Quasiclassical description of the nearest-neighbor hopping dc conduction via hydrogen-like donors in intermediately compensated GaAs crystals

Abstract

Expressions for the pre-exponential factor σ 3 and the thermal activation energy ε 3 of hopping electric conductivity of electrons via hydrogen-like donors in n-type gallium arsenide are obtained in the quasiclassical approximation. Crystals with the donor concentration N and the acceptor concentration KN at the intermediate compensation ratio K (approximately from 0.25 to 0.75) are considered. We assume that the donors in the charge states (0) and (+1) and the acceptors in the charge state (−1) form a joint nonstoichiometric simple cubic 'sublattice' within the crystalline matrix. In such sublattice the distance between nearest impurity atoms is R h = [(1 + K)N] −1/3 which is also the length of an electron hop between donors. To take into account orientational disorder of hops we assume that the impurity sublattice randomly and smoothly changes orientation inside a macroscopic sample. Values of σ 3 (N) and ε 3 (N) calculated for the temperature of 2.5 K agree with known experimental data at the insulator side of the insulator-metal phase transition.3 However, in GaAs with high concentration of irradiation-induced defects dc hopping conduction is observed [5] even at a temperature of 100 K.

Thermal ionization energy of hydrogen-like impurities in semiconductor materials

“… Средняя по объему кристаллического образца концентрация доноров в зарядовом состоянии (+1), согласно [28], определяется так: , , / a H -боровский радиус.…”

Drift-diffusion model of hole migration in diamond crystals via states of valence and acceptor bands

“…In this work in the weak electric field limit (e d k T B E  , where d is the mean hop length of electron via localized states) and when the thermal energy is greater than the fluctuation dispersion of energy levels of localized states it is shown that the ratio of the diffusion coefficient to the drift mobility is equal to k T e B . Finally, the values of effective hole or electron concentrations involved in hopping migration via hydrogenlike impurities in crystalline semiconductors are determined in [13,16,17,[28][29][30]. [31][32][33][34] used particular forms of the expressions for N hp and N hn that are only suitable for limiting values of the compensation ratio (K 1  or K 1 1 - ) of the majority impurity by the minority impurity.…”

“…According to [46,57] only the linear approximation of the screening charge density  . Taking into account equations (3) and (7), the radius of static screening of the Coulomb field of the impurity ion by v-band holes and holes of the acceptor band migrating over the crystal is determined by the following expression (see also [26,28,29,46]): = ---( ) according to equations (1) and (6) is the effective concentration of holes hopping via acceptors in the vicinity of the screening ion; p…”

“…parameters p x and h x characterize the deviation of the ratio of the diffusion coefficient to the drift mobility from the classical value k T e B. According to[26,28,29,46] these parameters areLet us note that in writing equations (1)-(21) we assumed that on the insulating side of the Mott transition vband holes and holes of acceptor band coexist in the crystal matrix separately. Consequently, in the derivation of equations(20) and(21)we assumed that the densities of states in the v-band g p and in the acceptor band a  are weakly (compared to the probabilities of filling hole states f p and f…”

“…, where T j is given by equation (35), we obtain the integral activation energy of hopping migration of holes via acceptors, from equation (38) taking into account equations (13), (17), (21), and (23), in the form [28,29] metallic state. One should bear in mind that the compensation ratio K of the majority impurity (boron atoms as acceptors) by the minority impurity (donors) usually decreases with the boron concentration in synthetic p-type diamond crystals.…”