V13. MBE growth and optical properties of III/V-II/VI hybrid core-shell nanowires

Alexander Pawlis and Mihail Ion Lepsa

Peter Grünberg Instutite (PGI-9, PGI-10)

JARA-Fundamentals for Information Technology

Research Center Jülich, 52425

Contents 1. Introduction ...... 2 2. Molecular beam epitaxy of semiconductor heterostructures ...... 3 2.1 Molecular beam epitaxy ...... 3 2.2 MBE growth...... 7 3. Growth, morphology and structural properties of GaAs/ZnSe core-shell nanowires ...... 12 3.1 Growth of self-catalyzed GaAs nanowires ...... 12 3.2 Growth of ZnSe shell ...... 14 3.3 Structural properties of GaAs/ZnSe core/shell nanowires ...... 15 4. Theoretical basis for describing optical properties of semiconductor nanostructures ...... 17 4.1 Energy gap, band structure and effective mass approximation ...... 17 4.2 Electron-photon interaction, transition matrix and oscillator strength ...... 19 4.3 Einstein coefficients, transition rates and radiative lifetime ...... 20 4.4 Band offset, heterostructures and 1-dim. confinement (quantum well)...... 21 5. Photoluminescence properties of the GaAs/ZnSe core/shell nanowires ...... 23 References ...... 25

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1. Introduction For electronic and optoelectronic applications, self-catalyzed grown semiconductor nanowires (NWs) especially from classical III/V compound semiconductors ((AlGa)As, InAs, InSb) have attracted much research interest in the last ten years. Measurements of the charge transport characteristics along the NW axis allows for studying quantum effects on the nanoscale as typically NW diameters are in the order of 10-100 nm. If those NWs are combined with certain contact designs, they provide a suitable base for a new class of modern devices such as field effect transistors or gate confined quantum dots. Regarding optical and optoelectronic applications, NWs are particularly suitable for nanolasers and single photon sources due to their high length-to-width aspect ratio, forming a build-in waveguide system. However, typical core-only NWs provide an extremely large surface/volume ratio. This leads to strong non-radiative surface recombination of carriers, which for optoelectronic applications drastically reduces the quantum efficiency of NW based devices. Therefore, suitable passivation techniques are required to enhance the optical quantum efficiency and to explore relevant quantum effects in the NWs. Efficient passivation is achieved by epitaxial co- verage of the core material with a shell material pro- viding a larger bandgap as the core and a small lattice mismatch (e.g. difference between the lattice para- meters of the core and shell material) to it. The most prominent core/shell NW system is GaAs/(Al,Ga)As. Here, the GaAs NWs are passivated by an epitaxial shell of (Al,Ga)As. The latter must be additionally capped with another GaAs layer to maintain chemical stability Fig. 1.1: Schematic drawing (right side) of a GaAs/ZnSe core/shell of the system, as (Al,Ga)As NW and calculation of the conduction band alignment (left side) rapidly oxidizes in air. Due between GaAs and ZnSe close to the interface (provided by Dr. N. to the improved surface Demarina). Considering a shell thickness of 70 nm, a core radius passivation, capped NWs of 35 nm and a shell n-type doping concentration of 5x10 17 cm -3, yield a noticeably enhanced electron wavefunctions (red, blue) are localized at the periphery of photoluminescence (PL) the GaAs core . emission. In time-resolved PL measurements of AlGaAs/GaAs NWs, carrier lifetimes up to multiple nanoseconds were demonstrated, which together with the enhanced emission intensity validates the passivation effect. A prominent alternative system to GaAs/AlGaAs is GaAs/ZnSe. The II/VI compound semiconductor ZnSe is also almost lattice matched with GaAs. Improved enhancement of the optical properties of a GaAs core NWs is possible since GaAs/ZnSe provides substantially larger band offsets than AlGaAs/GaAs. This results in improved carrier localization and balanced confinement of electrons and holes in the GaAs core. A schematic drawing of a GaAs/ZnSe core/shell NW and calculations of the conduction band alignment (see also Sec.4.4) of core and shell at the interface are shown in Fig. 1.1 Depending on the doping level of the shell, electron wave functions can be localized in the periphery of the GaAs core. 3

Additionally, the ZnSe shell provides a higher stability against oxidation without the need for additional GaAs capping. Finally, the extremely small lattice mismatch of 0.3 % between GaAs and ZnSe allows for engineering nearly perfect epitaxial interfaces between GaAs and ZnSe with extremely low dislocation densities. Although the radial interface between core and shell is nearly defect-free, the GaAs core itself can contain randomly stacked axial segments of wurtzite (WZ) and zincblende (ZB) crystal phase. This polymorphism (see also Sec.3.3) leads to twinning domains and stacking faults at the phase boundaries between the segments. In this course, the growth by molecular beam epitaxy (MBE) and optical properties of GaAs/ZnSe core-shell NWs are studied. Here, we introduce first the basics of the MBE growth with specific exemplification. In the following section the growth, morphology and structural properties of the GaAs/ZnSe core-shell NWs are considered. Then the theoretical basis for the understanding of the optical properties of the GaAs/ZnSe core-shell NWs are introduced. Finally, the PL properties of the GaAs/ZnSe core-shell NWs are discussed.

2. Molecular beam epitaxy of semiconductor heterostructures 2.1 Molecular beam epitaxy Molecular beam epitaxy is a refined form of physical vapor deposition for epitaxial growth of high quality semiconductor, metal and insulator thin films. The epitaxial growth refers to the deposition of a crystalline film on a crystalline substrate, the film being in registry with the substrate. The term epitaxy comes from the Greek roots epi, meaning "above", and taxis, meaning "in ordered manner". It can be translated "to arrange upon". Using MBE, high quality semiconductor layers are grown regarding purity, crystal phase, control of layer thickness and doping. The main characteristic features of the MBE are: - precise controlled atomic or molecular thermal beams react with a clean heated crystalline surface (substrate); - ultra high vacuum (UHV) conditions; - the beams are obtained by effusion from solid (sublimation) or liquid (evaporation) ultra pure material sources at high local temperature; - low growth rate (1 µm/h ~ 1 monolayer/s) which permit the surface migration of the impinging species resulting in the growth of atomically flat surfaces ; - the growth governed mainly by the kinetics of the surface processes , under conditions far from thermodynamic equilibrium; - ultra rapid shutters in front of the beam sources allowing nearly atomically abrupt transitions from one material to another and therefore, obtaining of abrupt interfaces . Historically, the basic concepts of the MBE growth process have been developed in 1958 by K. G. Günther at Siemens Research Laboratories (Erlangen) within so called ‘three temperature method’ . The foundation of the MBE was done in the mid-sixties, when the first semiconductor films were grown by J.R. Arthur and A.Y. Cho at Bell Laboratories while studying the interaction of Ga atoms and As 2 molecules with crystalline GaAs in UHV conditions. In the following, some of the characteristics of the MBE will be discussed.

a) Vapor pressure It is well known that in a closed volume, a liquid or solid element is in equilibrium with the above gas phase (see Fig.2.1a). The corresponding pressure of the gas is called the saturated or equilibrium vapor pressure, peq . Increasing the temperature, the vaporization will be 4

Fig. 2.1: (a) Illustration of the vaporization of a liquid or solid material in a closed volume resulting in the saturated vapor pressure of the gas phase. (b) Phase diagram of a single element. stimulated and peq will increase. Each element has a characteristic phase diagram, which describes the coexistence of different physical states of the element. This is shown in Fig. 2.1b. Only at one point, the so called triple point (T) the three different physical states coexist. The MBE method makes use of the vaporization of solid or liquid materials in ultrahigh vacuum (UHV) conditions. The vapors are directed to a crystalline substrate as atom (molecular) beams where they condense in the solid state. In Fig. 2.2, the vapor pressure of different elements as function of temperature is shown. Depending on the element, the vaporization results in molecules or atoms and a certain peq is reached by sublimation or evaporation at different -3 temperatures. For example, a peq of 10 torr is reached at 270 °C for As by sublimation of As 4 molecules, at 1082 °C for Ga and 1007 °C for Al, both by evaporation of atoms.

Fig. 2.2: Vapor pressure of different elements as function of temperature. The arrows indicate -3 the necessary temperatures to reach a vapour pressure of 10 torr for As 4 (red, 270°C, sublimation), Ga (green, 1082°C, evaporation) and Al (blue, 1007°C, evaporation).b) Molecular (atomic) beams.

The molecular (atomic) beams necessary for MBE are generated in the effusion cells. The latter exploit the evaporation process of condensed materials as molecular flux in vacuum. The understanding of the properties of real effusion cells is complicated and not straightforward, so, easier models are needed. The molecular (atomic) rate of evaporation per unit area from a liquid free surface, Ae, in equilibrium with its vapor, was first derived by Hertz and later modified by Knudsen obtaining: 5

dN N e = α ( p − p) A (2.1) A dt v eq 2πk MT e B where peq is the equilibrium vapor pressure at the absolute temperature T, p is the ambient hydrostatic pressure acting upon the evaporant in the condensed phase, M is the molar mass of the evaporating species, and NA and kB are the Avogadro constant and Boltzmann constant, respectively. The evaporation coefficient αv was introduced by Knudsen to account for the fraction of evaporant vapor molecules that are reflected by the condensed phase surface. αv is dependent on the microscopic status of the surface and is strongly unpredictable. The maximum evaporation rate is obtained for αv=1 and p=0. Langmuir has shown that the Hertz-Knudsen equation applies also to sublimation from solid free surfaces. Phase transitions of this type, which constitutes vaporization from free surfaces, as commonly referred to Langmuir or free evaporation. The free evaporation is isotropic. To force αv=1, Knudsen invented a technique,

Fig. 2.3: The ideal effusion source used by Knudsen to study atomic beams of Hg. in which the evaporation occurs as effusion from an isothermal enclosure with a sufficient small orifice (Knudsen cell, see Fig. 2.3). Under these conditions, the orifice represents an evaporation source with the evaporant pressure peq but without the ability to reflect vapor molecules. If Ae is the orifice area, the effusion rate, Γe, from the Knudsen cell is given by

dN N Γ = e = A ( p − p ) A (2.2) e e eq v π dt 2 kB MT with pv the pressure in the reservoir where the molecules effuse from the cell orifice. In UHV environment, it is reasonable to consider pv = 0. Then, the Knudsen effusion equation can be written in the most used form:

p A Γ = 22 eq e (2.3) e 33.8 x10 MT where all the quantities are in SI units. The Knudsen equation can be used to determine the impingement rate on a substrate from ideal effusion sources. In Fig. 2.4, two situations are shown, when the source orifice is oriented axially and non-axially with respect to the substrate. The impingement rate in the central point A is: Γ p A I = e = .2 653 ×10 22 eq e (2.4) A πr 2 2 A rA MT

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(c)

Fig. 2.4: Molecular flux on a substrate oriented axially (a) and non-axially (b) with respect to the orifice of the ideal effusion cell. (c) Molecular flux from a conical, Langmuir type non-equilibrium effusion cell tilted against the perpendicular substrate axis. where rA is the distance from the orifice to the substrate. The flux at the edge point B of the substrate can be calculated as:

Γ cos 2ϑ r 2 I = e ⋅ A = I cos 4ϑ (2.5) B πr 2 r 2 A B This is called the cosine law of effusion. Proceeding in an analogous way, the impingement rate from a source which is tilted by an angle ϕ from perpendicular to the substrate can be calculated:

(2.6) d) Ultra high vacuum Vacuum conditions are necessary in MBE for two reasons. First, the beam nature of the mass flow towards the substrate has to be preserved. This means that the highest admissible value of the residual gas pressure in the vacuum reactor should assure the condition that the mean free path of the molecules (atoms) of the reactant beam penetrating the environment of the residual gas has to be larger than the distance from the outlet orifice of the beam source to the substrate crystal surface. In standard MBE chambers, this distance is ~ 0.2 m and a maximum residual gas pressure of 5.7x10 -4 Torr can be estimated. It is evident that the beam nature of the mass transport is preserved even in high vacuum (HV) conditions. However, the low growth rates typical for the MBE technique (about 1 µm/h, or 1 monolayer (ML)/s) combined with the important requirement of negligible unintentional impurity incorporation in the crystallized epilayer lead to much more rigorous limitations for the total pressure of the residual gas in the MBE reactor. To get an estimation of this pressure we consider that the residual gas consists only of nitrogen molecules. The number of molecules which strike the unit area of the substrate can be expressed as: p = 22 N2 wN 8.33x10 (2.7) 2 MT where all the quantities are in SI units. At room temperature, T = 300 K, and a residual gas pressure of 10 -6 Torr, considering molar mass of the nitrogen molecule 28x10 -3 kg/mol, the overall flux is given by 7

w = 3.82x1014 molecules/cm 2s or 7.64x10 14 atoms/cm 2s. This corresponds approximately to N2 1 ML nitrogen atoms per second, which is also the typical growth rate in semiconductor epitaxy. These means that the background pressure has to be significantly lower than 10 -6 Torr. An acceptable value of the background doping for the growth of III-V semiconductor layers is of the order of 10 13 atoms/cm 3. On the other hand, the atom density of semiconductors is about 10 22 atoms/cm 3, hence nine orders of magnitude higher than the background doping level. So, we can conclude that the background pressure of the residual gas should be nine orders of magnitude lower than 10 -6 Torr, if the sticking coefficient of nitrogen atoms is 1, i.e. 10 -15 Torr. This pressure is technically unachievable. However, the sticking coefficient is in general less than one so achievable residual gas pressures of 10-12 Torr should be enough to obtain low background doping. These are UHV conditions.

2.2 MBE growth a) MBE system A typical MBE system is presented schematically in Fig. 2.5a. The chamber is from stainless steel. Inside, UHV is maintained at a background pressure lower than 10 −10 Torr using ion getter, titanium sublimation and cryo-pumps. Effusion cells are mounted symmetrically on a source flange. In Fig. 2.5b, a standard effusion cell is shown. The heating element is a tungsten wire being surrounded by several tantalum foils. These serve as a radiation shield to improve the power efficiency of the source and to reduce the heating of the surrounding cryo-panel (see below). A precise temperature control of each cell assures the desired constant vapor pressure and corresponding beam flux. The material is heated in pyrolytic boron nitride (PBN) crucibles (see Fig. 2.5c). Rapid shutters mounted in front of the effusion cells switch the atomic or molecular beams on and off. Each cell is surrounded by a cryo-shield continually cooled with liquid nitrogen at a temperature of 77K. A second cryo-panel forms an inner shield, so that the main MBE area is surrounded by cold walls operating as additional pumping units and minimizing spurious fluxes of atoms and molecules from the walls of the chamber. In the middle of the chamber, the rotatable substrate holder contains also the heater of the substrate. The pressure of the specific material can be measured with a Bayert-Alpert ion gauge, which can be positioned in the same place as the substrate holder. This pressure is often referred as the beam equivalent pressure (BEP) since the absolute value of the ion gauge reading is dependent on the geometry of the beam with

(a) (b)

<<<< (c)

Fig. 2.5. Schematic illustration of an MBE system (a), pictures of an effusion cell (b) and PBN crucibles (c). 8 respect to the ion gauge entrance slit and other properties, like the ionization probability of the material. The materials loaded in the effusion cells have very high purity. To grow III/V compound semiconductor layers, the effusion cells should contain materials like Ga, As, In, Al for the layer growth and Si and Be for intentional n-type and p-type doping, respectively. The UHV environment in the MBE is also ideal for many in-situ characterization tools, like reflection high energy electron diffraction (RHEED). The RHEED-system provides real time information about the state of the surface during the growth and can be used to determine the growth rate of different layers. b) Growth of GaAs The growth of GaAs is a good example to illustrate the MBE of III/V semiconductors. Surface processes involved in general in the MBE growth are schematically illustrated in Fig. 2.6. These are: - physical and chemical adsorption of the constituent atoms or molecules impinging the substrate surface; - surface migration and dissociation of the adsorbed molecules; - incorporation of the constituent atoms into the crystal lattice of the substrate (grown layer); - thermal desorption of species not incorporated into the crystal lattice.

Fig. 2.6: Surface processes involved in MBE growth.

GaAs is generally prepared in MBE by the evaporation of elemental, atomic Ga, and the sublimation of elemental arsenic which can either be dimeric (As 2) or tetrameric (As4). As 2 is obtained from As 4 by cracking. The growth is performed usually on heated GaAs-(100) substrates. The sticking coefficient of different species impinging the substrate is defined as the ratio between the adsorption rate to the impinging rate. Ga has the sticking coefficient of unity for the used growth temperatures. The incorporation of the arsenic depends of the involved species. When GaAs is grown from As 2 and Ga, As 2 is first adsorbed into a mobile, weakly bound precursor state (see Fig. 2.7a). Dissociation of adsorbed As 2 molecules can occur only when these encounter paired Ga lattice sites while migrating on the surface. In the absence of free surface Ga adatoms, As 2 molecules have a measurable surface lifetime and desorb. The sticking coefficient of As 2, is proportional with the Ga flux I Ga and tends to become unity when the surface is completely covered with one monolayer of Ga. Additionally, this increases with increasing substrate temperature. In this way, stoichiometric GaAs is grown when I As2 /I Ga ≥ 1. For the growth of GaAs with Ga and As 4, the process is more complex (see Fig. 2.7b). From the mobile precursor state, pairs of As 4 molecules react on adjacent Ga sites resulting in the incorporation of four As atoms and desorption of one As 4 molecule (second-order reaction). The sticking coefficient is always less than or equal to 0.5. Stoichiometric GaAs is obtained when IAs4/I Ga >> 1. Finally, the important conclusion of the presented models is that the growth of GaAs is kinetically controlled by adsorption of group-V element, while the growth rate is determined only by the group-III element flux. This is available also for the growth of other 9

(b) (a)

Fig. 2.7: Models for the growth of GaAs with As 2 (a) and As 4 (b).

III-V compound semiconductors. For similar reasons, the growth rate of most of the II/VI compound semiconductors depends on the flux of the group-II element.

c) RHEED RHEED is one of the most important in-situ analysis tools for physical vapor deposition. As already mentioned, RHEED is used in MBE to analyze the surface of the substrate/grown film obtaining fundamental information about surface geometry and chemistry, both in static and dynamic conditions (during growth) and to monitor the growth rate. The technique employs a high energy electron beam (several tens of keV), directed on the sample surface at grazing incidence (a few degrees); the diffraction pattern is imaged on a symmetrically placed fluorescent screen (see Fig. 2.5a). Thanks to the grazing incidence, the electron beam is scattered in the first few atomic layers, thus giving a surface-sensitive diffraction pattern. Besides, the grazing geometry avoids any interference of the RHEED apparatus with the molecular beams, making the technique suitable for real time growth analysis. A qualitative explanation of the origin of RHEED patterns can be seen in Fig. 2.8a. If electrons interact only with the first atomic layer of a perfectly flat and ordered surface, the three- dimensional reciprocal lattice points degenerate into parallel infinite rods. In the resulting

(a)

(b)

Fig. 2.8: a) Ewald sphere construction for a two-dimensional reciprocal lattice (side view). b) RHEED geometry and formation of a diffraction pattern. 10

Ewald construction, the intersection of the rods with the Ewald sphere (having a radius much larger than the inter-rod spacing for typical RHEED energies) consists therefore of a series of points placed on a half circle. In reality, thermal vibrations and lattice imperfections cause the reciprocal lattice rods to have a finite thickness, while the Ewald sphere itself has some finite thickness, due to divergence and dispersion of the electron beam. Therefore, even diffraction from a perfectly flat surface results in a diffraction pattern consisting in a series of streaks with modulated intensity, rather than points (Fig. 2.8b). If the surface is not flat, many electrons will be transmitted through surface asperities and scattered in different directions, resulting in a RHEED pattern constituted by many spotty features. Therefore, a first important information provided by RHEED regards the flatness of a surface. Furthermore, it is evident that diffraction from an amorphous surface (such as an oxide on top of a semiconductor) gives no diffraction pattern at all, and only a diffuse background will result. This is important, for example, for evaluating oxide desorption when a new substrate is initially heated up prior to growth in the MBE chamber, exposing the underlying, crystalline semiconductor surface. The RHEED diffraction pattern consists of main streaks with the bulk lattice periodicity (due to penetration of the beam in the first atomic layers), intercalated by weaker, surface reconstruction-related lines. Besides the structural information, RHEED can also provide information about the growth rate of atomic layer deposition. On a perfect laterally flat surface and under the assumption of a two dimensional growth mode, the surface condition varies during the growth periodically. It starts with a complete filled flat surface layer then it continues with half a monolayer coverage (”rough surface”) and finally back to a complete surface coverage (see Fig. 2.9a) after a monolayer growth. This periodical change in the surface conditions can be seen in RHEED intensity variations of a specular diffraction spot and can directly be used to calculate the growth rate as the inverse of the RHEED oscillation frequency (see Fig. 2.9b).

Growth rate r = 1ML/ ∆t

(a) (b)

Fig. 2.9: a) Schematic illustration of the appearance of the RHEED intensity oscillation during the growth of one monolayer. b) Evaluation of the growth rate from RHEED oscillations. d) Growth modes. The adsorbed atoms move on the surface of the substrate and also interact with each other. Depending on the interaction with the substrate and between atoms themselves, three possible modes of crystal growth may be distinguished. These modes are illustrated in Fig. 2.10. The layer-by-layer mode, or Franck van der Merwe mode, occurs when the atoms are more bound 11 to the substrate than to each other (see Fig. 2.10a). The island mode, or Volmer-Weber mode, displays the opposite characteristics. Small cluster are nucleated directly on the substrate and then growth into islands of the condensed phase (see Fig. 2.10b). This growth mode appears when the crystal lattice constant of the deposited material is significantly different from that of the substrate (lattice mismatched material systems). An intermediate case is the layer plus island mode, or Stranski-Krastanov. After forming a first monolayer, or a few monolayers, subsequent layer growth is unfavorable and islands are formed on top of this ‘intermediate’ wetting layer.

(c) (a) (b) Fig. 2.10: Schematic illustration of the crystal growth modes.

The real surface of the substrate is not ideally flat, monoatomic steps can be found on the surface, which are correlated with the surface orientation. On a crystal surface with cubic symmetry, the step width is depending on the surface misalignment with respect to a certain crystal orientation. The steps change the surface potential and have a strong influence on the growth. An adsorbed atom on such a step can move downwards or upwards to the edges of the step. In the case of the downward movement, the atom cannot fall onto the next step because it has to overcome the so called Schwöbel barrier (see Fig. 2.11). However, atoms moving in the upward direction can be incorporated into the crystal phase at the upper step edge. The relation between the step width, l, and the diffusion length, λ, depending on temperature, determines the growth mode: 2-D growth at lower temperatures and the step flow growth at higher temperatures. These are illustrated in Fig. 2.12 together with the corresponding RHEED intensity profiles. In the step flow growth mode no oscillations are observed.

Fig. 2.11: Surface potential at step edge referred as the Schwöbel barrier.

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Fig. 2.12: Illustration of the step growth mode and 2-D growth mode together with the corresponding RHEED intensity profiles.

3. Growth, morphology and structural properties of GaAs/ZnSe core- shell nanowires The growth of self-assembled 1-dimensional structures or nanowires (NWs) can be accomplished with different growth techniques, such as MBE, Chemical beam epitaxy (CBE) or Metal organic vapor phase epitaxy (MOVPE). Vertical nanowires are grown on (111) oriented substrates, which can be III/V compound semiconductors or Si. Also, different growth mechanisms were identified depending on growth technique and conditions and NW material, the most representative being vapor-liquid-solid (VLS), vapor-solid (VS) and solid-solid (SS) modes. In the VLS growth mode, small liquid droplets are used for the growth of NWs. The growth proceeds by supersaturating the droplet with the grown material. If the droplet is from a foreign material, e.g. Au, this acts as a catalyst. To avoid the incorporation of the foreign material in the NW, which can be detrimental, alternative methods have been developed for the growth of III/V NWs, using substrates covered with a thin layer of SiO x or a patterned thicker oxide. In the case of the growth on substrates covered with a thin SiO x, it is self- catalyzed, i.e. due to a droplet of the group-III element, which is saturated with the group V- element, and the NWs are randomly distributed on the substrate. The growth on patterned substrates is selective resulting in NW arrays. The NWs used in this experiment consist of GaAs and ZnSe combined in a core-shell geometry. The GaAs core NWs are grown self-catalyzed via VLS mechanism on SiO x/Si (111) substrates. For the growth of ZnSe shell, growth conditions are identified which favor the lateral growth on specific core facets.

3.1 Growth of self-catalyzed GaAs nanowires a) Vapor-liquid-solid growth mechanism A prerequisite of the growth of self-catalyzed nanowires via VLS mode is the existence of holes in the SiO x film, which cover the Si (111) substrate (pinholes in thin oxide or patterned holes in thicker oxide). A simple growth model is illustrated in Fig. 3.1. When the growth is started, Ga adatoms on the surface are mobile and can form droplets over/in the pinholes/holes (1). The droplets become saturated with As (2) and GaAs grows between the droplet and substrate (3). In this way, the droplet moves upwards and is continuously fed with Ga and As 13 leaving behind the grown NW. Typical growth conditions of the NWs are: substrate tempe- -5 rature in the range 620-645 °C, Ga rate (~flux) ~0.1 µm/h and As 4 BEP (~flux) ~10 mbar.

Fig. 3.1: Schematic illustration of the VLS growth of GaAs NWs.

In this growth window, GaAs NWs with diameter around <100 nm and length of a few µm in one hour are obtained. This growth rate is much higher than the growth rate of layers on GaAs- (001) under similar conditions, indicating that the main contribution to the axial growth does not come from the direct impingement but from surface diffusion. In this sense, a complex growth kinetics has to be considered, in which multiple processes of impingement, diffusion and desorption for the adatom contribution to the NW droplet are involved. These are schematically described in Fig. 3.2.

Fig.3.2: Different processes for adatom contribution (e.g. Ga and As) to the NW droplet: Direct impingement on the droplet (1, a); impingement on the side facets of the NW (2, b); diffusion from the side facets to the droplet (3, c); desorption from the side facets (4); impingement on the SiO x (5); diffusion from SiO x along the side walls to the droplet (6); desorption from SiO x (7) and desorption from SiO x and re-adsorption on the side facets and droplet.

Apart from NWs growing perpendicular on the substrate, NWs can grow inclined, in the equivalent (111) directions and crystallites are present after the growth (see Fig. 3.3a). In general, the vertical NWs are tapered, which means that the diameter changes continuously from bottom to the top (see Fig. 3.3b). They have a hexagonal prism morphology with side facets belonging to the {110} family (see Fig. 3.3c,d). The shape of the spherical Ga droplet determining the angle with the side-facets has influence on the crystal phase of the grown material being and is responsible for the specific polytypism present in the NWs. b) Selective area growth of GaAs nanowire arrays For selective area growth of GaAs NW arrays, Si-(111) substrates covered with a thicker SiO 2 layer (20 nm) are used. Two-dimensional, periodic arrays of nano-sized holes are patterned in the oxide film using E-beam lithography and dry and wet chemical etching. The 14 substrate preparation is crucial for achieving a high vertical NW yield. Here, the growth process follows the same VLS mechanism described above and similar growth parameters are used.

Fig. 3.3: . SEM images of GaAs NWs. (a) Overview of a typical sample showing NWs and crystallites, (b) single GaAs NW, (c) Ga droplet on top of the NW, (d) NW base showing the hexagonal morphology.

The pre-deposited Ga droplet has to fill the whole hole in the oxide with a contact angle of 90° (see Fig.3.4). High selectivity is obtained without any material growth on SiO 2 mask.

a) b)

Fig. 3.4: Ga droplet in a 80 nm hole in SiO 2 (a) and overview of a GaAs array (b).

3.2 Growth of ZnSe shell After the growth of the GaAs core NW the sample is transferred from the III/V to the II/VI MBE chamber. Separation of the two chambers is required since the group-III and group-V elements act as dopants of the II/VI material and vice versa. Since the structural morphology and geometry of the NW is already determined by the as grown GaAs core NWs, the ZnSe shell growth is performed under similar conditions as the normal 2-D layer growth. . Between the NWs, the surface usually consists of the thin layer of polycrystalline or amorphous SiO 2, on which the deposited ZnSe does not form an epitaxial, monocrystalline film. In contrast, a monocrystalline shell layer is obtained on the side facets of the GaAs core NWs and reveals the same morphology and crystal structure as those of the core. Although the shell growth is very similar to normal 2-D layer-by-layer growth of ZnSe on GaAs-(001) substrates, the corresponding II:VI flux ratios and growth rates are rather different. This is due to two main reasons: Firstly, the side facets of the NW have a different crystallographic orientation, which modifies the diffusion properties and sticking coefficients of Zn and Se adatoms on those side facets. Secondly, the flux is not only impinging in between the NWs but also directly on the 15

NW side facets. While the latter increases the adsorption efficiency of Zn and Se atoms on the NWs, the former can decrease the adsorption efficiency due to additional shadowing effects. The ZnSe shell is grown at lower temperatures than GaAs NWs, which is specific for the growth of II/VI compound semiconductors. The growth starts at a lower temperature than the temperature of the actual growth to minimize the interdiffusion of Ga and Zn atoms resulting in the formation of GaSe and ZnAs at the interface, which will hinder afterwards the layer-by- layer growth (Frank van der Merwe) of ZnSe. Optimal growth conditions have been found using a substrate temperature of 240/260 °C and a VI:II BEP ratio of 2.5-3.0 (Zn BEP was always 1x10 -6 mbar). At the bottom, the shell growth rate was lower; possible reasons being the WZ crystal phase of the corresponding GaAs segment and the influence of the polycrystalline ZnSe layer grown on the Si (111) substrate as it might change the diffusion of the atoms involved in the growth.

3.3 Structural properties of GaAs/ZnSe core/shell nanowires Most of the III/V and also the II/VI compound semiconductor epitaxial films have ZB crystal structure under normal growth conditions; only the nitrides crystallize in the WZ crystal structure. In contrast, both crystal phases are present along the III/V nanowires, depending on the growth conditions. The ZB structure can simply be described by two face centered (fcc) cubic sublattices translated along the body diagonal by 1/4a where ‘a’ is the lattice constant. Each sublattice is occupied by one of the elements. The group-III elements are at the position [0 0 0] while the group-V elements occupy the position [1/4a, 1/4a, 1/4a] (see Fig. 3.5, left side). The WZ structure is based on a hexagonal close packing. The unit cell is characterized by the lattice constants ‘a’ and ‘c’ and the internal lattice parameter ‘u’. The group-III and group-V elements are located at [1/3a, 2/3a, 0] and [1/3a, 2/3a, 3/8c], respectively (see Fig. 3.5, right side). The lattice constants of GaAs and ZnSe are listed in Table 3.1. One can observe that the two materials are almost lattice matched resulting in high quality interface when they are combined in heterostructures.

Fig. 3.5: Unit cells of the zinc blende and wurtzite crystal structures

GaAs ZnSe Zinc blende a=5.654 Å a=5.668 Å a=3.912 Å a=3.974 Å Wurtzite c=6.441 Å c=6.506 Å u=0.374 Å u=0.375 Å

Table 3.1: Lattice constants of ZB and WZ GaAs and ZnSe.

16

Both crystal structures are very similar to each other. This can be seen when the ZB structure is viewed in the [1-10] direction along the [111] one and the WZ structure in the [11-20] direction along [0001] one. As illustrated in Fig. 3.6, the characteristic stacking sequence in this views differentiates the two crystal structures: ...ABCABC… for ZB and ...ABAB... for WZ.

Fig. 3.6 : Zincblende structure viewed in the [1-10] direction and wurtzite structure viewed in the [11- 20] direction. Group-III and group-V atoms are shown in green and red, respectively. The unit cells are highlighted by solid lines.

Depending on the angle between the Ga droplet and the side-facets during NW growth, wurtzite or zincblende crystallization is energetically favorable. For contact angles around ~130 , ZB crystallization is favored, while WZ crystallization is preferred for contact angles slightly higher than ~90°. For contact angles between ~90° and ~130 , mixed phase (MP) occurs. Figure 3.7 shows a high resolution transmission electron microscopy image (HRTEM) of an about 250 nm long GaAs core NW section as grown by self-catalyzed epitaxy. ZB and WZ phases are observed and identified by the corresponding electron diffraction images (Fig. 3.7b and Fig. 3.7d). Segments of both pure crystal phases with axial dimensions >20 nm are typically separated by the MP regions (dashed lines in Fig. 3.7a and zoom-in in Fig. 3.7c). The MP regions contain a

Fig.3.7: Exemplary HRTEM micrographs of sections of a GaAs core NW as grown by self-catalyzed epitaxy on Si-(111) substrates. a) Overview of a middle section from the NW with zincblende (ZB), wurtzite (WZ) and mixed phase (MP) regions. b)-d) Zoom-in to the blue frames localized in three different regions of the NW and corresponding diffraction images. 17

Fig. 3.8: a) TEM overview image of a NW section with large WZ and smaller ZB segments as well as a mixed phase region. Core and shell are clearly distinguishable, the shell thickness is about 20 nm. HRTEM of a NW region with a ZB and WZ segment. The different stacking sequences reveal the corresponding crystal structure of core and shell . high density of rotational twins as well as stacking faults and in between those, small inclusions (axial dimension <20 nm) of WZ and ZB segments (blue (ZB) and orange (WZ) arrows in Fig. 3.7c) are found. Note, that due to different band gap energies of WZ-GaAs and ZB-GaAs, such small segments can induce additional axial confinement of the electrons discussed in Sec. 4.4 and Sec. 5.

Figure 3.8a shows a TEM micrograph of an as-grown GaAs/ZnSe core/shell NW with a shell thickness of about 20 nm. The different phase-pure regions are well distinguished in both, core and shell, by their different contrast (WZ bright, ZB dark). The ZB and WZ regions are separated by stacking faults in the GaAs core and in the ZnSe shell. Figure 3.8a also indicates that GaAs core and ZnSe shell share the same crystal phase in the phase-pure regions (e.g. if GaAs core is WZ/ZB than also ZnSe shell is WZ/ZB). For detailed analysis of the interface and crystal structure between core and shell, Fig. 3.8b depicts a HRTEM image with a ZB and WZ section and the core/shell interface. Different stacking sequences of both phases are clearly visible and confirm that core and shell grow in the same crystal phase. Note, that the radial GaAs/ZnSe core/shell interface (highlighted by the light grey line in the upper right corner) is defect-free along phase-pure segments; while at the boundaries between them stacking faults (grey arrow in Fig. 3.8b) are transferred through the core/shell interface.

4. Theoretical basis for describing optical properties of semiconductor nanostructures 4.1 Energy gap, band structure and effective mass approximation The polymorphism of the self-catalyzed GaAs/ZnSe core/shell nanowires can have substantial impact on the optical properties of the NWs as the band structures of WZ and ZB type GaAs are different (see also Sec. 5). In the following, a short review of the most important aspects regarding energy gap, band structure, effective mass approximation and band-to-band transitions is presented. 18

The movement of a single electron in the semiconductor band structure is described by the one-electron Hamiltonian

ℋ = + = , 4.1 where are electron wave function2 and energy eigenvalue of the n-th band of the , semiconductor and ℏ is the momentum operator. The potential V(r) reflects the periodic Coulomb potential of =the crystal∇ atoms and its periodicity depends on the lattice parameter and

crystal direction of the semiconductor. The Bloch-functions ∗ are solutions of Eq. 4.1 for the -th band and wavevector originated in the first, = Brillouin ,zone. Substitution of the Bloch-functions for in Eq. 4.1 results in the form , ℏ ∗ ℏ + + + , = ,, . 4.2 For the center of2 the Brillouin zone2 (e.g. , the -point in zincblende and wurtzite crystals) a complete orthonormal set of basic funct =ions 0 of theΓ form

+ , = ℋ, , = ,, = 1, 2 … 4.3 is obtained. Close2 to the absolute temperature available electron energy levels are occupied up to the valence band edge , while the conduction band is defined as the subsequent energetically higher empty band. The direct bandgap of a semiconductor is the minimum difference of the energy eigenvalues of conduction and valence band at the same wavevector ( = −for most of the ZB and WZ semiconductors). If the valence band and conduction band = extrema 0 are not at same , the bandgap is indirect and electron transitions across the bandgap require the absorption/emission of a phonon to satisfy momentum conversion (see also Sec. 4.2). For understanding direct band-to-band electron transitions involving absorption/emission of a photon close to the -point, we can restrict ourselves to consider the band structure only in a Γ tiny interval around , as the wavevector of light (e.g. ) is small compared to that of the electron. Therefore, = 0 Eq. 4.2 can be Taylor-expanded|| around = ℏ to the second order in k so that = 0

ℏ ℏ , ∙ , , = , + + . 4.4 2 , − , Note, that the sum in Eq. 4.4 involves contributions of all other bands to the dispersion of the -th band. The linear term in vanishes as is considered , as an extremum. Eq. 4.4 allows to calculate the band dispersion of a non-degenerate, band (e.g. any s-type electron band) around based on the band energy eigenvalues . This approach is the -method referring =to 0the scalar product in the third term in Eq. 4.4., The second and third term ∙ in Eq. 4.4 define a perturbation of the electron motion for small , as the electron would move like a particle with a different mass ∗. It is conventional to express Eq. 4.4 in this context, e.g.

ℏ , = , + ∗ , 4.5 with ∗ defined as the effective mass of the non-degenerat2 e band and parabolic dispersion around . Eq. 4.5 is valid to describe the conduction band . However, for description of degenerate = 0 bands (p-type), such as the valence band the spin-orbit interaction ℋ = ℏ must be considered in Eq. 4.2 as a further term, where are the Pauli spin × ∙ 19 matrices. Generally, this leads to a band dispersion of similar form as Eq. 4.5 but involving different effective masses for the hole states in the three valence bands ∗ ∗ ∗ that stem from the three p-type orbitals. , ,

4.2 Electron-photon interaction, transition matrix and oscillator strength Optical processes such as photon absorption or emission in a direct bandgap semiconductor can be well described by the electron- radiation-interaction Hamiltonian, when considering the electro- magnetic field of the photon as a small perturbation of the one- Fig. 4.1: Optical transitions of a single electron in a 2-level electron Hamiltonian Eq. 4.1. system with ground state energy E 1 and excited state energy Hereby, the momentum operator E2: a) Absorption, b) emission of a photon. in Eq. 4.1 is replaced by . The vector potential describes the electromagnetic wave of the photon = and + is chosen in the Coulomb gauge, approximation (e.g.

and and ) with the form = − = × ∙ = 0

, = ∙ = exp ∙− + exp −∙− . 4.6 The unit vector is parallel to the direction of the electric field and perpendicular to the photon wavevector . Moreover, fulfills the commuter relation so that , , = 0 insertion of Eq .4.6 in the Hamiltonian leads to ℋ , ℋ = ∗ + ∗ ∙ ∙ + = ℋ + ℋ , 4.7 where we considered only2 linear interaction of the electron with the electric field (e.g. neglect terms ). Using~ Eq. 4.7, we can exemplary calculate the probability of transition of an electron from a non-degenerate valence band state to a conduction band state per unit volume upon absorption of a photon: For that purpose we evaluate the transition matrix element with Bloch-functions of electrons in the conduction and holes (e.g. missing electrons)= | ∙in |the valence band, & , respectively. The | = , ∙ | = , ∙ probability of an electron transition is proportional to the expectation value after integration over time and over the unit cell of the semiconductor. Since the Bloch-functions| | are orthogonal and periodic within the crystal unit cell (e.g. ), the transition matrix element collapses to the following more simple integral = +

∗ || ∙ || = ∙ , − + ∙ , . 4.8 Note that the term in the exponential function of Eq. 4.8 refers to the momentum conservation in − any absorption+ or emission process. The transition matrix element is typically maximized for direct band-to-band transitions ( ). If the valence band maximum and the conduction band minimum are located at≪ different = wave vectors in the Brillouin zone (indirect bandgap semiconductors), indirect transitions are obtained. The latter additionally require the absorption/emission of a phonon with wavevector added to the exponential function of Eq. 4.8 to fulfil momentum conservation. For indirect semiconductors the relevant transition matrix elements are typically considerably smaller as in direct semiconductors like GaAs and ZnSe. Eq. 4.8 can be further simplified as the wavevector of 20 light is small compared to the size of the Brillouin zone. Expanding in a Taylor series and neglecting all terms except the first order term leads to | | = ||ℋ || = ∗ || ∙ || . 4.9 In the interaction picture of electron and photon the equation of motion of a time dependent operator can be expressed as . With the momentum operator = ℋ, in the form the transition matrix elementℏ results in ∗ = = | ⁄ | = |ℋ, | = | ∙ | . 4.10 Considering, that the electric fieldℏ is given by , the matrix element in Eq. 4.10 is equivalent to , the electric dipole = − approximation with commonly found in= literature.| ∙ Finally,| using Eq.4.10 we can rewrite Eq. 4.9 in theℋ′ form= ∙

| | = ||ℋ || = |||| , 4.11 which enables us to evaluate the matrix elements for band to band transitions, if the initial state (here ) and the final state (here ) of the electron are known. The transition matrix element is directly| proportional to the oscillator| strength of a transition defined in the classical picture of a Lorentz oscillator. Generally, for transitions between non-degenerate bands with energies the relationship between oscillator strength and transition matrix element is given by , ∗ 2 = |||| . 4.12 3ℏ 4.3 Einstein coefficients, transition rates and radiative lifetime The transition rate of electrons between two non-degenerate levels as drawn in Fig. 4.1 can be described by the Einstein coefficients for stimulated absorption , stimulated emission and spontaneous emission of unpolarized light. The conservation of energy requires that the energy of an absorbed/emitted photon matches the energy difference of the two levels e.g. . Theℏ processes = − of stimulated absorption/emission of a photon are induced by the presence of an external light field (e.g. incoming photon or laser field). In case of absorption, the energy of the incident photon is absorbed by an electron in the ground state and the electron is transferred to the excited state . Vice versa, an electron occupying the excited state can be stimulated by an incident photon to decay back to the ground state. The latter process is a coherent quantum mechanical effect in which the electron decays by emission of a photon that is in phase with the incident photon. Because of its coherent nature, stimulated emission is inherently different from the spontaneous emission described further below. The stimulated photon absorption/emission rate depends on the population of the initial state with electrons and the spectral energy density (e.g. intensity) of the incident light field. The rate equations for stimulated absorption/emission are

= − ; & = − . 4.13 Since the spectral energy density also depends nontrivially on time, the above differential equations have no intuitive simple solution. The spontaneous emission rate describes the instantaneous decay of an electron from the excited state to the ground state by emission of its excess energy into a photon. In contrast to the previously discussed stimulated absorption/emission, this statistically random process is 21 not coherent and does not need the presence of an external light field. Therefore, the photon emission rate is simply proportional to the population of the excited state with electrons and leads to the rate equation

= − . 4.14 The solution of this rate equation results in an exponential decay of the emission intensity with a correspondin = 0g characteristic exp − correlation time given by , which is the natural radiative lifetime of the electronic transition. If an = = 1 ensemble of electrons populate the excited state, the intensity of the 10 5 spontaneous emission decays τ 4 = 0.9 ns exponentially over time. The latter 10 rad can be measured by time-resolved 10 3 photoluminescence spectroscopy, a typical intensity decay curve is shown 10 2 in Fig. 4.2. With this method, intensity (counts) 10 1 important information of the origin and nature of the investigated 0 1 2 3 4 5 transition can be obtained. For time (ns) example, the radiative lifetime is Fig. 4.2: Typical intensity decay curve measured by time directly proportional to the transition resolved photoluminescence. In log.-scale the linear fit of matrix element between the two the decay (red line) yields the measured lifetime. energy levels (see also Sec. 4), e.g.

1 = = |2||1| . 4.15 3ℏ Consequently, time-resolved photoluminescence measurements provide a nice tool to evaluate the matrix elements of real electronic transitions experimentally. Moreover, it is important to mention that radiative recombination in semiconductors is typically accompanied by substantial non-radiative recombination that acts on much faster timescales (e.g. energy dissipation into phonons and heat). In combination of both processes the measured total lifetime of a selected transition is given by . Note, that Eq. 4.15 is 1 1 1 only valid, if the photon is emitted into free-spac =e and not + into a photonic resonator that modifies the photon density of states (and affects ). The three Einstein coefficients introduced above are all related to each other as in thermal equilibrium the rate of upward transitions (stimulated absorption) must exactly balance the rates of downward transitions (spontaneous & stimulated emission). Therefore the rates and in Eq. 4.13 can be obtained without additional information of , if the rate of spontaneous emission is experimentally known (e.g. by lifetime measurement). For non- degenerate energy levels, the relations between the three Einstein coefficients are

8ℎ = ; = . 4.16 4.4 Band offset, heterostructures and 1-dim. confinement (quantum well) Most of the present semiconductor devices require stacking of multilayer structures in specific geometries, which are composed of various materials with different tunable bandgap energies. The ordinary form of such heterostructures is a substrate material (e.g. GaAs, Si, etc.) on top of which a thin epitaxial layer of another semiconductor is deposited by standard growth 22 techniques (MBE, MOVPE). This planar heterostructure contains one interface with different absolute band energies of the substrate and the layer material. To define the electron transport across this interface, the bandgaps must be energetically aligned relative to a common reference energy. The latter, can , , be obtained either from the different chemical potential of the materials or from the same mid-bandgap impurity complex identified in both semiconductors. Three alignment cases of the two materials A and B are possible with inherently different transport and diverse optical properties as shown in Fig. 4.3. At the interfaces, the resulting energy offsets between the conduction and valence bands of the two materials are defined as the band offsets between them. For type-I alignment (Fig. 4.3a), electron (and hole) transport from semiconductor∆ ; ∆ A to B is obtained and radiative transitions of electrons in material B are strongly enhanced. Alternatively, type-II alignment (Fig. 4.3b) leads to electron transport from A to B in the conduction band, but hole transport from B to A in the valence

Fig. 4.3: Possible band alignments at the interface between two different semiconductors in a heterostructure. The arrows indicate the electron/hole transport and possible radiative transitions. a) Type-I, b) type-II, c) broken-gap band alignment. band. Consequently, both carrier types are localized at separated positions in the crystal. Radiative transitions of electrons from the conduction band to the valence band are still possible, but such spatially indirect optical transitions usually have a reduced oscillator strength (see also Sec. 4.2 and Sec. 5). Finally, the configuration in Fig. 4.3c shows the broken-gap alignment in which efficient electron transport is generated by direct band-to-band tunneling between both materials, while radiative band-to-band transitions are inhibited.

Most of the optoelectronic devices such as lasers and LEDs rely on heterostructures with minimum two interfaces, in which in growth direction (z-axis) semiconductor B is enclosed in two layers of material A with a bandgap and type-I band alignment. If the width of material B is comparable to the dimension, of, the electron or hole wavefunctions in B, additional 1-dim. localization of the electron (and hole) occurs and leads to an increase of the energy eigenvalues by a certain amount of confinement energy. Such heterostructures are known as quantum wells (QWs) and can be described by the 1-electron Hamiltonian Eq. 4.1, when the crystal potential is modified by a rectangular potential trap in z-direction

) , || 2 = , 4.17 with for electrons in the conduction0 , || band 2and for holes in the valence band of =semiconductor ∆ B, respectively. Note, that the crystal′ =potentials ∆ in x- and y-direction stay unchanged and lead to the same dispersion relationship as derived in the effective mass 23 approximation (see Eq. 4.5). Consequently, the total energy dispersion of a quantum well confined electron is then given by

ℏ = + ∗ + + . 4.18 2 The effective mass ∗ in Eq. 4.18 is that of the specific band of consideration (e.g. conduction or valence band) and without limitation can be defined as the band extremum of semiconductor B (most likely at ). The = confinement 0 of the electron in z- direction leads to an additional energy contributio = 0n we can separately calculate by solving the 1-dim. Schrödinger equation

ℏ − ∗ + | = | . 4.19 2 Eq. 4.19 can be solved analytically, if we assume that the kinetic energy of the confined electron (or hole) is much smaller than the depth of the potential trap ( ). In this case the amplitude of the confined particle wave function must vanish at the position→ ∞ , e.g. the interfaces between material A and B. Then, discrete solutions of the form = ± 2

2 ∙ sin = 2,4,6 ⋯ = , 4.20 2 ∙ cos = 1,3,5 ⋯ with the corresponding 1-dim. confinement energies

ℏ = ∗ , 4.21 are obtained. In summary, the additional2 1-dim. confinement that is induced by the square potential trap leads to the formation of an infinite number of discrete energy levels along the quantization direction z, while along the x- and y-axis the free electron dispersion in the semiconductor B is maintained. Finally, two remarks have to be taken into account once the above simplified model is used to calculate the energy levels in real QW structures: (1) Besides their bandgap energies most semiconductor materials have also different crystal lattice parameters. Epitaxial growth of one material on another therefore induces biaxial lattice deformations in both materials. This strain modifies the bandgap energy and lifts the degeneration of the heavy hole and light hole valence bands with corresponding effective masses ∗ ∗ at . (2) Generally, the band offsets between typical semiconductors can become , rather small, = especially 0 if additional strain is involved. Therefore, the potential trap depth likely is of the same order than the kinetic energy of the confined electron/hole. In this case, Eq. 4.19 can only be numerically solved as parts of the amplitude of the confined particle wave function penetrates into the barrier material. Considering this leads to two effects: Firstly a slight reduction of the 1-dim confinement energy due to weaker localization in the QW. Secondly, only a finite number of energy levels (typically 1-3) are stabilized in the potential trap. 5. Photoluminescence properties of the GaAs/ZnSe core/shell nanowires The general geometry of GaAs/ZnSe core/shell NWs is shown in Fig. 5.1a. Typical GaAs core diameters range between 40 and 80 nm width and the ZnSe shell thickness varies between 20 and 50 nm. The overall length of the NWs is about 1-4 µm and related to the size of the 24

GaAs core due to different com- peting axial (z-axis, growth direction) and radial (x,y-plane) growth rates. For the direct band-to-band transitions in such NWs, two directional band alignments (with different band offsets) close to the Γ -point of GaAs and ZnSe are relevant: In radial direction of the NW, a type- I band alignment is obtained, where the ZnSe ( eV) serves as the barrier4 material = 2.820 (Fig. 5.1b). Thus, efficient radiative recombination in the GaAs core ( eV) is 4 1.51 expected. In the case of our core/shell NWs, the additional confinement Fig. 5.1: Geometry in typical polymorph GaAs/ZnSe energy discussed for QWs in Sec. 4. is core/shell NWs and resulting band alignments (close to negligible small since the core diameter the Γ-point). a) Cross-section drawing. b) radial (x,y- is substantially larger than the size of the direction) band offsets between ZnSe and GaAs (type- exciton wavefunction in GaAs (e.g. I). c) Axial band alignment between small ZB and WZ regions in the GaAs core (type-II). Bohr radius ~12 nm). The situation is quite different along the axial direction of the GaAs core (Fig. 5.1c). Due to the polymorphism of the self-catalyzed grown GaAs NW cores discussed in Sec. 3.3, small zincblende and wurtzite segments with variable width are stacked on each other. The bandgap

Fig.5.2: Selection of low-temperature (5K) PL spectra of GaAs/ZnSe core shell NWs. a) The localized states related to axial confinement between ZB and WZ segments of GaAs are only visible at low excitation power (lower spectrum) while those saturate and vanish for high excitation power (upper spectrum). b) and c) are PL spectra of two NWs with most likely ZB and WZ phase in the GaAs core. 25 energies of the two crystal phases of GaAs differ from each other by about 10-20 meV and at the interface between them, type-II band alignment is predicted. The length of the smallest ZB or WZ segments is in the order of a few nanometer, so that tiny QW sections with substantial confinement energies are formed. Note, that the type-II alignment leads to spatially indirect band-to-band transitions (as indicated by the arrows in Fig. 5.1c) with only moderate oscillator strength between localized states in ZB and WZ segments. The special band alignment along the axial direction of the GaAs core has a strong impact on power-, temperature-dependent and time-resolved photoluminescence of GaAs/ZnSe core/shell NWs. Exemplary PL spectra are shown in Fig. 5.2. At low excitation power and low temperature, electrons and holes preferentially occupy the localized states in the type-II QWs. Consequently, sharp peaks are frequently observed in the PL spectrum (Fig. 5.2a, lower spectrum, red arrows), which stem from the spatially indirect WZ ‰ZB or ZB ‰WZ band-to- band recombination (assigned as “type-A” transitions). Those discrete emission lines vanish at high excitation powers due to saturation of the localized states. Then, efficient direct band-to- band recombination within large segments of the same crystal phase (e.g. WZ ‰WZ or ZB ‰ZB, “type-B” transitions) is observed (Fig. 5.2a, upper spectrum). Moreover, the spectral energy of the type-B transitions depend on the volume ratio of WZ phase and ZB phase in the GaAs core. The spectrum in Fig. 5.2b yielding a peak at 1.512 eV stems from a NW with a high volume fraction of ZB phase with a peak energy close to the ZB-GaAs bandgap energy of about 1.515 eV. In contrast, the spectrum in Fig. 5.2c is assigned to a NW containing most likely WZ phase of GaAs with a corresponding bandgap energy of about 1.5 eV. Finally, the oscillator strength of the spatially indirect type-A transitions is expected to be substantially smaller compared to that of the spatially direct type-B transitions. Consequently, both recombination pathways lead to different natural radiative lifetimes (see Sec. 4.3) that can be measured by time-resolved PL studies.

References

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