On the modification of the generalized Einstein relation for a semiconductor superlattice

Abstract

It is well-known that the Einstein relation for the diffusivity-mobility ratio of the carriers in semiconductors i s too frequently used in calculations on semiconductor devices and in computing diffusivity from the knowledge of mobility and vice-versa. That this relation should be modified under conditions of degeneracy was also shown for the first time by Landsberg (1) who derived a generalized form of the Einstein relation. In recent years, it has further been shown that the generalized relation takes different forms in degenerate semiconductors under the influence of magnetic quantization (2, 3) and in the presence of band tails at low temperatures (4). These contributions have created the interest for examining the validity of the generalized Einstein relation for a semiconductor superlattice in which alternate layers of two different degenerate materials (either n-or p-type) set up a periodic potential with aperiodicity many times the crystal lattice dimensions. Incidentally, it may be mentioned that the formation of a superlattice appeared (5 to 7) experimentally feasible with controlled parameters. In the present communication, an attempt is made for the first time to derive an expression for the diffusivitymobility ratio of the carriers in a semiconductor superlattice and to compare it with the generalized Einstein relation.According to the principle of detailed balance, the diffusivity-mobility ratio of the carriers in semiconductors can be expressed (8) a s where e i s the charge, n the carrier concentration, and E the Fermi energy.Thus it appears that for determining the D/JL ratio for a semiconductor superlattice, we are to determine first of all an expression for the carrier concentration in such 0 F

A simple theoretical analysis of the Einstein relation for the DMR (diffusivity-mobility ratio) in Nono compounds on the basis of k.p formalism

“…Using the equations (16) and (12) I get the same equation (15). For quantum wires and heterostructures with small charge densities, the relation between μ / D and G is again given by the equation (15).…”

“…For quantum wires and heterostructures with small charge densities, the relation between μ / D and G is again given by the equation (15). The equation (15) is also valid in the presence of quantizing magnetic field and also under cross-field configuration.…”

“…The suggestion for the experimental determination of the DMR for degenerate materials having arbitrary dispersion laws as given by equation (15) does not contain any band parameters. For a constant temperature, the DMR varies inversely as G .…”

“…Landsberg first pointed out that the Einstein relation for electronic materials having degenerate electron concentration is essentially determined by their energy band structures [4]. The nature of the variations of the DMR under different physical conditions has been studied in the literature [5][6][7][8][9][10][11][12][13][14][15][16][17][18] and some of the important features, which have appeard from these studies, are:…”