materials

Review Binary Phase Diagrams and Thermodynamic Properties of Silicon and Essential Doping Elements (Al, As, B, Bi, Ga, In, N, P, Sb and Tl)

Ahmad Mostafa 1 and Mamoun Medraj 1,2,* 1 Mechanical and Materials Engineering Department, Khalifa University of Science and Technology, Masdar Institute, Masdar City 54224, UAE; [email protected] 2 Mechanical Engineering Department, Concordia University, 1515 Rue Sainte Catherine West, Montreal, QC H3G 2W1, Canada * Correspondence: [email protected]; Tel.: +1-514-848-2424

Received: 15 May 2017; Accepted: 13 June 2017; Published: 20 June 2017 Abstract: Fabrication of solar and electronic silicon wafers involves direct contact between solid, liquid and gas phases at near equilibrium conditions. Understanding of the phase diagrams and thermochemical properties of the Si-dopant binary systems is essential for providing processing conditions and for understanding the phase formation and transformation. In this work, ten Si-based binary phase diagrams, including Si with group IIIA elements (Al, B, Ga, In and Tl) and with group VA elements (As, Bi, N, P and Sb), have been reviewed. Each of these systems has been critically discussed on both aspects of phase diagram and thermodynamic properties. The available experimental data and thermodynamic parameters in the literature have been summarized and assessed thoroughly to provide consistent understanding of each system. Some systems were re-calculated to obtain a combination of the best evaluated phase diagram and a set of optimized thermodynamic parameters. As doping levels of solar and electronic silicon are of high technological importance, diffusion data has been presented to serve as a useful reference on the properties, behavior and quantities of metal impurities in silicon. This paper is meant to bridge the theoretical understanding of phase diagrams with the research and development of solar-grade silicon production, relying on the available information in the literature and our own analysis.

Keywords: binary phase diagrams; doping diffusion; solar-grade silicon; thermochemical data

1. Introduction The primary energy sources for electrical power generation are recognized as unsustainable. For instance, combustion of fossil fuels (coal, petroleum, and natural gas) emit massive quantities of CO2 in the atmosphere that leads to severe climate changes, such as global warming, sea level rise and change in the rain fall patterns [1–3]. Nuclear power plants are more environmentally friendly (emit zero CO2. However, these plants can be extremely dangerous, if unsafely operated as was the case in the Chernobyl disaster in 1986 [4], or if natural disasters take place in events such as the Fukushima nuclear accident [5]. Storage of the highly radioactive waste is another serious issue that must be taken into consideration [1]. It is expected that both safety and high-level nuclear waste issues will be more seriously examined in the next generation of nuclear power reactors. For the reasons mentioned above, more use of clean and renewable energy sources is crucial. Sources of renewable energy, solar in particular, can provide vital solutions to problems associated with fuel combustion and nuclear fission. The solar energy is transferred into direct current electrical power via the photovoltaic (PV) effect [6], which was discovered and demonstrated by the Nobel Laureate Becquerel [7,8]. Solar cells are traditionally divided into three different generations, these are: silicon-based solar cells, thin-films solar cells and solar cells based on nano-crystals and nano-porous materials [2,3,6,9].

Materials 2017, 10, 676; doi:10.3390/ma10060676 www.mdpi.com/journal/materials Materials 2017, 10, 676 2 of 49

Most of the available solar cell modules for contemporary market demands are made of crystalline silicon (c-Si). Thin film solar cells (TFSC) [10,11], including: amorphous silicon (a-Si), copper indium gallium diselenide Cu(In,Ga)Se2 (CIGS), cadmium telluride (CdTe) and others, represent 10% of the solar cells market [1]. The third generation of solar cells, include dye-sensitized solar cells (DSSC), hybrid organic solar cells and quantum dot solar cells, and are still under research and development [1,3,9]. The PV industry is currently undergoing significant development. It is difficult to predict which technical pattern has to be followed to achieve the desired outcomes from PV devices. It is important to know which materials will be utilized and what conditions are suitable to ensure maximum efficiency and long-term energy provision. Photovoltaic efficiency is highly influenced by temperature, dopant amount and density of imperfections [1,12]. These conditions might be optimized using heuristic approaches. However, it will be a very long journey to design a perfect PV system. The major goal in solar cell fabrication is to design a process that can minimize the negative effects of impurities or at least passivate them through a better understanding of their relationships with silicon. In this work, we use our knowledge of phase diagrams, obtained by investigating several alloying systems, to understand basic concepts for improvement in PV device performance while also providing thermodynamic properties of the Si-based binary systems. In the course of this work, we focus on crystalline silicon solar cells and binary phase diagrams of silicon with different doping elements, such as Al, As, B, Bi, Ga, In, N, P, Sb and Tl. This should serve as a useful reference for the properties, behavior and quantities of metal impurities in silicon. It is worth mentioning that this work will not provide a theoretical background on c-Si solar cell fabrication or discussion associated to energy levels of semiconductors, but rather serves as a guideline to control the processing parameters of solar and electronic Si through understanding the phase diagram, thermodynamic and diffusion data.

2. Crystalline Silicon Solar Cells Although they have a theoretical efficiency limit of about 26% [12,13], due to the presence of surface recombination that depletes the minority carriers [14–16], crystalline silicon solar cells have dominated PV modules [17]. These cells constitute more than 85% of the worldwide PV market [1]. Dominance of c-Si in PV technology stems to a great extent from the development of Si for the microelectronic applications [18,19], besides its relatively low manufacturing cost, non-toxicity and availability [1,13,15,20]. Both laboratory and industrial-type crystalline silicon solar cells are divided into monocrystalline Si, block-cast polycrystalline Si, ribbon Si and thin-film polycrystalline Si according to the type of the starting silicon wafer [1,2,9,13,15]. Crystalline silicon is an indirect semiconductor and its electrical properties deteriorate largely by the level of defects (bulk and/or surface defects), because they form numerous clusters that capture charge carriers. These defects are classified as intrinsic and extrinsic [15]. Intrinsic defects in pure silicon can be vacancies or self-interstitials that play an important role in many defect processes, such as self or dopant diffusion, strain release in the lattice and radiation defects [17]. Extrinsic defects can be doping atoms, transition metals, interstitial oxygen atoms or carbon substitutional atoms [17,18,21]. The following will be an attempt to summarize a general understanding of impurities in silicon.

3. Impurity Atoms The concentration space of impurity atoms in the solar and electronic Si ranges from particle per billion (ppb), which represents a challenge to measure for some impurities [22], to few percentages. However, a small change in the impurity level of a PV junction can result in an unacceptable drop in performance. Impurities exist in the Si lattice, as substitutional or interstitial point defects, in the form of precipitates or at the surfaces of the silicon wafers. Their distribution depends on the solubility limits and diffusivity as functions of atomic size and affinity to form bonds with silicon atoms [23]. Solubility limits can be directly determined from a well-established phase diagram as a function of temperature. Processing temperatures can be optimized with the help of a phase diagram to achieve the desired concentration level of impurity atoms. Materials 2017, 10, 676 3 of 49

Solubility limits can be directly determined from a well-established phase diagram as a function ofMaterials temperature.2017, 10, 676 Processing temperatures can be optimized with the help of a phase diagram3 of to 49 achieve the desired concentration level of impurity atoms. Knowledge of diffusion mechanisms and diffusivity of impurity atoms is essential to understand Knowledge of diffusion mechanisms and diffusivity of impurity atoms is essential to understand the microstructural changes in solar and electronic silicon at any temperature, which can be the microstructural changes in solar and electronic silicon at any temperature, which can be supported supported by phase equilibrium studies. Three possible mechanisms of atomic diffusion were by phase equilibrium studies. Three possible mechanisms of atomic diffusion were established [24,25]. established [24,25]. These are: (1) the interstitial mechanism, where the small radius impurity can These are: (1) the interstitial mechanism, where the small radius impurity can move from one interstitial move from one interstitial position to another, such as group IA and group VIIIA elements; (2) the position to another, such as group IA and group VIIIA elements; (2) the vacancy mechanism, where vacancy mechanism, where substitutional impurity moves via neighboring vacant sites through the substitutional impurity moves via neighboring vacant sites through the host lattice; (3) interstitialcy host lattice; (3) interstitialcy mechanism (combined interstitial and vacancy mechanisms), where the mechanism (combined interstitial and vacancy mechanisms), where the diffusion occurs when a diffusion occurs when a substitutional impurity resides at an interstitial site replacing a silicon substitutional impurity resides at an interstitial site replacing a silicon atomand the replaced Si atom atomand the replaced Si atom undergoes self-interstitial within the regular lattice site [26]. The three undergoes self-interstitial within the regular lattice site [26]. The three diffusion mechanisms are diffusion mechanisms are illustrated in Figure 1. illustrated in Figure1.

(a) (b) (c)

FigureFigure 1. 1. ((aa)) Interstitial, Interstitial, ( (bb)) Vacancy Vacancy and and ( (cc)) interstitialcy interstitialcy diffusion diffusion mechanisms.

The diffusivity of impurity atoms depends exponentially on temperature according to Arrhenius The diffusivity of impurity atoms depends exponentially on temperature according to Arrhenius Equation (1), as follows: Equation (1), as follows:   Qd 2 D== D exp −− cmcm /s/s (1) (1) 0 RT where, QQdd isis the the activation activation energy energy and and DD0 is0 isthe the temperature-independent temperature-independent pre-exponential pre-exponential factor. factor. R andR and T Tareare the the universal universal gas gas constant constant and and the the absolute absolute temperature. temperature. Impurity Impurity with with high high diffusivity diffusivity tendstends to to move move toward toward nucleation sites and gives rise to structure relaxation [[23].23]. TheThe success of of producing or or refining refining Si materials to high purity levels depends heavily on on the availabilityavailability and and reliability of phase diagrams, thermodynamic and diffusion data. This information actact as an important tool in evaluating the effects of impurities on the phase equilibria in in solar and electronicelectronic Si systems. Many Many impurity impurity atoms atoms may may exis existt in in Si Si wafers, wafers, such such as as oxygen, oxygen, carbon, carbon, transition transition metals,metals, alkali alkali and and alkali-earth alkali-earth impurities impurities and and groups groups IIIA IIIA and and VA VA metals metals [27]. [27]. However, However, in in this this work, work, we focus on the impurity atoms of group IIIA (p-type) and group VAVA ((nn-type).-type).

4.4. Impurity Impurity Atoms Atoms from from Groups Groups IIIA IIIA and and VA AtomsAtoms of of these groups act as substitutional impu impuritiesrities in Si. When When an an atom atom from from group group IIIA IIIA replacesreplaces a a Si atom, the the remaining valence valence electrons electrons are are insufficient insufficient to to satisfy the four covalent neighboringneighboring bonds. bonds. This This gives gives rise rise to the to theformation formation of holes of holes that are that weakly are weakly tied to tiedgroup to IIIA group atoms. IIIA Thus,atoms. group Thus, IIIA group atoms IIIA are atoms acceptors. are acceptors. On the othe Onr the hand, other group hand, VA group impurity VA impurity atoms are atoms called are donors, called becausedonors, they because replace they a Si replace atom and a Si one atom electron and one rema electronins untied remains to group untied VA toatom. group This VA extra atom. electron This canextra be electron easily activated can be easily and sent activated to the conduction and sent to ba thend conduction [24]. Besides band their [24 suitability]. Besides as their donors suitability and/or acceptors,as donors and/orthe binary acceptors, phase diagrams the binary of phase Al, As, diagrams B, Bi, Ga, of In, Al, N, As, P, B, Sb Bi, and Ga, Tl In, with N, P, Si Sb exhibit and Tl some with similarities.Si exhibit some Thesimilarities. main similarity The mainbetween similarity some betweenof these somephase of diagrams these phase is diagramsthat the maximum is that the solubilitymaximum of solubility an impurity of an atom impurity occurs atomabove occurs the eute abovectic temperature. the eutectic temperature.This is due to Thisthe high is due entropy to the high entropy of the disordered state, which results in forming defects such as vacancies [28]. This behavior is called retrograde or inverse solubility [28,29]. The retrograde solubility phenomenon occurs Materials 2017, 10, 676 4 of 49 Materials 2017, 10, 676 4 of 49 of the disordered state, which results in forming defects such as vacancies [28]. This behavior is called retrograde or inverse solubility [28,29]. The retrograde solubility phenomenon occurs during during solidification and originates from a miscibility gap in the free energy of mixing [30]. Impurity solidification and originates from a miscibility gap in the free energy of mixing [30]. Impurity concentration in the melt varies with the fraction of melt solidified and the value of the impurity concentration in the melt varies with the fraction of melt solidified and the value of the impurity distribution coefficient, Ko, which is also known as the segregation or partition coefficient [31]. Ko of distribution coefficient, Ko, which is also known as the segregation or partition coefficient [31]. Ko of group IIIA and group VA dopants in Si is less than one, as listed in Table1[ 28,32]. When Ko is less than group IIIA and group VA dopants in Si is less than one, as listed in Table 1 [28,32]. When Ko is less one, impurities accumulate progressively at the liquid/solid interface during the continuous crystal than one, impurities accumulate progressively at the liquid/solid interface during the continuous pulling process. These impurities deplete when Ko is greater than one [28]. This provides insight on the crystal pulling process. These impurities deplete when Ko is greater than one [28]. This provides technical challenges related to producing large volume Si substrates with uniform dopant distribution. insight on the technical challenges related to producing large volume Si substrates with uniform From a refining point of view, impurities with a very low distribution coefficient can easily be removed dopant distribution. From a refining point of view, impurities with a very low distribution coefficient since they accumulate at the bottom end of the crystal and contamination does not occur. For those can easily be removed since they accumulate at the bottom end of the crystal and contamination does having higher distribution coefficients (close to unity), they remain in the melt and accumulate in not occur. For those having higher distribution coefficients (close to unity), they remain in the melt the upper end of the crystal. Thus, some separate chemical processes or multiple zone melting are and accumulate in the upper end of the crystal. Thus, some separate chemical processes or multiple required to clean them up [33]. zone melting are required to clean them up [33].

Table 1. Distribution coefficient (Ko) of studied elements in this work at melting point of Si. Table 1. Distribution coefficient (Ko) of studied elements in this work at melting point of Si.

ElementElement KoK[28o [28]] Element Element Ko [28]Ko [28] AlAl 0.002 0.002 In In 4 × 104 ×−4 10−4 1 −4 AsAs 0.3000.300 NN1 7 × 107 ×−4 10 BB 0.8000.800 P P 0.350 0.350 Bi 7 × 10−4 Sb 0.023 −4 GaBi 0.008 7 × 10 Sb Tl 0.023 - Ga1 0.008 Tl - Ko for nitrogen was taken from [32]. 1 Ko for nitrogen was taken from [32].

TheThe equilibriumequilibrium distributiondistribution coefficientcoefficient isis thethe ratioratio ofof thethe impurityimpurity concentrationconcentration inin thethe solid,solid, CCss, toto thatthat inin thethe liquid,liquid, CCoo,, atat aa givengiven temperature,temperature, e.g.,e.g., TT11 inin FigureFigure2 2.. KKoo can bebe obtainedobtained fromfrom aa phasephase diagramdiagram asas demonstrateddemonstrated inin FigureFigure2 .2.

FigureFigure 2.2. Determination ofof thethe distributiondistribution coefficientcoefficient usingusing aa phasephase diagram.diagram.

From a practical point of view, Ko is used to find the maximum molar solid solubility (Xm) of From a practical point of view, K is used to find the maximum molar solid solubility (X ) of impurities in silicon through the empiricalo relationship [34] given in Equation (2): m impurities in silicon through the empirical relationship [34] given in Equation (2): =0.1× (2) Xm = 0.1 × Ko (2) When the unit of atom/cm3 is used for the maximum solid solubility, CM, Equation (2) can be re- written as in Equation (3) [34]:

=(5.2×10 )× (3)

Materials 2017, 10, 676 5 of 49

3 When the unit of atom/cm is used for the maximum solid solubility, CM, Equation (2) can be re-written as in Equation (3) [34]:  21 CM = 5.2 × 10 × Ko (3)

This relation was extracted from the maximum solid solubility vs. distribution coefficient plot of the following group of elements: Fe, Zn, S, Mn, Au, Cu, Al, Ga, Li, Sn, Sb, As and P. Although it is not exact for some elements, it may be useful to predict one quantity, either Cm or Ko, if the other one is known, or to evaluate some experimental data [34]. For the aforementioned similarities, phase diagrams of groups IIIA and V elements are evaluated giving special attention to the Si-rich terminal side, due to its practical relevance to production of solar and electronic Si.

5. Phase Diagrams One of the major reasons to analyze Si binary phase diagrams is that doping elements have a steep temperature-dependent solid solubility limit that renders Si easily supersaturated with them upon cooling. Therefore, they tend to form crystal defects in form of complex precipitates at grain boundaries [1]. These defects are not preferable since they deteriorate solar cell efficiency. Knowledge of the phase equilibrium and thermodynamic properties of the Si-impurity binary phase diagrams is important for understanding and improving the refining process of metallurgical Si grade feedstock to solar cell grade. For instance, the solvent refining process is one of the metallurgical approaches used for solar-grade silicon production, especially when impurity precipitates exhibit very limited solubility in silicon [35]. In this methodology, the silicon alloy is kept at a temperature above the liquidus, and then the temperature is reduced to a value near the eutectic temperature. As a result, purification solidification takes place and leaves impurities in the liquid phase. This means that purification occurs due to impurity rejection by the solidification front [36]. The success of the solvent refining process depends on the Si-terminal solubility which is decided by careful examination of the solvus line of the equilibrium phase diagram. The accuracy of the solvus lines in an equilibrium phase diagram is highly dependent on the solubility limit measurements. If the solubility values of specific impurities for a specific system are unknown and/or difficult to determine experimentally, or their behavior cannot be extrapolated, thermodynamic modeling is used [37]. Solidification process parameters such as the composition of the alloy, temperature and influence of cooling rate on the microstructure controls the impurity level of the crystallized silicon and can be determined from a well-established phase diagram. In this work, binary phase diagrams of Si with p-type elements (Si-{B, Al, Ga, In, Tl}) and Si with n-type elements (Si-{N, P, As, Sb, Bi}) have been assessed based on the available experimental data and thermodynamic descriptions. Throughout the paper, solid blue color lines are used in the figures to represent our best understanding of the phase diagram and thermodynamic data. All data points, obtained from the literature, are presented in phase diagram and thermodynamic properties figures in order to illustrate the error range. Error bars are provided whenever they are available in the literature. The phase diagrams and thermodynamic properties plots are in mole fraction; whereas, concentrations of impurity elements in the text are in atomic percentage. The crystallographic data for solid phases of all systems are summarized in Table2. This table will be referred to during the discussion of each binary system. Materials 2017, 10, 676 6 of 49

Table 2. Crystallographic data of the solid phases in the binary systems covered in the current study.

Lattice Parameters (nm) Space Groupe System Phase Prototype Space Group Ref. a b c Number All systems (Si) C (diamond) 0.5430 227 Fd-3m [38,39] Al-Si (Al) Cu 0.4047 225 Fm-3m [38,39] AsSi AsSi 1.598 0.3668 0.953 12 C2/m [39–41] As2Si As2Ge 1.453 1.037 0.3728 55 Pbam [39,42] As-Si 1 As2Si FeS2 6.0232 205 Pa-3 [41,43] (As) αAs 0.3760 1.0682 166 R-3m [39,41,43] β-B β-B 1.101 2.3900 166 R-3m h [39,44] B Si B C 0.6319 1.2713 166 R-3m h [39,45] B-Si 3 4 B6Si B6Si 1.439 1.827 0.988 58 Pnnm [39,46] B Si n β-B 1.101 2.390 166 R-3m [39,47,48] n ≈ 23 Bi-Si Bi αAs 0.4546 1.1862 166 R-3m [49,50] (αGa) αGa 0.45192 0.76586 0.45258 Cmca [39,51] (βGa) 0.27713 0.80606 0.33314 15 C12/c1 [39,51] Ga-Si (γGa) γGa 1.0593 1.3523 0.5203 63 Cmcm [39,51] (δGa) 0.909 1.702 177 R-3m [39,51] In-Si (In) In 0.4599 0.4947 F4/mmm [52]

αSi3N4 Si3N4 0.7818 0.5591 159 P31c [53] N-Si βSi3N4 Si3N4 0.7595 0.2902 173 P63 [54] 1 γSi3N4 Fe3O4 0.7772 227 Fd-3m [39] P(red) P 0.9210 0.9250 2.2600 13 P12/c1 [39] SiP SiP 0.3511 2.0488 1.3607 36 Cmc2 [39,55] P-Si 1 SiP2 GeAs2 1.397 1.008 0.3436 55 Pbam [42] Si6P2.5 C5W12 0.616 1.317 162 P-31m [39] Sb-Si Sb αAs 0.4331 1.1374 166 R-3m [39,56] αTl Mg 0.3456 0.5526 194 P6 /mmc [39,57] Si-Tl 3 βTl W 0.3882 229 Im3m [39,57] 1 High-pressure phase.

5.1. The Al-Si System The Al-Si phase diagram in Figure3 was redrawn after Murray and McAlister [ 58] based on the available experimental and thermodynamic data in the literature. The dashed line represents the calculated system by Liang et al. [59]. The system exhibits a eutectic reaction and two terminal solid solutions. The eutectic occurs at 12.2 at % Al and 577 ◦C. Many researchers [60–65] studied the solvus line in the Al-rich side as shown in Figure4. The maximum solid solubility of Si in Al terminal solid solution is about 1.5 at % Si. The liquidus curve and the thermodynamic activity of the melts have been extensively reviewed and recalculated by Safarian et al. [66,67]. The solvus curve of the Si terminal solid solution among the different studies was inconsistent, as can be seen in Figure5. In addition to the experimental errors, the data scattering could be due to the presence of low concentration impurities, which reduce the accuracy of the measurements. Gudmundsen and Maserjian [29], using thermal gradient experiments and spectrophotometric analysis, measured the solubility of Al in Si as 2.9 × 10−4 and 2.4 × 10−4 at % at 715 ◦C and 720 ± 10 ◦C, respectively, as compared to Mondolfo [65] who reported the solubility of Al in Si to be ranging from 1 × 10−2 at % at 1327 ◦C to 1.15 × 10−2 at % at 997 ◦C. Navon and Chernyshov [68] measured the solubility of Al in Si in the 700–1200 ◦C temperature range using resistivity measurements. Their measurements showed fair agreement with the data of Miller and Savage [69] at 1200 ◦C but not at lower temperatures, due to the inaccuracy of diffusion measurements [69] at low temperatures. Navon and Chernyshov [68] further reported a retrograde behavior in the Si-rich side with a maximum of 1.7 × 10−2 at % Al at around 1204 ◦C. In their review, Murray and McAlister [58] estimated the maximum solubility of Al in Si, based on the experimental results of [65,68], to be 1.61 × 10−2 at % Al at about 1210 ◦C. In a recent study, Yoshikawa and Morita [70] measured the solid solubility of Al-Si melts, prepared by true gradient zone melting (TGMZ) method, using electron probe microanalyzer (EPMA) and Hall Materials 2017, 10, 676 7 of 49 measurements, and reported a similar retrograde solubility behavior to that of [68]. The solubility values obtained from the two measuring methods [70] were consistent with each other and gave maximum at 4.3 × 10−2 at % Al and 1177 ◦C. The same level as the solubility of Al in Si [70] was obtained by Nishi et al. [71] using inductively coupled plasma (ICP spectrometry. Although these values are higher than those in the literature, yet they are accepted in the current work, because Yoshikawa and Morita [70] formed Si single crystal using TGMZ method, which makes the hole mobility measurements possible. The crystallographic data of the terminal solid solutions in Al-Si system are listed in Table2. It is worth mentioning that silicon films formed from Al-Si melt are not suitable as PV materials, because of the high solubility of Al in liquid Si. In other words, the number of aluminum acceptors would increase dramatically upon cooling due to Al supersaturation in Si lattice. The solubility of Al can be lowered by adding other elements to the melt such as P, which reacts with aluminum to form small insoluble particles of AlP intermetallic [72]. It is provenMaterials 2017 experimentally, 10, 676 that the solubility of Si in Al can be increased using rapid7 of 49 quenching process ofMaterials Al-Si 2017 melts, 10, 676 under pressure [37]. Soma et al. [73], using first principle calculations,7 of 49 measured It is proven experimentally that the solubility of Si in Al can be increased using rapid quenching the solubilityprocessIt of is Siprovenof inAl-Si Al experimentally undermelts under pressure thatpressure the of solubility 0,[37]. 3, 5Soma and of Si 10et in al. GPa.Al [73],can They be using increased concluded first usingprinciple rapid that calculations, quenching the solid solubility of siliconprocess inmeasured aluminum of theAl-Si solubility extendsmelts underof Si from in pressureAl 1.6under to pressure[37]. ~30.0 Soma at of % 0,et 3, under al.5 and [73], 10 pressure GPa.using They first and concluded principle their resultsthatcalculations, the solid were in good agreementmeasuredsolubility with the theof availablesilicon solubility in aluminum of experimental Si in Al extends under pressure datafrom 1.6 [74 ofto,75 0,~30.0 ].3, No5 atand % information 10under GPa. pressure They aboutconcluded and their the that results Al the solubility weresolid in Si at solubilityin good ofagreement silicon in withaluminum the available extends fromexperiment 1.6 to ~30.0al data at %[74,75]. under pressureNo information and their about results the were Al high pressure could be found in the literature. insolubility good agreement in Si at high with pressure the available could be experimentfound in theal literature. data [74,75]. No information about the Al solubility in Si at high pressure could be found in the literature. 1600

1600 800 Liquid 1400 800 Liquid 700 Liquid 1400 Liquid 700 1200 600

1200 6000.00 0.05 0.10 0.15 0.20 0.25 0.30 1000 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Liquid+Diamond_Si 1000 800 Liquid+Diamond_Si 800 577oC Temperature (°C) Temperature 600 12.2 at.% Si 577oC Temperature (°C) Temperature 600 FCC_Al+Diamond_Si 1.5 at.% Si 12.2 at.% Si 400 FCC_Al+Diamond_Si 1.5 at.% Si Liang et al. [59] 400 Murray and McAlister [58] Liang et al. [59] 200 0.0 0.2 0.4 0.6Murray and 0.8 McAlister [58] 1.0 200 0.0 0.2 0.4Mole fraction 0.6 (Si) 0.8 1.0 Figure 3. The Al-Si phase diagram redrawn afterMole [58]; fraction -----: [59]; (Si) +: [65]; ○: [76]; □: [77]; Δ: [78]; : [79]; Figure 3. The Al-Si phase diagram redrawn after [58]; - - - - -: [59]; +:[65]; :[76]; :[77]; ∆:[78]; Figure: [80]; 3. ●The: [81]; Al-Si ■: [82]; phase ▲ :diagram [83,84]; ▼redrawn: [85]; ♦ :after [86]. [58]; -----: [59]; +: [65]; ○: [76]; □: [77]; Δ: [78]; : [79]; 5:[79]; :[80]; :[81]; :[82]; :[83,84]; :[85]; :[86]. # : [80]; ●: [81]; ■: [82]; ▲: [83,84];N ▼: [85];H ♦: [86].  700 Liquid 700 Liquid 600 Liquid+Diamond_Si

600 FCC_Al Liquid+Diamond_Si 577°C 1.5 at.% Si 500 FCC_Al 577°C 1.5 at.% Si 500

400 FCC_Al+Diamond_Si

Temperature (°C) 400 FCC_Al+Diamond_Si 300 Temperature (°C) Liang et al. [59] 300 Murray and McAlister [58] 200 Liang et al. [59] 0.00 0.01 0.02Murray 0.03 and McAlister [58] 0.04 200 0.00 0.01Mole fraction 0.02 (Si) 0.03 0.04 Figure 4. Al-rich side of the Al-Si phase diagram [58];Mole ----:fraction [59]; (Si) ×: [60]; *: [61]; ○: [62]; □: [63]; Δ: [64]; +: [65]. Figure 4. Al-rich side of the Al-Si phase diagram [58]; ----: [59]; ×: [60]; *: [61]; ○: [62]; □: [63]; Δ: [64]; +: [65]. Figure 4. Al-rich side of the Al-Si phase diagram [58]; - - - -: [59]; ×:[60]; *: [61]; :[62]; :[63]; ∆:[64]; +: [65]. #

Materials 2017, 10, 676 8 of 49 Materials 2017, 10, 676 8 of 49

Liquid 1400

1200

1000 Liquid+Diamond_Si

This work Temperature (°C) Temperature 800 Murray and McAlister [58] Liang et al. [59] Mey and kack [87]

Dorner et al. [88] o Diamond_Si 600 577 C

0.9995 0.9996 0.9997 0.9998 0.9999 1.0000 Mole fraction (Si) Figure 5. Magnified part of the Si-rich side of the Al-Si phase diagram; ―: [58]; -----: [59]; -·-·-: [87]; ····: Figure 5. Magnified part of the Si-rich side of the Al-Si phase diagram; —: [58]; - - - - -: [59]; -·-·-: [87]; [88]; ■: [29]; ●: [65]; □: [68]; ○: [69]; Δ (EPMA): [70], ▼ (Hall measurements): [70]; : [89]. ····:[88]; :[29]; :[65]; :[68]; :[69]; ∆ (EPMA): [70], H (Hall measurements): [70]; ♦:[89]. Aluminum is considered #the fastest diffusing acceptor dopant in silicon, thus it is used to Aluminumfabricate deep isconsidered n-p junctions the with fastest large diffusing thicknesses acceptor [90,91]. dopant Despite in silicon, their industrial thus it is usedimportance, to fabricate deepfabrication n-p junctions of aluminum with large n-p thicknesses junctions [requires90,91]. Despitehigh processing their industrial temperature importance, of about fabrication1250 °C, of aluminumcorresponding n-p junctions to the requiresmaximum high Al solubility processing in Figure temperature 5, and a of long about time 1250 of 40◦C, h [91]. corresponding These severe to the maximumconditions Al solubility give rise to in defect Figure formation5, and a and long to timepossible of 40 contamination. h [ 91]. These Furthermore, severe conditions new processing give rise to techniques, such as ion implantation [92], focus on shortening the diffusion time and lowering the defect formation and to possible contamination. Furthermore, new processing techniques, such as diffusion temperature. In order to achieve the optimum processing conditions, the diffusion behavior ion implantation [92], focus on shortening the diffusion time and lowering the diffusion temperature. of Al in Si must be very well understood. The diffusivity of aluminum in silicon was measured by In order to achieve the optimum processing conditions, the diffusion behavior of Al in Si must be very Krause and Ryssel [91] in the 850–1290 °C temperature range. They measured both intrinsic, , and well understood.extrinsic, ,The diffusion diffusivity coefficients of aluminum and the results in silicon are wassummarized measured in Table by Krause 3. The and diffusivity Ryssel of [91 ] in ◦ the 850–1290several elementsC temperature in silicon, range.including They those measured involved bothin the intrinsic, current work,Di, and has extrinsic,been reportedDex ,in diffusion the coefficientsliterature. and More the details results are are av summarizedailable in the works in Table of 3Fisher. The [93] diffusivity and Tang of et several al. [94]. elements in silicon, including those involved in the current work, has been reported in the literature. More details are available in the works of Fisher [Table93] and 3. Tang and et al. of[ aluminum94]. in silicon.

1 2 1 2 Temperature (°C) Intrinsic diffusivity (cm /s) Extrinsic diffusivity (cm /s) 900 Table 3. D 1.9i and × 10D−14ex of aluminum in silicon. 1.2 × 10−16 1000 2.5 × 10−13 1.4 × 10−15 Temperature (◦C) Intrinsic Diffusivity 1 D (cm2/s) Extrinsic Diffusivity 1 D (cm2/s) 1100 2.3 × 10−12 i 1.0 × 10−13 ex −14 −16 900 1 Diffusivity1.9 × 10 values reported by [91]. 1.2 × 10 1000 2.5 × 10−13 1.4 × 10−15 Chakraborti1100 and Lukas [95] critically2.3 × reviewed10−12 the available phase diagram1.0 × and10− thermodynamic13 data of Al-Si system in the literature. Using computational thermodynamics, enormous number of 1 Diffusivity values reported by [91]. Al-Si phase diagram calculations were performed [27,59,87,88,96–101]. The thermodynamic properties, enthalpy of mixing and activity, are calculated as shown in Figure 6a,b, respectively. The Chakrabortithermodynamic and parameters Lukas [95 of] criticallythe Al-Si system reviewed are thelisted available in Table phase4. diagram and thermodynamic data of Al-SiIn Figure system 6a, the in calculated the literature. enthalpy Using of mixing computational of the liquidthermodynamics, phase by Murray and enormous McAlister [58] number of Al-Siat 1427 phase °C agree diagram with the calculations reaction calorimetric were performed result of Bros [27,59 et, 87al., 88[102],96 –within101]. ±225 The J·mol thermodynamic−1 only at properties,mid-composition, enthalpy ofbut mixing differ 900 and J·mol activity,−1 fromare the calculatedresults of Korber as shown et al. in[58] Figure and 5006a,b, J·mol respectively.−1 from The thermodynamicGizenko et al. [103]. parameters In contrast, of theTang Al-Si et al. system [99] gave are higher listed weight in Table to4 .the experimental results of InRostovtsev Figure6a, and the Khitrik calculated at 1600 enthalpy °C [104]. ofOther mixing calculations of the liquid performed phase by by Safarian Murray et al. and [66] McAlister and Tang [ 58] at 1427et al.◦C [105] agree were with lower the than reaction any of calorimetric the reported resultvalues. ofThe Bros low etvalues al. [102 might] within be as a± result225 Jof·mol attempts−1 only at made by authors [66,105] to be consistent with the phase diagram data only. On the other hand, mid-composition, but differ 900 J·mol−1 from the results of Korber et al. [58] and 500 J·mol−1 from Gizenko et al. [103]. In contrast, Tang et al. [99] gave higher weight to the experimental results of Rostovtsev and Khitrik at 1600 ◦C[104]. Other calculations performed by Safarian et al. [66] and Tang et al. [105] were lower than any of the reported values. The low values might be as a result of Materials 2017, 10, 676 9 of 49

Materials 2017, 10, 676 9 of 49 attempts made by authors [66,105] to be consistent with the phase diagram data only. On the other experimentalhand, experimental points points given givenby Gizenko by Gizenko et al. [103] et al. showed [103] showed higher higher enthalpy enthalpy of mixing of mixing than others. than others. This mightThis might explain explain why why these these results results were were not not considered considered in inthermodynamic thermodynamic calculations calculations of of [66,99,105]. [66,99,105]. The calculated calculated enthalpy enthalpy of of mixing mixing in in the the present present work, work, taking taking into into account account all the all available the available data datasets, agreesets, agree with withthe experimental the experimental data data of [102] of [102 in] th ine the 58–100 58–100 at at% %Al Al range range and and consistent consistent with with the calculations of [58] [58] in the full composition range at 1427 °C.◦C. Thus, the calculations made in this work are more reliable for thermodynamicthermodynamic modelling purpose. The calculat calculateded activity in Figure 66bb agreesagrees very well with the experimental data of [[103].103]. Th Thee other data points might be scattered due to the difference in the measurement temperatures. The nega negativetive deviation from Raoult’s law indicates that the liquid solution is exothermic.

0 1.0 This work at 1427°C This work at 1427°C -500 [58] [66] [99] 0.8 -1000 [105] Ideal solution

-1500 0.6

-2000 aAl aSi

Activity 0.4 -2500

-3000 Enthalpy of mixing (J/mol) 0.2

-3500

-4000 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Mole fraction (Si) (a) (b)

Figure 6. ((a)) Calculated enthalpy of mixing of the Al-Si liquid; —:―: [[99]99] atat 16001600 ◦°C;C; ○::[ [104]104] at at 1600 1600 °C;◦C; □: [103] at 1547 ◦°C; Δ: [102] at 1427 ◦°C; -·-·-: [58]; -----: [66]; ····· : [105] at 1427 °C◦ and (b) Calculated :[103] at 1547 C; ∆:[102] at 1427 C; -·-·-: [58]; - - - - -: [66]; ····· :[105] at 1427 C# and (b) Calculated activity of Al and Si in the Al-Si liquid at 1427 ◦°C; -----: [99] at 1600 °C;◦ ○: [106]; □: [107] and Δ: [100] at activity of Al and Si in the Al-Si liquid at 1427 C; - - - - -: [99] at 1600 C; :[106]; :[107] and ∆:[100] 1427 °C;◦ ■: [103] at 1547 °C; ◦▲: [108] at 1700 °C.◦ at 1427 C; :[103] at 1547 C; N:[108] at 1700 C. #

TableTable 4. Optimized model parameters of the Al-Si system. Phase Excess Gibbs Energy Parameter (J/Mole) Ref. Phase0 Excess Gibbs Energy Parameter (J/Mole) Ref. , = −11 340.1 − 1.23394 0 liq 1 L = −11 340.1 − 1.23394 T Liquid , = −3Al 530.93,Si + 1.35993 [59,98] 1 liq Liquid 2 L = −3 530.93 + 1.35993 T [59,98] , = 2 265.39Al,Si 2 liq 0 L = 2 265.39 FCC_Al , = −3Al 143.78,Si + 0.39297 [59,98] Diamond_Si 00 =f cc 113= 246.16− − 58.0001+ This work FCC_Al , LAl,Si 3 143.78 0.39297 T [59,98] T is the absolute temperature0 Diamond in this table and throughout the paper. Diamond_Si LAl,Si = 113 246.16 − 58.0001 T This work T 5.2. The As-Si System is the absolute temperature in this table and throughout the paper. This phase diagram has been mainly studied under pressure, because the sublimation 5.2. The As-Si System temperature of arsenic at atmospheric pressure is low (614 °C) [109]. The melting under pressure of As occursThis phase at 940 diagram °C and has59.2 been atm mainly [110]. studiedTalc was under used pressure, as a solid because pressure-transmitting the sublimation temperaturemedium to generateof arsenic pressure at atmospheric inside the pressure test chamber is low (614[111].◦C) The [109 As-Si]. The equilibrium melting under phase pressure diagram of at As a occurspressure at of940 ~39.5◦C and atm 59.2 was atm evaluated [110]. Talc by wasOlesinski used as and a solid Abbaschian pressure-transmitting [112] based on medium the available to generate experimental pressure datainside [42,113–119] the test chamber and thermodynamic [111]. The As-Si descriptions equilibrium [120–123], phase diagram as shown at in a pressureFigure 7. ofThe ~39.5 liquid atm phase was boundaryevaluated of by the Olesinski As-Si system and Abbaschian in the Si-rich [112 side,] based up onto thethe availableeutectic point experimental at around data 56 at [42 %,113 Si,– 119was] drawnand thermodynamic as dotted line descriptionsin the work [of120 Olesinski–123], as an shownd Abbaschian in Figure 7[112]. The due liquid to the phase large boundary disagreement of the among the available data [113,115]. However, the liquidus in the As-rich side and solidus lines agree very well with the results of Ugay et al. [115], who performed vapor pressure measurements using a static manometric method and provided results with higher accuracy than those obtained by Klemm

Materials 2017, 10, 676 10 of 49

As-Si system in the Si-rich side, up to the eutectic point at around 56 at % Si, was drawn as dotted line in the work of Olesinski and Abbaschian [112] due to the large disagreement among the available data [113,115]. However, the liquidus in the As-rich side and solidus lines agree very well with the resultsMaterials of2017 Ugay, 10, 676 et al. [115], who performed vapor pressure measurements using a static manometric10 of 49 method and provided results with higher accuracy than those obtained by Klemm and Prscher [113] and Prscher Ugay et [113] al. [114 and]. Ugay The systemet al. [114]. includes The system two intermetallic includes two compounds intermetallic and compounds two terminal and solid two ◦ solutions.terminal solid The solutions. AsSi intermetallic The AsSi compoundintermetalli meltsc compound congruently melts congruently at 1113 C; while at 1113 As °C;2Si while undergoes As2Si peritecticundergoes transformation peritectic transformation at 977 ◦C. The at crystallographic977 °C. The crystallographic data of the solid data phases of the solid in the phases As-Si system in the As- are givenSi system in Table are given2. The in data Table of Beck2. The [ 40 data] and of WadstenBeck [40] etand al. Wadsten [42] for the et AsSial. [42] (monoclinic for the AsSi crystal (monoclinic system, AsSicrystal prototype system, AsSi and C2/m prototypespace and group) C2/m and space As2 group)Si (orthorhombic and As2Si (orthorhombic crystal system, crystal As2Ge system, prototype As and2Ge Pbamprototypespace and group) Pbam phases, space respectively,group) phases, at roomrespectively, temperature at room are acceptedtemperature in this are work. accepted It is in worth this mentioningwork. It is worth that thementioning stable high-pressure that the stable structure high-pressu of Asre2 Sistructure is pyrite-type, of As2Si which is pyrite-type, is not achievable which is undernot achievable ambient under conditions ambient [119 conditions]. [119].

FactSage [124] 1400 Olesinski and Abbaschian [112]

Liquid 1200 0.56 o Liquid+Diamond_Si 1113 C o 1108 C 1097oC 1000 979oC 0.60

o 977 C Diamond_Si 795oC

Temperature (°C) 800 797oC 0.047 0.098

(As)+As Si As Si+AsSi AsSi+Diamond_Si 600 2 2

0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Figure 7. The As-Si phase diagram at ~40 bar [112]; ----: [124]; ○: [113]; □: [114]; Δ: [115]. Figure 7. The As-Si phase diagram at ~40 bar [112]; - - - -: [124]; :[113]; :[114]; ∆:[115]. # The solubility of Si in As is considered negligible, whereas solubility of As in Si shows a The solubility of Si in As is considered negligible, whereas solubility of As in Si shows a retrograde retrograde behavior in liquid silicon. It can reach to around 3.25 at % at the eutectic temperature. behavior in liquid silicon. It can reach to around 3.25 at % at the eutectic temperature. Several research Several research works [118,125–131] focused on the Si-rich side to determine the solid solubility works [118,125–131] focused on the Si-rich side to determine the solid solubility limits of arsenic in limits of arsenic in silicon. According to Olesinski and Abbaschian [112], the maximum solubility of silicon. According to Olesinski and Abbaschian [112], the maximum solubility of As was reported as As was reported as 3.5 at % As at ~1200 °C based on the work of Sandhu and Reuter [117], who 3.5 at % As at ~1200 ◦C based on the work of Sandhu and Reuter [117], who determined the solvus line determined the solvus line from the vapor pressure measurements using radiotracer and chemical from the vapor pressure measurements using radiotracer and chemical methods. Other experimental methods. Other experimental points were excluded, because they were acquired by electrical points were excluded, because they were acquired by electrical conductivity methods that are known to conductivity methods that are known to give high error of measurements in this system. Tang et al. give high error of measurements in this system. Tang et al. [105] assessed the As-Si system based on the [105] assessed the As-Si system based on the experimental data of [113,114,117,118,125,126,131] and experimental data of [113,114,117,118,125,126,131] and the thermodynamic activity data of [116,117]. the thermodynamic activity data of [116,117]. They [105] re-evaluated the maximum solubility of As They [105] re-evaluated the maximum solubility of As in Si to be around 3.4 at % As at 1300 ◦C, favoring in Si to be around 3.4 at % As at 1300 °C, favoring the data of [118,130] over [117,126] without the data of [118,130] over [117,126] without providing any justification. The Si terminal solid solution providing any justification. The Si terminal solid solution was described [105] based on a was described [105] based on a substitutional solution with random mixing assumption. Although substitutional solution with random mixing assumption. Although Tang et al. [105] incorporated Tang et al. [105] incorporated several experimental points in their optimization, the assessment of several experimental points in their optimization, the assessment of Olesinski and Abbaschian [112] Olesinski and Abbaschian [112] is favorable in this work, because they are self-consistent. Figure8 is favorable in this work, because they are self-consistent. Figure 8 summarizes the solid solubility summarizes the solid solubility limits of As in Si and the acceptable solvus line in this work, which limits of As in Si and the acceptable solvus line in this ◦work, which provides a maximum solubility providesof 3.52 at a% maximum As at 1200 solubility °C. of 3.52 at % As at 1200 C.

Materials 2017, 10, 676 11 of 49

Materials 2017, 10, 676 11 of 49

Liquid 1400

1200 Diamond_Si

1000

800 AsSi+Diamond_Si Temperature (°C)

600 This work Tang et al. [105] Olesinski and Abbaschian [112] 400 0.96 0.97 0.98 0.99 1.00 Mole fraction (Si) Figure 8. Magnified part of the As-Si phase diagram; —: [105]; ----: [112]; □: [117]; : [118]; : [126]; Figure 8. Magnified part of the As-Si phase diagram; —: [105]; - - - -: [112]; :[117]; 5:[118]; :[126]; ○: [130]; Δ: [131].  ♦ :[130]; ∆:[131]. # It is worth mentioning that if As concentration is higher than the solubility limit, the electrical It isproperties worth mentioning of the heavily thatAs-doped if As Si concentration deteriorates due is to higherthe occurrence than the of electrically solubility inactive limit, arsenic the electrical clusters [125,132,133]. The electrically inactive cluster contains two As atoms and one vacancy properties of the heavily As-doped Si deteriorates due to the occurrence of electrically inactive position [125,134]. Furthermore, these clusters result in obstructing the phase equilibrium between Si arsenic clustersand the AsSi [125 ,compound132,133]. Theby blocking electrically the inactivenucleation cluster of AsSi contains precipitates. two AsHence, atoms it is and of onegreat vacancy positionimportance [125,134]. Furthermore,to determine the these maximum clusters solubility result in of obstructing As in Si precisely. the phase Nobili equilibrium and Slomi between [134] Si and the AsSidescribed compound the maximum by blocking As theconcentration, nucleation Csat of, in AsSi Si lattice precipitates. at equilibriumHence, with it AsSi is of by great importance=1.3× to (. ⁄) determine10 thee maximum cm solubility based on of the As best in Si fit precisely. equation given Nobili in Nobili’s and Slomi earlier [134 work] described [128] in the the 800– maximum 1050 °C temperature range. 23 (−0.42 eV/kT) −3 As concentration, Csat, in Si lattice at equilibrium with AsSi by Csat = 1.3 × 10 e cm Impurity atoms may occupy either substitutional or interstitial locations in Si lattice.◦ However, based onarsenic the best shows fit equationmixed vacancy-interstitial given in Nobili’s (i.e., earlier interstitialcy work as [128 illustrated] in the in 800–1050 Figure 1c) Cdiffusivity temperature in Si range. Impurity[26,135]. atoms It has almost may occupysimilar tetrahedral either substitutional radius as silicon or (As interstitial = 1.24 Å and locations Si = 1.18 in Å), Si thus lattice. it does However, arsenicnot shows strain mixed the silicon vacancy-interstitial lattice. However, at (i.e., high interstitialcyarsenic concentration, as illustrated clusters form in Figure and retard1c) diffusivity the in Si [26diffusivity,135]. It of has As almost in Si similar[136]. Intrinsic tetrahedral diffusivity radius of asAs siliconin Si (Ascan be = 1.24expressed Å and as Si = = 1.18 Å), (. /) thus it does22.9 × not straincm the/s silicon in the 900–1250 lattice. °C However, temperature at range high [137]. arsenic Arsenic concentration, diffusion in Si clustersis quiet form complex due to the change of diffusion mechanism depending on As concentration and temperature. and retard the diffusivity of As in Si [136]. Intrinsic diffusivity of As in Si can be expressed as Additional information about arsenic diffusion mechanisms can be found in Hull [138] and Fair [137]. (−4.1 eV/kT) 2 ◦ Di = 22.9 ×Thee As-Si systemcm was/s recalculatedin the 900–1250 using FTliteC temperaturethermodynamic range database [137 integrated]. Arsenic in FactSage diffusion® in Si is quietsoftware complex (version due to7.0, the Thermofact change and of diffusionGTT-Technologies, mechanism Montreal, depending Canada) [124]. on As In some concentration regions, and temperature.the calculated Additional phase informationdiagram showed about reasonable arsenic ag diffusionreement with mechanisms the experimental can beresults found presented in Hull [138] and Fairby [137 Ugay]. et al. [115]. However, many discrepancies were detected. Figure 7 shows both versions of Thethe As-Si As-Si system phase wasdiagram recalculated [112,124] and using Table FTlite 5 summarizes thermodynamic the differences database between integrated these in two FactSage ® versions. As can be seen from Figure 7 that the liquidus curve presented by [112] is more convincing software (version 7.0, Thermofact and GTT-Technologies, Montreal, Canada) [124]. In some regions, than that of [124], because it matches better with the experimental points on both composition the calculatedextremes. phase Furthermore, diagram due showed to the retrograde reasonable behavior agreement of the Si-rich with thesolvus experimental line, the shape results of Si-rich presented by Ugayliquidus et al. [ 115in [112]]. However, is more appropriate many discrepancies when considering were the detected. limiting Figureslopes theory7 shows [139]. both versions of the As-Si phase diagram [112Table,124 5. ]Comparison and Table between5 summarizes the available the As-Si differences phase diagram between data. these two versions. As can be seen fromFeatures Figure7 that the liquidusOlesinski and curve Abbaschian presented [112] by [ FTlite112] isDatabase more convincing[124] than that of [124], becauseSi terminal it solid matches solution better with Retrog the experimentalrade behavior points on Typical both composition behavior extremes. Furthermore, dueSi-rich to the eutectic retrograde behavior 60 of at the% Si Si-rich at 1097 solvus°C line, 56the atshape % at 1108 of Si-rich°C liquidus in [112] is more appropriateAs-rich eutectic when considering 9.8 the at % limiting Si at 797 slopes°C theory 4.7 [ 139at %]. Si at 795 °C As2Si peritectic temperature 977 °C 979 °C Table 5. Comparison between the available As-Si phase diagram data.

Features Olesinski and Abbaschian [112] FTlite Database [124] Si terminal solid solution Retrograde behavior Typical behavior Si-rich eutectic 60 at % Si at 1097 ◦C 56 at % at 1108 ◦C As-rich eutectic 9.8 at % Si at 797 ◦C 4.7 at % Si at 795 ◦C ◦ ◦ As2Si peritectic temperature 977 C 979 C Materials 2017, 10, 676 12 of 49 Materials 2017, 10, 676 12 of 49

The thermodynamic properties, enth enthalpyalpy of mixing and activity of As-Si liquids, are calculated using FTlite databasedatabase andand presented presented in in Figure Figure9. 9. No No experimental experimental enthalpy enthalpy of mixingof mixing or activity or activity of the of theliquid liquid As-Si As-Si alloys alloys could could be foundbe found in the in the literature literature to compareto compare with. with. The The calculated calculated activity activity curve curve of ofliquid liquid As As and and Si Si alloys alloys at at 1600 1600◦C °C shows shows a a negative negative deviation deviation fromfrom thethe idealideal behavior.behavior. The negative deviation from Raoult’s law could be duedue toto thethe strongerstronger molecularmolecular interactioninteraction betweenbetween As/SiAs/Si atoms than the interactions between Si/Si and and As/As As/As atoms. atoms. The enthalpy of formation of the As-Si intermetallic compounds was determined by Fitzner and Kleppa [140] [140] using using direct direct synthesi synthesiss drop drop calorimetry. calorimetry. The The actual actual value value of ofenthalpy enthalpy of offormation formation of theof theAsSi AsSi compound compound could could be higher be higher thanthan that thatlisted listed in Table in Table 6, because6, because the measurements the measurements were wereperformed performed on an onalloy an containing alloy containing a mixture a mixtureof AsSi + of As AsSi2Si rather + As 2thanSi rather on a pure than AsSi on a compound. pure AsSi Thesecompound. experimental These experimental results were results compared were with compared those predicted with those by predicted Niessen byet Niessenal. [141] etusing al. [141 the] semi-empiricalusing the semi-empirical theory of. theory The of.predicted The predicted results results are significantly are significantly higher higher than than those those obtained experimentally by Fitzner and Kleppa [140], [140], as indi indicatedcated in Table 6 6.. TheThe largelarge negativenegative valuesvalues ofof thethe calculated enthalpies of formation are because the liquid arsenic that should occur under under atmospheric atmospheric pressure was not considered. It is worth mentioning that the liquid arsenic was treated as a solvent in the work of Niessen et al.al. [[141].141]. Based on ourour state of knowledge of this system we recommend further experimental efforts to measure the enthalpy of mixing of the liquid solution, the activities in the liquid phase and most importantly the maximum solubility of As in Si. After this is done, a new thermodynamic modeling considering all thethe newnew datadata shouldshould bebe carriedcarried out.out.

0 1.0

-500

0.8 -1000 Ideal solution

-1500 aAs aSi 0.6 -2000

-2500

Activity 0.4 -3000

Enthalpy of mixing (J/mol) of mixing Enthalpy -3500 0.2

-4000

-4500 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Mole fraction (Si) (a) (b)

Figure 9. (a) Enthalpy of mixing of the As-Si liquid and ( b) activity of As and Si in the As-Si liquid ® calculated in this work at 1600 ◦°CC using FactSage ® softwaresoftware [124]. [124].

Table 6. The enthalpy and entropy of formation of the As-Si intermetallic compounds (at 298 K and Table 6. The enthalpy and entropy of formation of the As-Si intermetallic compounds (at 298 K and 1 atmospheric pressure). Enthalpy of Formation Entropy of Formation Compound Enthalpy of Formation Entropy of Formation Ref. Compound −1 Ref. kJ·(Mole·Atom)kJ·(Mole·Atom)− 1 (J/Mole(J/Mole·Atom·K)·Atom·K) Experimental −5.4 ± 1.2 - [140] Experimental −5.4 ± 1.2 - [140] AsSi CalculatedAsSi Calculated −114.0−114.0 -- [141] [141] CALPHADCALPHAD 1 1 −5.9−5.9 30.6430.64 [124] [124] ExperimentalExperimental −3.7− 3.7± 2.3± 2.3 - - [140] [140] As2Si Calculated −89.0 - [141] As2Si CalculatedCALPHAD −89.0−4.3 33.8- [124] [141] CALPHAD −4.3 33.8 [124] 1 Calculations of phase diagram. 1 Calculations of phase diagram.

Materials 2017, 10, 676 13 of 49

5.3. The B-Si System Boron is a primary p-type doping element in silicon wafers, with the highest solid solubility in silicon as compared to all elements in group IIIA [90]. According to Zaitsev and Kodentsov [142], the solid solubility of B in Si can reach up to 3.5 at % B at 1362 ◦C. The B-Si phase diagram was assessed by Olesinski and Abbaschian [143] based on the previous experimental data [118,144–147] and thermodynamic calculations [148–150]. Three intermetallic compounds were reported. Two of ◦ ◦ them, BnSi (14 < n < 40) and B6Si, form peritectically at 2020 C and 1850 C, respectively. Whereas, ◦ the third intermetallic compound, B3Si, was found to form by a peritectoid reaction at 1270 C. The crystallographic data of the intermetallic compounds in the B-Si system are listed in Table2. B3Si and BnSi were represented as intermediate solid solutions with unknown solubility ranges [143] while B6Si was represented as stoichiometric compound. In the work of [151], B3Si was reported as B4Si Olesinski and Abbaschian [143] suggested that different formulae were due to difficulty in phase separation of B3Si from B6Si, which shows a molar ratio of B to Si of around 4. However, X-ray analysis [45,152] revealed the composition of this compound as B3Si. Hence, in the current work, this compound is considered as B3Si. The BnSi compound was given the formula B14Si after Dirkx and Spear [153], who provided thermodynamic formation data for the B-Si intermetallic compounds. According to these authors [153], the intermediate phases were treated as line compounds and their formation enthalpies and entropies were assumed to be independent of temperature, claiming that it is a good approach when compounds exhibit narrow homogeneity ranges, although BnSi seems to have significant homogeneity range. Zaitsev and Kodentsov [142] modeled the B-Si phase diagram, based on their own thermodynamic measurements, shown as dashed lines in Figure 10. The modeled phase diagram [142] exhibits reasonable agreement with the assessment of Olesinski and Abbaschian [143] in the B-rich side up to 63.0 at % B. However, differences in other parts of the B-Si phase diagram could be observed. For instance, Zaitsev and Kodentsov [142] lowered the eutectic temperature from 1385 to 1362 ◦C with a shift in the eutectic composition from 86 to 92 at % Si, and therefore the liquid curve was suppressed in the 40–86 at % Si composition range. Moreover, Zaitsev and Kodentsov [142] treated BnSi as a stoichiometric compound, whereas Olesinski and Abbaschian [143] presented the compound with an appreciable homogeneity range. A comparison between the two phase diagrams [142,143] can be found in [154]. In this work, however, Figure 10 compares both recent calculated phase diagram versions by [155] and [142] with respect to the available experimental data [142,144,147]. The solid lines presented in Figure 10 are for the B-Si phase diagram calculated by Fries and Lukas [155] using the thermodynamic parameters presented in Table7. These parameters are available in the FTlite database of FactSage® software [124] and generate similar B-Si phase diagram to that of [155]. Equally, Seifert and Aldinger [156] performed a comprehensive review on the experimental and thermodynamic data of the B-Si system and presented a similar phase diagram. The calculated phase diagram [155] is in good agreement with the liquidus experimental results of [147] in the B-rich side as shown in Figure 10 and with those of the solvus reportedby [146,148,157] in the Si-rich side shown in Figure 11. However, the calculated liquidus line in the 70–92 at % Si composition range does not agree with the experimental points of Zaitsev and Kodentsov [142] and Brosset and Magnusson [144]. According to the limiting slopes of phase boundaries theory [139], the Si-rich liquid phase cannot be as flat as given by the experimental points of Brosset and Magnusson [144] and the calculations of Zaitsev and Kodentsov [142], because the liquidus is expected to be pushed upward by ◦ the peritectic formation of B6Si at 1850 C. Thus, the liquidus at the Si-rich side must show steeper slope due to the relatively low eutectic point at 92 at % Si and 1348 ◦C. The thermodynamic calculations of the B-Si phase diagram, given by [155], are accepted in this work, because they better describe the phase diagram along with other thermodynamic properties of the solution phases and available experimental results. Materials 2017, 10, 676 14 of 49 Materials 2017, 10, 676 14 of 49

2250 2037°C Materials 2017, 10, 6762000 Liquid 14 of 49 2020°C β−B 1850°C 2250 1750 2037°C 2000 Liquid 2020°C 1500β−B 1850°C 92.0 at.% 1385°C 1750 1362°C 86.0 at.% 1250 1270°C 1500 92.0 at.% 1385°C Temperature (°C) Temperature B Si n B3Si+Diamond_Si 1000 1362°C 86.0 at.% 1250 1270°C B3Si

Temperature (°C) Temperature B Si B Si+Diamond_Si 750 n B Si 3 Zaitsev and Kodentsov [142] 1000 6 Fries and Lukas [155]

B3Si 0.00.20.40.60.81.0 750 B6Si Zaitsev and Kodentsov [142] Fries and Lukas [155] Mole fraction (Si) 0.00.20.40.60.81.0 Figure 10. The B-Si phase diagram redrawn after [155]; ----: [142]; □: [144]; ○: [147]; Δ: [142]. Figure 10. The B-Si phase diagram redrawnMole after fraction [155]; -(Si - -) -: [142]; :[144]; :[147 ]; ∆:[142]. # The B solubilityFigure 10. in The Si B-Si data phase is scattered diagram redrawn and contradictory. after [155]; ----: [142]; The □solid: [144]; solubility ○: [147]; Δ :of [142]. boron in silicon The B solubility in Si data is scattered and contradictory. The solid solubility of boron in silicon as as a function of temperature was first presented by Vick and Whittle [153]. According to these a functionThe of B temperature solubility in wasSi data first is scattered presented and by contradictory. Vick and Whittle The solid [153 solubility]. According of boron to thesein silicon authors, authors, the solid solubility varies from 9.0 × 10−4 at % at 700 °C to 1.4 × 10−2 at % at 1151 °C. Olesinski the solidas a solubilityfunction of varies temperature from 9.0 was× 10first−4 presenteat % atd 700 by◦ CVick to 1.4and× Whittle10−2 at [153]. % at According 1151 ◦C. Olesinski to these and and Abbaschian [139], using different sources [114,141,142], estimated the B solubility in Si to be ~3.0 Abbaschianauthors, [ 139the solid], using solubility different varies sources from 9.0 [114 × ,10141−4 at,142 % ],atestimated 700 °C to 1.4 the × 10 B− solubility2 at % at 1151 in Si°C. to Olesinski be ~3.0 at %. at %. Whereas, Zaitsev and Kodentsov [138] reported maximum solubility of 3.5 at % B at 1362 °C, Whereas,and Abbaschian Zaitsev and [139], Kodentsov using different [138] reported sources [114,141,142], maximum solubility estimated ofthe 3.5 B solubility at % B at in 1362 Si to◦ beC, ~3.0 favoring favoringat %. the Whereas, results Zaitsev of Samsonov and Kodentsov and Sleptsov [138] reported [141] only. maximum Although, solubility the calculatedof 3.5 at % Bsolubility at 1362 °C, of B in the results of Samsonov and Sleptsov [141] only. Although, the calculated solubility of B in Si by Fries Si byfavoring Fries and the resultsLukas of[151] Samsonov is in goodand Sleptsov agreement [141] only.with Although,the data thofe [144,153]calculated solubilityat 1.6 at of%, B furtherin and Lukas [151] is in good agreement with the data of [144,153] at 1.6 at %, further investigation of investigationSi by Fries of andthis Lukasregion [151] is highly is in goodrecommended. agreement withSince the the data results of [144,153] of Armas at 1.6et al.at [143]%, further and Vick this region is highly recommended. Since the results of Armas et al. [143] and Vick and Whittle [152] and Whittleinvestigation [152] of support this region one is another, highly recommended. a solvus line consistentSince the results with ofthem Armas is adopted et al. [143] in and this Vick work. supportand oneWhittle another, [152] support a solvus one line another, consistent a solvus with line them consistent is adopted with them in this is work.adopted in this work.

Liquid 1385°C 1385°C 1400 Liquid 1400 1362°C 1362°C 98.4 at.% Si 96.5 at.% Si 98.4 at.% Si B Si+Diamond_Si 96.5 at.% Si 13001300 6B6Si+Diamond_Si 1270°C1270°C

Diamond_SiDiamond_Si 12001200 Temperature (°C) Temperature Temperature (°C) Temperature B3Si+Diamond_Si B3Si+Diamond_Si 1100 1100

Zaitsev and Kodentsov [142] ZaitsevFries and LukasKodentsov [155] [142] 1000 Fries and Lukas [155] 1000 0.90 0.92 0.94 0.96 0.98 1.00 0.90 0.92 0.94 0.96 0.98 1.00 Mole fraction (Si) Mole fraction (Si) ■ FigureFigure 11. Magnified 11. Magnified part part of of the the B-Si B-Sisystem system near the the Si-rich Si-rich side side [155]; [155 ----:]; -[142]; - - -:[ Δ142: [118];]; ∆:[ 118: [157];];  □:[: 157]; [144]; : [145]; : [146]; ○: [148]. Figure:[144 ];11.5 Magnified:[145]; ♦:[ part146]; of :[the148 B-Si]. system near the Si-rich side [155]; ----: [142]; Δ: [118]; ■: [157]; □: [144]; : [145]; : [146]; ○: #[148]. Boron is a fast diffuser in silicon. The intrinsic diffusivity of boron in silicon as function of Borontemperature is a fast was diffuser represented in silicon. by the The equation intrinsic diffusivity=0.76× of(. boron⁄) in silicon cm/s as [26]. function Van-Hung of temperature et al. Boron is a fast diffuser in silicon. The intrinsic diffusivity of boron in silicon as function of was represented[158] calculated by the the equation diffusionD coefficients= 0.76 × eof(− 3.46boroneV/ kTin) siliconcm2/s [based26]. Van-Hung on interstitial et al. and [158 vacancy] calculated temperature was represented by thei equation =0.76×(. ⁄) cm/s [26]. Van-Hung et al. the diffusionmechanisms coefficients using statistical of boron moment in silicon method. based The temperature on interstitial dependence and vacancy activation mechanisms energy and using [158] calculated the diffusion coefficients of boron in silicon based on interstitial and vacancy mechanisms using statistical moment method. The temperature dependence activation energy and

Materials 2017, 10, 676 15 of 49 statistical moment method. The temperature dependence activation energy and diffusion coefficients results [158] were compared with the available [26,159–162] literature data. They concluded that the dominant diffusion mechanism of B in Si is the interstitial mechanism [26,159,163]. It is worth mentioning that boron atom has 0.75 relative mismatch ratio with respect to, which is relatively large enough to produce high strain in silicon lattice. The induced lattice strain can reduce the level of other unwanted impurities by a trapping mechanism [26]. For example, high concentrations of boron are particularly good to combat iron impurities in Si [164].

Table 7. Thermodynamic model parameters of the B-Si system.

Phase Excess Gibbs Energy Parameter (J/Mole) [155] Liquid 0L = 17 631.92 − 1.76321 T Liquid B,Si 1 Liquid LB,Si = −3 526.99 − 0.3527 T 0 Dia−Si Diamond_Si LB,Si = 57 978.16

G (B : Si) = −6 160.245 + 0.6160245 T + 93.0 GHSERB + 12.0 GHSERSi β-B 0 β−B LB:B,Si = −725 614 + 72.5614 T

G (B : Si : B) = 112 000 + 12.0 GHSERB + 2.0 GHSERSi B3Si G (B : Si : Si) = 112 000 + 6.0 GHSERB + 8.0 GHSERSi 0 B3Si LB:Si:B,Si = −2400 475 + 240.0475 T

G (B : Si : B) = 729 824.4 − 72.98244 T + 258.0 GHSERB + 23.0 GHSERSi B6Si G (B : Si : Si) = 5454 560 − 545.456 T + 210.0 GHSERB + 71.0 GHSERSi 0 B6Si LB:Si:B,Si = −15715 630 + 1571.563 T

G (B : Si : B) = −89 819.86 + 8.981986 T + 69.0 GHSERB + GHSERSi BnSi G (B : Si : Si) = −176 659.7 + 17.66597 T + 61.0 GHSERB + 9.0 GHSERSi 0 Bn Si LB:Si:B,Si = −281 573.6 + 28.15736 T GHSER is Gibbs free energy values at reference state (1 atm and 298.15 K) for a pure element.

The enthalpy of mixing of B-Si melts, presented by a solid line in Figure 12a, was calculated by Olesinski and Abbaschian [143], who tried to fit their calculations with the experimental points given by Esin et al. [150]. Another set of experimental points were presented by Beletskii et al. [165], whose results agreed well with that of Esin et al. [150]. Later, Kudin et al. [166] determined the mixing ◦ enthalpies of B-Si melts in the 0.6 < XSi < 1.0 composition range at 1600 C using isoperibolic calorimetry. The enthalpy of mixing experimental data [166] were different from that of [143,150,165]. This could be attributed to the low purity of amorphous boron used by [166], which was about 98%. However, it is not logical to see a gradual increase and then decrease in the enthalpy of mixing curve [150,165] at the Si-rich side. Such behavior may result from the inaccurate measurements of the interaction energies in boron binary melts [166]. The recent thermodynamic assessments of the B-Si system [167] showed a positive enthalpy of mixing at 2127 ◦C as presented by a dashed line in Figure 12a. It seems that the liquid phase was treated as a random mixture, because the calculated enthalpy of mixing (4.4 kJ/mole) [167] was relatively small, which is not an accurate representation of the mixing in the B-Si melts. In this work, the enthalpy of mixing experimental results of Kudin et al. [166] are accepted for the B-Si system. The activities of boron and silicon in the liquid phase were measured by Zaitsev and Kodentsov [142] using Knudsen effusion mass spectrometry in the 1249–1607 ◦C temperature range. The average activities of B-Si melts established by Zaitsev and Kodentsov [142] at 1577 ◦C show small deviation from Raoult’s low (negative for B and positive for Si), as shown in Figure 12b. The amount of deviation was found to increase with a decrease in temperature and increase in B concentration. It is important to note that the boron activity data points must obey Henry’s law in the Si side and not as reported by Zaitsev and Kodentsov [142]. Thus, we recommend further experimental efforts to Materials 2017, 10, 676 16 of 49 measure the activity of B in the liquid phase. Due to the lack of reliable activity data, the boron and silicon activities at 2127 ◦C, reported by Franke and Neuschütz [167], are presented as dashed lines in Figure 12b. Both boron and silicon activities [167] show positive deviation from ideality, indicating that theMaterials solution 2017, 10 is, endothermic,676 which is contradictory to the enthalpy of mixing measurements of16 [166 of 49].

5000 1.0

0 0.8 aB -5000 aSi 0.6

-10000

Activity 0.4 -15000 Enthalpy of mixing of mixing (J/mole) Enthalpy 0.2 o -20000 This work [167] at 2127 C [143] [167] -25000 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Mole fraction (Si) (a) (b)

Figure 12. (a) Enthalpy of mixing of the B-Si liquid; —: [143]; □: [166,168] and ○: [150,165] at 1600 ◦°C; Figure 12. (a) Enthalpy of mixing of the B-Si liquid; —: [143]; :[166,168] and :[150,165] at 1600 C; ◦ ------: - - - -: [167] [167 ]at at 2127 2127 °C;C; ( (bb)) Average Average activity activity values values of of B and Si in thethe B-SiB-Si liquid;liquid;# boronboron ((□) andand siliconsilicon ((○)[) [142]142] at 1577 ◦°C;C; ----: - - - -:[167] [167 ]at at 2127 2127 °C◦C. # According to data assessment in the current study, the B-Si phase diagram presented by Fries According to data assessment in the current study, the B-Si phase diagram presented by Fries and and Lukas [155] is accepted, since it matches with the phase diagram experimental and Lukas [155] is accepted, since it matches with the phase diagram experimental and thermodynamic thermodynamic data. However, the calculated phase diagram [155] showed the maximum solubility data. However, the calculated phase diagram [155] showed the maximum solubility of B in Si as of B in Si as 1.6 at % B at 1385 °C (as opposed to 3.5 at % at 1362 °C [142]), trying to fit their calculations 1.6 at % B at 1385 ◦C (as opposed to 3.5 at % at 1362 ◦C[142]), trying to fit their calculations with with the experimental points of [146,148]. The enthalpies and entropies of formation of the the experimental points of [146,148]. The enthalpies and entropies of formation of the intermetallic intermetallic compounds values from different authors are scattered as could be seen in Table 8 and compounds values from different authors are scattered as could be seen in Table8 and Figure 13. Figure 13.

Table 8. The enthalpy and entropy of formation of the B-Si intermetallic compounds. Table 8. The enthalpy and entropy of formation of the B-Si intermetallic compounds.

Enthalpy of Formation Entropy of Formation Compound Enthalpy of Formation Entropy of Formation Ref. Compound · · −1 · · Ref. kJ·(Mole·Atom)kJ (Mole Atom)−1 (J/Mole(J/Mole·Atom·K)Atom K) −6.150−6.150 − − [124[124,155],155] −11.119 −3.68 [153] CALPHAD B3Si −11.119 −3.68 [153] CALPHAD B3Si −6.025 - [169] −−6.02527.350 −16.18- [170[169]] −27.350 −16.18 [170] B4Si −18.16 - [171] B4Si −18.16 - [171] −4.230 - [124,155] −21.186−4.230± 1.07 -- [124,155] [142] −21.186−17.286 ± ±1.076.85 −5.31- [148[142]] B Si 6 −17.286−6.616 ± 6.85 -−5.31 [169[148]] B6Si −6.616−8.380 −1.43- [153] CALPHAD[169] −17.457 - [171] −8.380 −1.43 [153] CALPHAD B14Si −17.457−3.825 -- [153] CALPHAD[171] BnBSi,14Sin = 15.67 −12.304−3.825± 1.37 -- [153] [142CALPHAD] BnSi, n = 36 −1.810 - [124,155] BnSi, n = 15.67 −12.304 ± 1.37 - [142] BnSi, nB 15= Si36 −13.563−1.810± 4.84 −3.78- [124,155] [148]

B15BSi12 Si −13.563−4.316 ± 4.84 -−3.78 [169[148]] B12Si −4.316 - [169]

MaterialsMaterials2017 2017, 10,, 10 676, 676 1717 of 49of 49 Materials 2017, 10, 676 17 of 49

10 Materials 2017, 10, 676 10 17 of 49 BnSi B6Si B3Si BnSi B6Si B3Si 10

) 0

) 0 BnSi B6Si B3Si e.atom )

l 0 e.atom l -10 mo

/ -10 mo / J J e.atom l (k (k -10 mo on / on i i J -20

(k -20 on ormat ormat i f f

f

f -20

ormat -30-30 f

f Heat o Heat Heat o Heat -30

Heat o Heat -40-40 0.000.00 0.05 0.05 0.10 0.10 0.15 0.15 0.20 0.20 0.25 0.25 0.30 0.30 -40 Mole fraction (Si) 0.00 0.05 0.10Mole 0.15 fraction 0.20(Si) 0.25 0.30 Figure 13. Enthalpy of formation of intermetallic compounds of the B-Si phase diagram; □: [155]; ○: FigureFigure 13. 13.Enthalpy Enthalpy of of formation formation of of intermetallic intermetalliMole fractionc compounds compounds (Si) ofof thethe B-SiB-Si phasephase diagram;diagram; □::[ [155];155]; ○: [153]; Δ: [169]; : [170]; : [171]; : [142]; ◁: [148]. :[[153];Figure153]; Δ ∆13.::[ [169]; 169Enthalpy]; 5: :[[170]; 170of formation]; ♦::[ [171];171]; of  intermetalli:[: [142];142]; C◁:[: [148].c148 compounds]. of the B-Si phase diagram; □: [155]; ○: # [153]; Δ: [169]; : [170]; : [171]; : [142]; ◁: [148]. 5.4. The Bi-Si System 5.4.5.4. The The Bi-Si Bi-Si System System 5.4. TheBismuth Bi-Si System atom is one of the shallow donor impurities in silicon. Bismuth-doped-silicon (Si:Bi) BismuthBismuth atom atom is is one one of of the the shallow shallow donor donor impurities impurities in in silicon. silicon. Bismuth-doped-silicon Bismuth-doped-silicon (Si:Bi) (Si:Bi) gained increasing interest due to its superior properties over the phosphorus/arsenic-doped-silicon gainedBismuth increasing atom interest is one of due the to shallow its superior donor primpuritiesoperties overin silicon. the phosphorus/arsenic-doped-silicon Bismuth-doped-silicon (Si:Bi) gained(Si:P/Si:As) increasing junctions interest [172–175]. due to its superiorThe importan propertiesce of over bismuth-doped-si the phosphorus/arsenic-doped-siliconlicon stems from its gained increasing interest due to its superior properties over the phosphorus/arsenic-doped-silicon (Si:P/Si:As)(Si:P/Si:As)technological junctions junctions application [172 –[172–175].175 as an]. Theinfrared importanceThe photoconducting importan of bismuth-doped-siliconce detectorof bismuth-doped-si [176]. The stems Bi-Silicon from phase its stemsdiagram technological from was its (Si:P/Si:As) junctions [172–175]. The importance of bismuth-doped-silicon stems from its applicationtechnologicalconstructed as anby application infraredOlesinski photoconducting asand an Abbaschianinfrared photoconducting detector [50] based [176 on]. Thedetectorthe Bi-Siavailable [176]. phase experimentalThe diagram Bi-Si phase was results constructed diagram and was technological application as an infrared photoconducting detector [176]. The Bi-Si phase diagram was byconstructedthermodynamic Olesinski and by Abbaschian Olesinskicalculations and [50in ]Abbaschianthe based literature on the [50][ available120,177–179]. based experimentalon Figurethe available 14 resultsshows experimental the and calculated thermodynamic results Bi-Si and constructed by Olesinski and Abbaschian [50] based on the available experimental results and calculationsthermodynamicphase diagram in the obtained literature calculations from [120 ,FTlite177in the–179 database literature]. Figure and 14[120,177–179]. FactSage shows the® software calculated Figure [124], Bi-Si13 showswhich phase isthe diagram consistent calculated obtained with Bi-Si thermodynamic calculations in the literature [120,177–179]. Figure 14 shows the calculated Bi-Si fromphasethat FTlite of diagram [50]. database The obtained system and exhibits FactSage from FTlite a® monotecticsoftware database [transformation124 and], which FactSage is consistentat® software96.6 at % with [124],Si and that which 1402 of [°C; 50is ].consistentas The well system as a with phase diagram obtained from FTlite database and FactSage® software [124], which is consistent with exhibitsthateutectic of a [50]. monotectictransformation The system transformation atexhibits 1.7 × 10 a− 7monotectic atat 96.6% Si atand % transformation Siabout and 271.4 1402 °C◦C; at [66]. as 96.6 well The at as %solid aSi eutectic and solubility 1402 transformation °C; of Bias inwell Si as a that of [50]. The system exhibits a monotectic transformation at 96.6 at % Si and 1402 °C; as well as a ateutectic 1.7showed× 10 transformationa− retrograde7 at % Si and behavior at about 1.7 and× 271.4 10 its−7 maximumat◦C[ %66 Si]. and The was about solid estimated 271.4 solubility to°C be [66]. ofaround Bi The in 1.8 Sisolid × showed 10 solubility−3 at % a Bi retrograde at of 1350 Bi in Si eutectic transformation at 1.7 × 10−7 at % Si and about 271.4 °C [66]. The solid solubility of Bi in Si behaviorshowed°C. Although and a retrograde its the maximum calculated behavior was [124] estimatedand and its assessed maximum to be [50] around was maximum estimated 1.8 × 10solubility− to3 at be % around of Bi Bi at in 1350 1.8 terminal ×◦ C.10− Although3 atSi %side Bi areat the 1350 showed a retrograde behavior and its maximum was estimated to be around 1.8 × 10−3 at % Bi at 1350 °C.consistent, Although the the solvus calculated line described [124] and by Olesinski assessed and [50] Abbaschian maximum [50]solubility is more of representative, Bi in terminal because Si side are calculated°C. Although [124] the and calculated assessed [124] [50] and maximum assessed solubility [50] maximum of Bi insolubility terminal of SiBi sidein terminal are consistent, Si side are the it matches better with the experimental data of [118,179] as demonstrated in Figure 15. solvusconsistent,consistent, line described thethe solvussolvus by line line Olesinski described described and by by Olesinski Abbaschian Olesinski and and Abbaschian [50 Abbaschian] is more [50] representative, [50] is more is more representative, representative, because itbecause matches because The terminal solid solubility of Si in Bi is considered negligible [50,124]. The crystallographic betteritit matchesmatches with the betterbetter experimental withwith the the experimental experimental data of [118 data,179 data] of as of[118,179] demonstrated [118,179] as asdemonstrated demonstrated in Figure 15in .Figure in Figure 15. 15. data of the end-members of the Bi-Si system are given in Table 2. TheThe terminal terminal solid solidsolid solubility solubility solubility of of Si of inSi Si Biin in isBi Bi consideredis isconsidered considered negligible negligible negligible [50 [50,124].,124 [50,124].]. The The crystallographic Thecrystallographic crystallographic data ofdatadata the end-members of the end-membersend-members of the1800 Bi-Siof of the the system Bi-Si Bi-Si system system are given are are given in given Table in inTable2. Table 2. 2.

180016001800 Liquid#1 + Liquid#2 1402°C 160014001600 Liquid#1Liquid#1 + Liquid#2 + Liquid#2 1402°C1402°C 96.6 at.% Si 140012001400 3.3 at.% Si

3.3 at.% Si 96.6 at.%96.6 Si at.% Si 120010001200 3.3 at.% Si Liquid+Diamond_Si 10001000800 Liquid+Diamond_Si

Temperature (°C) Temperature Liquid+Diamond_Si 800600800 Temperature (°C) Temperature

Temperature (°C) Temperature 600400 Bi+Diamond_Si 600 271.4°C 400200 Bi+Diamond_Si 400 Bi+Diamond_Si 0.0 0.2 0.4 0.6271.4°C 0.8 1.0 271.4°C 200 Mole fraction (Si) 2000.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Figure 14. The calculated Bi-SiMole phase fraction diagram (Si) [124]; ○: [120]. Mole fraction (Si) ○ FigureFigure 14. 14.The Thecalculated calculated Bi-Si phase diagram diagram [124]; [124]; : [120].:[120 ]. Figure 13. The calculated Bi-Si phase diagram [124]; ○: [120]. #

Materials 2017, 10, 676 18 of 49 Materials 2017, 10, 676 18 of 49 Materials 2017, 10, 676 18 of 49 1500 Liquid#2 1500 1414oC Liquid#2 1400 o 1414 C 1400 Diamond_Si o 1300 1400 C Diamond_Si 1300 1400oC

1200 1200 Temperature (°C) Temperature Temperature (°C) Temperature Liquid+Diamond_Si 11001100 Liquid+Diamond_Si

FactSageFactSage [124] [124] OleainskiOleainski and and Abbaschian Abbaschian [50][50] 10001000 0.999980.99998 0.9999850.999985 0.99999 0.9999950.999995 1.0 1.0 MoleMole fraction ( Si(Si) ) Figure 15. Magnified part of the Bi-Si system in the Si-rich side [50]; ----: [124]; ○: [179]; □: [118]. FigureFigure 15.15. MagnifiedMagnified partpart ofof thethe Bi-SiBi-Sisystem systemin inthe theSi-rich Si-richside side[ 50[50];]; - ----: - - -: [124]; [124]; ○::[ [179];179]; □: :[[118].118]. # Diffusion of Bi in silicon was investigated by several authors [179–181]. Fuller and Ditzenberger Diffusion[179] expressed of of Bi Biinthe siliconin diffusivity silicon was ofinvestigated was bismuth investigated in bythe several 1220–1380 by authors several °C temperature [179–181]. authors [rangeFuller179–181 as and ]. =Ditzenberger 1030Fuller × and ◦ [179]Ditzenberger expressed(. / ) [179 the cm] expressed diffusivity/s with an the estimatedof diffusivitybismuth error in ofof the about bismuth 1220–1380 ±40%. in This the °C 1220–1380large temperature error valueC temperaturerange was attributed as = range 1030to as × (. / ) (−1.109 eV/ kT) 2 D = the1030 concentration× cme /s withmeasurements ancm estimated/s withat the erroran junction estimated of about depth ±40%. error due to ofThis the about largepossibility± error40%. of value Thisa Kirkendall largewas attributed error effect value to wasthe concentration attributed[182], which to would measurements the concentrationshift the reference at the measurements diffusion junction in deterface.pth at thedue Ghoshtagore junction to the possibility depth[180] concluded due of to a theKirkendall that possibility bismuth effect of [182],a Kirkendalldiffusion which would effectin silicon shift [182 obeys], the which thereference point-defect would diffusion shift mechanism. the interface. reference He measuredGhoshtagore diffusion the diffusivity interface.[180] concluded of Ghoshtagore Bi in the that 1190– bismuth [180] diffusionconcluded1394 in that °Csilicon bismuthtemperature obeys diffusionthe point-defectrange inand silicon mechanism.expressed obeys the Hethe point-defect measureddiffusion the mechanism.equation diffusivity asHe of =1.08×Bi measured in the 1190– the (.±. / ) 1394diffusivity °C oftemperature Bi in thecm /s 1190–1394 . Ishikawarange ◦etandC al. temperature [181]expressed could describe range the the anddiffusion diffusivity expressed ofequation Bi the in Si, diffusion in theas 1050–1200 equation=1.08× as °C temperature range, as = 2.0 × 10 ×(. / ) cm/s. The temperature dependent diffusion D(.±. / ) = 1.08 × e(−3.85cm±0.06/s.eV Ishikawa/ kT) cm 2et/s al.. Ishikawa[181] could et describe al. [181] the could diffusivity describe of the Bi in diffusivity Si, in the of1050–1200 Bi in Si, coefficient of Bi in Si from different sources are plotted in Figure 16. °Cin thetemperature 1050–1200 range,◦C temperature as = 2.0 ×range, 10 as×D(. / )= 2.0 × cm10−4/s×. Thee(−2.5 temperatureeV/ kT) cm2 /sdependent. The temperature diffusion The measured diffusion coefficients were found to vary within one order of magnitude in the coefficientdependentoverlapped of diffusion Bi intemperature Si coefficientfrom different range. of It Bi sourcesis in interesting Si from are differentplotted to note thatin sources Figure if these are16. measurements plotted in Figure are extrapolated, 16. Themeasurements measured of diffusion [179] appear coefficients coefficients to be consistent were found with [181]to vary at high within temperature one order (~1650 of magnitude K) and with in the overlapped[180] at temperaturelow temperature range. (~1460 It It K).is is interesting The slopes of to to th note e three that curves, if these representing measurements the activation are extrapolated, energy measurementsof bismuth, of ofshow [179[179] reasonable] appear appear to agreementto be be consistent consistent with witheach with [other.181 [181]] atHowever, highat high temperature the temperature activation (~1650 energy (~1650 K) of and K)bismuth withand [with180] [180]at low wasat temperature low found temperature much (~1460 smaller (~1460 K). than The K). that The slopes of P,slopes As of and the of threethB, ealthough three curves, curves, they representing show representing similar the diffusion the activation activation coefficient energy energy of ofbismuth, bismuth,values. show Thisshow reasonable was reasonable attributed agreement agreement to the Bi withatom-vacancy with each each other. other.pairing However, However, mechanism the activationthe [181]. activation energy energy of bismuth of bismuth was wasfound found much much smaller smaller than thatthan ofthat P, Asof P, and As B, and although B, although they show they similarshow similar diffusion diffusion coefficient coefficient values. Thisvalues. was This attributed was attributed to the Bi to atom-vacancy the Bi atom-vacancy Fuller pairing and Ditzenberger mechanismpairing [179] mechanism [181]. [181]. Ghoshtagore [180] Ishikawa et al. [181] 1E-11

/s) Fuller and Ditzenberger [179] 2 Ghoshtagore [180] Ishikawa et al. [181] 1E-11 /s)

2 1E-12

1E-12 Diffusion coefficient (cm coefficient Diffusion 1E-13

1300 1400 1500 1600 1700

Diffusion coefficient (cm coefficient Diffusion Temperature (K) 1E-13

Figure 16. The temperature dependence of the diffusion coefficients, DBi, in silicon; □: [179]; ○: [180];

Δ: [181]. 1300 1400 1500 1600 1700

Temperature (K)

FigureFigure 16. The 16. The temperature temperature dependence dependence of the of diffusion the diffusion coefficients, coefficients,DBi, inDBi silicon;, in silicon;:[179 □: ];[179];:[180 ○: ];[180];∆:[181 ]. Δ: [181]. #

Materials 2017, 10, 676 19 of 49 Materials 2017, 10, 676 19 of 49

Recently, thethe Bi-Si Bi-Si binary binary phase phase diagram diagram was calculatedwas calculated by Kaban by etKaban al. [183 et] usingal. [183] the parametersusing the ofparameters liquid phase of fromliquid the phase work from of Olesinski the work and of Abbaschian Olesinski and [50] givenAbbaschian in Table [50]9. The given enthalpy in Table of mixing 9. The andenthalpy activity of ofmixing liquid and silicon activity and bismuth of liquid are silicon presented and in bismuth Figure 17 area,b, presented respectively. in InFigure Figure 17a,b, 17a, threerespectively. enthalpy In ofFigure mixing 17a, curves three [enthalpy50,120,124 of] aremixi presented.ng curves [50,120,124] Olesinski and are Abbaschian presented. Olesinski [50] accepted and theAbbaschian thermodynamic [50] accepted parameters the th ofermodynamic Thurmond [120parameters] in their of calculations. Thurmond Differences[120] in their in thecalculations. enthalpy ofDifferences mixing values in the are enthalpy due to theof mixing use of differentvalues are thermodynamic due to the use parameters of different for thethermodynamic liquid phase byparameters [50,120] asfor shown the liquid in Table phase9. Nevertheless,by [50,120] as theshown calculated in Table enthalpy 9. Nevertheless, of mixing the of thecalculated Bi-Si liquid enthalpy [ 50] isof inmixing good of agreement the Bi-Si withliquid that [50] of is [ 124in good] at 2600 agreement◦C. The with Bi and that Si of activities [124] at in2600 the °C. liquid The phaseBi and are Si presentedactivities in in the Figure liquid 17 phaseb based are on presented the work in of Figure [67] at 17b 1414 based◦C, whichon the arework identical of [67] toat 1414 that of°C, [124 which] at theare identical same temperature. to that of [124] Additionally, at the same the temperature. Bi and Si activitiesAdditionally, in the the liquid Bi and phase Si activities were calculated in the liquid at 2600phase◦ C[were124 calculated] to verify theat 2600 findings °C [124] in Figure to verify 17a. the The findings positive in enthalpy Figure 17a. implies The thatpositive the mixingenthalpy is endothermicimplies that the and mixing the attractive is endothermic interaction and betweenthe attractive molecules interaction of different between species molecules are weaker of different than thosespecies between are weaker molecules than those of the between same molecules species. This of the strong same interaction species. This between strong interaction the pairs of between similar atomsthe pairs is reflectiveof similar ofatoms the presenceis reflective of of immiscibility the presence in of the immiscibility liquid phase. in the The liquid shape phase. of activity The shape plot indicatesof activity the plot presence indicates of athe two-phase presence fieldof a two-phase at 1414 ◦C, field which at is1414 liquid °C, #1 which and liquidis liquid #2 as#1 inferredand liquid from #2 theas inferred Bi-Si phase from diagram the Bi-Si in phase Figure diagram 14. in Figure 14.

1.0 16000 1414°C

14000 0.8 2600°C 12000

10000 0.6 aSi 8000 aBi

Activity 0.4 6000 Ideal solution 4000 [50] Enthalpy of Enthalpy (J/mole)mixing [120] 0.2 2000 [124] at 2600oC

0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Mole fraction (Si) (a) (b)

Figure 17. (a) Calculated enthalpyenthalpy ofof mixingmixing ofof the the Bi-Si Bi-Si liquid liquid [ 124[124]] at at 2600 2600◦ C;°C; —: ―: [ 50[50];]; - ----: - - -: [[120]120] and ((b)) calculatedcalculated activityactivity ofof BiBi andand SiSi inin thethe Bi-SiBi-Si liquidliquid atat 14141414 ◦°CC andand 26002600 ◦°CC[ [124].124].

Table 9.9. Thermodynamic parameters of thethe liquidliquid phasephase inin Bi-SiBi-Si system.system. Phase Excess Gibbs Energy Parameter (J/Mole) Ref. Phase Excess Gibbs Energy Parameter (J/Mole) Ref. 0 = 46 370 + 2.26 [50] ,liq Liquid 0 0 LBi,Si = 46 370 + 2.26 T [50 ] Liquid , = 62 090 − 8.62 [120] 0 liq LBi,Si = 62 090 − 8.62 T [120] 5.5. The Ga-Si System 5.5. The Ga-Si System Gallium, as a p-type dopant in silicon, is attaining great interest for the PV industry, because siliconGallium, thin films as acanp-type be grown dopant in inGa silicon, melts by is liquid attaining phase great epitaxy interest [85,184]. for the The PV Ga-Si industry, binary because phase silicondiagram, thin shown films in can Figure be grown 18, was in Garedrawn melts after by liquid Franke phase and epitaxy Neuscütz [85 [185],,184]. who The Ga-Siaccepted binary the phase diagram,diagram data shown reported in Figure by Olesinski18, was redrawn et al. [51]. after The Franke system and is described Neuscütz as [185 a simple], who eutectic accepted that the occurs phase diagramat 99.994 dataat % reportedGa and 29.7 by Olesinski°C [185]. The et al. solid [51]. solubility The system of isgallium described in silicon as a simple shows eutectic typical thatretrograde occurs ◦ atbehavior, 99.994 at as % demonstrated Ga and 29.7 C[in Figure185]. The 19, solidand was solubility estimated of gallium as ~0.08 in at silicon % at around shows typical 1200 °C retrograde [51]. The ◦ behavior,solubility asof silicon demonstrated in gallium in Figureis negligible, 19, and because was estimated the liquid as phase ~0.08 almost at % at degenerate around 1200 on theC[ 51Ga]. Theterminal solubility side. ofThe silicon crystallographic in gallium is data negligible, of the end because members the liquid of the phase Ga-Si almost system degenerate are given in on Table the Ga 2. terminalThe liquid side. phase The crystallographicwas experimentally data investigated of the end members through of thermal the Ga-Si analysis system are[186], given and in thermal Table2. analysis and metallography [187]. The liquid solubilities were determined by a weighing technique

Materials 2017, 10, 676 20 of 49

The liquidMaterials phase 2017, 10 was, 676 experimentally investigated through thermal analysis [186], and thermal20 of analysis 49 Materials 2017, 10, 676 20 of 49 and metallography [187]. The liquid solubilities were determined by a weighing technique in the in the 300–800 °C temperature range [178,188]. The liquidus of Ga-Si phase diagram [185] shows a 300–800 ◦C temperature range [178,188]. The liquidus of Ga-Si phase diagram [185] shows a reasonable reasonablein the 300–800 agreement °C temperature with the rangeexperimental [178,188]. data Th eof liquidus [178,186,188]. of Ga-Si However, phase diagram Savitskiy [185] et al.shows [187] a agreementreportedreasonable with lower agreement the values experimental duewith tothe impuritiesdata experimental of [178 in ,the186 data ,st188arting of]. [178,186,188]. However, elements. SavitskiyIt However, is worth et mentioningSavitskiy al. [187] reportedet thatal. [187] the lower valuesretrogradereported due to impuritieslower solubility values of in dueGa the in to starting Si impurities is an elements.indication in the Itofstarting isa worthlarge elements. entropy mentioning ofIt isthe wo thatSi-Garth thementioning solid retrograde solution that with solubility the of Gatemperatureretrograde in Si is an solubility indication[189]. of ofGa a in large Si is entropyan indication of the of Si-Ga a large solid entropy solution of the with Si-Ga temperature solid solution [189 with]. temperature [189]. 1500 1500

1250 Liquid 1250 Liquid

1000 1000

750 750 Liquid+Diamond_Si Liquid+Diamond_Si 500

Temperature (°C) 500 Temperature (°C) 250 250 Eutectic 99.994 at.% Ga o Eutectic 99.994 at.% Ga 29.7 C 0 29.7oC 00.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2Mole 0.4 fraction ( 0.6Si) 0.8 1.0 Mole fraction (Si) FigureFigure 18. 18.The The Ga-Si Ga-Si phase phase diagram diagram [[185];185]; □: :[[186];186 ];Δ:∆ [188];:[188 ];: 5[187]::[187 ○:]: [178].:[178 ]. Figure 18. The Ga-Si phase diagram [185]; □: [186]; Δ: [188]; : [187]: ○: [178]. # Liquid 1400 Liquid 1400

1200 1200 Diamond_Si Diamond_Si 1000 1000

800 800

Temperature (°C) 600 Temperature (°C) 600 Liquid+Diamond_Si Liquid+Diamond_Si 400 400

0.9990 0.9992 0.9994 0.9996 0.9998 1.0000 0.9990 0.9992 0.9994 0.9996 0.9998 1.0000 Mole fraction (Si) Mole fraction (Si) Figure 19. Magnified part of the calculated Ga-Si phase diagram [185]; □: [118]; Δ: [85]. Figure 19. Magnified part of the calculated Ga-Si phase diagram [185]; □: [118]; Δ: [85]. Figure 19. Magnified part of the calculated Ga-Si phase diagram [185]; :[118]; ∆:[85]. Gallium was used at the beginning of the semiconductor industry for making alloy junctions, becauseGallium of its washigh used diffusion at the coefficientbeginning ofand the low semiconductor eutectic temperature industry for[90]. making However, alloy the junctions, use of Galliumbecause of was its usedhigh diffusion at the beginning coefficient of and the low semiconductor eutectic temperature industry [90]. for However, making alloythe use junctions, of gallium is limited, because of its high diffusivity in SiO2, which is commonly used for layer masking because[190].gallium of The itsis diffusion limited, high diffusion because of gallium of coefficientits in highsilicon diffusivity was and first low ininvestigated SiO eutectic2, which by temperature is Fuller commonly and Ditzenberger used [90]. for However, layer [179] masking who the use of galliumdescribed[190]. The is thediffusion limited, diffusion of because gallium coefficient in of silicon of its galliu high wasm first diffusivityin the investigated 1105–1360 in by SiO°C Fuller 2temperature, which and Ditzenberger is range commonly as =3.6×[179] usedwho for layerdescribed(./) masking cmthe [190 diffusion/s].. In The agreement coefficient diffusion with of ofgalliu Fuller galliumm inand the in Ditzenbe1105–1360 siliconrger was °C [179],temperature first Pichler investigated range [90] asderived by=3.6× Fuller the and (./) Ditzenbergerdiffusivity [179 cmof gallium]/s who. In described underagreement intrinsic the with diffusion and Fuller inert coefficient conditionsand Ditzenbe ofin galliumsiliconrger [179], from in the Pichlerseveral 1105–1360 studies[90] derived◦ C[179,191– temperature the diffusivity of gallium(. /) under(− intrinsiceV kT) and inert conditions in silicon from several studies [179,191– 194] as =3.81× 3.5 / cm /s, in2 the 800–1380 °C temperature range. range as D = 3.6 ×(. /)e cm /s. In agreement with Fuller and Ditzenberger [179], 194] as =3.81× cm /s, in the 800–1380 °C temperature range. Pichler [90] derived the diffusivity of gallium under intrinsic and inert conditions in silicon from several (−3.552 eV/kT) 2 ◦ studies [179,191–194] as Di = 3.81 × e cm /s, in the 800–1380 C temperature range. Materials 2017, 10, 676 21 of 49 Materials 2017, 10, 676 21 of 49 Enthalpy of mixing of the liquid Ga-Si binary alloys were measured at 1487 ± 5 °C by KanibolotskyEnthalpy et of al. mixing [195], ofusing the liquidhigh-temperature Ga-Si binary isoperibolic alloys were calorimetry, measured up at 1487to 0.6%± 5Ga.◦C The by Kanibolotskyenthalpy of mixing et al. [ 195for], the using melt high-temperature of these alloys was isoperibolic found positive, calorimetry, as shown up to in 0.6% Figure Ga. The20a, enthalpywhich is ofan mixing indication for the of meltan endothermic of these alloys mixing. was found In a positive,recent investigation, as shown in FigureSudavtsova 20a, which et al. is[196] an indication reported ofmixing an endothermic enthalpies mixing.of the Ga-Si In a recent melt in investigation, the full composition Sudavtsova range, et al. using [196] reportedisoperibolic mixing calorimetry enthalpies at of1477 the °C, Ga-Si and melt their in results the full were composition in good agreement range, using with isoperibolic those of Kanibolotsky calorimetry atet al. 1477 [195].◦C, andThus, their the resultsenthalpies were of in mixing good agreementdetermined with by [195,196] those of Kanibolotsky using calorimetric et al. [measurements195]. Thus, the are enthalpies recommended of mixing in determinedthis work as by they [195 are,196 more] using reliable. calorimetric The activities measurements of gallium are recommendedand silicon in the in thismelts work at 1477 as they °C areare moregiven reliable.in Figure The 20b. activities Sudavtsova of gallium et al. [196] and siliconcalculated in the the melts Si activity at 1477 from◦C arethe givencoordination in Figure of 20 theb. Sudavtsovaliquidus line et using al. [196 Schröder’s] calculated equation, the Si while activity the from Ga activity the coordination was calculated of the using liquidus the lineanalytical- using Schröder’snumerical equation,Gibbs-Duhem while integration. the Ga activity The was calculated calculated activities using the of analytical-numericalGa-Si melts by Safarian Gibbs-Duhem et al. [67] integration.were based on The the calculated work of Sudavtsova activities of et Ga-Si al. [196]. melts The by recently Safarian assessed et al. [67 activities] were based of Ga onand the Si in work the ofmelts Sudavtsova [185] deviate et al. from [196 ].the The calculations recently assessedof [67,196] activities and show of Ganearly and ideal Si in behavior. the melts This [185 deviation] deviate fromcould the be calculationsdue to that of Sudavtsova [67,196] and et show al. [196] nearly treated ideal behavior.the Ga-SiThis melt deviation as quasi-regular could be duesolutions. to that SudavtsovaMoreover, they et al. correlated [196] treated the the positive Ga-Si meltdeviation as quasi-regular from ideality solutions. to the absence Moreover, of compounds they correlated and/or the positivesolid solutions deviation in fromthe system ideality and to theto the absence degenerate of compounds eutectic and/orin the Ga-rich solid solutions side. The in optimized the system andmodel to theparameters degenerate for eutecticthe liquid in thephase, Ga-rich listed side. in Table The optimized 10, were adopted model parameters by Franke forand the Neuscütz liquid phase, [185] based listed inon Table the work 10, were of Olesinski adopted byet al. Franke [51]. and Neuscütz [185] based on the work of Olesinski et al. [51].

[51] 1.0 6000 [120] [121] [122] 5000 [185] 0.8 [195] and [196] aSi aGa [197] 4000 0.6

3000

Activity 0.4 2000 Ideal solution

Enthalpy of mixing (J/mole) 0.2 1000 [67] [185] [196] 0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.00.20.40.60.81.0 Mole fraction (Ga) Mole fraction (Ga) (a) (b)

Figure 20. (a) Enthalpy of mixing of the Ga-Si liquid at 1477 °C; ―◦ : [185]; □: [195] and [196] at 1487 ± Figure 20. (a) Enthalpy of mixing of the Ga-Si liquid at 1477 C;—:[ 185]; :[195] and [196] at 14875 °C; ±-·-5·- ◦: C;[121];-·-·- -:[··-··121-: [120];]; -··-·· -----:-:[120 [122];]; - -  - -: -: [197]; [122]; ····5 ::[ [51]197 at]; ····>1414:[51 °C] atand >1414 (b) Activity◦C and of (b )gallium Activity and of galliumsilicon in and the silicon Ga-Si liquid; in the Ga-Si ―: [185]; liquid; -·-·-:— [196]:[185 and]; -·------·-: [196 : [67]] and at -1477 - - - -: °C. [67 ] at 1477 ◦C.

Table 10.10. OptimizedOptimized modelmodel parametersparameters ofof thethe Ga-SiGa-Si system.system. Phase Excess Gibbs Energy Parameter (J/Mole) Ref. Phase Excess0 Gibbs Energy Parameter (J/Mole) Ref. Liquid , = 14 900 + 4.9 [51] 0 liq Liquid LGa,Si = 14 900 + 4.9 T [51] 5.6. The In-Si System 5.6. TheIndium In-Si Systemis a p-type impurity in silicon from group IIIA of the periodic table. Indium has been usedIndium for the isfabrication a p-type impurity of infrared in silicon detectors, from beca groupuse IIIA of its of thehigh periodic ionization table. energy Indium [90]. has The been binary used forIn-Si the phase fabrication diagram of was infrared assessed detectors, by Olesinski because et of al its. [52] high using ionization the experimental energy [90]. data The of binary the liquid In-Si phasephase diagramfrom [120,178,186,188] was assessed byand Olesinski the solubility et al. data [52] usingof In in the Si experimentalfrom [198,199]. data The of In-Si the binary liquid phasephase fromdiagram [120 ,178shown,186 ,188in Figure] and the 21 solubility was calculated data of In usin in Sig fromFTlite [198 thermodynamic,199]. The In-Si binarydatabase phase [124]. diagram The showncalculated in Figure phase 21 diagram was calculated [124] is consistent using FTlite with thermodynamic the assessment database of Olesinski [124]. et The al. calculated[52]. The system phase diagramshows a [flat124 ]liquidus, is consistent which with indicates the assessment the existence of Olesinski of a metastable et al. [52]. Themiscibility system showsgap in a the flat liquid. liquidus, A whicheutectic indicates transformation, the existence occurs of at a metastable4 × 10−3 at % miscibility Si and very gap close in theto the liquid. melting A eutectic temperature transformation, of In. The crystallographic data of the end members of the In-Si system are listed in Table 2. The intrinsic

Materials 2017, 10, 676 22 of 49 occurs at 4 × 10−3 at % Si and very close to the melting temperature of In. The crystallographic data Materials 2017, 10, 676 22 of 49 of the end members of the In-Si system are listed in Table2. The intrinsic diffusivity of indium in silicondiffusivity as function of indium of temperature, in silicon fromas function experimental of temperature, measurements from experimental of [179,200 –measurements202], was derived of by (−3.668 eV/kT) 2 (. ⁄) Pichler[179,200–202], [90] to be as was follows: derivedD byi = Pi3.13chler× [90]e to be as follows:cm /s. =3.13× cm /s.

1400 Liquid

1200

1000

800 Liquid+Diamond_Si 600

Temperature (°C) 400

200 156.8°C 0.004 (In)+Diamond_Si 0 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Figure 21. The calculated In-Si phase diagram ―: [124] based on the assessment of [52]; ○: [186]; □: Figure 21. The calculated In-Si phase diagram—:[ 124] based on the assessment of [52]; :[186]; [120]; Δ: [188]; : [178]. :[120]; ∆:[188]; 5:[178]. # Different maximum solid solubility values of indium in silicon were reported by Backenstoss Different[198] as 8 × maximum 10−4 at % using solid neutron solubility activation values analysis of indium and in by silicon Jones et were al. [199] reported as 5 × by 10− Backenstoss3 at % at 1330 [198] as 8 ×°C 10using−4 at a gradient % using transport neutron solution activation growth analysis process. and Pichler by Jones [90] provided et al. [199 values] as 5 for× the10− solid3 at % at 1330 ◦solubilityC using of a gradientindium in transport silicon from solution resistivity growth combined process. with Pichler Hall-effect [90 ]measurements provided values [200–206] for the or solid capacitance-voltage profiling [207] at different concentrations and temperatures. Later, the solid solubility of indium in silicon from resistivity combined with Hall-effect measurements [200–206] solubility of In in Si was calculated by Yoshikawa et al. [208], considering the results from the work or capacitance-voltage profiling [207] at different concentrations and temperatures. Later, the solid of Scott and Hager [204], as shown in Figure 22. In their calculations [208], the liquidus was presented solubilityas a dashed of In in line Si due was to calculated the lack of byexperimental Yoshikawa data et [204] al. [208 at high], considering temperatures. the The results maximum from the values work of Scottof and indium Hager solubility [204], as in shown silicon, inreported Figure by 22 Scott. In their and Hager calculations [204], was [208 only], the up liquidus to 1300 °C, was because presented of as a dashedthe furnace line due limitations to the lack and of problems experimental in quartz data ampoules. [204] at This high explains temperatures. why the Theshape maximum of In solubility values of indiumcurve solubility did not indecrease silicon, to reported zero at the by Si Scott melting and te Hagermperature [204 ],(i.e., was retrograde only up tosolubility) 1300 ◦C, as because typically of the furnaceobserved limitations in other and systems, problems such in as quartz Al-Si, ampoules. As-Si, Ga-Si This and explains Sb-Si. Later, why Cerofolini the shape et of al. In [200], solubility using curve did notresistivity decrease and to zeroHall atmeasurements, the Si melting reported temperature lower (i.e.,indium retrograde solubility solubility) in silicon asdue typically to the high observed in otherdiffusivity systems, of suchIn atoms as Al-Si, in Si As-Si, lattice, Ga-Si which and allows Sb-Si. the Later, existence Cerofolini of a metastable et al. [200 state,], using observed resistivity by and Cerofolini et al. [209], in the In-Si system. The solubility limits of indium in silicon [200] were Hall measurements, reported lower indium solubility in silicon due to the high diffusivity of In atoms measured using ion implantation followed by thermal annealing. Although this technique is operated in Si lattice, which allows the existence of a metastable state, observed by Cerofolini et al. [209], in the at low temperatures, which means that doping can be performed without influencing previously In-Sidiffused system. regions The solubility and produce limits uniform of indium In-doped in silicon layers, [the200 solvus] were line measured is considered using inaccurate. ion implantation This followedconclusion by thermal was drawn annealing. from Figure Although 22. The experimental this technique data is point operated at 1200 at °C low [200] temperatures, indicate that the which meanssolubility that doping of In did can not be start performed at the Si melting without poin influencingt. On the other previously hand, Scott diffused and Hager regions [204] prepared and produce uniformindium-doped-silicon In-doped layers, using the solvus a gradient-transport line is considered solution inaccurate. growth Thisprocess conclusion in the 950 was to 1300 drawn °C from Figuretemperature 22. The experimental range and measured data point the In at solubility 1200 ◦C[ using200] indicate Hall measurements. that the solubility Although of this In didtechnique not start at the Sipromotes melting point.structural On defects the other with hand, increasing Scott andtemperature, Hager [204 the] solubility prepared measurements indium-doped-silicon of indium usingin a gradient-transportsilicon proves to solution be accurate growth for processthe whole in thetemp 950erature to 1300 range◦C as temperature can be seen rangein Figure and 22. measured In agreement with [204], the accepted Si-rich solvus line in the current study is presented by a solid line the In solubility using Hall measurements. Although this technique promotes structural defects with in Figure 22. increasing temperature, the solubility measurements of indium in silicon proves to be accurate for the whole temperature range as can be seen in Figure 22. In agreement with [204], the accepted Si-rich solvus line in the current study is presented by a solid line in Figure 22.

Materials 20172017,, 1010,, 676676 23 of 49 Materials 2017, 10, 676 23 of 49 Liquid 1400 Liquid 1400 Diamond_Si Diamond_Si 1200 1200 Temperature (°C) Temperature (°C) 1000 1000 Liquid+Diamond_SiLiquid+Diamond_Si

YoshikawaYoshikawa et et al. al. [208] [208] This work 800 This work 800 10-4 10-5 10-6 10-7 10-4 10-5 10-6 10-7 Mole fraction (In) Mole fraction (In) Figure 22. Magnified part of the In-Si phase diagram; -----: [208]; □: [204]; ○: [200]; Δ: [198]. FigureFigure 22. 22.Magnified Magnified part part of of the the In-Si In-Si phase phase diagram; diagram; ------: - - -: [208]; [208]; □::[ [204];204]; ○: :[[200];200]; Δ∆: :[[198].198]. # The thermodynamic properties of the In-Si system were reviewed by Frank and Neuschütz [210] Thebased thermodynamic on the work of Olesinski propertiesproperties et ofal.of thethe[52] In-Siand Tmar system et al. were [197]. reviewed Enthalpy byby of Frank mixing and and Neuschütz activity are [[210]210] basedgiven on the in Figure work work 23a,b,of of Olesinski Olesinski respectively. et et al. al. The [52] [52 enthalpy ]and and Tmar Tmarof mixing et etal. al.values [197]. [197 ofEnthalpy]. In-Si Enthalpy melts of found mixing of mixing in the and literature and activity activity are aregiven given[52,66,120] in Figure in Figure support23a,b, 23 respectively. a,b,one another respectively. and The thus enthalpy The are enthalpy accept of mixinged in of the mixingvalues current of values work. In-Si meltsThe of In-Si results found melts of inThurmond foundthe literature in the literature[52,66,120][121] [were52 support,66 not,120 considered ]one support another in one the and another current thus areevaluation and accept thus,ed arebecause in accepted the they current show in the work. different current The enthalpy results work. Theof mixingThurmond results of Thurmond[121] valueswere not[of121 aboutconsidered] were 6000 not J/mole consideredin the atcurrent mid-composition in the evaluation current , evaluation,from because other they result because shows [52,66,120]. theydifferent show The enthalpy different Si-In liquid of enthalpy mixing solution is endothermic as indicated by the positive enthalpy of mixing and positive deviation of ofvalues mixing of valuesabout 6000 of about J/mole 6000 at J/mole mid-composition at mid-composition from other from result others [52,66,120]. results [52,66 The,120 Si-In]. The liquid Si-In activities from Raoult’s law. The optimized model parameters for the liquid phase [52] are listed in liquidsolutionTable solution is 11, endothermic which is endothermic represent as indicated the as most indicated accept by theable by positi the data positive vefor enthalpythe In-Si enthalpy phase of mixing of diagram. mixing and and positive positive deviation deviation of ofactivities activities from from Raoult’s Raoult’s law. law. The The optimized optimized model model parameters parameters for for the the liquid liquid phase phase [52] [52] are listed in TableTable 1111,, whichwhich representrepresent thethe mostmost acceptableacceptable datadata forfor the1.0the In-SiIn-Si phasephase diagram. diagram. 12000

0.81.0 10000 12000

8000 0.60.8 10000

6000 aSi Activity 0.4 8000 0.6 aIn 4000 Ideal solution

6000 o [52] at 1427 C 0.2 Enthalpy of mixing (J/mole) of mixing Enthalpy 2000 aSi [66] Activity 0.4 aIn [120] at 1427oC [124] and [210] at 1427°C [67] at 1427°C 4000 [121] Ideal solution 0 0.0 0.0 0.2[52] 0.4 at 1427oC 0.6 0.8 1.0 0.20.0 0.2 0.4 0.6 0.8 1.0 Enthalpy of mixing (J/mole) of mixing Enthalpy 2000 Mole[66] fraction (Si) Mole efraction (Si) [120] at 1427oC [124] and [210] at 1427°C [121](a) [67](b )at 1427°C 0 0.0 0.0Figure 23. 0.2 (a) Enthalpy 0.4 of mixing 0.6 of In-Si 0.8 melts 1.0 at 1427 °C0.0 [52]; -·-·-: 0.2 [121]; ····: 0.4 [120]; -----: 0.6 [66] at 0.81427 1.0 °C and (b) ActivityMole of fraction In and (Si) Si in the liquid In-Si phase [124,210]; -----: [67]Mole at 1427 efraction °C. (Si) (a) (b) Table 11. Model parameters of the In-Si system. Figure 23. (a) Enthalpy of mixing of In-Si melts at 1427 °C◦ [52]; -·-·-: [121]; ····: [120]; -----: [66] at 1427 Figure 23. (a) EnthalpyPhase of mixing Excess of In-SiGibbs melts Energy at 1427 parameterC[52 ];(J/mole) -·-·-: [121 Ref.]; ···· :[120]; - - - - -: [66] at °C and◦ (b) Activity of In and Si in the liquid In-Si phase [124,210]; -----: [67] at 1427 °C. ◦ 1427 C and (b) Activity of In and Si in the0 liquid In-Si phase [124,210]; - - - - -: [67 ] at 1427 C. Liquid , = 45 100 + 12.8 [52]

Table 11.11. Model parametersparameters ofof thethe In-SiIn-Si system.system. Phase Excess Gibbs Energy parameter (J/mole) Ref. Phase Excess Gibbs Energy Parameter (J/mole) Ref. 0 Liquid , = 45 100 + 12.8 [52] liq Liquid 0L = 45 100 + 12.8 T [52] Ga,Si

Materials 2017, 10, 676 24 of 49

Materials 2017, 10, 676 24 of 49 5.7.Materials The N-Si 2017, System10, 676 24 of 49 5.7. The N-Si System 5.7.Nitrogen The N-Si System gas is often used as inert atmosphere during post implantation annealing and as a carrier gasNitrogen in semiconductor gas is often diffusionused as inert technology atmosphere [211]. during Therefore, post theimplantation commercial annealing silicon may and contain as a Nitrogen gas is often used as inert atmosphere during post implantation annealing and as a nitrogencarrier ingas dissolved in semiconductor form if no diffusion measures technology for cleaning [211]. are Therefore, taken [32 ].the Kaiser commercial and Thurmond silicon may [212 ] carrier gas in semiconductor diffusion technology [211]. Therefore, the commercial silicon may foundcontain that nitrogen nitrogen in indissolved silicon haveform if donor no measures properties for cleaning when it are reacts taken with [32]. liquid Kaiser silicon and Thurmond and forms contain nitrogen in dissolved form if no measures for cleaning are taken [32]. Kaiser and Thurmond silicon[212] nitride found that (Si Nnitrogen). The in thin silicon film have silicon donor nitrides properties are attractive when it reacts for applications with liquid silicon in microelectronic and forms [212] found that 3nitrogen4 in silicon have donor properties when it reacts with liquid silicon and forms andsilicon optoelectronic nitride (Si3N devices,4). The thin because film silicon they performnitrides are as attractive gate dielectric for applications layers, intermetal in microelectronic insulators, siliconand optoelectronic nitride (Si3N4 ).devices, The thin becaus film silicone they nitridesperform are as attractive gate dielectric for applications layers, intermetal in microelectronic insulators, passivation films, diffusion barriers or optical matching layers [213,214]. The N-Si phase diagram, andpassivation optoelectronic films, diffusiondevices, barriersbecause orthey optical perform matching as gate layers dielectric [213,214]. layers, The N-Siintermetal phase diagram,insulators, in in Figure 24, was developed by Ma et al. [214], using Calphad method at 1 atmosphere, taking into passivationFigure 24, films,was developed diffusion barriersby Ma etor al.optical [214], matching using Calphad layers [213,214].method at The 1 atmosphere,N-Si phase diagram, taking into in considerationFigure 24, was the developed available databy Ma [215 et– 222al. ].[214], At the using same Calphad pressure, method the system at 1 atmosphere, exhibits a eutectic taking reactioninto consideration the available data [215–222]. ◦At the same pressure, the system exhibits a eutectic ofconsideration L → Diamond the Si +available Si3N4 at data around [215–222]. 1413.94 AtC the and same 0.012 pressure, at % N as the demonstrated system exhibits in the a N-Sieutectic partial reaction of L → Diamond Si + Si3N4 at around 1413.94 °C and 0.012 at % N as demonstrated in the N- phasereactionSi partial diagram of phaseL → for Diamond diagram extremely Si for + lowSiextremely3N4 N at concentrations around low N1413.94 concentrations redrawn°C and 0.012 afterredrawn at Yatsurugi% N after as demonstrated Yatsurugi et al. [32 et] in inal. Figurethe [32] N- in 25 . −6 UsingSiFigure partial zone-melting 25. phase Using diagram zone-melting experiments, for extremely experiments, the maximum low N theconcentrations solubilitymaximum of solubilityredrawn N in Si afterof was N Yatsurugi foundin Si was to beetfound al. 9 ×[32] 10to inbe at %Figure at9 × the 10 −25.6 eutectic at Using% at the temperature zone-melting eutectic temperature [ 32experiments,]. The [32]. extremely theThe maximum extr lowemely solubility solubilitylow solubility of of N N in of in Si N Si wasin was Si attributedwas found attributed to tobe the 9 × 10−6 at % at the eutectic temperature [32]. The extremely low solubility of N in Si was attributed highto stabilitythe high stability of Si3N4 ofbesides Si3N4 besides the large the difference large difference in the in atomic the atomic radii radii of N of and N Siand [32 Si]. [32]. Atthe At samethe eutectictosame the higheutectic temperature, stability temperature, of Kaiser Si3N4 andKaiser besides Thurmond and the Thurmond large [212 difference] reported[212] reported in the a much atomic a much lower radii lower solubility of solubilityN and of Si N [32].of in N solid Atin solid the Si as − 2 ×sameSi10 as eutectic29 ×at 10 %−9 andtemperature,at %a and higher a higher Kaiser N concentration N and concentration Thurmond of 0.02 of [212 0.02 at] reported %at in% liquidin liquid a much Si Si due lower due to to thesolubility the detectability detectability of N in solidlimit limit of −9 theSiof measurements.as the 2 ×measurements. 10 at % and a higher N concentration of 0.02 at % in liquid Si due to the detectability limit of the measurements. 3500 3500 Gas Gas 3000 3000 2500 2500 Liquid+Gas

Liquid+Gas o 2000 1877 C 2000 1877oC Liquid+Si N 1500 3 4 1413.94oC Liquid+Si N 1500 3 4 1413.94oC

Temperature (°C) 1000 4 Temperature (°C) 1000 N 3 4 Si N

Si N +Gas3 Si N +Diamond_Si 500 3 4 3 4 Si N +GasSi Si N +Diamond_Si 500 3 4 3 4 0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Mole fraction (Si) Figure 24. The N-Si binary phase diagram calculated by Ma et al. [214] at 1 atm; ○: [221]; □: [223]. Figure 24. Figure 24.The The N-Si N-Si binary binary phasephase diagram calcul calculatedated by by Ma Ma et et al. al. [214] [214 at] at 1 1atm; atm; ○: [221];:[221 □];: [223].:[223 ]. # 1414.04 1414.04 Liquid Liquid 1414.00

~ 1414.00 ~ ~ 1413.96

Liquid+Diamond_Si~ Liquid+Si3N4 Liquid+Diamond_Si 1413.96 Liquid+Si3N4 ~ ~ ~ ~ 1413.92 Diamond_Si 1413.92 Temperature (°C) Temperature Si N +Diamond_Si Diamond_Si Temperature (°C) Temperature 3 4 1413.88 Si3N4+Diamond_Si 1413.88

1413.84 0.00018 0.00012 0.00008 12 8 4 1413.84 0.00018 0.00012 0.00008 12 8 -8 4 Mole fraction (N) x10 -8 Mole fraction (N) x10 Figure 25. The N-Si partial phase diagram for the extremely low N concentration after Yatsurugi et FigureFigureal. 25. [32].The 25. The N-Si N-Si partial partial phase phase diagram diagram for for the the extremely extremely low low N concentrationN concentration after after Yatsurugi Yatsurugi et et al. [32]. al. [32].

Materials 2017, 10, 676 25 of 49

Despite their low solubility, nitrogen impurities strongly interact with vacancies in Si lattice altering the size and kinetics of the voids causing gate oxide failure [224]. Using dislocation unlocking experiments, Alpass et al. [225] expressed the effective diffusivity of nitrogen in Si in the 500–750 ◦C (−3.24 ev/kT) 2 temperature range as: De f f = 200 000 × e cm /s. According to Fujita et al. [224], the di-interstitial nitrogen defect was found to be the dominant diffusion mechanism of nitrogen in Si. In this mechanism, two nitrogen interstitial atoms bind into Si lattice due to their rapid diffusion. The defects of this type are known to be stable up to 900 ◦C[224]. Nevertheless, they do not possess any deep donor or acceptor properties [226]. So far, the Si3N4 [227] is the only confirmed intermetallic compound in the N-Si system [228]. The presence of other silicon nitrides, such as SiN [229,230], Si3N2 [230], Si3N[231] and Si(N3)4 [232], was uncertain and not supported by other studies. The compound Si3N4 exists in three polymorphic forms, α, β and γ phases [233]. Analogous to cubic boron nitride, cubic γSi3N4 with a spinel-type structure exists but only at high pressure (above 15 GPa) and temperature (exceeding 2000 K) [234]. Therefore, it will only be mentioned briefly here and more importance will be given to α and β structures. According to Grün [54], βSi3N4 is the more stable phase at room temperature and αSi3N4 is a metastable phase. The crystallographic data of Si3N4 phases are presented in Tables2 and 12. In principle, both α and β silicon nitride phases exist as stoichiometric compositions with Si12N16 for α-phase and Si6N8 for β-phase [235], representing the 28 and 14 atoms in the unit cells, respectively. Whilst αSi3N4 has trigonal symmetry with space group P31c (No. 159) [235] and Pearson symbol hP28 [39], βSi3N4 has hexagonal symmetry with space group P63 (No. 173) [235] and Pearson symbol hP14 [39]. Figure 26 is drawn to describe the crystal structure of the three forms of Si3N4 based on the crystallographic data from Table2 and site occupancies from [ 39] in Table 12. It can be depicted from the crystallographic data and the graphic presentation of silicon nitride phases that Si3N4 tetrahedra in the α structure appear as interconnected cavities as opposed to tunnels in β structure parallel to the c-axis of the unit cell. The length of c parameter in αSi3N4 is almost double that of βSi3N4. This is attributed to the occupancy of additional Si2 atoms on 6c sites of the unit cell. The N-Si phase diagram in Figure 24 shows that Si3N4 has no true melting temperature at ◦ atmospheric pressure. It rather decomposes to liquid and N2 gas at 1877 C[214,221], which is only 23 ◦C lower than the measurement reported by Forgeng and Decker [223] as 1900 ◦C. Although, in this work we consider the values reported by [214,221,223] are consistent, the variation between them could be due to the pressure difference between these measurements. For instance, Forgeng and Decker [223] did not specify the pressure in their work; while both [214,221] performed their calculations at the atmospheric pressure. Because of no other compounds in the N-Si system, it is expected that Si3N4 melts congruently at high enough nitrogen pressure as shown in the calculated condensed N-Si phase diagram [214] in Figure 27. The maximum calculated congruent melting temperature of Si3N4 is 5318 ◦C at about 7.5 × 109 Pa.

Table 12. Atom positions in the unit cell of Si3N4.

Phase Symmetry Pearson Symbol Atom Wyckoff Position x y z N1 6c 0.0424 0.3891 0.0408 N2 6c 0.3169 0.3198 0.2712 N3 2b 0.3333 0.6667 0.3649 αSi N Hexagonal hP28 3 4 N4 2a 0.0000 0.0000 1.0000 Si1 6c 0.0821 0.5089 0.3172 Si2 6c 0.1712 0.2563 0.0274 N1 6c 0.0298 0.3294 0.2680 βSi3N4 Hexagonal hP14 N2 2b 0.3333 0.6667 1.0000 Si 6c 0.7686 0.1744 0.2550 N 32e 0.8676 0.8676 0.8676 γSi3N4 Cubic cF56 Si1 8a 0 0 0 Si2 16d 0.6250 0.6250 0.6250 Materials 2017, 10, 676 26 of 49 Materials 2017, 10, 676 26 of 49

N

Si

b c a

(a)

b c a

(b)

b

c a

(c)

Figure 26. Crystal structure and unit cell of (a) αSi3N4, (b) βSi3N4, showing the hexagonal symmetry, Figure 26. Crystal structure and unit cell of (a) αSi3N4,(b) βSi3N4, showing the hexagonal symmetry, and (c) γSi3N4. and (c) γSi3N4. Because of the very small solid solubility of N in Si , the Diamond Si terminal solid solution was Because of the very small solid solubility of N in Si , the Diamond Si terminal solid solution treated as pure Si in the calculated N-Si phase diagram of Ma et al. [214]. However, the calculated was treated as pure Si in the calculated N-Si phase diagram of Ma et al. [214]. However, the composition of the L → Diamond Si + Si3N4 eutectic is in good agreement with that of Yatsurugi et al. calculated composition of the L → Diamond Si + Si N eutectic is in good agreement with that [32] at 0.012 at % N. This consistency indicates that 3the4 eutectic composition is not affected by the ofpressure. Yatsurugi Overall, et al. [32 the] atN-Si 0.012 phase at % diagram N. This optimized consistency by indicates Ma et al. that [214] the is eutecticacceptable composition in this work. is not The affected by the pressure. Overall, the N-Si phase diagram optimized by Ma et al. [214] is acceptable in optimized model parameters and enthalpy and entropy of formation of Si3N4 are listed in Table 12 thisand work. 14, respectively. The optimized The model Gibbs parametersenergy of the and gas enthalpy phase is and taken entropy from ofSGTE formation substance of Si 3databaseN4 are listed [236] inand Tables that 13of andthe pure 14, respectively. elements are The from Gibbs Dinsdale energy [237]. of theThe gas enthalpies phase is and taken entropies from SGTE of formation substance for database [236] and that of the pure elements are from Dinsdale [237]. The enthalpies and entropies Si3N4 reported by Ma et al. [214] were mainly taken from the work of Pehlke and Elliott [216] and the ofheat formation capacity for values Si3N 4werereported from byGuzman Ma et et al. al. [214 [217].] were mainly taken from the work of Pehlke and Elliott [216] and the heat capacity values were from Guzman et al. [217].

Materials 2017, 10, 676 27 of 49 Materials 2017, 10, 676 27 of 49

Liquid 5000

4000

3000

Liquid+Si N Liquid+Si3N4 3 4 Temperature (°C) Temperature 2000

1413.94oC

1000 Si3N4+Diamond_Si

0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si)

9 FigureFigure 27.27. TheThe calculatedcalculated condensedcondensed N-SiN-Si phasephase diagramdiagramat at7.5 7.5× × 109 PaPa [214]. [214].

Table 13.12. Optimized model parametersparameters ofof thethe N-SiN-Si system.system. Phase Excess Gibbs Energy Parameter (J/Mole) [214] Phase Excess Gibbs Energy Parameter (J/Mole) [214] Liquid 0 = −87 631 − 22.359 liq , Liquid 0 =− − LN,Si0 87= 631 −788 513.00922.359 T + 733.225 − 121.79 ln() − 0.020 65 + : − − Si N Si3N4 0GSi3N4 = −788 513.009 + 733.225 T − 121.79 T ln(T) − 0.020 65 T2 + 1666 886.4 T 1 + 6.9938 × 10 7 T3 3 4 N:1666 886.4 Si + 6.9938 × 10

Table 14.13. The enthalpy and entropy of formationformation ofof thethe N-SiN-Si intermetallicintermetallic compounds.compounds.

EnthalpyEnthalpy of of Formation Formationk EntropyEntropy of Formation of Formation CompoundCompound Ref. Ref. kJ·(Mole·Atom)J·(Mole·Atom)−−1 1 (J/Mole(J/Mole·Atom·K)·Atom·K)

Si3N4 Si3N4 −103.400−103.400 −45.000−45.000 [216] [216]

5.8. The P-Si System Silicon-doped-phosphorus is very important for the power semiconductors [90] [90] application. Phosphorus is the fastest diffusing donor impurity in silicon. However, the maximummaximum required limit of phosphorus forfor solar-gradesolar-grade SiSi isis almostalmost 1010−−5 atat %. %. At At higher higher concentration, concentration, phosphorus introduces latticelattice strainstrain due toto thethe tetrahedraltetrahedral mismatchmismatch ratioratio betweenbetween PP andand SiSi atomsatoms ofof aboutabout 93%.93%. The misfitmisfit latticelattice strainstrain narrowsnarrows thethe bandband gap,gap, andand reducesreduces thethe (PV)(PV)−− pair dissociation [[26].26]. This infinitesimally infinitesimally small amountamount makes makes phosphorus phosphorus refining refining process proces durings recyclingduring recycling very difficult, very because difficult, phosphorus because phosphorus has a relatively large segregation coefficient, Ko, in silicon of about 0.35 [238,239]. has a relatively large segregation coefficient, Ko, in silicon of about 0.35 [238,239]. Diffusivity ofof phosphorus phosphorus in siliconin silicon has beenhas measuredbeen measured using severalusing experimentalseveral experimental and analytical and techniquesanalytical techniques as reviewed as byreviewed Christensen by Christensen [240]. The intrinsic[240]. The diffusivity intrinsic ofdiffusivity phosphorus of phosphorus in silicon was in silicon was expressed, by Fair [137], as:(− D3.66i =eV/kT 3.85) × 2e(−3.66 eV/kT) cm2/s. Later, Van-Hung et al. [158] expressed, by Fair [137], as: Di = 3.85 × e cm /s. Later, Van-Hung et al. [158] calculated the diffusioncalculated coefficients the diffusion of phosphoruscoefficients inof siliconphosphorus by interstitial in silicon and by vacancyinterstitial mechanisms and vacancy using mechanisms statistical momentusing statistical method. moment They concluded, method. They by comparing concluded, their by owncomparing results their with own the available results with data the [26 ,available159,163], thatdata the[26,159,163], dominant that diffusion the dominant mechanism diffusion of P in Simech is theanism interstitial of P in mechanism, Si is the interstitial similar to mechanism, boron. similarThe to phase boron. diagram and thermodynamic properties of the P-Si system are still under investigation, becauseThe ofphase the difficultdiagram experimental and thermodynamic requirements properties due to of the the presence P-Si system of liquid-vapor are still phaseunder boundariesinvestigation, [55 because]. First version of the ofdifficult the P-Si experimental binary phase requirements diagram was due revealed to the by presence Giessen andof liquid-vapor Vogel [241]. Accordingphase boundaries to these [55]. authors, First the versio eutecticn of temperaturethe P-Si binary and phase the liquidus diagram were was determined revealed by using Giessen thermal and analysisVogel [241]. in the According 0 to 28.0 atto %these P composition authors, the range. eutectic No temperature or very limited and solubility the liquidus of P were in the determined Si terminal using thermal analysis in the 0 to 28.0 at % P composition range. No or very limited solubility of P in the Si terminal side was assumed and a stoichiometric intermetallic compound of SiP was proposed

Materials 2017, 10, 676 28 of 49 side was assumed and a stoichiometric intermetallic compound of SiP was proposed based on the lever rule calculations [241]. Additionally, they attempted to measure the equilibrium gas composition by quenching alloys from liquid-vapor region using the knowledge of the starting composition, liquid composition and mass change in P-Si alloys. Olesinski et al. [242] reproduced the P-Si phase diagram at ambient pressure based on the liquidus and eutectic data from Giessen and Vogel [241] and the solubility of P in Si from Kooi [243] data, as their solubility limits [243] were found more convincing by [242]. Whereas, the solubility of Si in P is considered negligible [242]. The solubility of P in the Si terminal side was investigated by many authors [118,243–255] but the reported data show large discrepancies among each other due to sample oxidation, the presence of impurities, or other experimental difficulties. According to Trumbore [118], the solid solubility of phosphorus in silicon shows a retrograde behavior with a maximum value of about 2.50 at % P at 1180 ◦C, which is close to 2.4 at % obtained by Kooi [243], who studied the diffusion behavior of P in Si in the 920 to 1310 ◦C temperature range using a neutron activation analysis. Abrikosov et al. [244] used the microhardness measurements to determine the solubility of P in Si with a maximum of about 1.0 at % at 900 ◦C. On the other hand, lower concentrations were obtained by Uda and Kamoshida [245] and Tamura [249] at 1100 ◦C as about 0.3 at % and 0.6 at % P, respectively, upon measuring the P concentration in the ion-implanted and annealed Si crystals. Solmi et al. [246] used secondary neutral mass spectrometry measurements to determine the solubility of P in Si from 800 to 1000 ◦C. Nobili et al. [253] used Hall effect and resistivity measurement to determine the solubility of P in an ion-implanted Si specimens. The high values reported by [118,243] were not reliable as Nobili et al. [253] pointed out. The problem in Trumbore’s [118] data was due to using unjustified error function when the surface concentration was calculated. Moreover, the data given by Kooi [243] were related to O-P-Si ternary and not for P-Si system, due to the presence of an oxide film on the substrate. Although these data were criticized by Nobili et al. [253], they were used by Olesinski et al. [242] and Jung and Zhang [256] for P-Si system evaluation and optimization. Safarian and Tangstad [255] reinvestigated the liquidus and solidus of the Si-rich side of the P-Si phase diagram, up to 5.47 at % P, using thermogravimetric and differential thermal analysis (TG/DTA) experiments. According to these authors, the solubility of P in Si shows a retrograde behavior with 0.06 at % P at the eutectic temperature 1129 ± 2 ◦C and 0.09 distribution coefficient of P in Si. Furthermore, they [255] estimated the solubility line below eutectic based on the data of Borisenko and Yudin [254], because they [255] considered the high P solubility values as coexisting P in SiP precipitates. More recently, Liang and Schmid-Fetzer [257] in their optimized P-Si phase diagram classified the experimental solubility data into lower and higher solid solubilities near the eutectic temperature and thus used two different sets of thermodynamic parameters for the diamond-Si phase optimization. Figure 28 compares different sets of experimental and calculated data in the Si-rich side of the P-Si binary phase diagram. Thus far, the available experimental and calculated solubility limits data of P in Si are scattered and difficult to use to draw a common diamond-Si phase boundary. However, the experimental points provided by Safarian and Tangstad [255] are more convincing for the following reasons. The purity of the starting materials was 99.9999 wt % Si and 99.999 wt % P. Furthermore, authors used precise characterization techniques, such as wavelength dispersive spectroscopy (WDS) over many points for each measurement to determine the composition of the alloys and TG-DTA to determine the liquidus and solidus phase boundaries in the Si-rich side. The DTA results gave logical linear liquidus and solidus relationships below 5.5 at % P if the limiting slope theory is considered. Only one intermetallic compound, SiP, exists in the P-Si system at ambient pressure as presented by Olesinski et al. [242]. However, Liang and Schmid-Fetzer [257] reported two intermetallic compounds, SiP2 and SiP, in their calculated phase diagram at 0.5, 1, and 200 bar. The compound Si2P was only reported by Fritz and Berkenhoff [258], using X-ray and infra-red (IR) spectra, to form at 450 ◦C ◦ and decompose into Si and SiP at 600 C. Due to the limited information, the compound Si2P was not included in different versions [55,242,256,257] of the P-Si phase diagram. SiP single crystal was obtained by Beck and Stickler [40], who determined the structure of SiP as orthorhombic using X-ray Materials 2017, 10, 676 29 of 49

Materialsdiffraction 2017, 10 (XRD), 676 and transition electron microscopy (TEM). The crystal structure of SiP in Table2 was29 of 49 reported based on Wadsten [259] investigations. The SiP2 phase was first reported by Wadsten [42], confirmedwho investigated the existence the phosphide of SiP2 by alloys synthesizing using XRD. a large Later, crystal SpringThorpe of orthorhombic [260] confirmed structure the using existence vapor Materials 2017, 10, 676 29 of 49 transport technique [261]. The SiP2 crystal developed by SpringThorpe [260] was twice longer in b- of SiP2 by synthesizing a large crystal of orthorhombic structure using vapor transport technique [261]. direction (b = 2.006 nm) as that proposed by Wadsten [42] (b = 1.008 nm). It could be that the confirmed the existence of SiP2 by synthesizing a large crystal of orthorhombic structureTheSiP using2 crystal vapor developed by SpringThorpe [260] was twice longer in b-direction (b = 2.006 nm) as measurements of [42] and [260] were performed on a deformed crystal. In the current study, the transport technique [261]. The SiP2 crystal developed by SpringThorpe [260] was twicethat proposed longer in by b- Wadsten [42](b = 1.008 nm). It could be that the measurements of [42] and [260] were direction (b = 2.006 nm) as that proposed by Wadsten [42] (b = 1.008 nm). Itaccepted couldperformed be crystal that on the a deformedstructure crystal.of SiP2 Inwas the based current on study, the thework accepted of Wadsten crystal structure[42], since of SiPit was2 was used based and measurements of [42] and [260] were performed on a deformed crystal. In therepublished currenton the workstudy, by of the Wadsten[39]. A [new42], since silicon it was phosphide used and republishedSi12P5, with by rhombohedral [39]. A new silicon symmetry phosphide and Si 12CP55W, 12 12 5 accepted crystal structure of SiP2 was based on the work of Wadsten [42], sincestructure, withit was rhombohedral used was reportedand symmetry by Carlsson and C et5W al.12 [262].structure, The phase was reported Si P was by Carlssonfound to etform al. [ 262in an]. The amorphous phase ◦ republished by [39]. A new silicon phosphide Si12P5, with rhombohedral symmetryP-SiSi12 alloyP5 andwas thin C found 5filmW12 after to form annealing in an amorphous at 1000 °C P-Si for 30 alloy min thin and film dissociates after annealing at above at 1050 1000 °C.C forHence, 30 min only ◦ structure, was reported by Carlsson et al. [262]. The phase Si12P5 was found to formtwo andin anintermetallic dissociates amorphous at compounds, above 1050 C.SiP Hence, and onlySiP2, twoare intermetallicaccepted in compounds,the current SiPwork and for SiP 2the, are equilibrium accepted P-Si alloy thin film after annealing at 1000 °C for 30 min and dissociates at above 1050phasein °C. the diagram Hence, current only of work the forP-Si the system, equilibrium because phase their diagram formation, of the structure P-Si system, and properties because their have formation, been well two intermetallic compounds, SiP and SiP2, are accepted in the current work fordescribedstructure the equilibrium and and confirmed properties in have the been literature well described [40,42,259,260]. and confirmed in the literature [40,42,259,260]. phase diagram of the P-Si system, because their formation, structure and properties have been well described and confirmed in the literature [40,42,259,260]. Liquid 1400 Liquid 1400 Liquid+Diamond_Si Diamond_Si Liquid+Diamond_Si 1200 Diamond_Si 1131°C 0.06 at.%P 1200 1131°C 0.06 at.%P 1000

1000 (°C) Temperature SiP+Diamond_Si Temperature (°C) Temperature 800 SiP+Diamond_Si This work 800 Olesinski et al. [242] This work Olesinski et al. [242] 0.95 0.96 0.97 0.98 0.99 1.00 0.95 0.96 0.97 0.98 0.99 1.00 Mole fraction (Si) Mole fraction (Si) Figure 28. Assessed Si-terminal solid solution in relation to the available data; -·-·-·-: [242]; □: [118]; ■: Figure 28. Assessed Si-terminal solid solution in relation to the available data; -·-·-·-: [242]; :[118]; Figure 28. Assessed Si-terminal solid solution in relation to the available data; -·-·-·-: [242]; [241];□: [118];:[ 241Δ: ■[243];];: ∆:[ 243: [244];]; ♦:[ 244: [245];]; 5:[ ×245: [246];]; ×:[ +:246 [247];]; +: ▲ [247: [248];]; N:[ *:248 [250];]; *: ▼ [250: [252];]; H:[ ○252: [249];]; :[ ♦249: [253];];  :[◄253: [254];]; [241]; Δ: [243]; : [244]; : [245]; ×: [246]; +: [247]; ▲: [248]; *: [250]; ▼: [252]; ○: [249]; ♦: [253];● :◄ [255].:[: [254];254 ]; :[255]. # ●: [255]. TheThe vapor vapor composition composition and and thermodynamic properties properties of of the the P-Si P-Si melt, melt, containing containing 0.09–26.5 0.09–26.5 at % at The vapor composition and thermodynamic properties of the P-Si melt, containing% P,P, were were 0.09–26.5 investigated investigated at by by Zaitsev Zaitsev et al. et [ 263al. ][263] in the in 1234–1558 the 1234–1558◦C temperature °C temperature range. Therange. chosen The range chosen % P, were investigated by Zaitsev et al. [263] in the 1234–1558 °C temperature rangerange.covers covers The almost chosen almost the liquid the liquid phase ph field.ase field. The GibbsThe Gibbs energies energies of phase of phase transitions transitions of phosphorus of phosphorus and range covers almost the liquid phase field. The Gibbs energies of phase transitionsandsilicon ofsilicon phosphorus were were taken taken from from [264 [264,265].,265]. The The calculated calculat phosphorused phosphorus activities activities were in were good in agreement good agreement with and silicon were taken from [264,265]. The calculated phosphorus activities were withintheir good their [ 263agreement [263]] own own experiments. experiments. However, However, Zaitsev Zaitsev et al. [et263 al.] calculated[263] calculated the equilibrium the equilibrium of liquid, of solidliquid, with their [263] own experiments. However, Zaitsev et al. [263] calculated the equilibriumsolidsilicon silicon and of liquid,and vapor vapor phases phases at 1166 at 1166◦C, which °C, which washigher was higher than that than reported that reported by Giessen by Giessen and Vogel and [241 Vogel] solid silicon and vapor phases at 1166 °C, which was higher than that reported by[241] Giessenas 1131as 1131and◦C. Vogel The°C. The variation variation could could be due be todue the to difficulty the difficulty in differentiating in differentiating between between the eutectic the eutectic and [241] as 1131 °C. The variation could be due to the difficulty in differentiating betweenandprimary primary the solidificationeutectic solidification in this in system.this system. Franke Franke and Neuschütz and Neuschütz [55] presented [55] presented a calculated a calculated P-Si phase P-Si and primary solidification in this system. Franke and Neuschütz [55] presented a calculated P-Si phasediagram diagram based based on the on literature the literature data [ 114data,115 [114,115,239,241,242,263].,239,241,242,263]. Similar Similar version version was obtained was obtained using phase diagram based on the literature data [114,115,239,241,242,263]. Similar version was obtained usingFTlite FTlite thermodynamic thermodynamic database database in FactSage in FactSage® software® software [124]. According[124]. According to [55], to the [55], terminal the terminal solid using FTlite thermodynamic database in FactSage® software [124]. According to [55], the terminal solidsolution solution in thein the Si-rich Si-rich side side was was represented represented as aas typical a typical solid solid solution, solution, with with maximum maximum solubility solubility solid solution in the Si-rich side was represented as a typical solid solution, with maximum solubility at atthe the eutectic eutectic line, line, and and not not as a as retrograde a retrograde solution. solution. Jung Jung and andZhang Zhang [256] [256 reassessed] reassessed the P-Si the P-Siphase at the eutectic line, and not as a retrograde solution. Jung and Zhang [256] reassessed the P-Si phase diagramphase diagramusing the using modifi theed modified quasi-chemical quasi-chemical model model[266] for [266 the] for liquid the liquidphase phase and compound and compound energy diagram using the modified quasi-chemical model [266] for the liquid phase and compoundenergy formalism energy [267] for Si-rich phase assuming P substitutes Si. According to these authors, formalism [267] for Si-rich phase assuming P substitutes Si. According to formalismthese authors, [267] the for Si-rich phase assuming P substitutes Si. According to these authors, the thermodynamicthe thermodynamic properties properties of SiP of were SiP re-optimized were re-optimized using usinglow-temperature low-temperature heat capacity heat capacity of Ugai of et thermodynamic properties of SiP were re-optimized using low-temperature heat capacityUgai et of al. Ugai [268 ]et and the modified high-temperature heat capacity parameter of Knacke et al. [269]. al. [268] and the modified high-temperature heat capacity parameter of Knacke etal. al. [268] [269]. and Whereas, the modified high-temperature heat capacity parameter of Knacke et al. [269]. Whereas, the thermodynamic properties of SiP2 were based on the heat capacity measurementsthe thermodynamic of Philipp and properties of SiP2 were based on the heat capacity measurements of Philipp and Schmidt [270]. The evaporation and gas composition data [241] were not taken Schmidtinto account [270]. in Thethe evaporation and gas composition data [241] were not taken into account in the thermodynamic modeling of Jung and Zhang [256], because they [256] could thermodynamicnot reproduce the modeling of Jung and Zhang [256], because they [256] could not reproduce the experimental results. experimental results.

Materials 2017, 10, 676 30 of 49

Whereas, the thermodynamic properties of SiP2 were based on the heat capacity measurements of Philipp and Schmidt [270]. The evaporation and gas composition data [241] were not taken into account in the thermodynamic modeling of Jung and Zhang [256], because they [256] could not reproduce the Materials 2017, 10, 676 30 of 49 experimental results. Recently,Recently, Liang and Schmid-Fetzer [257] [257] remodeled the P-Si phase diagram considering no no short-range-orderingshort-range-ordering in the liquid phase. In In their their work, work, the the liquid liquid phase phase and and Si-rich Si-rich terminal terminal solution solution were described using the substitutional solution model, SiP and SiP 2 werewere treated as stoichiometric compoundscompounds and and the the gas phase was described as an idealideal gasgas mixture.mixture. Furthermore, Furthermore, new new set set of of thermodynamicthermodynamic parametersparameters were were provided provided [257 [257],], because because they discoveredthey discovered some errors some in errors the published in the publishedparameters parameters by Jung and by ZhangJung and [256 Zhang]. The optimized[256]. The optimized P-Si phase P-Si diagram phase at diagram 200 bar [at257 200] along bar [257] with alongthe experimental with the experimental data [255,268 data] is [255,268] shown in is Figure shown 29 in. TheFigure optimized 29. The modeloptimized parameters model parameters of the P-Si ofphase the P-Si diagram phase are diagram listed in are Table listed 15 .in Table 15.

1500 This work 1414°C Liang and Scmid-Fetzer [257], 200 bar Liquid 1250 1178°C 1170°C 1132°C 1125°C Diamond_Si 1000 2 SiP SiP Temperature (°C) Temperature 750 Diamond_Si+SiP

579°C (Red P) 500 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Δ: [268]; : FigureFigure 29.29. TheThe P-SiP-Si phasephase diagramdiagram withoutwithout gasgas phasephase atat 200200 bar;bar; ------: - - - -: [257]; [257]; ∆:[268];○ :[[255].255]. # In agreement with [256], the corresponding gas composition points [241] were not used by Liang In agreement with [256], the corresponding gas composition points [241] were not used by Liang and Schmid-Fetzer [257] in their optimization, because the data were considered inaccurate. At 200 and Schmid-Fetzer [257] in their optimization, because the data were considered inaccurate. At 200 bar, bar, both SiP and SiP2 compounds melt congruently at 1161 °C and 1169 °C, respectively, which are both SiP and SiP compounds melt congruently at 1161 ◦C and 1169 ◦C, respectively, which are slightly slightly below the2 experimental data [268] as shown in Figure 29. In this work, modified phase below the experimental data [268] as shown in Figure 29. In this work, modified phase boundaries boundaries are based on the experimental data of Ugai et al. [268], who measured the congruent are based on the experimental data of Ugai et al. [268], who measured the congruent melting of SiP melting of SiP and SiP2 to be 1170 °C and 1178 °C, respectively, and the SiP + SiP2 eutectic at 1125 °C. and SiP to be 1170 ◦C and 1178 ◦C, respectively, and the SiP + SiP eutectic at 1125 ◦C. The enthalpy The enthalpy2 and entropy of formation of the P-Si compounds are given2 in Table 15. It is worth noting and entropy of formation of the P-Si compounds are given in Table 16. It is worth noting that the that the enthalpy and entropy of formation of SiP, used in the calculations of Liang and Schmid- enthalpy and entropy of formation of SiP, used in the calculations of Liang and Schmid-Fetzer [257], Fetzer [257], were similar to those given by [256]. Whereas, the thermodynamic parameters of SiP2 were similar to those given by [256]. Whereas, the thermodynamic parameters of SiP were slightly were slightly modified by [257] to fit with the experimental congruent melting point as 2given by Ugai modified by [257] to fit with the experimental congruent melting point as given by Ugai et al. [268]. et al. [268]

Table 14. Optimized model parameters of the P-Si system.

Phase Excess Gibbs Energy Parameter (J/Mole) [257] , = 327 729.700 − 24.71 − 20.67 () −8.5×10 +ln(10 ×) , = 132 066.5 + 27.5674 − 36.30 () −4.0×10 +2.05×10 + ln (10 ×) , = 30 174.8 + 275.871 − 81.84 () −3.4×10 +6.70×10 + ln (10 ×) , Gas = 444 756.1 − 36.2676 − 19.80 () −5.05×10 −1.05×10 + ln (10 ×) , = 579 613.8 + 1.2671 − 34.50 () + ln (10 ×) , = 619 571.9 + 101.1376 − 55.10 () +ln(10 ×) , = 646 000.0 − 292.8000 + ln(10 ×) , , = −20 801.04 + 4.1172 Liquid , , = 13982.31 − 2.7877 () ,_ =30+ () Diamond_Si , = −40 498.48 + 21.8079 ( ) () , = 10 594.1 − 25.17 ( ) , SiP : = −77 110.5 + 228.49 − 38.34 () − 0.00544 + 2.825 × 10 , SiP2 : = −100 809.0 + 389.8 − 67.00 () − 0.00855 P is the pressure in Pascal

Materials 2017, 10, 676 31 of 49

Table 15. Optimized model parameters of the P-Si system.

Phase Excess Gibbs Energy Parameter (J/Mole) [257] 0,Gas −5 2 −5
GP = 327 729.700 − 24.71 T − 20.67 T ln(T) − 8.5 × 10 T + RT ln 10 × P 0,Gas −4 2 5 −1 −5
GP2 = 132 066.5 + 27.5674 T − 36.30 T ln(T) − 4.0 × 10 T + 2.05 × 10 T + RT ln 10 × P 0,Gas −4 2 5 −1 −5
GP4 = 30 174.8 + 275.871 T − 81.84 T ln(T) − 3.4 × 10 T + 6.70 × 10 T + RT ln 10 × P 0,Gas −4 2 5 −1 −5
Gas GSi = 444 756.1 − 36.2676 T − 19.80 T ln(T) − 5.05 × 10 T − 1.05 × 10 T + RT ln 10 × P 0,Gas −5
GSi2 = 579 613.8 + 1.2671 T − 34.50 T ln(T) + RT ln 10 × P 0,Gas −5
GSi3 = 619 571.9 + 101.1376 T − 55.10 T ln(T) + RT ln 10 × P 0,Gas −5
GSi4 = 646 000.0 − 292.8000 T + RT ln 10 × P 0,Liq LP,Si = −20 801.04 + 4.1172 T Liquid 1,Liq LP,Si = 13982.31 − 2.7877 T (Si) 0,white_P GP = 30 T + GP (Si) Diamond_Si LP,Si = −40 498.48 + 21.8079 T (Model I) (Si) LP,Si = 10 594.1 − 25.17 T (Model II) 0,SiP 2 5 −1 SiP GP:Si = −77 110.5 + 228.49 T − 38.34 T ln(T) − 0.00544 T + 2.825 × 10 T 0,SiP2 2 SiP2 GP:Si = −100 809.0 + 389.8 T − 67.00 T ln(T) − 0.00855 T P is the pressure in Pascal

Table 16. The enthalpy and entropy of formation of the P-Si intermetallic compound.

Enthalpy of Formation Entropy of Formation Compound Ref. kJ·(Mole·Atom)−1 (J/Mole·Atom·K) −61.118 15.016 [55] −71.128 - [271] −61.923 32.635 [124,242] SiP −63.300 34.735 [256] −63.300 34.740 [257] −63.220 29.400 [272] −80.070 64.050 [257] SiP2 −79.300 67.000 [256] −84.300 69.900 [270]

Very limited experimental data on the activity of P-Si in the melts could be found in the literature. Zaitsev et al. [263] investigated the activity of the P-Si melts in the 0.09 < P < 26.5 at % composition range at different temperatures, ranging between 1423 and 1558 ◦C, using Knudsen effusion mass spectrometry [273]. However, both [256,257] considered the activity data of Zaitsev et al. [263] not reliable, because it predicts (Si-rich solid + Gas) two phase field in the 1125 to 1220 ◦C temperature range, which is not the case as could be proven by Safarian and Tangstad [255] using DTA measurements. The authors [256,257] gave higher weight to the experimental results of Miki et al. [239] in the thermodynamic modeling of P-Si system. The enthalpy of mixing of the P-Si liquid at 1427 ◦C[55] is shown in Figure 30a. The experimental results of activity measurements of P and Si in the P-Si liquid at 1427 ◦C[263] are given in Figure 30b. The activity calculations of Franke and Neuschütz [55] are consistent with these experimental results, therefore Franke and Neuschütz’ curves are adopted in this work. Materials 2017, 10, 676 31 of 49

Table 15. The enthalpy and entropy of formation of the P-Si intermetallic compound.

Enthalpy of Formation Entropy of Formation Compound Ref. kJ·(Mole·Atom)−1 (J/Mole·Atom·K) −61.118 15.016 [55] −71.128 - [271] −61.923 32.635 [124,242] SiP −63.300 34.735 [256] −63.300 34.740 [257] −63.220 29.400 [272] −80.070 64.050 [257] SiP2 −79.300 67.000 [256] −84.300 69.900 [270]

Very limited experimental data on the activity of P-Si in the melts could be found in the literature. Zaitsev et al. [263] investigated the activity of the P-Si melts in the 0.09 < P < 26.5 at % composition range at different temperatures, ranging between 1423 and 1558 °C, using Knudsen effusion mass spectrometry [273]. However, both [256,257] considered the activity data of Zaitsev et al. [263] not reliable, because it predicts (Si-rich solid + Gas) two phase field in the 1125 to 1220 °C temperature range, which is not the case as could be proven by Safarian and Tangstad [255] using DTA measurements. The authors [256,257] gave higher weight to the experimental results of Miki et al. [239] in the thermodynamic modeling of P-Si system. The enthalpy of mixing of the P-Si liquid at 1427 °C [55] is shown in Figure 30a. The experimental results of activity measurements of P and Si in the P-Si liquid at 1427 °C [263] are given in Figure 30b. The activity calculations of Franke and Neuschütz [55] are consistent with these experimental results, therefore Franke and Neuschütz’ Materials 2017, 10, 676 32 of 49 curves are adopted in this work.

0 1.0

-1000 0.8

-2000 0.6

-3000

Activity 0.4

aSi

Enthalpy of mixing (J/mole) -4000 0.2 aP

o [55] at 1427 C [55] at 1427°C -5000 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Mole fraction (Si) (a) (b)

Figure 30.30. ((aa)) CalculatedCalculated enthalpyenthalpy ofof mixingmixing ofof thethe P-SiP-Si liquidliquid at at 1427 1427◦ °C;C;- ----: - - -: [55]; [55]; ( b) activity of SiSi and P in the P-Si liquid at 1427 ◦°C; ----: [55]; □ and Δ: [263]. and P in the P-Si liquid at 1427 C; - - - -: [55];  and ∆:[263].

5.9. The Sb-Si System Antimony-silicon system seems to have no particular technological importance in its own right. However, understanding its thermodynamic properties is essential to model possible interactions However, understanding its thermodynamic properties is essential to model possible interactions between Si and Sb in electronic applications, such as in soldering processes [56]. The Sb-Si phase between Si and Sb in electronic applications, such as in soldering processes [56]. The Sb-Si phase diagram was critically assessed by Olesinski and Abbaschian [274] based on the experimental results diagram was critically assessed by Olesinski and Abbaschian [274] based on the experimental results of [118,120,177,178,275,276]. Several authors calculated the Sb-Si phase diagram [101,120,274,277]. of [118,120,177,178,275,276]. Several authors calculated the Sb-Si phase diagram [101,120,274,277]. Wang et al. [277] reassessed the Sb-Si system, shown in Figure 31, to achieve compatibility among the Wang et al. [277] reassessed the Sb-Si system, shown in Figure 31, to achieve compatibility among the binaries in the Au-Sb-Si system, using data from Dinsdale [237] for the pure elements and binaries in the Au-Sb-Si system, using data from Dinsdale [237] for the pure elements and substitutional solution model to describe the liquid and solid solution phases. The optimized model parameters are listed in Table 17. The calculated liquid phase boundaries show very good agreement with most of the experimental data. Wang et al. [277] presented a modified Si-rich solvus line, different than that in [274], based on the experimental results of Nobili et al. [278]. The magnified part of the calculated Sb-Si phase diagram [277], near Si-rich side, associated with the experimental points is shown in Figure 32. Nobili et al. [278] measured the solid solubility of antimony in silicon by carrier density measurements on poly silicon films doped by ion implantation in the 850–1300 ◦C temperature range. Their measurements [278] proved to be accurate determination of the solubility values in this system. Therefore, the solvus line calculated by Wang et al. [277] is considered more accurate presentation of the Sb solubility in Si. The calculated Sb-Si phase diagram [277] exhibits a eutectic transformation at 0.3 at % Si and 630 ◦C. The solid solution of Si in Sb is considered negligible. The solid solubility of antimony in silicon showed retrograde behavior with a maximum of about 0.1 at % Sb at 1300 ◦C. The shape of the liquidus line indicates a likelihood of metastable miscibility gap with positive enthalpy of mixing [56] as could be seen in Figure 33a. The crystallographic data of the end-members of the Sb-Si system are listed in Table2. Antimony has a low diffusivity in silicon, compared to arsenic, for example, and it is known to diffuse via a vacancy mechanism. The diffusivity data of antimony in silicon was reviewed by Pichler [90] (−4.158 eV/kT) 2 who expressed the intrinsic diffusivity of antimony by the equation: Di = 40.9 × e cm /s. Materials 2017, 10, 676 32 of 49 Materials 2017, 10, 676 32 of 49 substitutional solution model to describe the liquid and solid solution phases. The optimized model substitutional solution model to describe the liquid and solid solution phases. The optimized model parameters are listed in Table 16. The calculated liquid phase boundaries show very good agreement parameters are listed in Table 16. The calculated liquid phase boundaries show very good agreement with most of the experimental data. Wang et al. [277] presented a modified Si-rich solvus line, with most of the experimental data. Wang et al. [277] presented a modified Si-rich solvus line, different than that in [274], based on the experimental results of Nobili et al. [278]. The magnified part different than that in [274], based on the experimental results of Nobili et al. [278]. The magnified part of the calculated Sb-Si phase diagram [277], near Si-rich side, associated with the experimental points of the calculated Sb-Si phase diagram [277], near Si-rich side, associated with the experimental points is shown in Figure 32. Nobili et al. [278] measured the solid solubility of antimony in silicon by carrier is shown in Figure 32. Nobili et al. [278] measured the solid solubility of antimony in silicon by carrier density measurements on poly silicon films doped by ion implantation in the 850–1300 °C density measurements on poly silicon films doped by ion implantation in the 850–1300 °C temperature range. Their measurements [278] proved to be accurate determination of the solubility temperature range. Their measurements [278] proved to be accurate determination of the solubility values in this system. Therefore, the solvus line calculated by Wang et al. [277] is considered more values in this system. Therefore, the solvus line calculated by Wang et al. [277] is considered more Materialsaccurate2017 presentation, 10, 676 of the Sb solubility in Si. 33 of 49 accurate presentation of the Sb solubility in Si.

1400 1400 Liquid Liquid

1200 1200

1000 1000

800 Liquid+Diamond_Si 800 Liquid+Diamond_Si Eutectic at 99.7at.% Sb 630°C 630°C 600 Eutectic at 99.7at.% Sb

Temperature (°C) Temperature 600 Temperature (°C) Temperature

400 Sb+Diamond_Si 400 Sb+Diamond_Si

200 200 0.00.20.40.60.81.0 0.00.20.40.60.81.0 Mole fraction (Si) Mole fraction (Si) Figure 31. The calculated Sb-Si binary phase diagram by Wang et al. [277]; ○: [177]; □: [275]; Δ: [120]; Figure 31. The calculated Sb-Si binary phase diagram by Wang et al. [277]; ○: [177]; □: [275]; Δ: [120]; Figure: 31.[178].The calculated Sb-Si binary phase diagram by Wang et al. [277]; :[177]; :[275]; ∆:[120]; ♦:[178]. : [178]. # 1500 1500 Liquid 1400 Liquid 1400 1300 Diamond_Si 1300 Diamond_Si 1200 1200 1100 1100 Liquid+Diamond_Si 1000 Liquid+Diamond_Si 1000 900

Temperature (°C) Temperature 900 Temperature (°C) Temperature 800 Wang et al. [277] 800 WangOlesinski et al. and [277] Abbaschian [274] Olesinski and Abbaschian [274] 700 700 0.9980 0.9985 0.9990 0.9995 1.0000 0.9980 0.9985 0.9990 0.9995 1.0000 Mole fraction (Si) Mole fraction (Si) Figure 32. Magnified portion of the calculated Sb-Si phase diagram [277]; ----: [274]; Δ: [179]; ○: [276]; Figure 32. MagnifiedMagnified portion ofof thethe calculatedcalculated Sb-SiSb-Si phasephase diagram diagram [ 277[277];]; - ----: - - -: [[274];274]; ∆Δ::[ [179];179]; ○::[ [276];276]; □: [118]; : [278]. □::[ [118];118]; ♦:[: [278].278]. # The calculated Sb-Si phase diagram [277] exhibits a eutectic transformation at 0.3 at % Si and 630 ExperimentalThe calculated thermodynamic Sb-Si phase diagram properties [277] ofexhibits the Sb-Si a eutectic system transformation could not be found at 0.3 in at the% Si literature. and 630 °C. The solid solution of Si in Sb is considered negligible. The solid solubility of antimony in silicon The°C. The calculated solid solution thermodynamic of Si in Sb properties, is considered enthalpy negligible. of mixing The andsolid activity solubility at 1477 of antimony◦C, using in different silicon models are shown in Figure 33a,b, respectively. Thurmond [121] used the regular solution model and calculated the molar enthalpy of mixing based on the data of Williams [177]. However, the measured values by Williams [177] are considered not accurate, because low purity silicon was used. Olesinski and Abbaschian [274] modified the thermodynamic model parameters of [120,121] in order to be consistent with the experimental phase diagram data [118,120,177,178,275,276]. The liquid phase parameters were modified by Safarian et al. [66] in an attempt to keep the eutectic temperature and composition as that given by Olesinski and Abbaschian [274] at 629.7 ◦C and 0.3 at % Si. Yet, their calculated values were closer to those of [120]. The available activities of antimony and silicon [56,67], in Figure 33b, are inconsistent but show positive deviation from Raoult’s law, which is expected for Materials 2017, 10, 676 33 of 49 showed retrograde behavior with a maximum of about 0.1 at % Sb at 1300 °C. The shape of the liquidus line indicates a likelihood of metastable miscibility gap with positive enthalpy of mixing [56] as could be seen in Figure 33a. The crystallographic data of the end-members of the Sb-Si system are listed in Table 2. Antimony has a low diffusivity in silicon, compared to arsenic, for example, and it is known to diffuse via a vacancy mechanism. The diffusivity data of antimony in silicon was reviewed by Pichler

[90] who expressed the intrinsic diffusivity of antimony by the equation: =40.9× (. ⁄) cm/s. Experimental thermodynamic properties of the Sb-Si system could not be found in the literature. The calculated thermodynamic properties, enthalpy of mixing and activity at 1477 °C, using different models are shown in Figure 33a,b, respectively. Thurmond [121] used the regular solution model and calculated the molar enthalpy of mixing based on the data of Williams [177]. However, the measured values by Williams [177] are considered not accurate, because low purity silicon was used. Olesinski and Abbaschian [274] modified the thermodynamic model parameters of [120,121] in order to be consistent with the experimental phase diagram data [118,120,177,178,275,276]. The liquid phase parameters were modified by Safarian et al. [66] in an attempt to keep the eutectic temperature and composition as that given by Olesinski and Abbaschian [274] at 629.7 °C and 0.3 at % Si. Yet, their Materialscalculated2017 values, 10, 676 were closer to those of [120]. The available activities of antimony and silicon [56,67],34 of 49 in Figure 33b, are inconsistent but show positive deviation from Raoult’s law, which is expected for such flatflat liquidus.liquidus. Thus, Thus, experimental experimental investigations investigations of of the the enthalpy of mixing and activities are required to verifyverify thesethese thermodynamicthermodynamic properties.properties.

1.0 5000

0.8 4000

0.6 3000 y

2000 Activit 0.4 aSi aSb [121] [274]

Enthalpy of mixing (J/mole) mixing of Enthalpy 1000 [120] [66] 0.2 [56] [67] 0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Mole fraction (Si) Mole fraction (Si) (a) (b)

Figure 33. ((aa)) Enthalpy Enthalpy of of mixing mixing of of the the Sb-Si Sb-Si liquid liquid at at1427 1427 °C;◦ C;-----: - - -[121]; - -: [121 ···· ];: [120];···· :[ 120˗·˗·˗];: [274]; -·-·-: [˗274··˗··˗];: -[66]··-·· -:and [66 (]b and) activity (b) activity of Sb and of Sb Si and in the Si inSb-Si the li Sb-Siquid liquid at 1477 at °C 1477 [277];◦C[ ----:277 ];[56]; - - - ····: -: [56 [67].]; ···· :[67].

Table 16. Optimized model parameters of the Sb-Si system [277].

PhaseTable 17. Optimized Excess model Gibbs parameters Energy Parameter of the Sb-Si (J system/Mole) [277]. Ref. Liquid ° = 15 463.82 + 4.805 [277] Phase Excess Gibbs, Energy Parameter (J/Mole) Ref. Diamond_Si ° = 67 795.81 [277] liq , Liquid ◦ L = 15 463.82 + 4.805 T [277] Sb ObtainedSb,Si from SGTE database [237] ◦ Diamond Diamond_Si LSb,Si = 67 795.81 [277] Sb Obtained from SGTE database [237] 5.10. The Tl-Si System

5.10.According The Tl-Si System to Zhao et al. [279], thallium could be the most suitable impurity atom in crystalline Si solar sell industry, because it provides deep level of impurity photovoltaic effect, which improves the solarAccording cell efficiency. to Zhao etSilicon al. [279 and],thallium thallium could are virtually be the most immiscible. suitable The impurity liquid atom miscibility in crystalline gap in Sithe solar Si-Tl sell system industry, was becausedescribed it providesby Savitskiy deep et level al. [187] of impurity and Thurmond photovoltaic and effect,Kowalchik which [120], improves with thesome solar variations. cell efficiency. Savitskiy Silicon et al. [187] and reported thallium the are monotectic virtually immiscible. transformation The temperature liquid miscibility at 1414 gap °C, in the Si-Tl system was described by Savitskiy et al. [187] and Thurmond and Kowalchik [120], with some variations. Savitskiy et al. [187] reported the monotectic transformation temperature at 1414 ◦C, while it was reported by Thurmond and Kowalchik [120] to be 1387 ◦C. Olesinski and Abbaschian [57] have constructed a tentative Si-Tl phase diagram, shown in Figure 34, based on the thermal analysis of Tamaru [280] and Savitskiy et al. [187]. Later on, the Si-Tl phase diagram assessed by Olesinski and Abbaschian [57] was accepted by Predel [281]. The Si-Tl phase diagram shows a eutectic transformation near the melting point of thallium and a monotectic transformation near the melting point of silicon. The solubilities of both silicon and thallium are very infinitesimal [282]. However, Schmit and Scott [282] developed a novel method, including adding of a second metal (tin) to thallium, to grow silicon-doped semiconductor for 3–5 µm infrared radiation detector, which can operate above 77 K. The diffusion of thallium in silicon was reviewed by Hull [138], who described the diffusivity of thallium in the 1105–1360 ◦C temperature range by the equation D = 16.5 × e(−3.896 eV/kT) cm2/s, based on the work of Fuller and Ditzenberger [179]. However, Ghoshtagore [283] expressed the diffusion coefficient of thallium in silicon in the 1244–1338 ◦C temperature range as D = 1.37 × e(−3.896 eV/kT) cm2/s. The difference in these two sets of results could be due to oxidation/reduction reactions on the Si surface. Materials 2017, 10, 676 34 of 49 Materials 2017, 10, 676 34 of 49 while it was reported by Thurmond and Kowalchik [120] to be 1387 °C. Olesinski and Abbaschian while it was reported by Thurmond and Kowalchik [120] to be 1387 °C. Olesinski and Abbaschian [57] have constructed a tentative Si-Tl phase diagram, shown in Figure 34, based on the thermal [57] have constructed a tentative Si-Tl phase diagram, shown in Figure 34, based on the thermal analysis of Tamaru [280] and Savitskiy et al. [187]. Later on, the Si-Tl phase diagram assessed by analysis of Tamaru [280] and Savitskiy et al. [187]. Later on, the Si-Tl phase diagram assessed by OlesinskiOlesinski and and Abbaschian Abbaschian [57][57] waswas accepted byby PredelPredel [281]. [281]. The The Si-Tl Si-Tl phase phase diagram diagram shows shows a a eutecticeutectic transformation transformation near near thethe meltingmelting point ofof thalliumthallium and and a amonotectic monotectic transformation transformation near near the the meltingmelting point point of of silicon. silicon. TheThe solubilitiessolubilities of bothboth siliconsilicon and and thallium thallium are are very very infinitesimal infinitesimal [282]. [282]. However,However, Schmit Schmit and and Scott Scott [282] [282] developeddeveloped aa novelnovel method, method, including including adding adding of ofa second a second metal metal (tin) (tin) to tothallium, thallium, to to grow grow silicon-doped silicon-doped semiconductorsemiconductor for for 3–5 3–5 μ μmm infrared infrared radiation radiation detector, detector, which which can can operateoperate above above 77 77 K. K. TheThe diffusion diffusion of of thallium thallium inin siliconsilicon was reviewedreviewed by by Hull Hull [138], [138], who who described described the the diffusivity diffusivity of of thalliumthallium in in the the 1105–1360 1105–1360 °C °C temptemperature range byby the the equation equation D D = =16.5 16.5 × e×(− 3.896e(−3.896 eV/kT) eV/kT) cm cm2/s,2 /s,based based on on thethe work work of of Fuller Fuller and and DitzenbergerDitzenberger [179]. HoweHowever,ver, Ghoshtagore Ghoshtagore [283] [283] expressed expressed the the diffusion diffusion coefficientcoefficient of of thallium thallium in in silicon silicon inin the 1244–1338 °C°C temperature temperature range range as as D D= 1.37= 1.37 × e ×(− 3.896e(−3.896 eV/kT) eV/kT) cm 2cm/s. 2/s. MaterialsTheThe difference2017 difference, 10, 676 in in these these twotwo setssets ofof results couldcould bebe due due to to oxidation/reduction oxidation/reduction reactions reactions on onthe the Si35 ofSi 49 surface.surface.

1600 1600 1414°C Liquid#1+Liquid#2 1414°C Liquid#1+Liquid#2

1200 1200 Diamond_Si+Liquid Diamond_Si+Liquid 800 800 Temperature (°C) Temperature

Temperature (°C) Temperature 400 304°C 400 Diamond_Si+βTl 304°C 234°C α Diamond_Si+ Tl Diamond_Si+βTl 234°C 0.0 0.2 0.4Diamond_Si+ 0.6αTl 0.8 1.0 0.0 0.2Mole 0.4 fraction (Tl) 0.6 0.8 1.0 Mole fraction (Tl) Figure 34. The Si-Tl phase diagram redrawn after Olesinski and Abbaschian [57]. □: [280]. Figure 34. The Si-Tl phase diagram redrawn after Olesinski and Abbaschian [57]. :[280]. Figure 34. The Si-Tl phase diagram redrawn after Olesinski and Abbaschian [57]. □: [280]. Very limited thermochemical data of the Si-Tl system could be found in the literature. Thurmond VeryandVery Kowalchik limited limited thermochemical thermochemical[120] attempted data todata describe of of the the Si-Tl Si-Tlthe systemSi-T systeml liquid couldcould in beterms found found of in inregular the the literature. literature. solution Thurmond model. Thurmond andand KowalchikHowever, Kowalchik Olesinski [120 [120]] attempted andattempted Abbaschian to describe to describe [57] the considered Si-Tl the liquidSi-Tl theliquid in termscalculations in ofterms regular of [120]regular solution speculative solution model. However,model.and OlesinskiHowever,inaccurate and OlesinskiAbbaschian without providing and [57 Abbaschian] considered enough justification. [57] the calculationsconsidered The enthalpy the of [120calculations of] speculativemixing curveof [120] and is shown inaccuratespeculative in Figure without and providinginaccurate35 [120]. enough withoutThe positive justification. providing enthalpyThe enough of enthalpy mixing justification. indicates of mixing The the curve enthalpy existence is shown of of mixing a inmiscibility Figure curve 35 gapis[ shown120 in]. the The in Si-Tl Figure positive system, which agrees with the Si-Tl phase diagram shown in Figure 34. The model parameters of the enthalpy35 [120]. of mixingThe positive indicates enthalpy the existence of mixing of indicates a miscibility the existence gap in the of Si-Tl a miscibility system, whichgap in agrees the Si-Tl with liquid phase reported by [120] are listed in Table 17. thesystem, Si-Tl phase which diagram agrees with shown the Si-Tl in Figure phase 34diagram. The shown model in parameters Figure 34. The of the model liquid parameters phase reported of the byliquid [120] are phase listed reported in Table by 18[120]. are20000 listed in Table 17.

18000 20000 16000 18000 14000 16000 12000

1400010000

120008000

100006000

Enthalpy of mixing (J/mol) of mixing Enthalpy 80004000

60002000

0 Enthalpy of mixing (J/mol) of mixing Enthalpy 4000 0.0 0.2 0.4 0.6 0.8 1.0 2000 Mole fraction (Si) 0 Figure 35. Calculated enthalpy of mixing0.0 of 0.2 the Si-Tl 0.4 liquid 0.6 using thermodynamic 0.8 1.0 coefficients from [120]. Mole fraction (Si)

FigureFigure 35. 35.Calculated Calculated enthalpy enthalpy of of mixing mixing of of the theSi-Tl Si-Tl liquidliquid using thermodynamic coefficients coefficients from from [120]. [120 ].

Table 18. Model parameters of the Si-Tl system.

Phase Excess Gibbs Energy Parameter (J/Mole) Ref. 0 liq = + Liquid LSi,Tl 69 500 15.9 T [120]

6. Discussion It is concluded from the analyzed data in this paper that the melts of Si with Al, As, B and P (IIIA group) are exothermic and their activities deviate negatively from Raoult’s ideal solution, whereas the melts of Si with Bi, Ga, In, Sb and Tl (VA group) are endothermic in behavior and deviate positively from Raoult’s law. Furthermore, it can be said that the atoms of the VA group do not prefer to form homogenous mixtures with silicon upon melting. Positive enthalpy of mixing in this case is due to the de-mixing effect, by which Si and VA group atoms in Si-VA group mixtures favor to form bonds between similar atoms. This was observed in systems where the liquid curve tends to be flat indicating a metastable miscibility gap or when the liquid miscibility gap is stable. Materials 2017, 10, 676 35 of 49

Table 17. Model parameters of the Si-Tl system.

Phase Excess Gibbs Energy Parameter (J/Mole) Ref. 0 Liquid , = 69 500 + 15.9 [120]

6. Discussion It is concluded from the analyzed data in this paper that the melts of Si with Al, As, B and P (IIIA group) are exothermic and their activities deviate negatively from Raoult’s ideal solution, whereas the melts of Si with Bi, Ga, In, Sb and Tl (VA group) are endothermic in behavior and deviate positively from Raoult’s law. Furthermore, it can be said that the atoms of the VA group do not prefer to form homogenous mixtures with silicon upon melting. Positive enthalpy of mixing in this case is due to the de-mixing effect, by which Si and VA group atoms in Si-VA group mixtures favor to form bonds between similar atoms. This was observed in systems where the liquid curve tends to be flat indicating a metastable miscibility gap or when the liquid miscibility gap is stable. In agreement with [105], Figure 36 shows a graphical summary of best representation of solid solubility of Al, As, B, Bi, Ga, In, N, P and Sb impurity atoms in silicon. No data regarding the solubility of thallium in silicon could be found in the literature. Boron, arsenic and phosphorus exhibit highest solid solubility in silicon than other impurity atoms included in this study, although they occupy substitutional positions in silicon lattice [26]. Here, the distribution coefficient, Ko in Materials 2017, 10, 676 36 of 49 Table 1, is chosen to compare the relative tendencies of various impurities to dissolve in solid silicon. B, As and P possess higher distribution coefficient values compared to other impurity atoms. InFurthermore, agreement withBurton [105 et al.], [284] Figure suggested 36 shows a rough a graphical correlation summary between the of distribution best representation coefficient of of solid an impurity atom and its tetrahedral radius at the melting point of silicon as demonstrated in Figure solubility of Al, As, B, Bi, Ga, In, N, P and Sb impurity atoms in silicon. No data regarding the 37. The trend goes toward higher solubility as the radius of impurity atom decreases. solubility ofThe thallium temperature-dependent in silicon could diffusion be found coefficients in the literature. of the studied Boron, doping arsenic elements and phosphorusin silicon are exhibit highestplotted solid solubilityin Figure 38. in This silicon plot is thanuseful other for comparing impurity relative atoms diffusivities included of in several this study,impurities. although The they occupyparameters substitutional used positionsin calculating in siliconthese coefficients, lattice [26 listed]. Here, in the the embedded distribution table, coefficient, were taken fromKo in the Table 1, is chosenliterature to compare [26,138,180]. the relative The inset tendencies shows the of variouslow nitrogen impurities diffusivity to in dissolve the 500–750 in solid °C temperature silicon. B, As and range. The diffusivity of co-diffusing atoms is greatly influenced by the size mismatch between P possess higher distribution coefficient values compared to other impurity atoms. Furthermore, silicon and the diffusing species [26]. The presence of size mismatch, irrespective to its value, leads Burtonto et lattice al. [284 strain,] suggested which may a roughinfluence correlation the diffusivity between of the impurity the distribution atom [26]. Table coefficient 18 presents of an the impurity atom andrelative its tetrahedral atomic size radiusof studied at the elements melting to pointsilicon. of It siliconis concluded as demonstrated that Al is the infastest Figure diffusing 37. The trend goes towardacceptor higher impurity solubility in Si followed as the by radius Ga. Moreover, of impurity the fastest atom diffusing decreases. donor impurity in Si is P.

1500

1400 As

1300 Bi Al In 1200 B 1100 Ga 1000 Temperature (°C) Temperature 900 N

800 Sb P

700 1×10-1 1×10-2 1×10-3 1×10-4 1×10-5 1×10-6 1×10-7 1×10-8 1×10-9 1×10-10 0 Mole fraction of impurity Figure 36. Summary of solid solubility of impurity atoms in silicon. Materials 2017, 10, Figure676 36. Summary of solid solubility of impurity atoms in silicon. 36 of 49

1 B P As VA ) 0.1 o K IIIA Sb 0.01 Ga

1E-3 Al N Bi In Distribution coefficient( 1E-4 Group IIIA elements Group VA elements

0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 Tetrahedral radius (nm) Figure 37. Distribution coefficients vs. tetrahedral radii of impurity atoms (except N) at the melting Figure 37. Distribution coefficients vs. tetrahedral radii of impurity atoms (except N) at the melting point of silicon. point of silicon. Table 18. Size of impurity atom relative to silicon.

The temperature-dependentGroup Element diffusion Tetrahedral coefficients Radius (nm) of the studied Size Ratio doping to Si elements Ref. in silicon are plotted in Figure 38. This plotB is useful for0.085 comparing relative diffusivities 0.72 of[284] several impurities. Al 0.126 1.07 [26,284] The parameters usedIII A in calculating these coefficients, listed in the embedded table, were taken from Ga 0.126 1.07 [26,284]◦ the literature [26Acceptors,138,180 ]. The inset shows the low nitrogen diffusivity in the 500–750 C temperature In 0.144 1.22 [26,284] range. The diffusivity of co-diffusing atoms is greatly influenced by the size mismatch between silicon Tl 0.144 1.22 [284] and the diffusing species [26N]. The presence of0.071 size mismatch, irrespective 0.60 to its value,[285] leads to lattice strain, which may influenceP the diffusivity of0.111 the impurity atom [26 0.94]. Table 19 presents[284] the relative V A atomic size of studied elementsAs to silicon. It0.118 is concluded that Al 1.00 is the fastest[284] diffusing acceptor Donors impurity in Si followed by Ga.Sb Moreover, the0.136 fastest diffusing donor 1.15 impurity in Si[26] is P. Bi 0.151 1.28 [284]

10-10 10-11 B

-13 N -11 10 Al 10

10-15 Tl 10-12 Bi 500 600 700 /s)

2 Ga 10-13 D =A e(B eV/kT) cm2/s -14 i 10 Element A B Al 0.317 -3.023 10-15 As 8.85 -3.97 P B3.79-3.645 Bi 1.08 -3.85 Diffusivity (cm -16 10 Ga 3.81 -3.552 In In 3.13 -3.668 -17 N 200000 -3.24 10 P1.03-3.507 Sb Sb 40.9 -4.158 -18 10 As Tl 1.37 -3.7

800 900 1000 1100 1200 1300 1400 Temperature (°C) Figure 38. Summary of diffusivity of the studied elements in silicon. The parameters used in the diffusion equation are listed in the embedded table.

Materials 2017, 10, 676 36 of 49

1 B P As VA ) 0.1 o K IIIA Sb 0.01 Ga

1E-3 Al N Bi In Distribution coefficient( 1E-4 Group IIIA elements Group VA elements

0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 Tetrahedral radius (nm) Figure 37. Distribution coefficients vs. tetrahedral radii of impurity atoms (except N) at the melting point of silicon.

Table 18. Size of impurity atom relative to silicon.

Group Element Tetrahedral Radius (nm) Size Ratio to Si Ref. B 0.085 0.72 [284] Al 0.126 1.07 [26,284] III A Ga 0.126 1.07 [26,284] Acceptors In 0.144 1.22 [26,284] Tl 0.144 1.22 [284] N 0.071 0.60 [285] P 0.111 0.94 [284] V A As 0.118 1.00 [284] Donors Sb 0.136 1.15 [26] Materials 2017, 10, 676 37 of 49 Bi 0.151 1.28 [284]

10-10 10-11 B

-13 N -11 10 Al 10

10-15 Tl 10-12 Bi 500 600 700 /s)

2 Ga 10-13 D =A e(B eV/kT) cm2/s -14 i 10 Element A B Al 0.317 -3.023 10-15 As 8.85 -3.97 P B3.79-3.645 Bi 1.08 -3.85 Diffusivity (cm -16 10 Ga 3.81 -3.552 In In 3.13 -3.668 -17 N 200000 -3.24 10 P1.03-3.507 Sb Sb 40.9 -4.158 -18 10 As Tl 1.37 -3.7

800 900 1000 1100 1200 1300 1400 Temperature (°C)

FigureFigure 38. 38. SummarySummary of of diffusivity diffusivity of of the the studied studied elemen elementsts in in silicon. silicon. The The parameters parameters used used in in the the diffusiondiffusion equation equation are are listed listed in in the the embedded embedded table. table.

Table 19. Size of impurity atom relative to silicon.

Group Element Tetrahedral Radius (nm) Size Ratio to Si Ref. B 0.085 0.72 [284] Al 0.126 1.07 [26,284] III A Ga 0.126 1.07 [26,284] Acceptors In 0.144 1.22 [26,284] Tl 0.144 1.22 [284] N 0.071 0.60 [285] P 0.111 0.94 [284] VA As 0.118 1.00 [284] Donors Sb 0.136 1.15 [26] Bi 0.151 1.28 [284]

7. Summary The success of producing or refining Si materials to high purity levels depends heavily on the availability and reliability of phase diagram, thermodynamic and diffusion data that serve as important tools in evaluating the effect of impurities on the phase equilibria in solar and electronic Si systems. In this work, ten Si-based binary phase diagrams, including Si with group IIIA elements (B, Al, Ga, In and Tl) and with group VA elements (N, P, As, Sb and Bi), have been reviewed. Each of these systems has been critically discussed in both aspects of phase diagram and thermodynamic properties. The available experimental data and thermodynamic parameters in the literature have been summarized and assessed thoroughly to provide comprehensive understanding of each system. Some systems were re-calculated to obtain the best evaluated phase diagram. As doping levels of solar and electronic silicon are of high technological importance, diffusion data have also been presented to serve as useful references on the properties, behavior and quantities of metal impurities in silicon. This paper is meant to bridge the understanding of phase diagrams with the information needed by the industry and research for development of solar-grade and electronic silicon, relying on the available information in the literature as well as our own analysis.

Acknowledgments: Authors would like to thank Kayode Orilomoye and Benjamin Wallace from TMG group of Concordia University for their help in providing some of the necessary references. Raiyan Seede from Masdar Institute is also acknowledged for improving the English language of the paper. Materials 2017, 10, 676 38 of 49

Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

Al Aluminum As Arsenic a-Si Amorphous silicon B Boron Bi Bismuth Calphad Calculations of phase diagram CdTe Cadmium telluride CIGS Copper indium gallium diselenide Cm Maximum solid solubility CO2 Carbon dioxide c-Si Crystalline silicon Csat Saturation concentration Cu(In,Ga)Se2 Copper indium gallium diselenide D Diffusivity D0 Temperature-independent pre-exponential factor Deff Effective diffusivity Dex Extrinsic diffusivity Di Intrinsic diffusivity DSSC Dye-sensitized solar cells DTA Differential thermal analysis EPMA Electron probe microanalyzer Ga Gallium GHSER Gibbs free energy values at reference state (1 atm and 298.15 K) for a pure element ICP Inductively coupled plasma In Indium IR Infra-red k Boltzmann constant Ko Distribution coefficient N Nitrogen P Phosphorus P Pressure ppb Particle per billion PV Photovoltaic Qd Activation energy R Universal gas constant Sb Antimony Si Silicon Si:As Arsenic-doped-silicon Si:Bi Bismuth-doped-silicon Si:P Phosphorus-doped-silicon T Absolute temperature TEM Transition electron microscopy TFSC Thin film solar cells TG Thermogravimetric TGMZ True gradient melting zone Tl Thallium WDS Wavelength dispersive spectroscopy Xm Maximum molar solid solubility XRD X-ray diffraction Materials 2017, 10, 676 39 of 49

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