First principles based multiparadigm modeling of electronic structures and dynamics

Electronic structures and dynamics are the key to linking the material composition and structure to functionality and performance.

An essential issue in developing semiconductor devices for photovoltaics is to design materials with optimal band gaps and relative positioning of band levels. Approximate DFT methods have been justified to predict band gaps from KS/GKS eigenvalues, but the accuracy is decisively dependent on the choice of XC functionals. We show here for CuInSe₂ and CuGaSe₂, the parent compounds of the promising CIGS solar cells, conventional LDA and GGA obtain gaps of 0.0-0.01 and 0.02-0.24 eV (versus experimental values of 1.04 and 1.67 eV), while the historically first global hybrid functional, B3PW91, is surprisingly the best, with band gaps of 1.07 and 1.58 eV. Furthermore, we show that for 27 related binary and ternary semiconductors, B3PW91 predicts gaps with a MAD of only 0.09 eV, which is substantially better than all modern hybrid functionals, including B3LYP (MAD of 0.19 eV) and screened hybrid functional HSE06 (MAD of 0.18 eV).

The laboratory performance of CIGS solar cells (> 20% efficiency) makes them promising candidate photovoltaic devices. However, there remains little understanding of how defects at the CIGS/CdS interface affect the band offsets and interfacial energies, and hence the performance of manufactured devices. To determine these relationships, we use the B3PW91 hybrid functional of DFT with the AEP method that we validate to provide very accurate descriptions of both band gaps and band offsets. This confirms the weak dependence of band offsets on surface orientation observed experimentally. We predict that the CBO of perfect CuInSe₂/CdS interface is large, 0.79 eV, which would dramatically degrade performance. Moreover we show that band gap widening induced by Ga adjusts only the VBO, and we find that Cd impurities do not significantly affect the CBO. Thus we show that Cu vacancies at the interface play the key role in enabling the tunability of CBO. We predict that Na further improves the CBO through electrostatically elevating the valence levels to decrease the CBO, explaining the observed essential role of Na for high performance. Moreover we find that K leads to a dramatic decrease in the CBO to 0.05 eV, much better than Na. We suggest that the efficiency of CIGS devices might be improved substantially by tuning the ratio of Na to K, with the improved phase stability of Na balancing phase instability from K. All these defects reduce interfacial stability slightly, but not significantly.

A number of exotic structures have been formed through high pressure chemistry, but applications have been hindered by difficulties in recovering the high pressure phase to ambient conditions (i.e., one atmosphere and room temperature). Here we use dispersion-corrected DFT (PBE-ulg flavor) to predict that above 60 GPa the most stable form of N₂O (the laughing gas in its molecular form) is a 1D polymer with an all-nitrogen backbone analogous to cis-polyacetylene in which alternate N are bonded (ionic covalent) to O. The analogous trans-polymer is only 0.03-0.10 eV/molecular unit less stable. Upon relaxation to ambient conditions both polymers relax below 14 GPa to the same stable non-planar trans-polymer, accompanied by possible electronic structure transitions. The predicted phonon spectrum and dissociation kinetics validate the stability of this trans-poly-NNO at ambient conditions, which has potential applications as a new type of conducting polymer with all-nitrogen chains and as a high-energy oxidizer for rocket propulsion. This work illustrates in silico materials discovery particularly in the realm of extreme conditions.

Modeling non-adiabatic electron dynamics has been a long-standing challenge for computational chemistry and materials science, and the eFF method presents a cost-efficient alternative. However, due to the deficiency of FSG representation, eFF is limited to low-Z elements with electrons of predominant s-character. To overcome this, we introduce a formal set of ECP extensions that enable accurate description of p-block elements. The extensions consist of a model representing the core electrons with the nucleus as a single pseudo particle represented by FSG, interacting with valence electrons through ECPs. We demonstrate and validate the ECP extensions for complex bonding structures, geometries, and energetics of systems with p-block character (C, O, Al, Si) and apply them to study materials under extreme mechanical loading conditions.

Despite its success, the eFF framework has some limitations, originated from both the design of Pauli potentials and the FSG representation. To overcome these, we develop a new framework of two-level hierarchy that is a more rigorous and accurate successor to the eFF method. The fundamental level, GHA-QM, is based on a new set of Pauli potentials that renders exact QM level of accuracy for any FSG represented electron systems. To achieve this, we start with using exactly derived energy expressions for the same spin electron pair, and fitting a simple functional form, inspired by DFT, against open singlet electron pair curves (H₂ systems). Symmetric and asymmetric scaling factors are then introduced at this level to recover the QM total energies of multiple electron pair systems from the sum of local interactions. To complement the imperfect FSG representation, the AMPERE extension is implemented, and aims at embedding the interactions associated with both the cusp condition and explicit nodal structures. The whole GHA-QM+AMPERE framework is tested on H element, and the preliminary results are promising.

Polaron hopping in olivine phosphates studied by nuclear resonant scattering

Valence fluctuations of Fe²⁺ and Fe³⁺ were studied in a solid solution of Li_xFePO₄ by nuclear resonant forward scattering of synchrotron x rays while the sample was heated in a diamond-anvil pressure cell. The spectra acquired at different temperatures and pressures were analyzed for the frequencies of valence changes using the Blume-Tjon model of a system with a fluctuating Hamil- tonian. These frequencies were analyzed to obtain activation energies and an activation volume for polaron hopping. There was a large suppression of hopping frequency with pressure, giving an anomalously large activation volume. This large, positive value is typical of ion diffusion, which indicates correlated motions of polarons, and Li⁺ ions that alter the dynamics of both.

In a parallel study of Na_xFePO₄, the interplay between sodium ordering and electron mobility was investigated using a combination of synchrotron x-ray diffraction and nuclear resonant scattering. Conventional Mossbauer spectra were collected while the sample was heated in a resistive furnace. An analysis of the temperature evolution of the spectral shapes was used to identify the onset of fast electron hopping and determine the polaron hopping rate. Synchrotron x-ray diffraction measurements were carried out in the same temperature range. Reitveld analysis of the diffraction patterns was used to determine the temperature of sodium redistribution on the lattice. The diffraction analysis also provides new information about the phase stability of the system. The temperature evolution of the iron site occupancies from the Mossbauer measurements, combined with the synchrotron diffraction results give strong evidence for a relationship between the onset of fast electron dynamics and the redistribution of sodium in the lattice.

Measurements of activation barriers for polaron hopping gave fundamental insights about the correlation between electronic carriers and mobile ions. This work established that polaron-ion interactions can alter the local dynamics of electron and ion transport. These types of coupled processes may be common in many materials used for battery electrodes, and new details concerning the influence of polaron-ion interactions on the charge dynamics are relevant to optimizing their electrochemical performance.

Phase behavior of complex superprotonic solid acids

Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb3H(SO4)2-RbHSO4 system, Rb3H(SeO4)2-Cs3H(SeO4)2 solid solution system, and Cs6(H2SO4)3(H1.5PO4)4. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.

Rb3H(SO4)2 is an atypical member of the M3H(XO4)2 class of compounds (M = alkali metal or NH4+ and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb3H(SO4)2-RbHSO4 system have revealed the disproportionation products to be Rb2SO4 and the previously unknown compound Rb5H3(SO4)4. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs5H3(SO4)4 [2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.

The compounds Rb3H(SeO4)2 and Cs3H(SeO4)2, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.

The compound Cs6(H2SO4)3(H1.5PO4)4 is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH2PO4) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H2O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs6(H2SO4)3(H1.5PO4)4 undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.

References

[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.

[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.

[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).