Equilibrium point defect and charge carrier concentrations in a material determined through calculation of the self-consistent Fermi energy

Abstract

Classification: 16.1 Structure and properties, 23 Statistical Physics and Thermodynamics Nature of problem: To determine the self-consistent Fermi energy and equilibrium defect and carrier concentrations given a set of point defect formation energies in a crystalline system, assuming the constraint of charge neutrality. Solution method: The concentrations of each defect in each charge state are calculated, as are the free carrier concentrations. These concentrations are functions of the Fermi energy. The code, using an interative search algorithm, determines the Fermi energy that satisfies the charge neutrality constraint (the self-consistent Fermi energy). The defect and carrier concentrations at that Fermi energy are then reported, as well as the Fermi energy itself. Restrictions: Thermodynamic equilibrium is assumed. The defect formation enthalpies and electronic density of states of the pristine system must be known. Additional comments: The concentrations of defects can be fixed to a particular value, thus modelling 'frozen-in' defects formed by e.g. kinetic processes. This procedure is facilitated by the related program, FROZEN-SC-FERMI, which is identical to SC-FERMI apart from the additional defect concentration fixing routine. Running time: Less than one second.

Native Defects and Their Doping Response in the Lithium Solid Electrolyte Li7La3Zr2O12

“…1, 2, 4, 5, and 6 are available under the MIT licence. 71 Our analysis codes use the matplotlib, 72 numpy, 73 pandas, 74 pymatgen, 75 scipy, 76 tqdm, 77 and vasppy 78 Python packages, and SC-Fermi and Frozen SC-Fermi 45,46 for calculating self-consistent defect concentrations.…”

“…1 or 2, but instead by a set of equations that describe the defect populations, to be solved self-consistently under the constraint of thermodynamic equilibrium. 40,[44][45][46] To better understand the native defect chemistry and doping response of lithium-garnet solid-electrolytes, we have performed a computational study of a broad range of defects in the prototypical system LLZO. We have used hybrid density functional theory (DFT) to calculate formation energies for a range of intrinsic defects, including lithium and oxygen vacancies and interstitials, lanthanum and zirconium vacancies, and cation anti-sites.…”

Upper limit to the photovoltaic efficiency of imperfect crystals from first principles

“…Thus we calculate the equilibrium concentrations of defects and carriers, and the Fermi level self-consistently under the constraint of charge neutrality condition for overall system of defects and charge carriers using SC-FERMI. 31 For a given Fermi level, the equilibrium concentration of a defect N(D q ) is given by…”

Intrinsic point defects and the n - and p -type dopability of the narrow gap semiconductors GaSb and InSb

“…84 We calculate the E f [X] at two extremes: Sb rich, where ∆µ Sb = 0 eV, corresponding to an excess of Sb in the growth environment and absence of pure In, and Sb poor, the opposite extreme, where ∆µ Sb = ∆H[MSb]. From the calculated defect formation energies and DOS, we used the code SC-FERMI [85][86][87][88] to determine the equilibrium carrier and defect concentrations. SC-FERMI employs Fermi-Dirac statistics to calculate the concentrations, which are functions of E F .…”