Theory of Electronic States and Transport in Graded Mixed Semiconductors

Abstract

Semiconductors which are slowly graded in composition can be shown to have position-dependent band gaps and position-dependent effective masses, describable in terms of an effective Hamiltonian in an effectivemass equation. The effective Hamiltonian previously obtained is, in the present work, rendered Hermitian. Electronic minority-carrier transport for graded systems is described in terms of an effective field which includes the electrostatic field plus a term in the gradient of the band edge and another in the gradient of the effective mass. The local radiative-recombination lifetime and local density of states for inhomogeneous semiconductors are discussed. The equation for the excess minority-carrier concentration in an inhomogeneous semiconductor is deduced and is found to differ from that in an homogeneous system, by the effective field replacing the electric field, by the position dependences of lifetime and mobility, and by terms in the mobility gradient. Some phenomena specific to graded mixed semiconductors are considered on the basis of the theoretical analysis.

Exact solutions of deformed Schrödinger equation with a class of non-central physical potentials

“…Later on, this formalism has been widely used in different fields of physics such as quantum liquids 2 , 3 H e clusters 3 , quantum wells, wires and dots 4,5 , metal clusters 6 , graded alloys and semiconductor heterostructures [7][8][9][10][11][12][13] , the dependence of energy gap on magnetic field in semiconductor nano-scale quantum rings 14 , the solid state problems with the Dirac equation 15 and others [16][17][18][19][20][21] . Recently, it has been applied to study nuclear collective states within Bohr Hamiltonian with Davidson potential and Kratzer potential [22][23][24] .…”

Valence-band mixing in first-principles envelope-function theory

“…Certain terms are larger than others, however. As shown by Leibler,16,17 to linear order only the BenDaniel-Duke operator 44 T BD = 1 2 pm −1 p and the Gora-Williams operator 22 …”

“…Morrow and Brownstein 20,21 have argued that only exponents satisfying ␣ = ␥ are physically permissible in abrupt heterostructures, which would rule out seemingly reasonable possibilities such as 22 …”

Osciladores quânticos com massa dependente da posição

“…Por exemplo, em 1966, BenDaniel e Duke [11] consideraram α = γ = 0, β = −1. Em 1969, Gora e Williams [12] estudaram o caso α = −1, β = γ = 0. Zhu e Kroemer [13], em 1983, analisaram sistemas com α = γ = − [14].…”