Nonlinear dielectric response to a point-donor impurity of an electron-gas-model semiconductor that includes the effect of the Dirac-Slater exchange correlation

Abstract

The Thomas-Fermi statistical theory, including the Dirac-Slater local-density treatment of exchange correlation, has been applied to the problem of nonlinear screening of a donor point charge embedded in an electron-gas-model semiconductor. The nonlinear screening equation is solved numerically, giving spatial dielectric functions and screening radii with exchange-correlation strength and ion-charge state as parameters. Illustrations and tabulations of these results are given for five semiconductors, four ion charges, and two nonzero values of the exchange-correlation strength corresponding to the Kohn-Sham and Slater exchange potentials. A variational principle equivalent of the nonlinear equation leads to approximate analytical expressions for the spatial dielectric functions which are in close agreement with the exact results. Variational parameters are given for a subset of the semiconductors and charge states. Dielectric functions of silicon are used to illustrate typical comparisons between the two methods of solution.

Thomas - Fermi-type dielectric screening of statistical atomic models of donor-specific impurities in a semiconductor-like valence electron gas at zero temperature

“…From ( 5), ( 8) and ( 9), the ground-state energy and the bound-electron charge density are determined now in terms of the parameters Z, p and . A parallel calculation of β, E a and α in terms of the screened Coulomb form of ρ e (r) given by (6) shows that β = 4/7, while the only changes in ( 8) and ( 9) are the replacement of the numerical quantities 784b and 28b by 196c and 14c, respectively, where c is an abbreviation for (1/2)(3π/4) 2/3 (3/5) 7/3 (4/3). Not surprisingly, it is found in general (p = 1) that the exponential density distribution leads to atomic energies (screening lengths) that are less negative (smaller) than their screened Coulomb counterparts.…”

“…Clearly, this statement coincides with the definition of V (r) given above in the context of the variational principle. Before proceeding to the TF and TFD theories of dielectric screening of statistical models of donor impurities, it is emphasized that the basic equations for n(r) and V (r) presented here are the same as those used in previous works [6,18] for the point-charge-impurity case of ( 14). The significant new feature here is the dependence of a nonpointlike v Z,p (r) on natural parameters identifying the donor atom or ion.…”

“…Modifications of the TF theory include exchange-correlation in the Dirac-Slater X α approximation [6] and a Weizsäcker-type gradient correction to the kinetic energy functional [7]. In the former case, an exchange-correlation potential of a shallow-donor impurity and the exchange interaction of the donor electron with the valence electrons are used in an effective-mass variational calculation of the binding energy.…”

On-top density in the nonlinear metallic screening and its implication on the exchange-correlation energy functional

“…An atom, especially hydrogen, immersed into the otherwise homogeneous electron gas (EG) has been investigated for more than four decades not only in the density functional theory (DFT), mostly in its local-density approximation (LDA) [1][2][3][4][5][6][7][8][9][10][11][12][13][14] , but also in various forms of many-body theories [15][16][17][18][19][20][21] , including diffusion Monte Carlo (DMC) 22 and variational Monte Carlo (VMC) 23 simulations. The primary motivation of those studies is to construct an appropriate theory for the nonlinear response of metallic electrons to an impurity point charge +Ze, but the basic physical concept with which they were concerned remains the same as that in the linear-response theory, known as Thomas-Fermi (TF) 24,25 (or Debye and Hückel 26 ) screening of the impurity charge with a short screening length λ TF which is about the same as k −1 F , where k F is the Fermi wave number of EG.…”