Shear Deformation Potential Research Articles

Uniaxial stress dependence of exciton emission from seeded physical vapor transport ZnSe

Uniaxial stress dependence of photoluminescence has been employed to study the exciton emission in seeded physical vapor transport ZnSe. By examining the stress behavior of the photoluminescence line Ix , it is suggested that this line is due to recombination of a deep donor-bound exciton. From measurements of the π- and σ-polarized luminescence spectra the heavy-hole and light-hole components of the exciton emissions were followed as a function of applied stress. From these data the linear hydrostatic and shear deformation potential constants were calculated to be a=−5.1 and b=−0.74 eV, respectively.

Pressure tuning of strain in CdTe/InSb epilayer: A photoluminescence and photomodulated reflectivity study

The heavy-hole and light-hole excitons of a CdTe epilayer, pseudomorphically grown on an InSb epilayer by molecular beam epitaxy, are studied with a diamond anvil cell as a function of applied hydrostatic pressure via photoluminescence (PL) and photomodulated reflectivity (PR) spectroscopies. They are compared with the excitonic features in the simultaneously measured PL spectra of a sample of bulk CdTe. Under applied pressure, the lattice mismatch-induced splitting between the light-hole and heavy-hole related transitions increases in a continuous and reversible manner because of the additional pressure-induced compression due to the difference in the compressibilities of CdTe and InSb. The unusually large strain sustained by the CdTe epilayer under pressure is discussed in the light of various models. The PR signal vanishes after the InSb epilayer goes through a structural phase transition at approximately 20 kbar, while the PL signal persists until it is irreversibly quenched by the CdTe epilayer undergoing a structural phase transition at approximately 30 kbar. For pressures between 20 and 30 kbar, the behavior of the CdTe epilayer is similar to that of the bulk sample; the strain appears to have been relaxed due to the structural phase transition which has taken place in InSb. Values of the first- and second-order pressure coefficients for bulk CdTe and for the CdTe epilayer as well as values of the hydrostatic and shear deformation potentials are obtained at 14 and 80 K and compared with previously quoted values.

Valence band structure calculations of GaAs/Ga xIn 1-xP strained-layer quantum wells

Valence band structure of GaAs/Ga xIn 1-xP strained-layer quantum wells are investigated within an envelope function formalism which takes into account the valence subbands mixing through the Luttinger-Kohn Hamiltonian and the strain effects due to the lattice-mismatch through the Pikus-Bir Hamiltonian. For a Ga mole fraction x greater than 0.516 (compression), the top valence band is heavy-hole-like. For x less than 0.516 (tension strain), the top valence subband can be either heavy-hole-like or light-hole-like, depending on the well width and on the shear deformation potential. Interesting features are also obtained for the effective masses of the valence subbands from ϵ( K → ) energy dispersion calculations along the in-plane K → direction.

Piezoreflectivity investigation of CdTe/(Cd,Zn)Te heterostructures

The deformation potentials of CdTe are such that a (001) or (111) in-plane biaxial strain strongly shifts the energies of the light hole states and leaves nearly unchanged the heavy hole states. As a consequence, in strained CdTe-based heterostructures, from piezoreflectivity measurements combined with first-order derivatives of the reflectivity structures, we identify in terms of heavy and light hole excitons all features associated with optically active layers (epilayers, substrates, buffer layers, quantum wells and/or superlattices). This appears of crucial relevance in the CdTe/(Cd,Zn)Te heterostructures (with a zinc composition of less than 0.15) because the lattice mismatch-induced splitting, the electron-hole Coulomb interaction and the valence band offset have the same order of magnitude. This produces a complex situation relating to the electronic states of the valence band. From the analysis of our experimental data via the envelope function formalism, including the specific strain effects, we find (i) new shear deformation potentials of CdTe; (ii) unambiguous identification of the character (heavy or light, type I or II) of excitonic ground states, in CdTe/(Cd,Zn)Te quantum wells and strained-layer superlattices; (iii) an accurate value of the chemical band offset between CdTe and (Cd,Zn)Te; (iv) finally, period dependence of the heavy and light hole exciton binding energies.

Piezospectroscopy of a GaAs/Ga 0.73Al 0.27As single quantum well structure: Piezoelectric effects

We have investigated the effects of large uniaxial stress (⇀T) along [100] (≈10 kbar) and [110] (≈16 kbar) on the photoreflectance spectra at 300K of a (001) GaAs/Ga 0.73Al 0.27As single quantum well structure. For ⇀T‖[100] the stress-induced shifts can be explained using only deformation potential theory while for ⇀T‖[100] there also are effects due to the piezoelectric field generated along the growth direction. However, the magnitude of this field is considerably smaller than predicted by theory, indicating the presence of screening charges. Also the hydrostatic (a) and shear (b) deformation potentials of the direct gap of Ga 0.73Al 0.27As have been evaluated.

Phonon conductivity of doped germanium under uniaxial stress in the

The relaxation-rate expressions for elastic, inelastic, and absorption phonon-electron processes in n-type germanium have been derived under [110] directional uniaxial tension. Using these expressions, the phonon conductivity of Sb-doped Ge under tension is evaluated and compared with the experimental results given by Keyes and Sladek. It is found that a slight increase of Bohr radii of the upper two levels of the donor ground states and decrease of shear deformation potential ${\mathit{E}}_{\mathit{u}}$ with stress can give better agreement with the experimental results. This work suggests that the theory of electron-phonon interaction is not a failure, as suspected by earlier workers.

Reflectivity studies of the strain dependence on E0 and E0+ Delta 0 excitonic transitions in ZnSe/GaAs.

The optical properties of ZnSe epilayers grown on (100) GaAs are greatly influenced by residual stress. Reflectance spectra of ${\mathit{E}}_{0}$ (light-hole and heavy-hole) and ${\mathit{E}}_{0}$+${\mathrm{\ensuremath{\Delta}}}_{0}$ excitonic transitions for layers thicker than 1 \ensuremath{\mu}m allow the determination of the ratio of the shear deformation potential (b) to the hydrostatic deformation potential (a). The value of the spin-orbit interaction (${\mathrm{\ensuremath{\Delta}}}_{0}$) is also determined for each layer that suffers two-dimensional tensile stress due to the difference in the thermal-expansion coefficients. The polarization characteristics of excitonic transitions reveal the misorientation of the layer and allow unambiguous identification of the light-hole and heavy-hole excitonic transitions.

Tellurium-based II-VI compound semiconductors and heterostructures under strain

Reviews work on some of the electronic and structural properties of CdTe-(CdZn)Te and CdTe-(CdMn)Te strained-layer quantum wells and superlattices under high pressure. The hydrostatic pressure dependence of the band gap of CdTe is deduced to be Eg=Ego+76P (meV GPa-1)-4P2(meV GPa-2) consistent with all the available data, and for ZnTe is Eg=Ego+105P-2P2. Results obtained by piezomodulation of the subband structure of such systems are also presented. The authors determine the values of the CdTe shear deformation potentials: b=-1.17 eV and d=-3.20 eV.

Efficient band-structure calculations of strained quantum wells.

The effective-mass equations using the Luttinger-Kohn Hamiltonian taking into account the strain effects are solved exactly by making a unitary transformation. Using this method, we need to solve two 2\ifmmode\times\else\texttimes\fi{}2 matrices instead of the original 4\ifmmode\times\else\texttimes\fi{}4 matrix. The eigenvalues and eigenvectors for the heavy hole and the light hole can be expressed analytically. When applied to heterojunctions such as quantum wells, the reduction in the number of unknowns makes the method a more efficient approach to the calculations of valence-band structures, which takes into account the valence-band mixing and the strain effects with proper boundary conditions. Detailed numerical results and significant features for strained ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As grown on an ${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{As}}_{\mathit{y}}$${\mathrm{P}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$ lattice matched to InP are presented. For a Ga mole fraction x less than 0.468 (compression), the top subband is heavy-hole-like. For x greater than 0.468 (tension strain), the top band can be either a heavy-hole or a light-hole subband, depending on the well width and the shear deformation potential. Interesting subband structures, which show a negative effective mass in the top subband, are discussed.

Piezo-photoreflectance of the direct gaps of GaAs and Ga 0.78Al 0.22As

We have investigated the effects of compressive uniaxial stress (T) on the photoreflectance spectra at 300K of the fundamental direct band gap (E o) and its spin-orbit split component (E o + Δ o) of GaAs and Ga 0.78Al 0.22As for T along [001] and [110]. From the stress-induced shifts and splittings we have deduced the hydrostatic ( a ) and shear ( b and d ) deformation potentials of these materials.

Theoretical and experimental study of the longitudinal uniaxial stress dependence of I-V characteristics in GaAs-AlxGa1−xAs-GaAs heterojunction barriers

Tunneling and thermionic emission through n+-GaAs–i-AlxGa1−xAs–n-GaAs heterojunction barriers are studied as a function of temperature from 77 to 200 K and as a function of externally applied uniaxial stress up to 10 kbar. A procedure to extract parameters for theoretical calculations is also proposed. The parameters extracted from the I-V characteristics of these heterostructures grown on (100) GaAs substrates with different aluminum mole fractions from 0.3 to 0.8 and thicknesses from 300 to 400 Å agree well with those of previous reports. The dependence of the I-V characteristics on uniaxial stress in the 〈100〉 direction perpendicular to the heterojunction plane has also been measured. The experimental results show good agreement with theoretical calculations assuming there is a linear stress-dependent decrease of the energy-band edges of the longitudinal X valleys (Xl) in AlGaAs with respect to the Γ valley in GaAs. The slope of the decrease is found to be 14±2 meV/kbar. This results in an X-valley shear deformation potential of 9.6±1.8 eV, which is believed to be the most accurate measured value to date.

Excess current in n +GaAsAl xGa 1− xAsnGaAs heterojunctions

Current versus longitudinal stress characteristics with 〈100〉 stress direction for four n + GaAsAl x Ga 1− x AsnGaAs heterojunc grown on (100) substrates are measured and compared with theory. Our samples have the AlGaAs barriers with aluminum concentrations x=0.30, 0.32, 0.50 and 0.80 and the thickness range from 300–400 Å. The agreement between theory and experiment is good, if we assume an X-valley shear deformation potential of 9.6 eV. However, x=0.32 and 0.50 samples need about 5 kbar of stress offset to match our experimental results with theory, which may be due to the excess current through impurities whose energy level is coupled to the X-valleys.

Photoreflectance and Double Crystal X-Ray Study of Strained InGaAsP Layers on InP Substrates

ABSTRACTDetermining the composition of quaternary epitaxial films requires accurate measurements of both the lattice parameter and the bandgap energy. Complications arise in lattice-mismatched material, because the mismatch produces tetragonal distortion of the epi-layer and splitting of the valence band energies in a manner which depends on the film composition. We present studies on strained InGaAsP grown on (100) InP. Using room temperature photoreflectance (PR) we observe shifting of the band gap and splitting of the valence band energies, and using the (115) and (004) reflections from double crystal x-ray diffraction (DXRD) we determine the values of the parallel and perpendicular lattice constants. By combining the lattice parameter measurements with band splitting data, we accurately determine the quaternary composition from a self-consistent model using an iterative procedure. By linear interpolation of the elastic-stiffness constants, C11 and C12. as well as the shear and hydrostatic deformation potentials for the four binary compounds in the InGaAsP system, we relate the state of biaxial stress to the induced shifts in the valence band energies.

Piezospectroscopy of GaAs-AlAs superlattices.

Piezospectroscopic studies of type-I and type-II GaAs-AlAs superlattices have been made for stress lying along the plane or along the growth axis. Ground and excited states have been studied by means of reflectivity for type-I superlattices. In type-II superlattices the X symmetry of the conduction subband has been observed. A reversal of the ordering of the ${X}_{z}$- and ${X}_{x}$,y-type conduction subband has been found to appear when the thickness of the AlAs slab is changed. This was interpreted as a contribution of the internal strain experienced by the AlAs slabs lattice matched to the GaAs substrate. Stress-induced switching of ordering between ${X}_{z}$ and ${X}_{x}$,y conduction states was observed in the case of stress perpendicular to the growth axis of the superlattice. We deduce the tetragonal shear deformation potential of AlAs conduction band: ${E}_{2}$=5.1\ifmmode\pm\else\textpm\fi{}0.7 eV.

Uniaxial stress dependence of current-voltage characteristics in GaAs-AlxGa1−xAs-GaAs heterojunction barriers

Current-voltage characteristics of nGaAs-iAlxGa1−xAs-nGaAs heterojunction barriers grown on (100) substrates have been measured under uniaxial stress along 〈100〉 at 77 K. The results show that thermionic emission current through longitudinal X valleys becomes dominant over Fowler–Nordheim tunneling current through Γ or transverse X valleys, as stress increases. From the stress-dependent thermionic emission current the rate of change with stress of the band-edge energy difference between Γ in GaAs and longitudinal X in AlGaAs is deduced to be 14±2 meV/kbar, which leads to an X-valley shear deformation potential of 9.6±1.8 eV.

Effect of biaxial strain on exciton transitions of AlxGa1−xAs epitaxial layers on (001) GaAs substrates

From the analysis of spectroscopic ellipsometry measurements in the temperature range between 16 and 300 K, the exciton splittings and shifts due to lattice mismatch in the AlxGa1−xAs/GaAs alloy system grown by liquid-phase epitaxy are obtained. The temperature dependence of the Ev10 and Ev20 exciton transitions shows that the difference in the expansion coefficients of the two materials does not play a significant role in the induced internal stress. The internal stresses are evaluated from an x-ray double-crystal diffraction technique. The shear deformation potential values of AlxGa1−xAs determined from the experimental results are in disagreement with those found in the literature.

Lattice strain and its effects on energy band structure in MBE-ZnS xSe 1− x/GaAs

ZnS x Se 1− x layers with various compositions ( x = 0−0.13) and layer thicknesses (0.1–3.5 μm) were grown on (100)GaAs by MBE. Lattice strain and its effects on energy band structure of the epilayers are studied. The lattice constants normal to the substrate revealed that the thin layers (0.1-0.3 μm) grew coherently. Splitting and shifting of exciton emissions due to two-dimensional strain were observed, and hydrostatic and shear deformation potentials were determined. The thick lattice-mismatched layers consist of thin coherently grown layers and remaining relaxed layers. The strain in the relaxed layers are affected both by the mismatches of lattice constants and by the difference in thermal expansion coefficients. The residual strain of the epilayers can be determined by the exciton emission energies using the deformation potentials.

Thermal emission of holes from defects in uniaxially stressed p-type silicon.

Iron-acceptor pair defects in silicon are insensitive to stress. These defects therefore provide convenient reference points from which to measure the effects of uniaxial stress on the valence-band structure in silicon. Despite the strong mixing of light- and heavy-hole bands at low values of stress, we find that for thermal emission the stress-split valence band can be approximated as two independent bands that displace rigidly with increasing stress according to the shear deformation potentials. The spherical approximation for the effective masses is not consistent with these deformation potentials because the approximation incorrectly partitions the density of states between the two bands. We establish the correct partitioning of the density of states numerically, and find stress-dependent density of states that approximately conserve the center of gravity of the split valence bands. Uniaxial stress data on the Fe-Al defects in silicon are used to experimentally verify the numerical results. The analysis described in this paper can be easily generalized to determine the stress properties of hole traps in any p-type semiconductor.

Properties of strained layer InxAl1−xAs/InP heterostructures

X-ray diffraction and photoluminescence measurements were made on InxAl1−xAs layers grown by molecular-beam epitaxy whose lattice constants are matched, in tension, or in compression, relative to their (100)-oriented InP substrates. Using a linear interpolation between the InAs and AlAs elastic stiffness coefficients, hydrostatic pressure coefficients, and shear deformation potentials, the strain-dependent fundamental band gaps were calculated and shown to be in good agreement with the experimentally measured data within the pseudomorphic limit. The calculated composition-dependent critical thickness for the onset of plastic deformation of these layers is shown to be in better agreement with the energy balance model of People and Bean than the mechanical equilibrium model of Matthews and Blakeslee.

Structural properties of GeTe at T=0.

The equilibrium lattice parameters, bulk modulus, shear elastic constant ${C}_{44}$, and cohesive energy of GeTe are calculated with use of the ab initio scalar relativistic pseudopotential in the local-density approximation. The convergence of the structural properties in basis-set size and Brillouin-zone averaging is discussed. For the rocksalt structure, valence charge densities and the band structure are presented. For the rhombohedral structure, the band structure is presented and the shear deformation potential is calculated. Good agreement of calculated quantities with available experimental results is obtained.