Scissor Correction Research Articles

Ab initio calculation of two-photon absorption in semiconductors

A theoretical derivation of two-photon absorption (2PA) from semiconductors, based on the length gauge analysis and the electron density operator, is formulated; the intraband ${\mathbit{r}}_{i}$ part and the interband ${\mathbit{r}}_{e}$ part of the position operator $\mathbit{r}$ are properly accounted for. Within the independent-particle approximation, the nonlinear third-order susceptibility tensor ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ and the two-photon absorption coefficient are calculated, including the scissors correction needed to correct the well-known underestimation of the local-density-approximation band gap. Using time-reversal symmetry, it is shown that the expression for ${\ensuremath{\chi}}^{\mathrm{a}\mathrm{b}\mathrm{c}\mathrm{d}}(\ensuremath{-}\ensuremath{\omega};\ensuremath{-}\ensuremath{\omega},\ensuremath{-}\ensuremath{\omega},\ensuremath{\omega})$ is finite at $\ensuremath{\omega}=0$, avoiding nonphysical divergences presented in previous calculations when $\ensuremath{\omega}\ensuremath{\rightarrow}0$. Ab initio band structure calculations using different pseudopotential schemes that include spin-orbit coupling are used to calculate the 2PA for several semiconductors, and the calculations are compared with available experimental results for photon energies that are below the optical band gap.

Strong bulk photovoltaic effect and second-harmonic generation in two-dimensional selenium and tellurium

Few-layer selenium and tellurium films have been recently prepared, and they provide a new platform to explore novel properties of two-dimensional (2D) elemental materials. In this work, we have performed a systematic first-principles study on the electronic, linear, and nonlinear optical (NLO) properties of atomically thin selenium and tellurium films within the density-functional theory with the generalized gradient approximation plus scissors correction using the band gaps from the relativistic hybrid Heyd-Scuseria-Ernzerhof functional calculations. Interestingly, we find that few-layer Se and Te possess large second-harmonic generation (SHG), linear electro-optic effect, and bulk photovoltaic effect. In particular, trilayer (TL) Te possesses large SHG coefficient, being more than 65 times larger than that of GaN, a widely used NLO material. Bilayer (BL) Te has huge static SHG coefficient, being more than 100 times larger than that of GaN. Furthermore, monolayer (ML) Se possesses large SHG coefficient. Moreover, we predict that TL Te exhibits strong bulk photovoltaic effect (BPVE), being greater than that of GeS, a polar system with the largest BPVE found so far. Although the shift current conductivities of bulk and 2D Se are comparable, the shift current conductivities of TL Te are five times larger than those of bulk Te. Finally, an analysis of the calculated electronic band structures indicates that the strong NLO responses of 2D Se and Te materials are primarily derived from their low-dimensional structures with high anisotropy, directional covalent bonding, lone-pair electrons, and relatively small band gaps. These findings provide a practical strategy to search for excellent NLO and BPVE materials.

First-principles study of strain effect on the thermoelectric properties of LaP and LaAs.

Rare-earth monopnictides have attracted much attention due to their unusual electronic and topological properties for potential device applications. Here, we study rock-salt structured lanthanum monopnictides LaX (X = P, As) by density functional theory (DFT) simulations. We show systematically that a meta-GGA functional combined with scissor correction can efficiently and accurately compute the electronic structures on a fine DFT k-grid, which is necessary for converging thermoelectric calculations. We also show that strain engineering can effectively improve the thermoelectric performance. Under the optimal conditions of 2% isotropic tensile strain and carrier concentration n = 3 × 1020 cm-3, LaP at a temperature of 1200 K can achieve a figure of merit ZT value >2, which is enhanced by 90% compared to the unstrained value. With carrier doping and strain engineering, lanthanum monopnictides thereby could be promising high-temperature thermoelectric materials.

Crystal growth, electronic and optical properties of Tl2CdSnSe4, a recently discovered prospective semiconductor for application in thin film solar cells and optoelectronics

Abstract A single crystal of the non-centrosymmetric low-temperature modification of Tl2CdSnSe4 (space group I 4 ‾ 2m) was grown, for the first time, and its electronic and optical properties were studied from both experimental and theoretical viewpoints. The Tl2CdSnSe4 crystal was grown from the solution-melt by vertical Bridgman-Stockbarger method. Centimeter dimensions of the crystal allow its application in practice. The bandgap energy, Eg = 1.32 eV, estimated from the optical absorption coefficient agrees well with the value of Eg = 1.29 eV calculated from the photosensitivity measurements. X-ray photoelectron spectroscopy (XPS) was used to investigate the electronic structure and charge states of atoms composing the crystal under consideration. To detect the best agreement of the curve of total densities of states (DOS) with the experimental XPS spectrum of valence electrons of Tl2CdSnSe4, we performed theoretical calculations within a density functional theory (DFT) framework treating different models for exchange correlation (XC) potential. Our findings yield that the best agreement of the experimental and theoretical distributions of the valence electronic states is derived when using in the computation procedure for XC potential the modified Becke-Johnson potential in the form of Tran-Blaha (TB-mBJ), which involves also the Hubbard parameter U for strongly correlated d electrons and spin-orbit coupling (SOC) effect (TB-mBJ + U + SOC model). Based on this approach, we calculated partial densities of states, energy band dispersion, and main optical constants of Tl2CdSnSe4. Importantly, the TB-mBJ + U + SOC model reveals the Eg value which is close to those determined experimentally; therefore, scissors correction adjustment is not required when performing DFT calculations of the optical constants in such a case. The present experimental XPS measurements of the treated with middle-energy Ar+-ions Tl2CdSnSe4 crystal surface and the theoretical DFT calculations data indicate, in spite of its rather hazardous chemical elements, thallium and cadmium, the crystal surface is rather stable and, coupled with suitable energy band gap, makes quaternary selenide under discussion a very promising material for using in thin film solar cells and optoelectronics as well as in highly efficient photocatalytic devices.

Ab initio investigation of optical properties of As2S3 and Ag doped As2S3

The density functional theory along with generalized gradient approximation is used to calculate the optical properties of As2S3 and Ag0.25As1.75S3. The effective band gap of Ag0.25As1.75S3 is reduced as compared to As2S3. The scissor correction of 1 eV is used to calculate the optical properties. The dielectric function of Ag0.25As1.75S3 enhances significantly at low energies while at higher energies there is constant shift in the peak positions of Ag0.25As1.75S3 as compared to As2S3. Similar enhancements at low energies and shift at higher energies are found in the refractive index, optical conductivity, absorption coefficient and reflectance of Ag0.25As1.75S3 as compared to As2S3. The optical parameters are found more anisotropic at low energies however at higher energies the anisotropy nearly vanishes. The Ag0.25As1.75S3 is found more birefringent than As2S3. The calculated results closely agree with the available experimental estimates of crystalline, amorphous and thin films of As2S3 and Ag0.25As1.75S3.

Effects of strain on electronic and optical properties of LiNbO3: a first principles study

The exchange-correlation functions of local density approximation and generalized gradient approximation using density functional theory were performed to calculate electronic and optical properties of lithium niobate crystal. To correct the underestimated value of band gap, a reverse scissor correction procedure was performed based on the experimental refractive index value because it is more suitable for compound with polar crystal. It is found that underestimated electronic band gap ∼4.76 eV was generated due to nature of generalized gradient approximation (GGA) exchange correlation. Based on density of states calculation, Li ion tends to diffuse into substrate as it possesses pure ionic character. Thus, the chemical bonding in LiNbO3 crystal has a mixed covalent-ionic character. The effect of strain on a-axis of the crystal and thus, its electronic and optical properties were investigated. The a-axis of the crystal is more sensitive towards the strain compared to c-axis as the band gap largely changes upon the applied strain. The optical properties such as dielectric function, refractive index, extinction coefficient, and absorption were calculated and explained in detail. The positive and negative strains do shift the optical spectrum either to higher or lower frequency depending on specific properties. These results would assist to provide the fundamental explanation about the effect of strain on the properties of lithium niobate crystal.

Thermoelectric characterization of ZnSb by first-principles method

The thermoelectric properties of semiconducting compound ZnSb are studied using crystalline orbitals program based on the periodic linear combination of atomic orbitals method. The calculations are done under the framework of density functional theory. We calculate the electronic band structure and the density of states. The k-space eigenvalues are coupled with Boltzmann transport equations to calculate transport coefficients such as the Seebeck coefficient, power factor and electronic thermal conductivity under the constant relaxation time and the rigid band approximations. Effect of the scissor correction on the transport coefficients is examined. We have found that ZnSb behaves as n-type thermoelectric. A comparison with available measurements is done and a good agreement is found. The thermoelectric performance is compared with other materials by means of the electronic fitness function which suggests ZnSb to be a good thermoelectric material.

Large second-harmonic generation and linear electro-optic effect in trigonal selenium and tellurium

Trigonal selenium and tellurium crystalize in helical chain-like structures and thus possess interesting properties such as current-induced spin polarization, gyrotropic effects and nonlinear optical responses. By performing systematic ab initio calculations based on density functional theory in the generalized gradient approximation plus scissors correction, we study their linear and nonlinear optical (NLO) properties. We find that the two materials exhibit significant second-harmonic generation (SHG) and linear electro-optic (LEO) effect. In particular, the SHG coefficients of tellurium are huge in the photon energy range of 0 ~ 3 eV, with the magnitudes of SHG(xxx) being as large as 3640 pm/V, which are about sixteen times larger than that of GaN, a widely used NLO material. On the other hand, trigonal selenium is found to possesses large LEO coefficients r(xxx,0) which are more than six times larger than that of GaN.Therefore, trigonal tellurium and selenium may find valuable applications in NLO and LEO devices such as frequency conversion, electro-optical switch and light signal modulator.The energy positions and shapes of the principal features in the calculated optical dielectric functions of both materials agree rather well with the available experimental ones, and are also analyzed in terms of the calculated band structures especially symmetries of the involved band states and dipole transition selection rules.

Real time scissor correction in TD-DFT

We demonstrate how the scissor correction to the optical band gap, common in linear-response time-dependent density functional theory (TD-DFT), may be extended to the domain of real-time TD-DFT. This requires modifying both the eigenvalues and momentum matrix elements of the underlying basis set. It provides a simple and computationally economical approach for calculating accurate electron dynamics in solids. We demonstrate the importance of this correction for prototypical semiconductors, diamond and silicon, where the energy absorption in both the linear and non-linear regimes is examined. We also show that for a particular system, ZnSe, using the adiabatic local density approximation together with a scissor correction can be advantageous over other approximations, as the underlying quasi-particle band structure is more accurate.

First-principles calculations of second-order nonlinear optical coefficients in the static limit and Pockels coefficients in III-N and II−IV−N2 compounds

The second-order nonlinear optical coefficients in the static limit are evaluated using density functional perturbation theory from the electronic response to a static electric field for the group-III nitrides and several $\mathrm{II}\text{\ensuremath{-}}\mathrm{IV}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ ternary nitrides. They are compared with literature results using the sum over states approach including local field effects. The effects of the scissor correction are evaluated. Good agreement is obtained for GaN, AlN, and w-BN. For InN, the small or even negative gap in the LDA at $\mathrm{\ensuremath{\Gamma}}$ causes an extreme sensitivity to the k point summation and pseudopotentials. Similar problems occur for other very small gap $\mathrm{II}\text{\ensuremath{-}}\mathrm{IV}\text{\ensuremath{-}}{\mathrm{N}}_{2}$ semiconductors. The nonlinear optics coefficients are showing a general trend of increasing values with smaller gaps but no clear scaling relation with the direct gaps is obtained. In addition, unexpected changes in sign are found for the Si-based compounds, similar to the case of AlN, compared to the expected signs of ${d}_{33}$ in GaN. The Pockels coefficient, which includes in addition to the electronic response the phonon and piezoelectric response, is also evaluated. They show that the phonon and electronic contributions to the response in these materials are comparable in magnitude but in many cases of opposite sign.

Theoretical studies on structural, electronic and optical properties of kesterite and stannite Cu2ZnGe(S/Se)4 solar cell absorbers

Structural, electronic and optical properties of Cu2ZnGe(S/Se)4 semiconductor materials in their kesterite and stannite phase have been investigated using density functional theory (DFT) approach using full potential linearized augmented plane wave (FP-LAPW) method. Modified Becke-Johnson (mBJ) exchange correlation is used for computing physical properties. These kesterite and stannite Cu2ZnGeS4 and Cu2ZnGeSe4 are direct band semiconductors with band gap values ∼1.15 eV and 1.0 eV for Cu2ZnGeS4 and 0.64 eV and 0.24 eV for Cu2ZnGeSe4, respectively at Γ point. A scissor correction of 1 eV raised these band gap values equal to the experiment values. Optical properties are investigated in terms of refractive index, extinction coefficient, reflectivity, optical conductivity, and optical absorption using dielectric constant.

Scaling of the self-energy correction to the HOMO-LUMO gap with magnesium cluster size and its potential for extrapolating to larger magnesium clusters

This paper presents a computational method for the estimation of the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of metallic nano-clusters using efficient density functional computations with the high accuracy of the GW method. Electronic structures of magnesium nano-clusters Mgn (n = 1–22, 25, 30, 35, and 40) are computed using the density functional theory (DFT) and the quasiparticle GW method. It is found that the energy difference between the DFT and GW results, defined as the scissors operator or correction, is only dependent on the cluster size and independent of the electronic shell filling effect. The scissors operators of HOMOs and LUMOs of metallic clusters can thus be fitted by using simple power functions of the cluster size n. Therefore, the HOMOs and LUMOs of metallic clusters can be efficiently calculated using DFT with a modification of scissors operators. The scissors operators are also demonstrated to be applicable to occupied and unoccupied states near the Fermi level.

Thermoelectric transport of GaAs, InP, and PbTe: Hybrid functional with k·p̃ interpolation versus scissor-corrected generalized gradient approximation

Boltzmann transport calculations based on band structures generated with the density functional theory are often used in the discovery and analysis of thermoelectric materials. In standard implementations, such calculations require dense k-point sampling of the Brillouin zone and are therefore typically limited to the generalized gradient approximation (GGA), whereas more accurate methods such as hybrid functionals would have been preferable. GGA variants, however, generally underestimate the band gap. While a premature onset of minority carriers can be avoided with scissor corrections, the band gap also affects the band curvature. In this study, we resolved the k-point sampling issue in hybrid-functional based calculations by extending our recently developed k·p̃ interpolation scheme [K. Berland and C. Persson, Comput. Mater. Sci. 134, 17 (2017)] to non-local one-electron potentials and spin-orbit coupling. The Seebeck coefficient generated based on hybrid functionals was found to agree better than GGA with experimental data for GaAs, InP, and PbTe. For PbTe, even the choice of hybrid functional has bearing on the interpretation of experimental data, which we attribute to the description of valley convergence of the valence band.

Second harmonic generation property of monolayer TMDCs and its potential application in producing terahertz radiation.

Second harmonic generation (SHG) properties in two-dimensional (2D) transition-metal dichalcogenides (TMDCs) have aroused great interest. However, until now SHG for TMDC monolayer alloys is seldom investigated. Meanwhile, there is considerable controversy over the static SHG coefficients of monolayer MoS2. The feasibility to produce terahertz (THz) radiation via SHG in pure and alloyed TMDCs has never been reported. We first calculate the SHG coefficients of monolayer MoS2, MoSe2, and MoS2(1-x)Se2x using the independent particle approximation plus scissors correction. We then simulate their THz absorption by applying density function perturbation theory plus the Lorentzian line and try to calculate their zero-frequency THz refractive index and birefringence. The physical property of MoS2(1-x)Se2x alloys is simulated by considering various combinations. Results indicate that monolayer MoS2, MoSe2, and MoS2(1-x)Se2x possess large static SHG coefficients and THz birefringence and display low absorption over broadband THz frequencies. Therefore, they have applications in producing THz radiation via SHG. This study demonstrates that THz radiation can be attained in a large number of monolayers and few-layers and will extend applications of 2D materials. Moreover, it is possible to identify the magnitude of static coefficients of single-layer MoS2 by measuring THz intensities.

Electronic structure and optical properties of iron based chalcogenide FeX2 (X = S, Se, Te) for photovoltaic applications: a first principle study

In present work, the electronic structure and optical properties of the FeX2 (X = S, Se, Te) compounds have been evaluated by the density functional theory based on the scalar-relativistic full potential linear augmented plane wave method via Wien2K. From the total energy calculations, it has been found that all the compounds have direct band nature, which determined by iron 3d states at valance band edge and anion p dominated at conduction band at Γ-point and the fundamental band gap between the valence band and conduction band are estimated 1.40, 1.02 and 0.88 eV respectively with scissor correction for FeS2, FeSe2 and FeTe2 which are close to the experimental values. The optical properties such as dielectric tensor components and the absorption coefficient of these materials are determined in order to investigate their usefulness in photovoltaic applications.

Nature of the metallization transition in solid hydrogen

We present an accurate study of the static-nucleus electronic energy band gap of solid molecular hydrogen at high pressure. The excitonic and quasiparticle gaps of the $C2/c$, $Pc$, $Pbcn$, and $P6_3/m$ structures at pressures of 250, 300, and 350~GPa are calculated using the fixed-node diffusion quantum Monte Carlo (DMC) method. The difference between the mean-field and many-body band gaps at the same density is found to be almost independent of system size and can therefore be applied as a scissor correction to the mean-field gap of an infinite system to obtain an estimate of the many-body gap in the thermodynamic limit. By comparing our static-nucleus DMC energy gaps with available experimental results, we demonstrate the important role played by nuclear quantum effects in the electronic structure of solid hydrogen. Our DMC results suggest that the metallization of high-pressure solid hydrogen occurs via a structural phase transition rather than band gap closure.

Frequency-dependent dielectric function of semiconductors with application to physisorption

The dielectric function is one of the most important quantities that describes the electrical and optical properties of solids. Accurate modeling of the frequency-dependent dielectric function has great significance in the study of the long-range van der Waals (vdW) interaction for solids and adsorption. In this work, we calculate the frequency-dependent dielectric functions of semiconductors and insulators using the $GW$ method with and without exciton effects, as well as efficient semilocal density functional theory (DFT), and compare these calculations with a model frequency-dependent dielectric function. We find that for semiconductors with moderate band gaps, the model dielectric functions, $GW$ values, and DFT calculations all agree well with each other. However, for insulators with strong exciton effects, the model dielectric functions have a better agreement with accurate $GW$ values than the DFT calculations, particularly in high-frequency region. To understand this, we repeat the DFT calculations with scissors correction, by shifting DFT Kohn-Sham energy gap to match the experimental band gap. We find that scissors correction only moderately improves the DFT dielectric function in low-frequency region. Based on the dielectric functions calculated with different methods, we make a comparative study by applying these dielectric functions to calculate the vdW coefficients ($C_3$ and $C_5$) for adsorption of rare-gas atoms on a variety of surfaces. We find that the vdW coefficients obtained with the nearly-free electron gas-based model dielectric function agree quite well with those obtained from the $GW$ dielectric function, in particular for adsorption on semiconductors, leading to an overall error of less than 7% for $C_3$ and 5% for $C_5$. This demonstrates the reliability of the model dielectric function for the study of physisorption.

New understandings of third harmonic generation coefficient of bulk silicon: Implementation and application of the full ab initio band structure sum-over-states method

We make a full ab initio band structure analysis of interband and intraband contributions for the third-order nonlinear optical susceptibilities of bulk silicon by implementing the Aversa and Sipe sum-over-states formulism. The band structure and momentum matrix elements were calculated by using the highly accurate all-electron full potential linearized augmented plane wave method within the local density approximation. The convergence tests including the scissor correction with different k-points meshes and empty states were performed. Both real and imaginary parts of susceptibility were directly calculated and checked by the Kramers–Kronig relation. The converged results are compared with other theoretical and experimental ones and in agreement with the recent ab initio real-time-based calculation. The nonlinear optical coefficient comes from three parts: the pure interband contribution (P_inter), the modulation of interband terms by intraband terms (P_mod), and the intraband contribution (J_intra). For each part, the origin of enhanced peaks is explored by tracing the sum-over-states process. The interband contribution is found to be dramatically modulated by the intraband contribution.

A DFT study of the electronic and optical properties of a photovoltaic absorber material Cu2ZnGeS4 using GGA and mBJ exchange correlation potentials

The electronic and optical properties of Cu2ZnGeS4 are calculated by means of the full potential linearized augmented plane wave method (FP-LAPW) using the generalized gradient approximation (GGA) and the modified Becke–Johnson (mBJ) as exchange correlation functionals. The band structures, total and partial densities of states as well as optical properties are presented and discussed in the context of the available experimental data and theoretical calculations. Our calculations show that the conduction bands minima (CBM) is composed of contributions mainly from Ge–p states while the valence bands maxima (VBM) is dominated by Cu–d states. We find that Cu2ZnGeS4 possesses a direct energy band gap situated at the center (Γ point) of the Brillouin Zone (BZ). The calculated energy gaps of 0.50 eV (GGA) and 1.21 eV (mBJ) are much smaller than the experimental value of around 2.2 eV. We have shown anisotropic behavior of the compound using optical constants and birefringence plots and found that the Δn(0) in GGA and mBJ is about 0.06 and 0.08, respectively when applied scissors correction. We find that applying the scissors correction leads to better agreement with the experiment.

First-principles calculation of semiclassical thermoelectric properties of (AgSbSe2)n(AgSbTe2)n superlattices

In this research, we perform density functional – pseudo potential calculation within generalized gradient approximation (GGA) to investigate semiclassical thermoelectric properties of (AgSbSe2)n(AgSbTe2)n (n = 1,2) thin film superlattices. It is seen that GGA, GGA + U, and the modified Becke Johnson (mBJ) functionals as well as full-relativistic corrections are not able to describe properly the electronic structure of bulk AgSbSe2 and AgSbTe2, hence a scissor correction is used throughout this study. The Seebeck coefficient, electrical conductivity, and electronic part of the thermal conductivity of bulk compounds as well as superlattices are computed at different values of hole doping, in the fixed relaxation time approximation. It is argued that the (AgSbSe2)1(AgSbTe2)1 superlattice may exhibits improved Seebeck coefficient compared with the bulk compounds and (AgSbSe2)2(AgSbTe2)2 superlattice.