G-Doping-Based Metal-Semiconductor Junction

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Article G-Doping-Based Metal-Semiconductor Junction

Avtandil Tavkhelidze 1,* , Larissa Jangidze 1,2, Zaza Taliashvili 2 and Nima E. Gorji 3

1 Center of Nanotechnology for Renewable Energy, Ilia State University, Cholokashvili Ave. 3/5, Tbilisi 0162, Georgia; [email protected] 2 Institute of Micro and Nano Electronics, Chavchavadze Ave. 13, Tbilisi 0179, Georgia; [email protected] 3 School of Physics, Dublin City University, Dublin, Ireland; [email protected] * Correspondence: [email protected]; Tel.: +995-59958-7316

Abstract: Geometry-induced doping (G-doping) has been realized in semiconductors nanograting layers. G-doping-based p-p(v) junction has been fabricated and demonstrated with extremely low forward voltage and reduced reverse current. The formation mechanism of p-p(v) junction has been proposed. To obtain G-doping, the surfaces of p-type and p+-type silicon substrates were patterned with nanograting indents of depth d = 30 nm. The Ti/Ag contacts were deposited on top of G-doped layers to form metal-semiconductor junctions. The two-probe method has been used to record the I–V characteristics and the four-probe method has been deployed to exclude the contribution of metal-semiconductor interface. The collected data show a considerably lower reverse current in p-type substrates with nanograting pattern. In the case of p+-type substrate, nanograting reduced the reverse current dramatically (by 1–2 orders of magnitude). However, the forward currents are not affected in both substrates. We explained these unusual I–V characteristics with G-doping theory and p-p(v) junction formation mechanism. The decrease of reverse current is explained by the drop of carrier generation rate which resulted from reduced density of quantum states within the G-doped region. Analysis of energy-band diagrams suggested that the magnitude of reverse current reduction depends on the relationship between G-doping depth and depletion width. Citation: Tavkhelidze, A.; Jangidze, L.; Taliashvili, Z.; Gorji, N.E. Keywords: G-Doping-Based nanograting; G-doping; metal-semiconductor junction; reverse current Metal-Semiconductor Junction. Coatings 2021, 11, 945. https:// doi.org/10.3390/coatings11080945 1. Introduction Academic Editor: Maja Miˇcetić Current developments in nanotechnology have enabled patterning the surface of semiconductor layers by nanoscale gratings with periodical arrays of width smaller than Received: 9 July 2021 1 µm [1–4]. Nanograting (NG) patterns have been shown to dramatically change the Accepted: 4 August 2021 electronic [5–7], magnetic [8,9], optical [10–14], and electron emission [15,16] properties Published: 7 August 2021 of the semiconductor substrate when the grating depth becomes comparable with de Broglie wavelength of electrons. This can be attributed to the special boundary conditions Publisher’s Note: MDPI stays neutral enforced by the NG on the wave function. Solution of time-independent Schrodinger with regard to jurisdictional claims in equation has to satisfy additional boundary conditions. Eigenfunctions are modified and published maps and institutional affil- the probability of finding electrons in the proximity of NG reduces. NG partly forbids some iations. quantum states within the patterned region and reduces the density of quantum states (DOS) [17]. In this case, the rejected electrons have to occupy empty quantum states with higher energy. As a result, the Fermi energy rises under the patterned region because the electron concentration, n, in the conduction band increases. We call this geometry-induced Copyright: © 2021 by the authors. electron doping (G-doping) [5]. Within this concept, both n and Fermi energy increase Licensee MDPI, Basel, Switzerland. without any ionized external impurities, which promises an interesting doping approach This article is an open access article for hard-doping materials such as GaN or for impurity-sensitive materials such as for distributed under the terms and thermotunnelling and solar cell applications, especially for large-production commercial conditions of the Creative Commons lines. Attribution (CC BY) license (https:// Various phenomena related to G-doping were already reported for different configu- creativecommons.org/licenses/by/ rations of other periodic structures. They have been reported in disordered nanostructures 4.0/).

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Coatings 2021, 11, 945 2 of 9 Various phenomena related to G-doping were already reported for different config- urations of other periodic structures. They have been reported in disordered nanostructures obtainedobtained by wet-etching by wet-etching of p-Si [18], of p-Si as well [18], as as in well nearly as in periodic nearly periodic nanostructures nanostructures made made by laser byradiation laser radiation interaction interaction with surfaces with surfaces of Si, Ge, of Si,and Ge, SiGe and crystals SiGe crystals [19], in [ 19in-], in indium tin dium tin oxideoxide [20] and [20] graphene and graphene oxide oxide [21] layers. [21] layers. A dramatic A dramatic increase increase of conductivity of conductivity (n-type (n-type conductivity)conductivity) was observed was observed in the ZnO in the crystal ZnO after crystal the after formation the formation of nanoparticles of nanoparticles on its on its surface [11].surface We [ 11have]. We shown have that shown NG that changes NG changes the conductivity the conductivity of p-type of p-typesilicon siliconto to n+-type n+-type in thinin device thin device (SOI) (SOI)layer layer[6]. Temperature [6]. Temperature dependences dependences of resistivity of resistivity and and Hall Hall coefficient coefficient of SOIof SOI device device layers layers show show meta metallicllic behavior behavior and and the the ellipsometry ellipsometry measure- measurements indicate ments indicatethat that the the dielectric dielectric function function is is metallic metallic type type [10 [10,13].,13]. Strong Strong photoluminescence photolumines- spectra were cence spectra recordedwere recorded for SOI for nanograting SOI nanograting surfaces surfaces [10,14 ][10,14] and for and the for periodic the periodic nanocones [19]. It is nanocones [19].remarkable It is remarkable that the that photoluminescence the photoluminescence phenomenon phenomenon is observed is observed in indirect in band gap indirect band materials.gap materials. In our In measurementsour measurements on NG on samples, NG samples, we observed we observed additional addi- periodic peaks tional periodicin peaks the photoluminescence in the photoluminesce spectrumnce spectrum and the and peak the positions peak positions were found were to be in agree- found to be in agreementment with with G-doping G-doping theory theo [10ry,14 [10,14].]. Giant Giant negative negative magnetoresistance magnetoresistance was found in SOI was found in SOInanograting nanograting samples samples [8] and [8] and other other periodic periodic nanostructures nanostructures [9]. Work-function[9]. Work- reduction function reductionwas investigatedwas investigated in Si in nanograting Si nanograting devices devices [22] [22] and and a strong a strong field field emission emis- was observed sion was observedin Si in periodic Si period nanoconeic nanocone structures structures [15]. [15]. A general energy-bandA general diagram energy-band of an diagramintrinsic bulk of an semiconductor intrinsic bulk semiconductor with NG patterns with NG patterns on the surface onis shown the surface in Figure is shown 1a. Some in Figure of the1 a.energy Some levels of the in energythe valence levels band in the are valence band forbidden due areto reduced forbidden quantum due to states reduced (resulting quantum from states NG patterning), (resulting from and the NG rejected patterning), and the electrons mustrejected occupy the electrons higher mustenergy occupy levels,the which higher in turn, energy increases levels, the which electron in turn,con- increases the centration in conductionelectron concentration band (G-doping). in conduction Figure 1b bandrepresents (G-doping). an energy-band Figure1b diagram represents an energy- of a p-type semiconductorband diagram substrate of a p-type with semiconductor NG patterns substrate on the surface. with NG In patterns this case, on thethe surface. In this rejected electronscase, will, the first, rejected move electrons to the top will, of the first, valence move toband the and top ofcompensate the valence the band holes, and compensate + which raises thethe Fermi holes, energy which level. raises Figure the Fermi 1c is the energy diagram level. of Figurea p+-type1c issemiconductor the diagram of a p -type with NG patternssemiconductor on the surface, with which NG patternsonly quantitatively on the surface, differs which from onlythat quantitativelyof the p-type differs from that of the p-type semiconductor. semiconductor.

Figure 1. BasicFigure energy-band 1. Basic energy-band diagrams of diagrams NG layers of fabricated NG layers on fabricated the surface on ofthe (a )surface an intrinsic of (a) semiconductor,an intrinsic sem- (b) a p-type, and (c) a p+-type.iconductor, The green (b) a linesp-type, refer and to energy(c) a p+-type. levels occupiedThe green by lines electrons, refer to and energy red lines levels refer occupied to energy by levels elec- forbidden trons, and red lines refer to energy levels forbidden by NG patterns. by NG patterns.

We can state thatWe canG-doping state that is equivalent G-doping isto equivalent donor-doping to donor-doping of the semiconductor of the semiconductor as as the the Fermi energyFermi level energy of the level semiconductor of the semiconductor rises under rises the patterned under the area. patterned In Figure area. 1a, In Figure1a, an an i–n junctioni–n forms junction on the forms surface on theof intrin surfacesic ofsubstrate intrinsic with substrate NG patterns. with NG In patterns. Figure 1b, In Figure1b, (the (the p-type substrate),p-type substrate), depending depending on G-doping on level, G-doping a partly level, compensated a partly compensated p-p− junction, p-p − junction, a a fully compensatedfully compensated p-i junction, p-ior even junction, a p-n or junction even a p-ncan junctionform by cantuning form the by geometry tuning the geometry of of the NG pattern.the NG In pattern.the case In of the p+ case-type of substrate p+-type substrate (Figure 1c), (Figure a p1+c),-p ajunction p +-p junction can be can be formed. formed. It shouldIt should be noted be notedthat the that rejected the rejected electrons electrons are confined are conﬁned within within the NG the layer. NG layer. Charge Charge neutralityneutrality in close in proximity close proximity of the ofpatterned the patterned region region does not does allow not allowdeeper deeper pene- penetration of tration of chargescharges into intothe substrate the substrate and andbind bindss the carriers the carriers to the to characteristic the characteristic depth depth d as d as shown in shown in FigureFigure 1. 1.

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In our previous works we fabricated NG layers in bulk p-Si to form a G-doped p-p(v) junction [23]. Analysis of the experimental results has revealed that the G-doping level can be adjusted electrically [24]. Here, we report on the fabrication of G-doped metal- semiconductor junction in p-type and p+-type substrates. Metal-semiconductor junctions are majority carrier devices allowing very high-frequency operation. Low barrier height and thermionic emission mechanism result in low forward voltages. However, reverse currents are high because of the same reasons and Coatings 2021, 11, 945 limit applications to DC and microwave electronics. Reverse currents can be reduced by 3 of 9 G-doping which will allow wider application of Schottky diodes. G-doping can be used for p-n junctions as well. G-doping allows high carrier mobility, which will improve characteristics of diodes and transistors used in power electronics. Unique optical properties In our previous works we fabricated NG layers in bulk p-Si to form a G-doped p- of G-doped layers can be used to improve solar cells and other optoelectronic devices. p(v) junction [23]. Analysis of the experimental results has revealed that the G-doping 2. Samplelevel Preparation can be adjusted and Characterization electrically [24]. Here, we report on the fabrication of G-doped metal-semiconductor junction in p-type and p+-type substrates. + Two typesMetal-semiconductor of Si substrates, junctions p-type and are majorityp -type, carrier were devicesused for allowing samplevery preparation. high-frequency The p-typeoperation. substrate Low has barrier a resistivity height and of 1–10 thermionic Ω × cm emissioncorresponding mechanism to hole result concentration in low forward ≈ 15 −3 + p 3 ×voltages. 10 cm However,. The p -type reverse substrate’s currents areresistivity high because is 0.044 of theΩ × same cm corresponding reasons and limit to appli- 17 −3 p = 5 ×cations 10 cm toDC [25] and p.32. microwave Samples were electronics. cut in 20 Reverse mm × currents10 mm × can0.5 mm be reduced chips. Figure by G-doping 2 showswhich the cross-section will allow widerof the applicationsamples. Dist ofance Schottky between diodes. the nanograting G-doping can junction be used and for p-n the referencejunctions plain as well. junction G-doping is 10 allowsmm. Details high carrier of the mobility,junction’s which cross-section will improve are given characteristics in Figureof 2 diodesof Ref. and[23]. transistors Nanograting used on in the power left side electronics. induces Unique a G-doped optical area properties in close ofprox- G-doped imity, layerswhich canforms be useda p-p to(v) improve junction solar in the cells depth and (d other) of the optoelectronic substrate. Metal-semiconduc- devices. tor contacts were made using Ti metal. Similar contacts on the plain area (right side of the chip, Figure2. Sample 2) were Preparation made during and Characterizationthe same manufacturing processes to record the reference I–V characteristics.Two types of SiComparison substrates, of p-type the I–V and characteristics p+-type, were recorded used for from sample both preparation. NG area andThe reference p-type substrate plain area has provides a resistivity valuable of 1–10 dataΩ × tocm observe corresponding unique changes to hole concentrationin con- ductivityp ≈ of3 ×patterned1015 cm −surfaces.3. The p +-type substrate’s resistivity is 0.044 Ω × cm corresponding to NGp = patterns 5 × 1017 withcm− 3a[ depth25] p.32. of Samples30 nm and were a period cut in 20 of mm150 ×nm10 were mm ×introduced0.5 mm chips. on theFigure 2 surfaceshows of silicon the cross-sectionsubstrates using of the laser samples. interference Distance lithography between and the nanogratingsubsequent reactive junction and ion etchingthe reference as described plain in junction Ref. [6]. is A 10 negati mm.ve Details photoresist of the layer junction’s was used cross-section for interference are given in lithographyFigure 2to ofensure Ref. [ 23uniform]. Nanograting etching onof thethe leftwhole side chip’s induces surface a G-doped and the area indents in close [22]. proximity, This waswhich performed forms a to p-p exclude (v) junction the influence in the depthof reactive (d) of ion the etching substrate. through Metal-semiconductor comparison with thecontacts reference were area. made Both using Ti Ti(50 metal. nm thick) Similar and contacts Ag (1000 on thenm plain thick) area films (right were side grown of the chip, using FigureDC magnetron2) were made sputtering during during the same the manufacturing single vacuum processes process. Later, to record metal the contacts reference I–V were backedcharacteristics. at a substrate Comparison temperature of the ofI–V 250characteristics °C for 5 min. recorded Back ohmic from contacts both NG were area and made referenceusing Al metal plain areaand standard provides metallization valuable data process. to observe All uniquecontacts changes were shaped in conductivity using of photolithographypatterned surfaces. and lift-off processes.

(a) (b)

NG patterns with a depth of 30 nm and a period of 150 nm were introduced on the

surface of silicon substrates using laser interference lithography and subsequent reactive ion etching as described in Ref. [6]. A negative photoresist layer was used for interference lithography to ensure uniform etching of the whole chip’s surface and the indents [22]. This was performed to exclude the inﬂuence of reactive ion etching through comparison with the reference area. Both Ti (50 nm thick) and Ag (1000 nm thick) ﬁlms were grown using DC magnetron sputtering during the single vacuum process. Later, metal contacts were backed at a substrate temperature of 250 ◦C for 5 min. Back ohmic contacts were Coatings 2021, 11, x FOR PEER REVIEW 4 of 9

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Figure 2. Cross-section of the prepared sample: (a) representing p-p(v)-M junction and (b) representing reference junction. The I- and V- labels represent the location of the 2-probe and 4-probe mademeasurements. using Al metal and standard metallization process. All contacts were shaped using photolithography and lift-off processes. Figure 33aa showsshows metalmetal contactcontact layoutlayout andand wiringwiring bothboth forfor two-wiretwo-wire andand four-wirefour-wire measurement methods. There There are are two two windows windows opened opened in in SiO 22 contactcontact under under layer. layer. Nanograting is fabricated inside the left window only. The rightright windowwindow containscontains plainplain Si substrate.

Figure 3. (a) Front side metal contact layout. Nanograting is fabricated inside the window opened Figure 3. (a) Front side metal contact layout. Nanograting is fabricated inside the window opened in SiO2 layer. (b) Back side contact layout. in SiO2 layer. (b) Back side contact layout.

The I–V characteristicscharacteristics were recorded using two-probe and four-probe methods.methods. The two-probe methodmethod was was used used to to characterize characterize p-p(v)-M p-p(v)-M junction. junction. The The four-probe four-probe method method was usedwas used to exclude to exclude the contribution the contribution of metal-semiconductor of metal-semiconductor interface interface and and to record to record the I–Vthe curveI–V curve of the of purethe pure p-p(v) p-p(v) junction. junction. The voltageThe voltage and currentand current terminals terminals of I–V ofmeasurements I–V measure- arements shown are shown in Figure in 2Figure. A Keysight 2. A Keysight multimeter multimeter 34410 (input 34410 impedance (input impedance >1 G Ω )>1 and GΩ E3640) and currentE3640 current source source and homemade and homemade LabVIEW LabVIEW drivers drivers were used were to used record to recordI–V curves. I–V curves.

3. Results and Discussion Figure 44aa showsshows thethe I–VI–V curvescurves of of p-p(v)-M p-p(v)-M and and the the corresponding corresponding reference reference p-M p- Mjunction junction recorded recorded using using thethe two-pr two-probeobe method. method. Figure Figure 4b 4showsb shows the the I–V I–Vcurvescurves of the of thesame same junctions junctions recorded recorded using using the four-probe the four-probe method method which which allows allows excluding excluding the metal- the metal-semiconductorsemiconductor interface interface contribution contribution to the toI–V the measurements.I–V measurements. The curve’s The curve’s colors colorscorre- correspondspond to the to colors the colors of I− ofand I− V-terminaland V-terminal labels labels of Figure of Figure 2. Curves2. Curves recorded recorded on the on theNG NGarea areaare areshown shown in red in red and and green green colors. colors. Reference Reference I–VI–V curvescurves shown shown in in blue blue and violet colors were obtained from analogous measurementsmeasurements made on the reference plain side ofof the same chip (right side of Figure2 2).). ComparisonComparison of of the the two two pairs pairs of of curves curves (red (red vs. vs. blue blue and green vs. violet) allows the identificationidentification of the influenceinfluence of NGNG patterningpatterning onon I–VI–V characteristics (forward and reverse currents) separately for two-probetwo-probe andand four-probefour-probe measurements, respectively. As shown in Figure4a, the forward current ( IF) of the p-p(v)-M junction has not been affected by NG patterns. The forward currents of both NG and reference plain junction fit with10 the5 Shockley expression with ideality factor of105η = 1.25. The reverse current (IR) of the p-p(v)-M junctionexp(eV/ (FigureηKT)-14a) is affected by NG and is considerably lower than the reference 104 104 p-M junction. The reduction of I cannot be explained by the limiting effect of the p-p(v) R Forward junction,103 which is connectedReverse in series. This is evident103 from the reverse current-voltage

0 Forward Reverse 0 I/I dependence2 of the p-p(v) junction (Figure4b, greenI/I 2 curve). Reverse current of p-p(v)

10 10 junction is considerably higher than that of the p-p(v)-M junction, which can be seen by comparing101 Figure4a (red curves) and Figure4b (green101 curves). Note the difference in

x-axis10 scales.0 The reverse current-voltage dependence100 is stronger for the p-p(v) junction.

10-1 10-1 0246810 0123 (a) V [Volt] (b) V [Volt]

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Figure 3a shows metal contact layout and wiring both for two-wire and four-wire measurement methods. There are two windows opened in SiO2 contact under layer. Nanograting is fabricated inside the left window only. The right window contains plain Si substrate.

Figure 3. (a) Front side metal contact layout. Nanograting is fabricated inside the window opened in SiO2 layer. (b) Back side contact layout.

The I–V characteristics were recorded using two-probe and four-probe methods. The two-probe method was used to characterize p-p(v)-M junction. The four-probe method was used to exclude the contribution of metal-semiconductor interface and to record the I–V curve of the pure p-p(v) junction. The voltage and current terminals of I–V measurements are shown in Figure 2. A Keysight multimeter 34410 (input impedance >1 GΩ) and E3640 current source and homemade LabVIEW drivers were used to record I–V curves.

3. Results and Discussion Figure 4a shows the I–V curves of p-p(v)-M and the corresponding reference p-M junction recorded using the two-probe method. Figure 4b shows the I–V curves of the same junctions recorded using the four-probe method which allows excluding the metal- semiconductor interface contribution to the I–V measurements. The curve’s colors correspond to the colors of I− and V-terminal labels of Figure 2. Curves recorded on the NG area are shown in red and green colors. Reference I–V curves shown in blue and violet colors were obtained from analogous measurements made on the reference plain side of the same chip (right side of Figure 2). Comparison of the two pairs of curves (red vs. blue and green vs. violet) allows the identification of the influence of NG patterning on I–V Coatings 2021, 11, 945 characteristics (forward and reverse currents) separately for two-probe and four-probe5 of 9 Coatings 2021, 11, x FOR PEER REVIEWmeasurements, respectively. 5 of 9

105 105 Figure 4. The I–V curvesexp(eV/ ηofKT)-1 p-type sample: (a) two-probe; (b) four-probe measurements. The red color corresponds104 to the nanograting area recorded using10 two4 probes; the blue color refers to the I–V Forward recorded103 from the plain areaReverse using two probes; the green103 color refers to the nanograting area rec-

0 Forward Reverse orded using four probes, and the violet refers to the plain0 area recorded using four probes. Colors I/I 2 I/I 2 correspond10 to voltage and current terminals shown in Figure 10 2. Shockley equation fitting curve (for η = 1.25) is shown in black. 101 101

100 100 As shown in Figure 4a, the forward current (𝐼) of the p-p(v)-M junction has not been

affected10-1 by NG patterns. The forward currents of both10-1 NG and reference plain junction fit 0246810 0123 with the Shockley expression with ideality factor of η = 1.25. The reverse current (𝐼) of (a) V [Volt] (b) V [Volt] the p-p(v)-M junction (Figure 4a) is affected by NG and is considerably lower than the referenceFigure 4. p-MThe junction.I–V curves The of p-type reduction sample: of 𝐼 (a ) cannot two-probe; be explained (b) four-probe by the measurements. limiting effect The of red thecolor p-p(v) corresponds junction, to which the nanograting is connected area in recorded series. This using is twoevident probes; from the the blue reverse color refers current- to the

voltageI–V recorded dependence from the of plainthe p-p(v) area using junction two probes;(Figure the 4b, green green color curve). refers Reverse to the nanograting current of p- area p(v)recorded junction using is considerably four probes, and higher the violet than refers that toof the the plain p-p(v)-M area recorded junction, using which four can probes. be seen Colors bycorrespond comparing to Figure voltage 4a and (red current curves) terminals and Figure shown in4b Figure (green2. curves). Shockley Note equation the ﬁttingdifference curve in (for x-axisη = 1.25) scales. is shown The reverse in black. current-voltage dependence is stronger for the p-p(v) junction. + To explain the reduction of 𝐼, we repeated the same experiment on p -type sub- + strate. FigureTo explain 5a shows the reduction the I–V ofcurvesIR, we of repeatedp+-p(v)-M the and same the experiment corresponding on p reference-type substrate. p-M + junctionFigure 5measureda shows the usingI–V thecurves two-probe of p -p(v)-M method. and Figure the corresponding 5b shows the reference I–V curves p-M junctionof the samemeasured junctions using recorded the two-probe using the method.four-probe Figure method.5b shows The curve’s the I–V colorscurves correspond of the same to thejunctions colors of recorded voltage and using current the four-probe terminals shown method. in Figure The curve’s 2. colors correspond to the colors of voltage and current terminals shown in Figure2.

4 105 2x10

104 Forward 1x104 103 0 0 Reverse I/I I/I 2

10 0

101 exp(eV/ηKT)-1 -1x104 100

10-1 01234 -0.002 0.000 0.002 0.004 (a) V [Volt] (b) Voltage [Volt]

FigureFigure 5. The 5. The I–VI–V curvescurves of p+-type of p+-type sample: sample: (a) (two-probe;a) two-probe; (b) ( bfour-probe.) four-probe. The The red red color color corresponds corresponds to tothe the nanograting nanograting area area recorded recorded using using two two probes; probes; the the blue blue refers refers to tothe the plain plain area area recorded recorded using using twotwo probes; probes; the thegreen green color color refers refers to the to nanogratin the nanogratingg area recorded area recorded using four using probes; four probes;and the andviolet the refersviolet to refersthe plain to the area plain recorded area recorded using four using probes. four Colors probes. corresp Colorsond correspond to voltage to and voltage current and termi- current nalsterminals labels in labels Figure in 2. Figure Shockley2. Shockley equation equation fitting curve ﬁtting (for curve η = (for1.25)η is= shown 1.25) is in shown black incolor. black color.

ForwardForward current current of ofp+ p-p(v)-M+-p(v)-M junction junction (Figure (Figure 5a)5a) is isnot not affected affected by by the the NG. NG. Forward Forward currentscurrents of of p p+-p(v)-M+-p(v)-M junction junction and correspondingcorresponding reference reference junction junction ﬁt wellfit well with with the Shock- the Shockleyley expression, expression, with with close close ideality ideality factor factor values values (η = 1.25).(η = 1.25). Current-voltage Current-voltage dependence depend- of encep+-p(v) of p+-p(v) junction junction (green (green curve curve in Figure in Figure5b) indicates 5b) indicates that pthat+-p(v) p+-p(v) junction junction is ohmic is ohmic type typewith with a resistance a resistance higher higher than than the substrate the substrate resistance resistance (violet (violet curve incurve Figure in5 b).Figure However, 5b). However,p+-p(v) junctionp+-p(v) junction has much has lower much resistance lower resistance with respect with to respect the reverse to the biased reverse p+ biased-p(v)-M p+junction-p(v)-M junction (see voltage (see scalesvoltage in scales Figure in5 a,b).Figure Reverse 5a,b). Reverse currents currents of p +-p(v)-M of p+-p(v)-M junction junc- (red tioncurve) (red curve) are dramatically are dramatically lower lower with respectwith respect to reference to reference junction. junction. Reduction Reduction is as is large as largeas1–2 as 1–2 orders orders of of magnitude magnitude in in the the wide wide range range ofof reverse voltages (Figure (Figure 5a).5a). Reverse Reverse currentcurrent reduction reduction is much is much more more pronounced pronounced for forthe thep+-p(v)-M p+-p(v)-M junction junction with with respect respect to p- to p(v)-Mp-p(v)-M junction junction (Figure (Figure 4a).4 a).Consequently, Consequently, the the drop drop in in𝐼 IstronglyR strongly depends depends on on carrier carrier concentrationconcentration of ofthe the substrate. substrate. To explain the dependence on carrier concentration, we analyze the relationship between G-doping depth d and the depletion width 𝑊. The d value does not depend on

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To explain the dependence on carrier concentration, we analyze the relationship between G-doping depth d and the depletion width WD. The d value does not depend hole concentrationon hole as estimated concentration in Ref. as [24] estimated for d ≈ 240 in Ref. nm. [ 24However,] for d ≈ the240 depletion nm. However, width the depletion + width is 500 nm in p-type substrate+ and 40 nm in p -type (calculated for V = 1 V) [25] is 500 nm in p-type substrate and 40 nm in p -type (calculated for 𝑉 = 1 V) [25] p. 89. R Consequently,p. we 89. have Consequently, realized two we diverse have realized cases in two our diverseexperiments. cases inIn ourthe experiments.first case, In the ﬁrst + case, WD > d and in the second+ case, WD < d (p -type). Let us begin from the p-type 𝑊 >𝑑 and in the second case, 𝑊 <𝑑 (p -type). Let us begin from the p-type substrate: the energy-bandsubstrate: diagrams the of energy-band p-p(v)-M junction diagrams is given of p-p(v)-M in Figure junction 6 and isdisplays given in the Figure ther-6 and displays V V V mal equilibriumthe (V thermal = 0), forward equilibrium bias (V ( > =0), 0), and forward reverse bias bias ( (V> < 0), 0) and regimes. reverse bias ( < 0) regimes.

Figure 6. Energy-bandFigure 6. Energy-band diagram of p-p(v)-Mdiagram of junction: p-p(v)-M (a) junction: thermal equilibrium;(a) thermal equilibrium; (b) forward bias;(b) forward (c) reverse bias; bias. (c) Distances reverse bias. Distances and energies (except the eVR) are scaled according to their experimental val- and energies (except the eVR) are scaled according to their experimental values. ues. The p-p(v) junction falls within the depletion region as shown in Figure6a. Built-in The p-p(v)potential junction value falls within 0.04 eV the is takendepletion from region experimental as shown data in Figure [23]. Fermi 6a. Built-in energy is calculated potential valuefrom 0.04 theeV holeis taken concentration from experimental of the substrate, data [23]. and Fermi the metal-semiconductor energy is calculated barrier is taken from the hole concentrationfor Ti on Si [25 of] p.the 179. substrate, In the forwardand the metal-semiconductor biased regime in Figure barrier6b, the is voltagetaken drop across for Ti on Si [25]the p. p-p(v)179. In junctionthe forward is much biased lower regime than in in Figure the metal-semiconductor 6b, the voltage drop junction. across This follows the p-p(v) junctionfrom is the much comparison lower than of forwardin the metal-semiconductor voltage values from junction. Figure4a. This It is follows also confirmed by a from the comparisonlarge difference of forward in voltage ideality values factors from (η = 1.25Figure for 4a. p-p(v)-M It is also junction confirmed and byη = a 0.18 for p-p(v) large differencejunction). in ideality The factors voltage (η distribution= 1.25 for p-p(v)-M is different junction in the and reverse η = 0.18 bias for regime p-p(v) (Figure 6c). The junction). The dropvoltage in reversedistribution voltage is differen across p-p(v)t in the junction reverse andbias metal-semiconductorregime (Figure 6c). The are comparable, drop in reversewhich voltage is confirmed across p-p(v) by comparison junction and of metal-semiconductor reverse voltages in Figure are 4comparable,a,b (red and green curves). which is confirmedThis result by comparison is consistent of with reverse our previous voltages measurements in Figure 4a,b [23 (red]. Figure and6 cgreen indicates that only curves). This resulta part is of consistent the depletion with regionour previous falls within measurements the G-doping [23]. region. Figure Consequently, 6c indicates NG-induced that only a partchanges of the depletion in semiconductor region falls material within properties the G-doping apply onlyregion. to aConsequently, part of the depletion region. NG-induced changesNext, in semiconductor we analyze results material obtained properties from the apply p+-type only substrate.to a part of Energy-band the de- diagrams pletion region.of p+-p(v)-M junction are given in Figure7. In the forward bias regime, voltage drop across Next, we theanalyze p-p(v) results junction obtained is much from lower the p than+-type in substrate. the metal-semiconductor Energy-band diagrams junction. This follows of p+-p(v)-M junctionfrom a are comparison given in Figure of forward 7. In the voltage forward values bias regime, from Figure voltage5a. drop The sameacross is true for the + the p-p(v) junctionreverse is much bias regime.lower than The inI–V thecharacteristics metal-semiconductor of p -p(v) junction. is ohmic This which follows is explained by the + from a comparisonhigh of hole forward concentration. voltage values Generally, from the Figure voltage 5a.drop The same over theis true p -p(v) for the junction re- is negligible both in forward and reverse bias regimes. The energy-band diagrams in Figure7 reflect the verse bias regime. The I–V characteristics of p+-p(v) is ohmic which is explained by the high voltage drop at these junctions. Figure7c indicates that the whole depletion region falls hole concentration. Generally, the voltage drop over the p+-p(v) junction is negligible both within the G-doping region. Consequently, NG-induced changes in the material properties in forward andof reverse the semiconductor bias regimes. substrates The energy-band apply to diagrams the whole in depletion Figure 7 region. reflect Knowingthe this, we voltage drop at these junctions. Figure 7c indicates that the whole depletion region falls offer the following interpretation for the drop in IR The DOS reduces in the G-doped layer within the G-dopingand this region. increases Consequently, the carrier NG-i generationnduced changes lifetime. in Consequently,the material properties the carrier generation of the semiconductorcurrent substrates decreases asapply it is correspondinglyto the whole depletion related region. to lifetime Knowing [25] p. this, 97, we offer the following interpretation for the drop in 𝐼 The DOS reduces in the G-doped layer and this increases the carrier generation lifetime. Consequently,Jge = eniWD the/τg carrier generation cur- (1) rent decreases as it is correspondingly related to lifetime [25] p. 97, where ni is an intrinsic carrier concentration and τg is a carrier generation lifetime. In Equation (1) we ignore the𝐽 recombination=𝑒𝑛𝑊/𝜏 current component as it is negligible(1) in the case

where 𝑛 is an intrinsic carrier concentration and 𝜏 is a carrier generation lifetime. In Equation (1) we ignore the recombination current component as it is negligible in the case

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of Si (low ni value) and especially in the case of G-doping, which reduces ni even more [25]. of Si (low 𝑛 value)In the and case especially of G-doped in the semiconductor, case of G-doping, the intrinsic which carrierreduces concentration 𝑛 even more is given by, [25]. In the case of G-doped semiconductor, the intrinsic carrier concentration is given by, (NG) (NG) () n =()ni/G and τg = τgG (2) 𝑛 =𝑛/𝐺 iand 𝜏 =𝜏𝐺 (2) where G is the wheregeometryG is factor the geometry [26]. An factorincrease [26 in]. Ancarrier increase generation in carrier lifetime generation is a conse- lifetime is a consequence of a generalquence principle of a general called principle “Fermi’s called golden “Fermi’s rule” which golden states rule” that which all transition states that all transition rates are proportionalrates are to proportional DOS. Inserting to DOS. Equation Inserting (2) into Equation Equation (2) (1) into we Equation obtain, (1) we obtain, () 𝐽𝑒 = 𝐽 /𝐺( NG) 2 (3) Jeg = Jge/G (3)

Figure 7. Energy-bandFigure 7. Energy-band diagram for diagram p-p(v)-M for junction. p-p(v)-M (a )junction. Thermal ( equilibrium;a) Thermal equilibrium; (b) forward ( bias;b) forward (c) reverse bias; bias. (c) Distances reverse bias. Distances and energies (except eVR) are scaled according to their experimental values. and energies (except eVR) are scaled according to their experimental values.

Equation (3) explainsEquation that (3) the explains generation that thecurr generationent is reduced current 𝐺 -fold is reduced within Gthe2-fold G- within the G- doped area withdoped respect area to withthe conventionally respect to theconventionally doped areas. Estimated doped areas. value Estimated for geometry value for geometry factor is G = 3.3factor as presented is G = 3.3 in as Ref. presented [24]. Conseq in Ref.uently, [24]. Consequently,about one order about of magnitude one order of magnitude reduction in generationreduction current in generation is expected. current This is expected.explains our This results explains for the our drop results in for𝐼 in the drop in IR in the case of p-typethe casesubstrate of p-type Figure substrate 4a. It sh Figureould be4a. noted It should here bethat noted the reverse here that currents the reverse currents should be comparedshould for be the compared same 𝑊 for value the (for same theW sameD value VR).(for Consequently, the same V p-p(v)R). Consequently, junc- p-p(v) tion voltage dropjunction is considerable voltage drop and isshould considerable be determined and should from be Figure determined 4b (for the from same Figure 4b (for the current) and subtractedsame current) from andthe x-axis subtracted of Figure from 4a the before x-axis applying of Figure to4a the before green applying curve. to the green After this procedure,curve. reverse After this current procedure, reduction reverse (Figure current 4a) reductionincreases (Figureto roughly4a) increasesone order to roughly one of magnitude andorder is in of good magnitude agreement and with is in Equa goodtion agreement (3). In the with case Equation of a p-type (3). substrate, In the case of a p-type the depletion regionsubstrate, is relatively the depletion wide regionand includes is relatively a G-doped wide and region includes (Figure a G-doped 6c). Conse- region (Figure6c ). quently, the generationConsequently, current the reduces generation at a sm currentall part reduces of the atdepletion a small region. part of theIn case depletion of region. In p+-type substrate,case the of depletion p+-type substrate, region shrinks the depletion dramatically region and shrinks becomes dramatically a part of the and G- becomes a part doping region ofitself the (Figure G-doping 7c). regionHere, the itself ge (Figureneration7 c).current Here, is the reduced generation within current the whole is reduced within + depletion region.the This whole can depletion explain why region. 𝐼 reduction This can is explain more pronounced why IR reduction in p -type is more sub- pronounced in + strates. The Si-basedp -type G-doped substrates. Schottky The Si-based diodes G-dopedI–V curves Schottky are comparable diodes I–V to curvesI–V curves are comparable to obtained on theI–V basiscurves of more obtained advanced on the ma basisterials of more(AlN advancedand GaN) materials [27]. Further (AlN improve- and GaN) [27]. Further ment of G-doping-basedimprovement junctions of G-doping-based can be made junctions by tuning can be the made Fermi by tuning level theusing Fermi level using nanograting depthnanograting variation depth [22]. We variation plan to [22 tune]. We the plan Fermi to tunelevel the by Fermivarying level the byNG varying line the NG line width as well. width as well. Reduced reverseReduced currents reverse in G-doped currents junctions in G-doped can be junctions used to cansignificantly be used to increase signiﬁcantly increase the quality of themetal-semiconductor quality of metal-semiconductor diodes by eliminating diodes by eliminatingtheir main theirdrawback—rela- main drawback—relatively tively high reversehigh currents. reverse currents. We estimated We estimated G-doping G-doping depth as depthd ≈ 240 as nmd ≈ in240 Ref. nm [24] in and Ref. [24] and used used this valuethis to explain value tothe explain concept the throug concepth energy-band through energy-band diagrams. This diagrams. value fits This well value ﬁts well + between WD+= 40 nm for p -type and WD = 500 nm for a p-type substrate. However, the between 𝑊 = 40 nm for p -type and 𝑊 = 500 nm for a p-type substrate. However, the direct measurementdirect of measurement d is essential. of Wed is are essential. planning We th aree direct planning measurements the direct measurements of G-dop- of G-doping ing depth and itsdepth voltage and dependence its voltage dependence in our future in ourexperiments. future experiments.

4. Conclusions

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4. Conclusions We have fabricated and characterized G-doping-based metal-semiconductor junctions. The p-type and p+-type silicon substrates were used as semiconductor material and Ti as metallic electrode. To realize G-doping, nanograting was patterned on the surface of Si substrates. It was found that forward current-voltage dependence of p-p(v)-M and p+-p(v)-M junctions are well described by the Shockley equation. The reverse current of p-p(v)-M junction is considerably lower with respect to the p-M junction. Reverse current of p+-p(v)-M junction is reduced even more and is 1–2 orders of magnitude less with respect to the p+-M junction. Experimental results are in agreement with the G-doping theory and the p-p(v) junction formation mechanism developed earlier. Low reverse currents are explained by the reduction of carrier generation current within the depletion region, which itself is a consequence of reduced DOS within the G-doped region. Substrate carrier concentration dependence is analyzed using energy-band diagrams. In the case of a p-type substrate, the depletion region includes the G-doped region. In the case of p+-type substrate, the depletion region shrinks dramatically and becomes a part of the G-doping region itself. Reduced reverse currents can be employed to signiﬁcantly increase the quality of metal-semiconductor diodes widely used in high-frequency and general electronics.

Author Contributions: A.T.: writing—original draft, methodology, experimental research, funding acquisition; L.J.: methodology, experimental research; Z.T.: experimental research; N.E.G.: manuscript review, funding acquisition. All authors have read and agreed to the published version of the manuscript. Funding: Research was funded by Shota Rustaveli National Science Foundation (SRNSF) and Georgia National Innovation Ecosystem, grant number CARYS-19-218. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data sharing not applicable. Acknowledgments: The authors would like to thank G. Skhiladze, S. Sikharulidze, and N. Kitoshvili for supporting the project. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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