On the Concentration Dependence of the Thermal Impurity‐to‐Band Activation Energies in Semiconductors

Abstract

It is proved by Hall effect measurements on Te-doped GaP and on ZnSiP, that the thermal activation energies of the majority impurities depend on the minority impurity concentrations. A new theoretical explanation for this concentration dependence is presented.Mittels Halleffektmessungen an Te-dotiertem GaP und an ZnSiP, wird gezeigt, daB die thermischen Aktivierungsenergien der Majoritiitsstorstellen von der Konzentration der Minoritiitsstorstellen abhangen. Fur diese Konzentrationsabhiingigkeit wird cine neue theoretische E r k k u n g gegeben.It is well known that in doped and compensated semiconductors three types of conductivity mechanisms with different activation energies c3 < E~ < c1 can be found, in general (see e.g . [l]).To be specific we shall concentrate on a n n-type semiconductor in the following. I n this case c3 corresponds to the phonon-assisted hopping motion of electrons from neutral donors t o empty positive donors, the energy spread of the donor levels being caused by the fluctuating electric field of the charged impurities. This hopping motion is well understood on the basis of the theory of Miller and Abrahams The activation energy c1 is connected with the energy ED, necessary to excite an electron from a donor into the conduction band, and deviates from ED slightly due to the fact, that the temperature dependence of the mobility deviates from p -T P 3 l 2[5]. The energy E, or E D is of principle interest in semiconductor physics and technology. However, it is understood much less both theoretically and experimentally than cZ and E~: not only its absolute value for different impurities cannot be calculated theoretically in satisfying agreement with experimental results, but also its large concentration dependence (if measured as a thermal activation energy e.g. by Hall experiments) is not well established even experimentally as explained below.I n this paper we want to contribute both experimental results and a new theoretical explanation for the concentration dependence of E D of shallow impurities.The phenomenon of the concentration dependence of the thermal activation energy of impurity electrons into the nearest host energy band is known for more than

Hole Scattering in GaSb: Scattering on Space Charge Regions Versus Dipole Scattering

“…This is about 1.4 and 1.7 times larger respectively than the results of two model predictions f (K) = 2.6533K 1/3 [11] and f (K) = 2.1828K 1/3 [12], respectively. Our results therefore indicate a stronger decrease in the thermal ionization energy with increasing acceptor concentration than predicted by simple electrostatic interaction models.…”

“…Besides our results, some data culled from [13][14][15][16] are also included. The data displayed exhibit the f (K) ∼ K 1/3 like dependence, as implied by the models based on electrostatic interaction [10][11][12]. An envelope fit to [5], up full triangledata of [13], full circle -data of [14], diamond -data of [15], down full trianglesdata of [16].…”

“…deduced from the experiments are plotted in a function of the compensation degree K with E A0 = 34.5 meV and ε r = 15.7 [1][2][3] alongside with the relevant theoretical relationships [10,12]. Besides our results, some data culled from [13][14][15][16] are also included.…”

“…An envelope fit to [5], up full triangledata of [13], full circle -data of [14], diamond -data of [15], down full trianglesdata of [16]. Theoretical curves: full line -fit of electrostatic interaction model to our data, dash-dot line -model of [11], dash line -model of [12].…”

<title>Thermal ionization energy of Mg acceptors in GaN: effects of doping level and compensation</title>

“…It is proposed that these differences can be satisfactorily described using a simple electrostatic interaction model originally due to Pearson and BardeenI 0 and Debye and Conwell, I I and later discussed and generalized by Monecke et al, 12 and by the present author. 13-15…”