Density of Electron States in Thin Bi Films

Abstract

The energy spectrum of charge carriers in thin films differs from that in bulk specimens. This distinction shows itself in the quantum size effects. F o r the first time quantum size effects were found in thin B i films /l/.The authors of /1/ observed oscillations of the kinetic coefficients in dependence on the film thickness. These oscillations were due to sharp changes in the density of states when the energy of quantized levels was equal to the Fermi energy of charge carriers.It is well-known that the density of states is governed by the dispersion relation. For example, in the case of an ellipsoidal non-parabolic spectrum /2/ the density of electron states (per unit surface) in Bi films has the following form /3/:Here axis 1 is directed along the binary axis, axis 2 along the elongation of the constant energy surface, axis 3 along the trigonal axis (we neglected the tilt angle 'p%6 of the axis 3 t o the trigonal axis), g, = 2 is the spin degeneracy, gv = 3 is the valley degeneracy, n = 1, 2 . . . is the size 0 quantdm number, a = 1/E (E is the band g g m, side function, d is the film thickness, and EnWe must note that formula (1) is correct for the case when theJfilm a plane is normal to the trigonal axis. In the present note we restrict ourselves to this case only for simplicity.As it is seen from (1) the density of states is a step-like function of energy.The expression of N(E) for an ellipsoidal parabolic spectrum may be 1) prospekt Narimanova, 370143 Baku, USSR.

The Influence of the Size Quantization on the Cyclotron Effective Mass and the Density of States in Bi Films

“…The expression (21) coincides with that obtained in [4]. However, we must remember that when condition (5) is fulfilled the edge of the n-th subband is not at En but at E F .…”

“…However, we must remember that when condition (5) is fulfilled the edge of the n-th subband is not at En but at E F . This fact was overlooked by the authors of [4]. Consequently the expression for g,(E) obtained in the above paper is correct only for E > En.…”

“…Recently, Mustafaev and Shakhtakhtinskii [4] have also considered the problem of the density of states in Bi films with n 11 C , in the framework of the NENP model. However, they have primarily considered the energy dependence of g,.…”