Pressure Coefficient Of Band Gap Research Articles

Hydrostatic Pressure as a Tool for the Study of Semiconductor Properties-An Example of III-V Nitrides.

Using the example of III-V nitrides crystallizing in a wurtzite structure (GaN, AlN, and InN), this review presents the special role of hydrostatic pressure in studying semiconductor properties. Starting with a brief description of high-pressure techniques for growing bulk crystals of nitride compounds, we focus on the use of hydrostatic pressure techniques in both experimental and theoretical investigations of the special properties of nitride compounds, their alloys, and quantum structures. The bandgap pressure coefficient is one of the most important parameters in semiconductor physics. Trends in its behavior in nitride structures, together with trends in pressure-induced phase transitions, are discussed in the context of the behavior of other typical semiconductors. Using InN as an example, the pressure-dependent effects typical of very narrow bandgap materials, such as conduction band filling or effective mass behavior, are described. Interesting aspects of bandgap bowing in In-containing nitride alloys, including pressure and clustering effects, are discussed. Hydrostatic pressure also plays an important role in the study of native defects and impurities, as illustrated by the example of nitride compounds and their quantum structures. Experiments and theoretical studies on this topic are reviewed. Special attention is given to hydrostatic pressure and strain effects in short periods of nitride superlattices. The explanation of the discrepancies between theory and experiment in optical emission and its pressure dependence from InN/GaN superlattices led to the well-documented conclusion that InN growth on the GaN substrate is not possible. The built-in electric field present in InGaN/GaN and AlGaN/GaN heterostructures crystallizing in a wurtzite lattice can reach several MV/cm, leading to drastic changes in the physical properties of these structures and related devices. It is shown how hydrostatic pressure modifies these effects and helps to understand their origin.

Pressure dependence of band gap of (0 4 0) oriented TlI films

Perfectly (040) oriented Thallium iodide films grown by vacuum thermal evaporation were found to have strain and band gap uncorrelated with their film thicknesses. Band structure of orthorhombic TlI was calculated using Density functional Theory (DFT) with appropriate functional. Elastic constants were calculated for determining the residual stress from strain. Band gaps of films linearly correlate with their residual stress. Experimental stress free direct band gap 2.92 eV determined from band gap-residual stress correlation matches quite closely with calculated 2.88 eV. Pressure coefficient of band gap −1 eV/GPa was determined from the residual stress dependence of band gap.

Bandgap Pressure Coefficient of a CH3NH3PbI3 Thin Film Perovskite.

Recent scientific interest in examining the bandgap evolution of a MAPbI3 hybrid perovskite by applying hydrostatic pressure has mostly focused on a room-temperature tetragonal phase. In contrast, the pressure response of a low-temperature orthorhombic phase (OP) of MAPbI3 has not been explored and understood. In this research, we investigate for the first time how hydrostatic pressure alters the electronic landscape of the OP of MAPbI3. Pressure studies using photoluminescence combined with calculations within density functional theory at zero temperature allowed us to identify the main physical factors affecting the bandgap evolution of the OP of MAPbI3. The negative bandgap pressure coefficient was found to be strongly dependent on the temperature (α120K = -13.3 ± 0.1 meV/GPa, α80K = -29.8 ± 0.1 meV/GPa, and α40K = -36.3 ± 0.1 meV/GPa). Such dependence is related to the changes in the Pb-I bond length and geometry in the unit cell as the atomic configuration approaches the phase transition as well as the increasing phonon contribution to octahedral tilting as the temperature increases.

Pressure induced structural, electronic and optical properties of wurtzite beryllium monoxide (w-BeO) from first-principle calculations

All-electron density functional calculations of structural, electronic and optical properties of wutrzite beryllium oxide (w-BeO) are carried out at different applied hydrostatic pressure. Calculated lattice constants decrease (a, c), while bulk modulus increases with increasing pressure. Direct fundamental band-gap (Eg) of w-BeO increases with increasing pressure and vice versa and the variation provides first and second order pressure coefficient of band-gap. The calculated volume deformation potential of band-gap of w-BeO is −11.5972 eV. Optical properties of w-BeO at zero and high pressures have been studied in terms of dielectric function ε(ω) and related ancillary optical parameters. Each optical parameter is marginally anisotropic. Calculated components of refractive index at each pressure signify uniaxial characteristics of the w-BeO. Calculated components of static dielectric constant, refractive index and reflectivity decreases, while critical point energy in the spectra of each component of ε2(ω), k(ω), σ(ω) and α(ω) increases with increasing pressure and vice versa. Calculated optical energy-gap (Eopt) of w-BeO increases like Eg with increasing pressure and vice versa. The transmission cutoff energy (ECutoff) is shifted towards the higher energy region with increasing pressure.

Electronic band structure, elastic, optical and thermodynamic characteristic of cubic YF3: An ab initio study

We have calculated the bond lengths dF3→F5,7,8, dF4→F5,6,8, dF2→F5,7,8, dF1→F6,7,8, dF1→8−Y1,2,3, dF9→Y1,2,3, dF1→8−F9 and single-crystal elastic stiffness constants, Cij and polycrystalline elastic moduli at different pressures by using GGA-PBE, GGA-PBESOL and LDA approach for cubic YF3. Yttrium fluoride is found to be elastically stable in the pressure range 0–40 GPa. Shear modulus, linear compressibility and Poisson's ratio have maximum and minimum values along with different crystallographic directions, which explain their predicted anisotropy. The direct Γ-Γ band gap value 5.082 eV indicates towards the insulating character of YF3. The broad band gap is a sign that this compound should function as an emission center. We predicted the first and second-order pressure coefficients of direct and indirect band gaps using the GGA-PBE, GGA-PBESOL and LDA approaches. The estimated volumetric thermal expansion coefficient, constants volume and constant pressure heat capacities and entropy at zero pressure and 300 K are 1.66 × 105 K−1, 82.56 Jmol−1K−1 and 83.59 mol-1 K−1, respectively. The edge of the optical absorption is located at 48.5 nm which is caused by the V1−C1 transition at the Γ point in the Brillouin zone that corresponds very well to the direct band gap at Γ- Γ.

Improved thermoelectric performance in PbSe–AgSbSe2 by manipulating the spin-orbit coupling effects

Abstract The thermoelectric performance of a semiconductor is intrinsically limited by the coupling of the transport factors, originating in the mechanism of band gap opening. Here we report the anomalous semiconductor AgSbSe2-alloyed PbSe, in which the spin-orbit coupling (SOC) induced band gap allows the decoupling of electrical conductivity and Seebeck coefficient. In such a SOC semiconductor, the decrease of lattice constant increases the band gap from 0.23 eV up to 0.5 eV, seemingly in contrast to the previously measured negative pressure coefficient of band gap. Very different thermoelectric behaviors from the pristine PbSe were observed in PbSe–AgSbSe2, and finally a high peak ZT of 1.65 at 858 K and a remarkable average ZT (300–858 K) of 0.86 were obtained. This study reveals the novel relativistic effects in PbSe–AgSbSe2 system, and its thermoelectric performance is believed to have a large potential to be further improved.

Chemical ordering and pressure-induced isostructural and electronic transitions in MoSSe crystal

Isostructural transitions in layered $M{X}_{2}$ compounds are governed by competing van der Waals (vdW) and Coulomb interactions. While an isostructural transition (at $P\ensuremath{\sim}$ 20 GPa) has been observed before metallization in ${\mathrm{MoS}}_{2}$ when subjected to pressure, it is surprisingly missing in layered ${\mathrm{MoSe}}_{2}$ and ${\mathrm{MoTe}}_{2}$. Using synchrotron x-ray diffraction and Raman spectroscopic measurements of structural and vibrational properties of layered MoSSe crystals subjected to pressures up to 30 GPa and first-principles density functional theoretical analysis, we demonstrate a layer sliding isostructural transition from its $2{H}_{c}^{\ensuremath{'}}$ structure (space group ${P6}_{3}mc$) to a mixed-phase of $2{H}_{a}^{\ensuremath{'}}+2{H}_{c}^{\ensuremath{'}}$ at $P\ensuremath{\sim}$ 10.8 GPa, marked by discontinuity in lattice parameters, pressure coefficients of Raman modes, and accompanying changes in electronic structure. The origin of the unusually lower transition pressure of MoSSe compared with ${\mathrm{MoS}}_{2}$ is shown to be linked to chemical ordering of S and Se atoms on the anionic sublattice, possible because of moderate lattice mismatch between the parent compounds ${\mathrm{MoS}}_{2}$ and ${\mathrm{MoSe}}_{2}$ and large interlayer space in the vdW-bonded structure. Notably, we also report a lower-pressure transition observed at $P\ensuremath{\sim}3$ GPa and not reported earlier in the isostructural Mo-based chalcogenides, marked by a discontinuity in the pressure coefficient of the $c/a$ ratio and indirect band gap. The transition observed at $P\ensuremath{\sim}10.8$ GPa appears due to the change in the sign of the pressure coefficient of the direct band gap originating from inversion of the lowest-energy conduction bands. Our theoretical analysis shows that the phase transition at $P\ensuremath{\sim}18$ GPa marked by sharp changes in pressure coefficients of ${A}_{1}$ Raman modes is associated with the metallization of the $2{H}_{a}^{\ensuremath{'}}$ phase.

Theoretical investigation of structural, electronic and optical properties of (BeS)1/(BeSe)1, (BeSe)1/(BeTe)1 and (BeS)1/(BeTe)1 superlattices under pressure

The influence of hydrostatic pressure on structural, electronic and optical properties of short period (BeS)1/(BeSe)1, (BeSe)1/(BeTe)1 and (BeS)1/(BeTe)1 superlattices, has been investigated. The lattice parameters a and c for the tetragonal unit cell obtained by total energy calculations are in good agreement with the values calculated by macroscopic elasticity theory. The (BeS)1/(BeSe)1 superlattice possesses an indirect band gap while (BeSe)1/(BeTe)1 and (BeS)1/(BeTe)1 superlattices possess a direct band gap. The pressure ranges from 0 to 47 GPa for (BeS)1/(BeSe)1, 0 to 39 GPa for (BeSe)1/(BeTe)1, and 0 to 45 GPa for (BeS)1/(BeTe)1, meanwhile the pressure dependence of the energy band gap along different symmetry directions obey the equation Egp=Eg+ap+bp2. The pressure coefficient of the indirect band gap for (BeS)1/(BeSe)1 is −22.5675 × 10−3 eV(GPa)−1, while that of the direct band gap is estimated as −25.8581 × 10−3 eV(GPa)−1 and −24.4695 × 10−3 eV(GPa)−1 for (BeSe)1/(BeTe)1 and (BeS)1/(BeTe)1, respectively. The variation of the static dielectric constant with pressure is discussed.

Topological phase transition and evolution of edge states in In-rich InGaN/GaN quantum wells under hydrostatic pressure

Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.

Pressure dependence of the band-gap energy in BiTeI

The evolution of the electronic structure of BiTeI, a layered semiconductor with a van der Waals gap, under compression is studied by employing semilocal and dispersion-corrected density-functional calculations. Comparative analysis of the results of these calculations shows that the band-gap energy of BiTeI decreases till it attains a minimum value of zero at a critical pressure, after which it increases again. The critical pressure corresponding to the closure of the band gap is calculated, at which BiTeI becomes a topological insulator. Comparison of the critical pressure to the pressure at which BiTeI undergoes a structural phase transition indicates that the closure of the band gap would not be hindered by a structural transformation. Moreover, the band-gap pressure coefficients of BiTeI are computed, and an expression of the critical pressure is devised in terms of these coefficients. Our findings indicate that the semilocal and dispersion-corrected approaches are in conflict about the compressibility of BiTeI, which result in overestimation and underestimation, respectively. Nevertheless, the effect of pressure on the atomic structure of BiTeI is found to be manifested primarily as the reduction of the width of the van der Waals gap according to both approaches, which also yield consistent predictions concerning the interlayer metallic bonding in BiTeI under compression. It is consequently shown that the calculated band-gap energies follow qualitatively and quantitatively the same trend within the two approximations employed here, and the transition to the zero-gap state occurs at the same critical width of the van der Waals gap.

High pressure and time resolved studies of optical properties of n-type doped GaN/AlN multi-quantum wells: Experimental and theoretical analysis

High-pressure and time-resolved studies of the optical emission from n-type doped GaN/AlN multi-quantum-wells (MQWs) with various well thicknesses are analysed in comparison with ab initio calculations of the electronic (band structure, density of states) and optical (emission energies and their pressure derivatives, oscillator strength) properties. The optical properties of GaN/AlN MQWs are strongly affected by quantum confinement and polarization-induced electric fields. Thus, the photoluminescence (PL) peak energy decreases by over 1 eV with quantum well (QW) thicknesses increasing from 1 to 6 nm. Furthermore, the respective PL decay times increased from about 1 ns up to 10 μs, due to the strong built-in electric field. It was also shown that the band gap pressure coefficients are significantly reduced in MQWs as compared to bulk AlN and GaN crystals. Such coefficients are strongly dependent on the geometric factors such as the thickness of the wells and barriers. The transition energies, their oscillator strength, and pressure dependence are modeled for tetragonally strained structures of the same geometry using a full tensorial representation of the strain in the MQWs under external pressure. These MQWs were simulated directly using density functional theory calculations, taking into account two different systems: the semi-insulating QWs and the n-doped QWs with the same charge density as in the experimental samples. Such an approach allowed an assessment of the impact of n-type doping on optical properties of GaN/AlN MQWs. We find a good agreement between these two approaches and between theory and experimental results. We can therefore confirm that the nonlinear effects induced by the tetragonal strain related to the lattice mismatch between the substrates and the polar MQWs are responsible for the drastic decrease of the pressure coefficients observed experimentally.

Effect of internal stress on the electro-optical behaviour of Al-doped ZnO transparent conductive thin films

In this work, we will report on scientific efforts aimed at unraveling the quantitative effect of elastic strain on the electro-optical behaviour of Al-doped zinc oxide (AZO). AZO thin films have been deposited by reactive magnetron sputtering to thicknesses from 300 to 500 nm, both on extra-clear glass substrates as well as on oxidised Si wafers. This resulted in both cases in polycrystalline, strongly textured (002) films. During deposition, the internal stress evolution in the growing film was monitored in-situ using high resolution curvature measurements. The resulting growth-induced elastic strain, which was found to depend heavily on the oxygen partial pressure, could further be modulated by appropriately choosing the deposition temperature. The latter also induces an additional extrinsic thermal stress component, whose sign depends on the substrate used. As such, a wide range of biaxial internal stresses could be achieved, from −600 MPa in compression up to 800 MPa in tension. The resulting charge carrier mobilities, obtained independently from room temperature Hall measurements, were found to range between 5 and 25 cm2/V s. Interestingly, the maximum mobility occurred at the zero-stress condition, and together with a charge carrier concentration of about 8 × 1020 cm−3, this gave rise to a resistivity of only 300 μΩ cm. From the stress-dependent optical transmission spectra in the range of 200–1000 nm, the pressure coefficient of the optical bandgap was estimated from the corresponding Tauc plots to be 31 meV/GPa, indicating a very high strain-sensitivity as well.

Influence of hydrostatic pressure on the built-in electric field in ZnO/ZnMgO quantum wells

We used high hydrostatic pressure to perform photoluminescence measurements on polar ZnO/ZnMgO quantum well structures. Our structure oriented along the c-direction (polar direction) was grown by plasma-assisted molecular beam epitaxy on a-plane sapphire. Due to the intrinsic electric field, which exists in polar wurtzite structure at ambient pressure, we observed a red shift of the emission related to the quantum-confined Stark effect. In the high hydrostatic pressure experiment, we observed a strong decrease of the quantum well pressure coefficients with increased thickness of the quantum wells. Generally, a narrower quantum well gave a higher pressure coefficient, closer to the band-gap pressure coefficient of bulk material 20 meV/GPa for ZnO, while for wider quantum wells it is much lower. We observed a pressure coefficient of 19.4 meV/GPa for a 1.5 nm quantum well, while for an 8 nm quantum well the pressure coefficient was equal to 8.9 meV/GPa only. This is explained by taking into account the pressure-induced increase of the strain in our structure. The strain was calculated taking in to account that in-plane strain is not equal (due to fact that we used a-plane sapphire as a substrate) and the potential distribution in the structure was calculated self-consistently. The pressure induced increase of the built-in electric field is the same for all thicknesses of quantum wells, but becomes more pronounced for thicker quantum wells due to the quantum confined Stark effect lowering the pressure coefficients.

Structural and electronic properties of boron- bismuth compound under pressure

<p>In the present work, we report first principles calculations of the pressure effect on the structural and electronic properties of Boron- Bismuth (BBi) compound in its zincblende phase. The pseudopotential plane wave (PPW) method in the framework of the density func-tional theory (DFT) within the local density approximation for the exchange-correlation functional, and the Hartwigzen-Goedecker-Hutter (HGH) scheme for the pseudopotential were used in the calculation. The unit cell volume, the molecular and crystal densities, the equation of state and also the linear and quadratic pressure coefficients of the energy band-gaps are investigated.</p>

Effect of high pressure on thermoelectric performance and electronic structure of SnSe via HPHT

Polycrystalline SnSe bulks were synthesized by a simple and rapid High Pressure and High Temperature (HPHT) method in pressure range of 1–5 GPa, and the thermoelectric performances were assessed after high pressure was released. HPHT can not only sharply shorten synthetic time to 25 min, but also tune thermoelectric properties in a broad range. More importantly, the beneficial thermoelectric properties under high pressure are effectively retained to ambient conditions via “quenching” procedure. The intrinsically high electrical resistivity of SnSe is remarkably reduced by HPHT, which is ascribed to pressure-induced band gap narrowing. A minimum electrical resistivity of 0.1 Ω cm at 5 GPa and maximum power factor of 1 × 10−4 Wm−1K−2 at 3 GPa for SnSe0.98Te0.02 are achieved at ambient conditions. Besides, the first principle calculations reveal that high pressure can fundamentally shrink interatomic distances and lattice parameters, which thus lead to a decreased band gap. The pressure coefficient of band gap dEg/dP = −0.074 eV/GPa is obtained. The variations of electronic structure under high pressure are in accordance with the trend in measured thermoelectric properties.

Crystalline to amorphous phase transformation of Ta2O5 quantum dots driven by residual stress

Simple vacuum thermal evaporation technique was used to grow Ta2O5 quantum dots. The small dots with large voids between them in ultra-thin films were found to gradually grow in size with decreasing voids with increase in film thickness. The development of residual stress was observed with increasing dot size or film thickness. Residual stress effect on band gap of orthorhombic Ta2O5 quantum dots is studied. Both SAED and XRD confirm that the films thicker than 45 nm become amorphous. Significantly varying optical band gap with film thickness was observed by studying optical absorption of the films. The variation of residual stress with film thickness scales linearly very well with the varying band gap with film thickness. Stress free band gap (3.94 eV) and pressure coefficient of band gap (∂Eg/∂P)T = −26.4 meV/GPa) were determined from this study. Transformation from crystalline to amorphous phase in orthorhombic form of Ta2O5 has been determined to be at about 18 GPa. Both crystalline to amorphous transition and pressure coefficient of band gap for orthorhombic Ta2O5 driven by residual stress have been determined for the first time in the literature.

Electronic Topological Transition in Ag2Te at High-pressure.

Recently, Ag2Te was experimentally confirmed to be a 3D topological insulator (TI) at ambient pressure. However, the high-pressure behaviors and properties of Ag2Te were rarely reported. Here, a pressure-induced electronic topological transition (ETT) is firstly found in Ag2Te at 1.8 GPa. Before ETT, the positive pressure coefficient of bulk band-gap, which is firstly found in TIs family, is found by both first-principle calculations and in situ high-pressure resistivity measurements. The electrical resistivity obtained at room temperature shows a maximum at 1.8 GPa, which is nearly 3.3 times to that at ambient pressure. This result indicates that the best bulk insulating character and topological nature in Ag2Te can be obtained at this pressure. Furthermore, the high-pressure structural behavior of Ag2Te has been investigated by in situ high-pressure synchrotron powder X-ray diffraction technique up to 33.0 GPa. The accurate pressure-induced phase transition sequence is firstly determined as P21/c → Cmca → Pnma. It is worth noting that the reported isostructural P21/c phase is not existed, and the reported structure of Cmca phase is corrected by CALYPSO methodology. The second high-pressure structure, a long puzzle to previous reports, is determined as Pnma phase. A pressure-induced metallization in Ag2Te is confirmed by the results of temperature-dependent resistivity measurements.

Carrier mediated reduction of stiffness in nanoindented crystalline Si(100)

We report the observation of carrier mediated decrease in the stiffness of crystalline (c)-Si(100) under nanoindentation. The apparent elastic moduli of heavily doped (∼1 × 1021 cm−3) p- and n-type c-Si are observed to be lower by 5.3%–7.5% than the estimated value for intrinsic (∼1 × 1014 cm−3) c-Si. The deviation observed with respect to elastic modulus remarkably matches with the estimated value while considering the electronic elastic strain effect on carrier concentration as an influence of negative pressure coefficient of band gap for Si (Γ-X). The value is predominantly higher than the reported value of a decrease of 1%–3% in stiffness as an effect of impurity in c-Si.

Band gap bowing parameter in pseudomorphic AlxGa1−xN/GaN high electron mobility transistor structures

A method for evaluation of aluminium composition in pseudomorphic AlxGa1−xN layer from the measured photoluminescence (PL) peak energy is presented here. The layers were grown by metalorganic chemical vapor deposition and characterized by high resolution X-ray diffraction (HRXRD), PL, cathodoluminescence, and atomic force microscopy. We estimated the value of biaxial stress in pseudomorphic AlxGa1−xN layers grown on sapphire and silicon carbide substrates using HRXRD scans. The effect of biaxial stress on the room temperature band edge luminescence in pseudomorphic AlxGa1−xN/GaN layers for various aluminium compositions in the range of 0.2 < x < 0.3 was determined. The value of pressure coefficient of band gap was also estimated. The stress corrected bowing parameter in AlxGa1−xN was determined as 0.50 ± 0.06 eV. Our values match well with the theoretically obtained value of bowing parameter from the density functional theory.

Optical properties of scintillator material BaBr2 films

The BaBr2 films grown by vacuum thermal evaporation prefer three different completely (hkl) oriented growth at different growth parameters and each orientation develops strain due to residual stress. The optical absorption indicates a direct type band gap for these films. The band gap of each (hkl) orientation varies linearly with its uniaxial strain. The three (hkl) orientations show band gap anisotropy (2.94–4.25eV). The negative (for (101) and (111)) and positive (for (013)) pressure coefficients of band gap are attributed to the strain in Br–Br and Ba–Br bonds along [hkl] respectively. The average pressure coefficient of band gap of all three orientations found to be significantly smaller than that calculated by volumetric pressure dependence.