Band-gap Deformation Potentials Research Articles

First Principles Study of Elastic Properties, Mechanical Properties and Electronic Band Structures of LiGaO2 Phases

LiGaO2 (LGO) under different pressure conditions can be stable in different structures. The structures of LGO were named WZ′, HX′, BCT′ and RS′′ in analogous with the well-known phases as of ZnO. In this work, the structural, elasticity, mechanical properties and the electronic band structures of those phases were studied. We found that the band gap as well as the band gap type (direct/indirect) are strongly depending on the crystal structure. In addition, for selected crystal structures, the changes of the band gaps with respect to the pressure, i.e. the band gap deformation potentials, were studied. Our results illustrated that applying pressure in different conditions can modify the band gap of LGO. The details of elasticity and mechanical properties and electronic band structures for different phases of LGO and the pressure dependence of selected phases will be presented and discussed.

HSE hybrid functional calculation of band gap deformation potential in MgGeN2

The MgGeN2 has been proposed as an alternative wide band gap semiconductor of III-N due to its flexibility in electronic property engineering. In this work, we calculated the relative deformation potential of band gap (ag ) in MgGeN2 comparing with those in the well-known binary semiconductors such as GaN and ZnO which possess very close lattice parameters of MgGeN2. The calculations were performed by using the density functional theory (DFT) with Heyd-Scuseria-Ernzerhof hybrid functional (HSE) approach. As the results, the ag of MgGeN2 is predicted as -5.37 eV, which is between those of GaN (-7.45 eV) and ZnO (-2.67). This ag is useful for advanced study in band alignment, which is crucial quantity in all optoelectronic devices using semiconductor heterostructures.

Stress-induced bandgap renormalization in atomic crystals

Single atomic layers of two-dimensional (2D) transition metal dichalcogenides (TMDs) are promising candidates for integration of optical and electronic circuits due to their extraordinary optical oscillator strength and large exciton binding energy. Customizing the exciton energy of the TMDs is a direct way to control the light-matter interaction. Here we demonstrate that the electronic band gap of tungsten diselenide WSe2 can be tuned continuously with the application of the uniaxial tensile strain. The energy is redshifted with a rate of ∼62.5 meV/% strain for exciton A, determined by photoluminescence spectroscopy along with Finite Element Method modeling using the commercial software ANSYS. The uniaxial bandgap deformation potential (DP) of the electronic bandgap of monolayer WSe2 can be computed directly from our measurements and is about −6.3 ± 0.5 eV. Our results agree well with first-principles calculations. The ability to control the renormalization of the bandgap in 2D materials with strain could be used in flexible electronics or optoelectronic devices such as a TMDs based microcavity.

Strain Loading Mode Dependent Bandgap Deformation Potential in ZnO Micro/Nanowires.

The electronic-mechanical coupling in semiconductor nanostructures under different strain loading modes can modulate their photoelectric properties in different manners. Here, we report the systematic investigation on the strain mode dependent bandgap deformation potential of ZnO micro/nanowires under both uniaxial tensile and bending strains at room temperature. Uniaxial stretching-photoluminescence results show that the deformation potential of the smaller ZnO nanowire (with diameter d = 260 nm) is -30.6 meV/%, and is close to the bulk value, whereas it deviates the bulk value and becomes to be -10.6 meV/% when the wire diameter is increased to d = 2 μm. This unconventional size dependence stems from surface effect induced inhomogeneous strain in the surface layer and the core of the ZnO micro/nanowires under uniaxial tension. For bending load mode, the in situ high-resolution transmission electron microscope analysis reveals that the local strain distributes linearly in the bending cross section. Further cathodoluminescence measurements on a bending ZnO microwire (d = 1.8 μm) demonstrate that the deformation potential is -27 meV/%, whose absolute value is much larger than that of the ZnO microwire under uniaxial tension. Further analysis reveals that the distinct deformation potentials originate from the different deforming modes in ZnO micro/nanowires under bending or uniaxial tensile strains. Our results should facilitate the design of flexible optoelectronic nanodevices.

Analysis of high-temperature thermoelectric properties of p-type CoSb3 within a two-valence-band and two-conduction-band model

Experimental data on the thermoelectric properties of p-type CoSb3 reported by Caillat et al. [J. Appl. Phys. 80, 4442 (1996)] have been analyzed, assuming not only a pair of the first valence (v1) and the first conduction (c1) bands but also the second valence (v2) and the second conduction (c2) bands. By taking into account the excitation of carriers into the v2 and the c2 bands, the behavior of the Hall coefficient as well as that of the Seebeck coefficient at high temperatures is well explained. By taking into account the nonparabolicity of the v1 band, the temperature dependence of mobility is well explained with assuming scattering due to acoustic phonons, nonpolar and polar optical phonons, and ionized impurities. Furthermore, various material parameters of CoSb3, such as the band-gap energy, effective masses, and deformation potentials, have been deduced from fitting the calculation to the experimental data on the temperature dependences of the Hall coefficient, the mobility, and the Seebeck coefficient. Among them, the band-gap energy and the effective mass of the v1 band have been corrected from the original values estimated by Caillat et al. In addition, it is shown that the experimental data on the hole-concentration dependences of both the room-temperature Seebeck coefficient and the cyclotron mass are well reproduced by the theoretical calculation using the deduced values for the nonparabolic v1 band.

Thermoelectric properties of Sn-doped p-type Cu3SbSe4: a compound with large effective mass and small band gap

Sn-doped Cu3SbSe4 with enhanced zT possesses a large effective mass, small band gap and moderate deformation potential with a complex band structure.

Mechanical strain dependent electronic and dielectric properties of two-dimensional honeycomb structures of MoX2 (X=S, Se, Te)

Mechanical strain induced tunability in two-dimensional (2D) honeycomb structures of MoX2 (X=S, Se, Te) with a focus on dielectric properties have been investigated in the framework of density functional theory. Mechanical strains reduce the band gap of considered semiconductors by causing a direct-to-indirect band gap transitions and finally rendering them into metal at critical value depending on the types of applied strain. The ultimate tensile strength estimated for MoS2, MoSe2 and MoTe2 monolayers is ∼7GPa, ∼6GPa and ∼5GPa respectively. Band-gap deformation potentials have been found to posses strong dependence on the types of applied strain. Small tensile strains increases the exciton binding energies which can have importance in the applications of optoelectronics. Dielectric properties too get influenced by the type of applied strain as well as the type of material. Imaginary part of dielectric function (ϵ2) shows redshift in the structure peak energy on the application of strains with significant dependence on the types of applied strain. Static dielectric constant (ϵs) has been found to increase with the increase of tensile strains (both uniaxial and biaxial) and asymmetric biaxial strain. On the other hand, ϵs decreases for smaller magnitude of compression strains and show increase at higher magnitude. The change in the magnitude of ϵs particularly for compression strains remain material specific.

Size effects in band gap bowing in nitride semiconducting alloys

Chemical and size contributions to the band gap bowing of nitride semiconducting alloys (In${}_{x}$Ga${}_{1\ensuremath{-}x}$N, In${}_{x}$Al${}_{1\ensuremath{-}x}$N, and Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N) are analyzed. It is shown that the band gap deformation potentials of the binary constituents determine the gap bowing in the ternary alloys. The particularly large gap bowing in In-containing nitride alloys can be explained by specific properties of InN, which do not follow trends observed in several other binaries.

Diameter dependence of mechanical, electronic, and structural properties of InAs and InP nanowires: A first-principles study

Semiconductor nanowires (NWs) have ideal morphologies to act as active parts and connections in nanodevices since they naturally restrict the conduction channels and periodicity to one dimension. The advantages from the reduced spatial dimension can be greatly enhanced by wisely selecting the materials composing the NWs, through the knowledge of the properties of their bulk counterparts. NW's properties can still be tailored by managing (i) internal or intrinsic characteristics as diameters, growth directions, structural phases, and the faceting or saturation of surfaces, and/or (ii) external or extrinsic influences as applied electric, magnetic, thermal, and mechanical fields. Bulk InAs has one of the lowest electron effective-masses among binary III-V semiconducting materials while bulk InP shows excellent optical properties, which make InAs and InP NWs candidates for optoelectronic materials. In this work, we use first-principles calculations to study the structural, electronic, and mechanical properties of [111] zinc-blende InAs and InP NWs as a function of diameter (ranging from 0.5 to 2.0 nm). The influence of external mechanical stress on the electronic properties is also analyzed. The axial lattice constants of the NWs are seen to decrease with decreasing diameter, as a consequence of a shorter surface lattice constant of the NWs, as compared to their bulk values. The Young's modulus of both InAs and InP NWs is determined to decrease while the Poisson's ratio to increase with decreasing diameters, with deviations from the bulk Young's modulus estimated to occur for NWs with diameters lower than 15 nm. The increase in the band-gaps with decreasing diameters is seen to be slower than the expected from simple quantum-mechanical models ($1/{D}^{2}$, where $D$ is the diameter), mainly for the smallest $(<1.0\text{ }\text{nm})$ diameters. The electron effective-masses are seen to increase with decreasing diameters, due to a $k$-dependent energy shift of the conduction-band minimum. The calculated work functions for both NWs show a decrease with decreasing diameters. The change in the NWs' band-edge eigenvalues with axial strain is calculated and the band-gap deformation potentials are determined and shown to change in signal within the range of studied diameters. The influence of the mechanical strain on the electronic bands is analyzed in terms of electronic charge decompositions in directions parallel and perpendicular to the NWs' axes. Direct to indirect band-gap transitions are observed for compressive strains in very thin NWs. The hole effective-mass is seen to be lower than the corresponding electron effective-mass for the studied NWs.

Electronic properties of3R-CuAlO2under pressure: Three theoretical approaches

The pressure variation in the structural parameters, $u$ and $c/a$, of the delafossite ${\text{CuAlO}}_{2}$ is calculated within the local-density approximation (LDA). Further, the electronic structures as obtained by different approximations are compared: LDA, $\text{LDA}+U$, and a recently developed ``quasiparticle self-consistent $GW$''$(\text{QS}GW)$ approximation. The structural parameters obtained by the LDA agree very well with experiments but, as expected, gaps in the formal band structure are underestimated as compared to optical experiments. The (in LDA too high lying) $\text{Cu}\text{ }3d$ states can be down shifted by $\text{LDA}+U$. The magnitude of the electric field gradient (EFG) as obtained within the LDA is far too small. It can be ``fitted'' to experiments in $\text{LDA}+U$ but a simultaneous adjustment of the EFG and the gap cannot be obtained with a single $U$ value. $\text{QS}GW$ yields reasonable values for both quantities. LDA and $\text{QS}GW$ yield significantly different values for some of the band-gap deformation potentials but calculations within both approximations predict that $3R{\text{-CuAlO}}_{2}$ remains an indirect-gap semiconductor at all pressures in its stability range 0--36 GPa, although the smallest direct gap has a negative pressure coefficient.

Electronic structure and phase stability of MgTe, ZnTe, CdTe, and their alloys in theB3,B4, andB8 structures

The electronic structure and phase stability of MgTe, ZnTe, and CdTe were examined in the zinc-blende (B3), wurtzite (B4), and NiAs-type (B8) crystal structures using a first-principles method. Both the band-gap and valence-band maximum (VBM) deformation potentials of MgTe, ZnTe, and CdTe in the B3 structure were analyzed, revealing a less negative band-gap deformation potential from ZnTe to MgTe to CdTe, with a VBM deformation potential increase from CdTe to ZnTe to MgTe. The natural band offsets were calculated taking into account the core-level deformation. Ternary alloy formation was explored through application of the special quasirandom structure method. The B3 structure is found to be stable over all (Zn,Cd)Te compositions, as expected from the preferences of ZnTe and CdTe. However, the (Mg,Zn)Te alloy undergoes a B3 to B4 transition above 88% Mg concentration and a B4 to B8 transition above 95% Mg concentration. For (Mg,Cd)Te, a B3 to B4 transition is predicted above 80% Mg content and a B4 to B8 transition above 90% Mg concentration. Using the calculated band-gap bowing parameters, the B3 (Mg,Zn)Te [(Mg,Cd)Te] alloys are predicted to have accessible direct band gaps in the range 2.39(1.48)--3.25(3.02) eV, suitable for photovoltaic absorbers.

Electronic structure and phase stability of MgO, ZnO, CdO, and related ternary alloys

The electronic structure and phase stability of MgO, ZnO, CdO, and related alloys in the rocksalt (B1), zincblende (B3), and wurtzite (B4) crystal structures were examined within first-principles band structure theory; the thermodynamically stable phases are reproduced for each material. The band alignment and band-gap deformation potentials were analyzed, showing an increase in the valence band maximum from Mg to Zn to Cd. Ternary alloy formation was explored through application of the special quasirandom structure method. The B1 structure is stable over all (Mg,Cd)O compositions, as expected from the preferences of the binary oxides. The (Mg,Zn)O alloy undergoes a tetrahedral to octahedral transition above 34% Mg content, in agreement with experiment. For (Zn,Cd)O, a transition is predicted above 62% Cd content. These results imply that band-gap manipulation of ZnO from alloying with Mg (Cd) will be limited to 4.0 eV (1.6 eV), while preserving the tetrahedral coordination of the host.

Consistent set of band parameters for the group-III nitrides AlN, GaN, and InN

We have derived consistent sets of band parameters (band gaps, crystal field splittings, band-gap deformation potentials, effective masses, and Luttinger and ${E}_{P}$ parameters) for AlN, GaN, and InN in the zinc-blende and wurtzite phases employing many-body perturbation theory in the ${G}_{0}{W}_{0}$ approximation. The ${G}_{0}{W}_{0}$ method has been combined with density-functional theory (DFT) calculations in the exact-exchange optimized effective potential approach to overcome the limitations of local-density or gradient-corrected DFT functionals. The band structures in the vicinity of the $\ensuremath{\Gamma}$ point have been used to directly parametrize a $4\ifmmode\times\else\texttimes\fi{}4$ $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ Hamiltonian to capture nonparabolicities in the conduction bands and the more complex valence-band structure of the wurtzite phases. We demonstrate that the band parameters derived in this fashion are in very good agreement with the available experimental data and provide reliable predictions for all parameters, which have not been determined experimentally so far.

First-principles calculations of the temperature dependence of the band gap of Si nanocrystals

The temperature dependence of the band gap of hydrogen-passivated Si nanocrystals of radius $R=0.7$ and $1.1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ has been calculated from first principles using constant-temperature molecular-dynamics simulations. The band-gap change with temperature $\mathrm{\ensuremath{\Delta}}{E}_{g}(R,T)={E}_{g}(R,T)\ensuremath{-}{E}_{g}(R,0)$ is obtained by averaging over the configurations sampled during the molecular-dynamics simulation. We find that $\mathrm{\ensuremath{\Delta}}{E}_{g}(R,T)$ depends strongly on the nanocrystal size. At room temperature, the calculated $\mathrm{\ensuremath{\Delta}}{E}_{g}(R,T)$ is approximately $\ensuremath{-}150\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ for $R=1.1\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ nanocrystals, and $\ensuremath{-}210\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ for $R=0.7\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ nanocrystals, significantly larger in magnitude than in the case of bulk Si. We also find that in Si nanocrystals the band-gap deformation potential is positive, but smaller than in bulk Si.

Electronic properties of GaN at high-pressure from local density and generalized gradient approximations

Electronic properties of zinc-blende GaN under high-pressure up to 12 Gpa are obtained from density-functional-theory calculations using an ab initio total energy pseudopotential technique within the local-density and the generalized gradient approximations. Quantities such as, band-gap deformation potentials and pressure coefficients of main critical-point band gaps, valence band width, and electron effective mass are calculated. The obtained results are generally in good agreement with available experimental data. The gradient corrections to the local density approximation, included via generalized gradient approximation give significant improvement of the calculated pressure coefficients over the local density approximation.

Theoretical study of the band-gap anomaly of InN

Using a band-structure method that includes the correction to the band-gap error in the local-density approximation (LDA), we find that the band gap for InN is 0.8±0.1eV, in good agreement with recent experimental data, but is much smaller than previous experimental value of ∼1.9eV. The unusually small band gap for InN is explained in terms of the high electronegativity of nitrogen and, consequently, the small band-gap deformation potential of InN. The possible origin of the measured large band gaps is discussed in terms of the nonparabolicity of the bands, the Moss–Burstein shift, and the effect of oxygen. Based on the error analysis of our LDA-corrected calculations we have compiled the band-structure parameters for wurtzite AlN, GaN, and InN.

Breakdown of the band-gap-common-cation rule: The origin of the small band gap of InN

It is well accepted that the band gap of a semiconductor compound increases as the atomic number decreases. However, recent measurements of the small band gap of InN ${(E}_{g}\ensuremath{\sim}0.9\mathrm{eV})$ suggest that this rule may not hold for the common-cation In compounds. Using a band-structure method that includes band-gap correction, we systematically study the chemical trends of the band-gap variation in III-V semiconductors. The calculated InN band gap is $0.85\ifmmode\pm\else\textpm\fi{}0.1\mathrm{eV},$ much smaller than previous experimental value of $\ensuremath{\sim}1.9\mathrm{eV}.$ The InN band-gap anomaly is explained in terms of atomic-orbital energies and the band-gap deformation potentials.

Investigation of the piezoelectric polarization in (In,Ga)N/GaN multiple quantum wells grown by plasma-assisted molecular beam epitaxy

We have studied the structural and optical properties of a series of (In,Ga)/GaN multiple quantum wells with identical thicknesses but varied In content grown by plasma-assisted molecular beam epitaxy. Careful choice of the growth parameters returns samples with smooth and abrupt interfaces. The shift of the photoluminescence transition energy with externally applied biaxial tension was investigated. We observed a redshift for small In contents while a blueshift was detected for higher In contents. This result is in qualitative agreement with self-consistent band profile calculations taking into account both band gap deformation potentials and piezoelectric polarization charges in these structures. However, the reduction of the polarization induced quantum-confined Stark effect is well in excess of that conventionally calculated for this material system. We attribute this observation to a substantial deviation of the piezoelectric polarization constants of strained layers from those calculated for unstrained material. This finding is shown to be in agreement with recent calculations of the piezoelectric polarization charges for biaxially strained (Al,Ga,In)N layers.

Impact of In content on the structural and optical properties of (In,Ga)N/GaN multiple quantum wells grown by plasma-assisted molecular beam epitaxy

AbstractWe have studied the structural and optical properties of a series of (In,Ga)/GaN multiple quantum wells with identical thicknesses but varied In content grown by plasma-assisted molecular beam epitaxy. Careful choice of the growth parameters returns samples with smooth and abrupt interfaces. The shift of the photoluminescence transition energy with externally applied biaxial tension was investigated. We observed a red-shift for small In contents while a blue-shift was detected for higher In contents. This result is in qualitative agreement with band profile calculations taking into account both the band gap deformation potentials and the piezoelectric polarization in these structures. However, the magnitude of the shift is well in excess of the calculated one. We attribute this finding to a substantial deviation of the piezoelectric constants from those calculated for unstrained material. Finally, we estimate the piezoelectric polarization of InGaN/GaN for linear and non-linear terms in strain.

Effect of Pressure on Direct Optical Transitions of ?-InSe

We have investigated the effect of hydrostatic pressure on direct optical transitions of the layered semiconductor γ-InSe by photoreflectance (PR) spectroscopy (T = 300 K). In addition, electroreflectance (ER) measurements were performed at ambient pressure. Six structures are resolved in the ER spectra in the energy range from 1.1 to 3.6 eV. The pressure dependence of four of these structures was determined by PR spectroscopy for pressures up to 8 GPa. In order to assign the features observed above the fundamental gap we have carried out band structure calculations for InSe at ambient pressure using a full-potential linear augmented plane wave method. Based on calculated band gap deformation potentials for different uniaxial strains, we explain the strongly nonlinear pressure dependence of the fundamental band gap and the absence of such effects for the higher lying transitions which increase almost linearly with pressure.