An essential issue in the development of semiconductor devices for photovoltaics is to design materials with optimal band gaps and relative positioning of band planes. 35 3.6 The interface models and calculated band alignments of Cu5In9Se16/CdS and CuIn5Se8.
Fundamental band gap from KS/GKS scheme in DFT
The theoretical background for using the KS/GKS orbital energy gap as a prediction of the fundamental band gap is described in Sec. 2.3) rigorously justifies the use of the KS/GKS orbital energy gap as a direct prediction of the fundamental band gap for commonly used XC functionals (LDA, GGA and hybrid functionals), with the accuracy dictated by the levels of approximations used, although it should be noted that (2.3) does not hold for the exact XC functional, if ever known.
Choice of basis sets and ECPs for periodic calculations
Ideally, the exponents and coefficients in these molecular basis sets should be reoptimized in crystal calculations. Comparison of the performance of truncated and optimized basis sets on the structures and band gaps of CuInSe2, CuGaSe2 and CdS.
Key ingredients in XC functionals for performance
Egand ∆V% are the absolute and relative errors in band gap and volume, respectively, compared to experiment. Egand ∆V% are the absolute and relative errors in band gap and volume, respectively, compared to experiment. 68], using plane wave basis sets with USPP.
Benchmark on a set of 27 binary and ternary semicon- ductorsductors
Concluding remarks
A quantum chemical view of density functional theory. 1998) Relationship between Kohn-Sham eigenvalues and excitation energies. Insights into current limitations of density functional theory. 1996) Generalized Kohn-Sham schemes and the band-gap problem.
Methodology for calculating band offsets from interface modeling
We then fully optimized both the atomic positions and the supercell lattice parameters while using symmetry constraints to maintain a perfect match at the interface (all coordinates and symmetry constraints are available in the supplementary material of our paper [34]). We then averaged the electrostatic potential within the xy plane as a function of the direction of the interface, z, to obtain V(z). As shown in Table 3.2, we find that the use of core levels from different elements leads to some fluctuations, with changes in the predicted CBO of up to 0.07 eV (as observed previously [52]).
![Figure 3.1. Illustration of the computation of band offsets for the CuInSe 2 /CdS (110) interface: (a) supercell structure with 5 layers for each material where the vertical axis is the [001] or z axis, (b) electrostatic potential averaged over the xy plan](https://thumb-ap.123doks.com/thumbv2/123dok/11410635.0/44.918.58.812.230.525/illustration-computation-interface-supercell-structure-material-electrostatic-potential.webp)
Band offsets at pristine CIGS/CdS interfaces
This indicates that the potential shift of each semiconductor side in the interface is insensitive to the detailed local structure or dipole of the interface, whether it is nonpolar or polar. We were surprised to find that the 0.13 eV increase in the absorber band gap goes solely to reducing the VBO to 0.56 eV, while the CBO remains at 0.83 eV. The interface models and calculated band alignments of CuIn0.75Ga0.25Se2/CdS, where we see that the bandgap increase of 0.10 eV goes solely to decrease the VBO.
Bulk structures of defect CIGS
For Cu5In9Se16 we investigated all possible configurations and adopted the one with the lowest energy, while for CuIn5Se8 low energy configurations suggested by previous LDA and GGA studies[26, 27]. Here, the predicted B3PW91 band gap of 1.30 eV for the CuIn5Se8 phase is in excellent agreement with the experimental value of 1.27 eV[60]. Again, we calculated all possible configurations and selected those with the lowest total energy (details can be found in the supplementary material of our paper[34]).
Roles of defects in band offsets and energetics at CIGS/CdS interfacesinterfaces
Therefore, it is electrostatics that gives Na and K better ability to optimize CBO. However, both Na and K have larger ionic sizes than Cu, leading to an increased interfacial energy to 0.138J/m2 for Na and 0.151J/m2 for K. The CBO is coherently tuned with an increase in the band gap, most likely due to the Cu vacancy, while when Cd impurities do not seem to play a significant role.
Concluding remarks
We find that Cu vacancies eliminate the dominance of Cu 3d levels in VBM. Substrate influence on Cu(In,Ga)Se2 film texture. 2004) Study of the photoemission and bandgap of the CuInSe2(001)/CdS heterojunction.Appl. Theoretical analysis of the conduction band-shift effect of window/CIS layers on the performance of CIS solar cells using device simulation.
This chapter describes our work[16], in which we predict a one-dimensional all-nitrogen polymer phase with two planar conformations for N2O at high pressures, and determine the transition pressure of 60 GPa, above which the polymer phases are strongest. stable shape. Furthermore, we find that upon relaxation under ambient conditions, both planar polymers relax into the same nonplanar transpolymer, and the predicted phonon spectrum and dissociation kinetics validate its stability. The description of the valence bond suggests alternating single and double bonds (1.448 ˚A and 1.309 ˚A), which is what we find for the cis case; however, for the trans case we find that all NN bonds have the same bond distances (1.390 ˚A at 1 atm), indicating full resonance along the chain.
Transitions between molecular, ionic, and polymer phases of N 2 Oof N2O
However, the structure of NO+NO−3 has not yet been well established experimentally: experiments reported the formation of monoclinic P21/m-phase ionic salt from the high-pressure reaction (2 GPa) of a mixture of N2 and O2[31], while the original experiments on the dissociation of N2O under laser heating in a diamond anvil found an orthorhombic phase related to the aragonite that formed after cooling [15, 32]. Surprisingly, this combination of NO+NO−3 and N2 is more stable than the molecular NNO phases for all pressures up to 0 GPa. For the mixed phase, the ionic NO+NO−3 component is a dense solid, but the global compressibility of the mixed phase is dominated by the molecular phase of N2 (see Figure 4.A1), which only polymerizes above 110 GPa[ 2]. .
Relaxation of polymer phases to ambient conditions
However, as the pressure is released, both crystals develop imaginary phonon modes at ~14 GPa, and both relax to a single non-planar trans conformation (see Figure 4.7) at zero pressure, with a phonon spectrum attesting to its stability. . Both planarcis and transpolymer phases develop imaginary phonon modes, due to electrostatic repulsions and/or second-order Peierls deformation, and transform into the same non-planar transpolymer phase (see Figure 4.7), whose phonon spectrum at 0 GPa shows no imaginary modes. Here, the DOS (Figure 4.9) shows that at high pressures both planarcis and trans polymers are (quasi-) uniform bond charge-transfer insulators, with the VBM dominated by 2p orbitals of the negatively charged oxygen and bridging nitrogen atoms, while the CBM dominated by 2p.
Kinetic stability of the non-planar N 2 O polymer at am- bient conditionsbient conditions
To rule out finite size and end group effects, we also performed a TS search with an isolated periodic infinite chain of the nonplanar polymer using the CRYSTAL09 package (UB3LYP/6-311G(d)) and a barrier of 26.2 kcal/mol (see Fig. 4.A2 ). Indeed, we calculated (PBE-ulg) the non-planar N2Otrans-polymer to provide an internal energy release of 3.5 kJ/g when dissociated into N2 and O2, which is comparable to that of TNT (4.2 kJ/g). Thus, non-planar trans-NNO is a potential high-energy oxidant for new explosive composites and rocket propellants.
Concluding remarks
TS calculated for the dissociation of an isolated periodic infinite chain of the non-planar polymer. 2012) Proton disorder and superionicity in warm dense ammonia ice. 2007) Triggering dynamics of high-pressure benzene amorphization. For atoms with valence electrons with higher angular momenta, such as p-block elements, the FSG representation misses part of the interaction between the core and valence electrons due to the absence of explicit nodal structures.
Formulation of ECP models in eFF
5.5) where r in (5.4) is the distance between the thes-type pseudo-core and an interacting s-type valence electron, and in (5.5) it corresponds to the distance between the thes-type pseudo-core and the thes-type Gaussian representing one of the lobes of ap-type valence electron (see Figure 5.2). Therefore, the center of the ans-type valence electron is for the spherical Gaussian, while the center of the ap-type valence electron, which is the node, and its offset is determined by s2/√. 2, with the reasonable assumption that the center of the spherical Gaussian is exactly at the tip of the lobe.
Performance of optimized eFF-ECP parameters
- Al and Si with s-s ECP
- C with s-p ECP
- Oxygen with s-p ECP
- Silicon carbide with combined s-s and s-p eFF-ECP
In general, eFF-ECP improves the dependence of C–C and C–H bond lengths on the size of saturated hydrocarbons. The all-electron eFF predicts a large increase in both bond lengths as the hydrocarbon size increases, while eFF-ECP captures the correct trend. Comparison of eFF-ECP and eFF on geometries of carbon-containing molecular and bulk systems.
Conclusions
We arranged the stop domain between the time of impact and the reversal of momentum. An essential one is the semi-empirical design of the core of eFF, i.e. the Pauli potential: it is constructed with only the kinetic energy penalty at antisymmetry, based on the fact that the kinetic energy penalty is the dominant contribution, while the rest is partially accounted for by the parameters set and fitted against a set of molecules[ 1, 2]; however, we later found that the electron-electron Coulomb part contributes non-negligible stabilization of the same-spin electron pairs (the so-called exchange energy), and the nuclear-electron Coulomb part is crucial for unphysical fusion of the same-spin prevent electron. pairs; besides the extra parameterization. Another limitation is the lack of a single FSG representation of each electron, which lacks the cusp state[3] and explicit nodal structures; the former leads to weaker binding energies between nuclei and electrons, e.g. the IP of H is predicted to be only 11.5 eV by eFF (versus the exact value of 13.6 eV), and the latter leads to poor description of systems involving strongly higher angular momentum characters, e.g. multiple bonds (unsaturated hydrocarbons) and lone pairs (water molecule) in compounds of p-block elements.
Exact QM energies of same spin FSG electron pair
To achieve this, we started by reproducing the exact QM energies of the same and opposite spin FSG electron pairs, and then designed symmetric and asymmetric scaling factors to recover the correct QM total energy from direct summation of local energies for systems with more than two electrons. Indeed, the curve with only kinetic energy penalty (6.3) closely resembles the exact one (UHF), and on that basis the eFF parameterization works reasonably well to compensate for the left contributions and approximate the exact curve. In fact, this term plays a crucial role, which is shown more clearly in Figure 6.2, where electron wavefunctions are relaxed, that the n-e Coulomb penalty prevents the unphysical merging of the same spin FSG electrons (associated with sudden collapse in energies), while eFF and only kinetic energy penalty both predict such a violation of Pauli exclusion principle at an H–H distance of 1.6 Bohr.
Symmetric and asymmetric scaling factors for QM ener- gies of multiple pairs of same spin FSG electrons
With (6.9) and (6.10) aiming at fully symmetric cases (with identical overlaps), however, it is expected that for asymmetric transitions, as shown in Figure 6.5, the total energy deviates slightly from the exact values. Therefore, for both the elimination of these small errors and the completeness of framework, asymmetric scale factor functions were designed with the form, . Execution of asymmetric scale factor functions on (a) quartet H3 transition from D3htoC2vand (b) quintet H4transition fromTdtoC3v.
Design of opposite spin Pauli potential
The performance is shown in Figure 6.8 and there is excellent agreement between GHA-QM and B3LYP in the D∞h H3 doublet symmetric stretching curve, but GHA-QM gives a significant overestimation of the D4h singlet H4 case. GHA-QM performance of the asymmetric stretching modes in (a) D∞h doublet H3 and (b) D4h open singlet H4 TS, they result in dissociation into the reference molecule(s) H2 and the H atom. Summing up, the potential of the inverse of the Pauli rotation in the GHA-QM framework is evaluated as EPauli(↑↓) =Fasym(↑↓)Fsym(↑↓)EPaulibase This final equation captures the essence of the correlation and gives an accurate description of the represented FSG. electron pair with opposite spins, as in the H2 molecule, and accommodates the H3 and H4 TS description quite well.
The AMPERE extension
The first case in which we tested the GHA-QM+AMPERE framework is element H, because it is an obvious boundary condition stone. Note that only the equilibrium point of the curve is included in the data set for the AMPERE fit, but the rest of the curve is very well described by GHA-QM+AMPERE, which most likely benefits from the well-designed GHA baseline -QM. Performance comparison of GHA-QM+AMPERE, GHA-QM and eFF on the dissociation curve of the H2 molecule.
Concluding remarks and future work
A hybrid scheme to construct opposite spin Pauli potential
The fitting performance is shown in Figure 6.B1 and the resulting parameters are listed in Table 6.B1. The additional correlation beyond the UHF level was taken into account by the Wigner correlation function[6]. The performance of this hybrid scheme is shown in Figure 6.B2 for both UHF and B3LYP levels of open singlet H2 cases.
Integrals involved in energy evaluation with AMPERE
Continuing with the assumption that the overlap density is uniform, the correlation energy is simply evaluated as Here we do not follow the extension used in Ref. 13)), but use a coordinate system with the origin at R~c and the z-axis along R~cv,. Note that the solid angle part is already integrated by Yl0(θ, φ), and the coordinate system is changed to with the origin at R~c and the z-axis along R~cv.
Numerical implementation of AMPERE (pair eff ecp.h) in LAMMPS
This part of the code is largely based on the FORTRAN code of the error function written by Cody, who uses the algorithm in his 1969 paper [24]. Q(x) and the order of the polynomials P(x) and Q(x) sufficient for an exact fit depend on the target interval. With flexible array content, any combination can be created and tested to find the best AMPERA design.