Hydrostatic Deformation Potentials Research Articles

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.

Electronic structure of BeCN2: A proposed nearly direct wide-band-gap semiconductor.

The electronic band structure of a hypothetical compound ${\mathrm{BeCN}}_{2}$ in the chalcopyrite structure has been calculated using the linear-muffin-tin-orbital method and the local-density approximation (LDA) for exchange and correlation. The calculations predict a lattice constant of 3.67 A\r{}, a bulk modulus of 315 GPa, and a cohesive energy of 6.1 eV/atom. The band gap is found to be nearly direct at the \ensuremath{\Gamma} point. The conduction-band minimum, which occurs at k=2\ensuremath{\pi}/a(0.89,0,0), is only 0.03 eV below the lowest conduction-band state at the \ensuremath{\Gamma} point. The minimum band gap is estimated to be 5.7 eV including corrections beyond the LDA. The band-gap hydrostatic deformation potential is calculated to be 0.4 eV.

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.

Calculation of hydrostatic and uniaxial deformation potentials with a self-consistent tight-binding model for Zn-cation-based II-VI compounds.

A self-consistent tight-binding (SCTB) calculation of the deformation potentials is performed for ZnTe, ZnSe, and ZnS. Tight-binding bulk parameters reproducing photoemission and reflectivity experiments are given for these compounds. Then the strain effects are considered in the SCTB model, which allows the calculation of the hydrostatic deformation potential and of the nonlinear variation of the fundamental ${\mathit{E}}_{0}$ gap with the relative change in the lattice constant \ensuremath{\Delta}a/${\mathit{a}}_{0}$. The method is applied to the determination of the offset in the strained ZnS-ZnSe system. Results are in good agreement with experimental and other theoretical works.

Pressure dependence of photoluminescence in CdTe/Cd1-xZnxTe strained-layer heterostructures

The photoluminescence of CdTe/Cd1-xZnxTe (x approximately=0.1) strained-layer heterostructures has been studied at 1.8 K as a function of hydrostatic pressure up to 2.7 GPa. The pressure dependence of transitions related to the substrate has been measured separately, and this enables a direct determination of the hydrostatic deformation potential a=-3.55 eV for bulk CdTe. The pressure coefficients of the heavy hole direct and of the light hole indirect transitions are found to be similar and slightly lower than those of bulk CdTe. The weak influence of the confinement effect on the structure could explain the results.

Modulation spectroscopy of the complex photoluminescence band ofGa0.7Al0.3As:Si

The photoluminescence and reflectivity of ${\mathrm{Ga}}_{0.7}$${\mathrm{Al}}_{0.3}$As:Si have been studied in piezomodulation, wavelength-modulation, and photomodulation spectroscopy at low temperatures. We could identify the symmetry of the zero-phonon and phonon-assisted transitions by their comparative behavior in wavelength- and piezomodulated spectroscopy. The experimental results have been interpreted in the framework of an effective-mass model of the donor wave function in multivalley semiconductors similar to that proposed by Henning, Ansems, and Roksnoer [Semicond. Sci. Technol. 3, 361 (1988)]. Within this model, a value of the hydrostatic deformation potential of the L band in this alloy is deduced: -4.99\ifmmode\pm\else\textpm\fi{}0.07 eV.

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.

Hydrostatic pressure coefficients of the photoluminescence of InxGa1-xAs/GaAs strained-layer quantum wells.

The photoluminescence of strained ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells, with x up to 0.225, grown pseudomorphically between unstrained GaAs barriers, has been studied under high hydrostatic pressure in a diamond-anvil cell. The measured direct-band-gap pressure coefficients show a marked deviation from theoretical predictions; they decrease strikingly below the GaAs value of 10.7 meV/kbar as the well width or the indium content is increased; the pressure coefficient of the band gap in wide wells depends on well composition x as 10.7-6.0x meV/kbar in the samples studied, compared with a predicted variation of 10.7-1.7x meV/kbar calculated with use of third-order elasticity theory. The experimental data could correspond to a composition dependence of the band-gap hydrostatic deformation potential, scra, of -7.99(1-0.47x) eV for small x. We speculate that the anomalously low measured pressure coefficients may be due to an interplay of effects related to disorder and strain in the alloy quantum wells.

Calculation of band offsets in strained II–VI heterojunctions

The self-consistent tight-binding description of unstrained and strained heterojunctions has recently provided theoretical values for the offset of the average valence band Δ E av v which agree well with experimental data for III–V and II–VI semiconductor compounds. We present here calculations of Δ E av v in other strained heterojunctions with common anion or cation atoms such as ZnS, ZnSe, ZnTe, HgTe and CdTe. The charge transfer in the interface neighbourhood is taken into account by a self-consistent description using realistic values of the dielectric constant ε ( q). First, we have obtained the hydrostatic deformation potentials. Then the Δ E av v are calculated for different situations which can occur for strained heterojunctions according to the strain is confined (i) to one side of the heterojunction as, for instance, CdTe strained to ZnTe or (ii) to the other side: ZnTe strained to CdTe. Results are discussed and compared with those obtained for similar compounds and also to experimental values.

Pressure dependence of the electronic properties of cubic III-V In compounds.

Electronic and ground-state properties of the binary In compounds in the zinc-blende structure are reported. They are evaluated in the local-density approximation using norm-conserving nonlocal pseudopotentials. Besides the lattice constant, the bulk modulus, and its first and second pressure derivative, the first- and second-order pressure coefficients of the main band gaps (at \ensuremath{\Gamma}, X, and L) are given. The hydrostatic deformation potentials and the crossover pressure from direct to indirect band gap are presented and compared with recent experimental values.

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.

Type II to type I conversion of pseudomorphic GaAs on InP dependent on growth direction

Predictions of band offsets assign a type-II offset for the GaAs–InP interface without inclusion of strain effects, with the conduction- and valence-band-edge offsets approximately given by 0.4 and 0.3 eV, respectively. It has been demonstrated recently that pseudomorphic GaAs grown on [100]-oriented InP also has a type-II interface, but with the conduction-band offset reduced by the hydrostatic deformation potential of GaAs. Poisson’s ratio in GaAs for [111]-directed uniaxial stress is smaller by 40% than the value for [100]-directed stress. The lattice constant perpendicular to the growth interface is therefore not reduced as much for [111] growth compared with the [100]-growth case, leading to a consequently larger shift of the conduction-band-edge energy. Based on the recently measured value of −9 eV for the conduction-band-edge hydrostatic deformation potential in GaAs, the band offset for pseudomorphic GaAs grown on (111) InP has been calculated to be type I. This material system should therefore show type II to type I conversion dependent on the growth direction of the pseudomorphic layer. The issues involved in the growth and measurement of GaAs grown on (111) InP are discussed briefly.

Hydrostatic pressure dependence of CdTe

The pressure dependence of the direct band gap of CdTe has been measured by observing the direct exciton photoluminescence and donor-acceptor pair photoluminescence under hydrostatic pressures up to 35 kbar. A value of 6.5+or-0.2 meV kbar-1 was obtained corresponding to a hydrostatic deformation potential a=-2.74+or-0.09 eV. From a tight-binding calculation the authors estimate the valence and conduction band contributions to a.

Band offsets for pseudomorphic InP/GaAs

Recently determined band-edge hydrostatic deformation potentials are used to predict heterojunction band offsets for the pseudomorphic GaAs-InP system. The calculations include GaAs/InP, InP/GaAs, and strained-layer GaAs-InP superlattices for both [100] and [111] oriented epitaxial growth. The offsets are type II for the unstrained case. The large hydrostatic contributions to the stress-induced band offsets can convert the offsets to type I. This conversion is especially apparent for growth in the [111] direction because of the small Poisson ratio for biaxial stress in the (111) plane.

Γ andX bandgap hydrostatic deformation potentials for epitaxial In0.52Al0.48As on InP(001)

The pressure dependence of the direct and indirect bandgap of epitaxial In0.52Al0.48As on InP(001) substrate has been measured using photoluminescence up to 92 kbar hydrostatic pressure. The bandgap changes from Γ toX at an applied pressure of ∼ 43 kbar. Hydrostatic deformation potentials for both the Γ andX bandgaps are deduced, after correcting for the elastic constant (bulk modulus) mismatch between the epilayer and the substrate. For the epilayer we obtain $$(\Xi _d + \tfrac{1}{3}\Xi _u - a) as - (6 \cdot 92 + 0 \cdot 3) eV$$ and+(2.81±0.15)eV for the Γ andX bandgaps respectively. From the pressure dependence of the normalized Γ-bandgap photoluminescence intensity a Γ-X lifetime ratio, (τΓ/τ X ), of 4.1×10−3 is deduced.

Comment on volume relaxation around defects in silicon upon electron emission.

The calculation of volume relaxation requires knowledge of the value of the conduction-band-edge hydrostatic deformation potential. The purpose of this Comment is to calculate the volume relaxation of the Au acceptor and the oxygen-vacancy pair (A center) in silicon based on the recently determined conduction-band deformation potential.

Band-edge deformation potentials in a tight-binding framework.

We calculate, within the tight-binding approximation, hydrostatic and uniaxial deformation potentials for seven III-V compounds (GaAs, InAs, GaSb, AlSb, InSb, InP, and GaP). These deformation potentials are expressed in terms of (i) the usual tight-binding parameters describing the unstrained bulk, (ii) an analytical law for the dependence of these parameters upon distance, and (iii) (for the uniaxial [111] deformation potential only) the internal displacements. We show that it is possible to derive a "universal variation law" that provides deformation potentials in reasonable agreement with available experimental data.

Hydrostatic pressure effects on Mn in GaAs 1−xP x

Hydrostatic pressure has been applied to samples of Mn-doped GaAs and GaAs 1−xP x ( x=0.04). The charge transfer nature of the radiative recombination allows determination of the pressure derivative of the Mn acceptor level relative to the valence band edge. The pressure derivatives have been determined and are found to be identical for both the binary and ternary material, 1.1–1.2meV/kbar. This number is only a small fraction of the total pressure derivative of the Γ 1c−Γ 15v energy gap which amounts to 10.7meV/kbar. Using the Mn acceptor energy level as a reference we were able to determine the hydrostatic deformation potentials of the valence and conduction bands and found values of a v =+0.9 eV and a c =−7.7 eV respectively, in excellent agreement with recent theoretical values.

Deep-level defects in silicon and the band-edge hydrostatic deformation potentials.

Evidence for an energy reference level based on substitutional transition-metal defect levels in semiconductors is presented and used to obtain the values for the band-edge hydrostatic deformation potentials in silicon. From the pressure derivatives of Pt and Pd acceptors in silicon we derive values of ${\ensuremath{\Xi}}_{d}=\ensuremath{-}0.5$ eV and ${a}_{v}=+0.9$ eV. These values are consistent with recent theoretical calculations and with the analysis of acoustic-phonon-limited electron and hole mobility.

Band-edge hydrostatic deformation potentials in III-V semiconductors.

We report experimental values for the band-edge hydrostatic deformation potentials of GaAs and InP semiconductors. The deformation potentials are determined directly by observation of the universal pressure derivative of transition-metal defect levels and consideration of this pressure derivative in the context of recent models of heterojunction band lineup. We obtain values of -9.3 and -7.0 eV for the conduction-band deformation potentials of GaAs and InP, respectively, determined from the uniaxial-stress deep-level transient spectroscopy on defect levels of Ti and V.