Electron States of Group-V Donors in Germanium: Variational Calculation Taking into Account the Short-Range Potential
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INTERNATIONAL SYMPOSIUM “NANOPHYSICS AND NANOELECTRONICS”, NIZHNY NOVGOROD, MARCH 10–13, 2020
Electron States of Group-V Donors in Germanium: Variational Calculation Taking into Account the Short-Range Potential A. A. Revina,b, A. M. Mikhaylovaa,b, A. A. Konakova,b,*, and V. N. Shastinb a Lobachevsky
b
State University of Nizhny Novgorod, Nizhny Novgorod, 603950 Russia Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod, 603087 Russia *e-mail: [email protected] Received April 15, 2020; revised April 21, 2020; accepted April 21, 2020
Abstract—The wave functions of low-lying 1s (A1), 2s, 2p0, 2p±, and 3p0 states of P, As, and Sb shallow donor centers in germanium are calculated in the scope of the envelope-function approximation taking into account the short-range impurity potential. The latter is constructed individually for each impurity allowing for the spatial permittivity dispersion and the difference between the ion cores of germanium and the impurity center. The envelope-function equation is solved using the Ritz variational method; herewith, the selected test functions of orbitally nondegenerate s states are characterized by two spatial scales. The first scale, on the order of the donor effective Bohr radius, corresponds to the long-range part of the potential, and the second scale, which is smaller by an order of magnitude, simulates the electron response to the short-range part of the donor potential. The electron density in the donor ground state is shifted to the nucleus, which is due to allowance made for the attracting “central cell” potential. The envelope functions of p states are in turn constructed so that they are orthogonal to envelopes in the ground states for each impurity centers and are different for various donors in contrast with previous works. Keywords: germanium, shallow donors, short-range potential, envelope function approximation DOI: 10.1134/S1063782620090225
1. INTRODUCTION Experimental and theoretical investigation of the electronic properties of Group-V donors in covalent semiconductors (primarily silicon and germanium) was performed as far back as in the 1950s [1, 2]. These objects also cause considerable interest now in connection with their possible application in the field of designing quantum computers [3, 4], coherent THz radiation sources [5, 6], and single-atom transistors [7]. Conventionally, the electronic properties of shallow impurity centers in silicon are more actively investigated for various applications, which is due to its widespread material abundance in nature, the possibilities of its deep chemical and isotopic purification and control of the impurity-center concentration, as well as its orientation to the technological base of electronics. At the same time, weakly doped n-type germanium has a series of advantages. First, the spatial scale of wave functions of the ground state for electrons localized at donors is larger by a factor of ~4 for germanium when compared with silicon [8], which noticeably extends the possibi
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