A Model for Estimating Chemical Potentials in Ternary Semiconductor Compounds: the Case of InGaAs

Abstract

In ab initio modeling of doped semiconductors, estimation of defect formation energies involving substitutional sites of ternary compounds is ambiguous due to an approximate treatment of chemical potential of the substituted atoms. We propose a model of assigning fractions of the formation energy to individual atoms of a ternary semiconductor and test it on InGaAs. The accuracy of this approximation is on the order of 0.1 eV/atom and is expected to be sufficient for many practical purposes.

Dopant–dopant interactions in beryllium doped indium gallium arsenide: An ab initio study

“…In Ref. [ 27 ], we introduced a way of computing Ef from only structures and energies of compounds, similarly to what is typically done for defect in monoelemental materials [10][11][12][13][14][15][18][19][20][21][22][23][24][25][26] . This is achieved by assigning a fraction f of formation energy Eform of InGaAs (computed vs bulk In, Ga, As) is assigned to each type of constituent atoms (In, Ga, As) as Eform(InGaAs) = Eform (InGaAs)×( fIn+fGa+fAs) = (E(In)+E(Ga)+2E(As))/4…”

“…43 This gives (6) The residual R = Ac -B is then a measure of the accuracy of this approximation. Based on the eight compounds listed above, the errors in formation energies of all structures (computed from the residual R) are on the order of 0.05 eV/atom 27 and are acceptable for the purpose of this work.…”

“…In Ref. [ 27 ] we showed that the errors in formation energies are not very sensitive to the exact composition of the set of structures used to fit E(In), E(Ga), and E(As); for example, a fit using only four reference structures (InGaAs, In3Ga, GaAs, and InAs) resulted in errors in the formation energy of about 0.04 eV (mean absolute error) of the eight structures and values of E(In), E(Ga), and E(As) different by less than 0.05 eV from those listed above (Eq. ( 6)).…”

“…( 6)). 27 This essentially one-body approximation, which does not carry structural (or atomic coordination) information, is nonetheless useful for the specific purpose of this work, i.e. assigning fractions of the formation energy of a ternary compound to its constituent atoms.…”

“…One novelty proposed here is the use of a model we have previously introduced in Ref. [ 27 ] that allows considering Be-doped InGaAs as a closed system and uniquely define formation energies without recourse to chemical potentials. This allows us to compute fully ab initio and compare different types of defects (substitutional, interstitial, and their combinations).…”