Electronic structure of Ge1 − x − ySixSny ternary alloys for multijunction solar cells

Ternary group‐IV alloys have a wide potential for applications in infrared devices and optoelectronics. In connection with photovoltaic applications, they are among the most promising materials for inclusion in the next generation of high‐efficiency multijunction solar cells, because they can be lattice matched to substrates as GaAs and Ge, offering the possibility of a range of band gaps complementary to III–V semiconductors. Apart from the full decoupling of lattice and band structures in Ge_{1 − x − y}Si_xSn_y alloys, experimentally confirmed, they allow preparation in a controllable and large range of compositions, thus enabling to tune their band gap. Recently, optical experiments on ternary alloy‐based films, photodetectors measured the direct absorption edges and probed the compositional dependence of the direct gap. The nature of the fundamental gap of Ge_{1 − x − y}Si_xSn_y alloys is still unknown, as neither experimental data on the indirect edges nor electronic structure calculations are available, as yet. Here, we report a first calculation of the electronic structure of Ge_{1 − x − y}Si_xSn_y ternary alloys, employing a combined tight‐binding and virtual crystal approximation method, which proved to be useful to describe group‐IV semiconductor binary alloys. Our results confirm predictions and experimental indications that a 1eV band gap is indeed attainable with these ternary alloys, as required for the fourth layer plan to be added to present‐day record‐efficiency triple‐junction solar cells, to further increase their efficiency, for example, for satellite applications. When lattice matched to Ge, we find that Ge_{1 − x − y}Si_xSn_y ternary alloys have an indirect gap with a compositional dependence reflecting the presence of two competing minima in the conduction band. Copyright © 2013 John Wiley & Sons, Ltd.     

Liquidus isotherms,solidus lines and LPE growth in the Te-rich corner of the Hg-Cd-Te system

Liquidus isotherms for the Hg_1−xCd_xTe primary phase field in the Te-rich corner of the Hg-Cd-Te ternary system have been determined for temperatures from 425 to 600‡C by a modified direct observational technique. These isotherms were used to help establish conditions for the open-tube liquid phase epitaxial growth of Hg_1−xCd_xTe layers on CdTe_1−ySe_y substrates. Layers with x ranging from 0.1 to 0.8 have been grown from Te-rich HgCdTe solutions under flowing H₂ by means of a horizontal slider technique that prevents loss of Hg from the solutions by evaporation. Growth temperatures and times of 450–550‡C and 0.25–10 min, respectively, have been used. The growth solution equilibration time is typically 1 h at 550‡C. Source wafers, supercooled solutions, and (111)-oriented substrates were employed in growing the highest quality layers, which were between 3 and 15 Μm thick. Electron microprobe analysis was used to determine x for the epitaxial layers, and the resulting data, along with the liquidus isotherms, were used to obtain solidus lines. In addition to EMP data, optical transmission results are given. This work was sponsored by the Department of the Air Force and the U. S. Army Research Office.     

Determination of liquidus temperatures of Hg-rich Hg-Cd-Te alloys by differential thermal analysis

Liquidus temperatures have been measured for eight (Hg_1−xCd_x)_yTe_1−y compositions with 0.099 ≤ x ≤ 0.401 and 0.703 ≤ y ≤ 0.900 by differential thermal analysis (DTA). The measured liquidus temperatures are in good agreement with those calculated from the thermodynamic model of Tung et al. The change in liquid composition caused by mercury vaporization into the free volume of the DTA ampule introduces an error in the liquidus temperature of less than 1.5°C.     

Distinctive features of the far-infrared reflection spectra of the semimagnetic semiconductors Hg1−x MnxTe1−y Sey

Reflection spectra of single crystals of Hg_1−x Mn_xTe_1−y Se_y (0.01<x<0.14, y=0.01) in the far-infrared range (10–600 cm⁻¹) are investigated at 300 and 77 K. A series of new phonon modes is observed, in addition to the longitudinal and transverse modes corresponding to the ternary compounds. Fiz. Tekh. Poluprovodn. 32, 546–548 (May 1998)     

Characterization of AlxInyGa1−x−yN quaternary alloys grown on sapphire substrates by molecular-beam epitaxy

High-resolution X-ray diffraction (HR-XRD) with rocking curve, atomic force microscopy (AFM) and photoluminescence (PL) spectroscopy have been performed on high-quality quaternary Al_xIn_yGa_1−x−yN thin films at room temperature. The Al_xIn_yGa_1−x−yN films were grown on c-plane (0 0 0 1) sapphire substrates with AlN as buffer layers using a molecular beam epitaxy (MBE) technique with aluminum (Al) mole fractions x ranging from 0.0 to 0.2 and constant indium (In) mole fraction y=0.1. HR-XRD measurements confirmed the high crystalline quality of these alloys without any phase separation. The X-ray rocking curve of Al_xIn_yGa_1−x−yN films typically shows full widths at half maximum (FWHM) intensity between 14.4 and 28.8 arcmin. AFM measurements revealed a two-dimensional (2D) growth mode with a smooth surface morphology of quaternary epilayers. PL spectra exhibited both an enhancement of the integrated intensity and an increasing blueshift with increased Al content with reference to the ternary sample In_0.1Ga_0.90N. Both effects arise from Al-enhanced exciton localization. PL was used to determine the behavior of the energy band gap of the quaternary films, which was found to increase with increasing Al composition from 0.05 to 0.2. This trend is expected since the incorporation of Al increases the energy band gap of ternary In_0.1Ga_0.90N (3.004 eV). We have also investigated the bowing parameter for the variation of energy band gaps and found it to be very sensitive on the Al composition. A value of b=10.4 has been obtained for our quaternary Al_xIn_yGa_1−x−yN alloys.     

Study of defects in heterostructures with GaPAsN and GaPN quantum wells in the GaP matrix

Heterostructures with GaP/GaP_{1 − x} N _x and GaP/GaP_{1 − x − y} As _x N _y quantum wells grown by the MOCVD method are studied by methods of capacitance-voltage profiling and capacitive and current deep level transient spectroscopy. In heterostructures with GaP/GaP_{1 − x} N _x quantum wells, intrinsic defects with deep levels of 0.17 and 0.08 eV are revealed. It is shown that a considerable decrease in the concentration of these defects occurs with the substitution of a ternary GaP_{1 − x} N _x alloy forming the region of the quantum well by a GaP_{1 − x − y} As _x N _y quaternary alloy. The nature of emerging defects and mechanisms of decreasing their concentration are discussed.     

Ternary phase relations of the chalcopyrite compound CuGaSe2

The ternary Cu-Ga-Se phase diagram has been determined by DTA and x-ray analysis. In addition to two ternary solid solutions based on the binary compounds Cu_2.xSe and Ga₂Se₃, only one ternary phase, the chalcopyrite CuGaSe₂ (peritectic m.p. 1030°C), was encountered. The liquidus contains two regions of liquid immiscibility, one which extends from the Cu-rich (Cu, Se) binary liquid immiscibility to the Ga-rich (Ga, Se) binary immiscibility, and the other which is a minor extension of the Se-rich (Cu, Se) binary liquid immiscibility. The liquidus maxima include those at the binary boundaries: Cu (1087°C), Cu₆₇Se₃₃ (1148°C), GaSe (960°C); and a ternary liquidus maximum at Cu₁₉Ga_28.5Se_52.5 (1112°C), the maximum melting point of a solid solution based on the defect-zincblende phase of Ga₂Se₃. The primary phase fields are identified and the crystal growth of CuGaSe₂ solid solutions from nonstoichiometric melts is discussed, especially the most satisfactory Bridgman growth from the Cu₂Se-CuGaSe₂ join. Subsolidus phase relations are also proposed for the Cu-Ga-Se system, and probable similaritics in all I-III-VI ternary diagrams are suggested.     

Synthesis of Homogeneously Alloyed Cu2−x(SySe1−y) Nanowire Bundles with Tunable Compositions and Bandgaps

Bundles of homogeneously alloyed Cu_2?x(S_ySe_1?y) nanowires with various compositions (0 ≤ y ≤ 1) are controllably prepared via a simple water‐evaporation method under mild conditions. It is found that the nanowire bundles have similar copper contents (0.37 ≤ x ≤ 0.44) and morphologies, and the same face centered cubic (fcc) crystal structure and growth orientation of [110] over the entire composition range of y. To the best of the authors' knowledge, this is the first report on cubic phased ternary Cu_2?x(S_ySe_1?y) compounds. It is found that lattice parameter of the Cu_2?x(S_ySe_1?y) compound changes linearly with the S content. It is also shown that the direct and the indirect bandgaps of the nanowires vary quadratically with the S content and have bowing parameters of 0.20 and 0.21 eV respectively. Energy‐gap‐tuning via compositional change is achieved for both the direct (1.48?1.87 eV) and the indirect (0.50?0.90 eV) bandgaps. The trends of lattice parameter and bandgap variations are consistent with those described by Végard's Law.     

Growth of GaAs1−xPx/GaAs and InAsxP1−x/InP strained quantum wells for optoelectronic devices by gas-source molecular beam epitaxy

In this paper we show that pseudomorphically strained heterostructures of InAs _x P_1−x /InP may be an alternative to lattice-matched heterostructures of In_1−x Ga _x As _y P_1−y /InP for optoelectronic applications. We first studied the group-V composition control in the gas-source molecular beam epitaxy (GSMBE) of the GaAs_1-x P _x /GaAs system. Then we studied GSMBE of strained InAs _x P_1−x /InP multiple quantum wells with the ternary well layer in the composition range 0.15 <x < 0.75. Structural and optical properties were characterized by high-resolution x-ray rocking curves, transmission electron microscopy, absorption and low-temperature photoluminescence measurements. High-quality multiple-quantum-well structures were obtained even for highly strained (up to 2.5%) samples. The achievement of sharp excitonic absorptions at 1.06, 1.3 and 1.55μm at room temperature from InAs _x P_1−x /InP quantum wells suggests the possibility of long-wavelength optoelectronic applications.     

Group-V composition control for InGaAsP grown by gas source molecular beam epitaxy

Based on our kinetics models for gas source molecular beam epitaxy of mixed group-V ternary materials, the group-V composition control in In_yGa_1−yAs_1−xP_x epilayers has been studied. The P or As composition in In_yGa_1−yAs_1−xP_x (lattice matched to InP or GaAs) can be obtained from a simple equation for substrate temperatures below 500°C. This has been verified by a series of experimental results.     

Energy bandgap and lattice constant contours of II–VI quaternary alloys

Energy bandgap and lattice constant contours of A_1?x B_x C_1?y D_y and AB_1?x?y C_x D_y II-VI quaternary alloys were calculated by the interpolation method using ternary alloy parameters. Three interpolation methods were applied to A_1?x B_x C_1?y D_y alloy systems. The maximum energy differences between the three methods, which occur near the center of the composition plane, are 0.14, 0.24, and 0.33 eV for (ZnCd)(SSe), (ZnCd)(SeTe), and (ZnCd)(STe) alloy systems, respectively. The calculated results are compared with two sources of experimental data and were fitted within 0.23 eV for all the three methods. For AB_1?x?y C_x D_y alloy systems the calculated results based on two interpolation methods agreed very well within 0.03 eV.     

Calculation of energy band gaps in quaternary iii/v alloys

The dielectric theory of electronegativity is applied to the calculation of the compositional dependence of the energy band gap for quaternary III/V alloys of type A_l-xB_xC_1-yD_y and A_1-x-yB_xC_yD. The departure from linearity of E_G versus x and y is taken to be the sum of two terms, the intrinsic or virtual crystal term and the extrinsic term due to effects of aperiodicity which for one type of alloy may occur on both sublattices. Rather than simply treating the quaternary as an average of the bounding ternary systems, as has been common in the past, the intrinsic departure from linearity is calculated by assuming E_h,i,C, and D_av to vary linearly with x and y. The result is a smaller intrinsic deviation from linearity and a much better fit to existing data in the system Ga_1-xIn_xAs_1-y P_y. The calculation is also applied to three systems where no data exist but which are of great interest because of their potential application for the fabrication of lattice matched tandem solar cells: Ga_l-xA1_xAs_l-ySb_y. Ga_1-x-yA1_xIn_yAs, and GaAs_1-x-yP_xSb_y.     

Model-based analytical FOE determination

An analytical procedure for the estimation of the focus of expansion (FOE) location is introduced. The method is applied to a vector field which has been obtained from the analysis of the relative translational movement of a rigid body with respect to the acquiring camera (monocular system). A polynomial model is fitted to the vector field; the order and shape of the model are determined by the kinetic analysis of the Euclidean camera centered coordinate system in which the camera is moving, and some hypothesis concerning the approximation of the inverse of the depth function 1/Z(x, y). Two basic properties of complex differentiation theory are applied, assuming that each vector of the optic flow is a real-valued complex function of the form v(x, y)=v_x(x, y)+iv_y(x, y). These properties provide the set of points for which both components of the vector field v_x(x, y) and v_y(x, y) are harmonic and, as a subset, the set of points for which both components are zero. The use of perspective projection states that the FOE is the locus where v_x(x, y)=0=v_y(x, y) and, therefore, where the conditions stated by both properties meet.     

Thermodynamically self-consistent approximations to the liquidus and solidus of Hg1−xCdxTe

Based on liquidus and solidus temperatures and associated confidence limits reported by Brice, Capper, and Jones [J. Cryst. Growth, 75, 395 (1986)], we develop polynomial approximations to the liquidus and solidus curves for the pseudobinary material Hg_1−xCd_xTe. These approximations are “thermodynamically consistent” in that they satisfy the requirement that the liquidus and solidus temperatures must agree at x=0 and 1. A linear programming approach is used to find the lowest-degree polynomial approximations to the liquidus and solidus temperatures falling within the confidence limits of Brice et al. at each of their 21 compositions, and also satisfying the convexity requirement imposed by Brice et al. on their own manually-drawn curves. Finally, we present a twoparameter rational approximation that fits the tabulated segregation coefficients for Hg_1−xCd_xTe better than an earlier five-parameter polynomial approximation.     

Phase equilibria of the Si-Ge-Ti system relevant to the reactions between SiGe alloys and Ti

The semiconductor-rich region of the Si-Ge-Ti ternary isotherm at 900°C was determined by metallography, x-ray diffraction, and electron microprobe analysis. The sample alloys were prepared by arc-melting. These alloys were brought to equilibrium by annealing at 900°C for 400 h. It was confirmed that at 900°C, TiSi₂ and TiGe₂ form a continuous solid solution Ti(Si_1−yGe_y)₂ with the C54 crystal structure. It was also shown that, other than Ti(Si_1−yGe_y)₂ and Si_1−xGe_x, there is not any binary or ternary phase within the Si-Ge-TiGe₂-TiSi₂ trapezoid region. Between the Ti(Si_1−yGe_y)₂ and Si_1−xGe_x single-phase fields is the Ti(Si_1−yGe_y)₂-Si_1−xGe_x two-phase region. The tie-lines for this two-phase region were determined. The tie-lines tilt slightly toward the TiSi₂ and Ge corners. In other words, at equilibrium, the silicon to germanium atomic ratio is larger in Ti(Si_1−yGe_y)₂ than in Si_1−xGe_x (x>y). This tendency for tie-lines to tilt toward the TiSi₂ and Ge corners had been proposed in the literature as the reason for the interesting microstructure evolution during the reactions between SiGe alloys and Ti. In addition, the possible diffusion paths for the reactions between SiGe alloys and Ti were discussed based on the obtained isotherm. Recognizing Si and Ge have higher mobilities in Ti(Si_1−yGe_y)₂, it is predicted that for SiGe the extent of concentration change is large but occurs over a shorter distance, and for TiSi₂ the extent of concentration change is small but occurs over a longer distance.     

Engineering phase formation thermo-chemistry for crystal growth of homogeneous ternary and quaternary III–V compound semiconductors from melts

Based on intrinsic alloy phase formation chemistry and thermodynamics, a novel and unique way of producing compositionally homogeneous multi-component (binary, ternary, quaternary) semiconductor materials is presented. A free energy minimization computer program licensed from AEA Technology Engineering Software, Inc., has been employed to study the composition of the solidifying phases from Ga-In-As-Sb melts at different temperatures and with various liquid compositions. The solid phases have been identified (theoretically and experimentally) to be either ternary compounds of Ga_1−xIn_xAs_ySb_1−y depending on the melt temperature and composition. By engineering the thermochemistry of preferential phase formation in the Ga-In-As-Sb melt, compositionally uniform, single phase, crack free, large polycrystalline Ga_1−xIn_xSb and Ga_1−xIn_xAs have been grown.     

Multi-Mode behavior of optical phonons in II-VI ternary and quaternary alloys

Zone-center optical phonons of tetrahedrally coordinatedII-VI semiconductor ternary (AB_1-xC_x) and quaternary (AB_1-x-yC_xD_y) alloys display a variety of distinct multi-mode behavior patterns. A brief review of the modified random element isodisplacement model, which can satisfactorily account for the composition dependence of the frequencies of the zone-center optical phonons, is presented; in this model, one uses the macroscopic parameters of the binary end members and their LO-TO phonon frequencies. When a constituent is present in extreme dilution in a binary (or in a ternary), e.g., C in AB (or in AB_1-y D_y), one sees either a local or a gap mode associated with it. For higher concentrations, one can see two (three) LO-TO phonon pairs for the ternary (quaternary) in the first order Raman spectrum or in the infra-red deduced from an analysis of the reststrahlen bands, when the masses of B and C differ significantly but are lighter than that of A. We illustrate these features in the Raman spectra of Cd_1-xMg_xTe and Cd_1-x-y Mg_xMn_yTe. Also shown are the infra-red spectra of the local mode of Mg²⁺ and Mn²⁺ in Cd Te, where their isotopic nature is clearly manifested.     

Liquidus Projection and Solidification of the Sn-In-Cu Ternary Alloys

Sn-In alloys are promising low-melting-point Pb-free solders. Knowledge of the ternary Sn-In-Cu liquidus projection is important for Sn-In solder applications. Sn-In-Cu ternary alloys were prepared and their primary solidification phases and phase-transformation temperatures during heating were determined. The liquidus projection of the Sn-In-Cu ternary system was determined based on the primary solidification phase at different compositional regimes, the phase-transformation temperatures of the ternary alloys, the phase boundaries and reaction temperatures of the constituent binary systems, and the available ternary Sn-In-Cu data in the literature. No ternary compound was found in the as-cast alloys. The Sn-In-Cu liquidus projection has 11 primary solidification phase regions and seven ternary invariant reactions with the liquid phase, and η-(Cu₆Sn₅,Cu₂In) has a very large compositional regime as the primary solidification phase. A very interesting phenomenon that was also observed is that the solidification paths of some Sn-In-Cu alloys surpass the liquidus trough after their intersections.     

Spinodal decomposition and clustering in III/V alloys

The criteria for clustering and spinodal decomposition in III/V pseudobinary and quaternary solid alloys are examined. A chemical driving force for clustering and phase separation exists in some ternary and most quaternary alloys. However, single crystalline alloys are shown to be stabilized by the coherency strain energy inherent in any clustering or spinodal decomposition in alloys where lattice parameter is a function of composition. Analytical expressions are derived for T_s, the temperature above which no clustering or phase separation should occur. Most III/V pseudobinary and quaternary alloys are stable at all temperatures. Numerical techniques are used to calculate spinodal isotherms. Results are presented for the systems Ga_xIn_1−x As P_1−y, A1_xGa_1−xAs_ySb_1−y, and Ga_xIn_1−x As P_1−y. This work was supported by the Department of Energy, contract No. DE-AT 03-81 ER 10934.     

Transport phenomena in n-MnxHg1−x Te/Cd0.96Zn0.04Te epitaxial films

The results of an experimental study of samples of Mn_xHg_1−x Te films grown by liquid-phase epitaxy on a Cd_0.96Zn_0.04Te substrate are presented. It shows that, as a result of the diffusion of cadmium from the substrate, a Cd_xMn_yHg_1−x−y Te film with a variable band-gap layer is formed close to the 〈epitaxial-film〉-substrate interface. The appearance of this variable band gap is revealed by the transport phenomena. The temperature dependence of the band gap E _g (T) is determined in a linear approximation on T from the results of a theoretical analysis of the temperature dependences of the free-carrier concentration and mobility. It is shown that averaging the semiempirical dependences for the ternary compounds with the extreme compositions, using the virtual-crystal approximation, can produce large errors when determining E _g (T) in a specific semiconductor. Fiz. Tekh. Poluprovodn. 31, 268–272 (March 1997)