This paper presents a calculation of the lifetimes (τ) of excess electrons and holes in a semiconductor aaanming the Auger effect between bands (electron-electron and hole-hole collisions) to be the only recombination mechanism. If pair annihilation, and the corresponding reverse process of pair creation, are counted separately, there are four classes of processes to be considered. The suitably weighted algebraic sum of the rates of these processes yields a net recombination rate R . If N be the non-equilibrium number of pairs, then τ = N/R . In the calculation the effect of traps is neglected, and the group of electrons in the conduction band and the group in the valence band are each assumed to be in equilibrium among themselves, but not with each other, by the use of quasi-Fermi levels. Bloch functions ψk = u(k, r) exp (ik.r) are used. The matrix element of the Coulomb interaction is obtained as a multiple sum over reciprocal lattice vectors. Most of these terms correspond to Umklapp-type processes whose probability of occurrence is shown to be small. The dominant term, after integration over all initial and final states, yields the dependence of lifetime on temperature, carrier concentration, energy gap and other parameters. The absolute value of the lifetime depends also on an overlap intergral of the form S u *(k, r) u(k', r) dr where k, k' are in different bands. This integral is estimated on the basis of a one-dimensional model. The theory is compared with experimental lifetimes in InSb, and shows that the mechanism envisaged may dominate radiative recombination above 240 °K and accounts for the order of magnitude of the observed lifetimes (~ 10 -8 s) in the neighbourhood of the highest temperature (330 °K) at which recombination in InSb has so far been studied.
Theoretical calculations of Auger transition rates are complicated by the interconnection of energy and momentum conservation. The use of a flat valence band where the heavy holes have infinite mass decouples energy and momentum conservation and greatly simplifies the calculation. This flat valence band model has been used to obtain a simple analytic approximation for Auger transition rates. It requires just two parameters to cover a wide range of temperature and carrier Fermi levels (both degenerate and nondegenerate) and their values may be found either by comparison with an accurate calculation or from Auger lifetimes determined experimentally. The results have been applied to InSb and Cd0.2188Hg0.7812Te where good agreement with accurate theoretical values using realistic band structures has been attained. The same model has also been used to provide a simple analytic approximation for impact ionization probability rates, again agreeing well with accurately determined values. Such approximations will prove to be useful in modeling semiconductor transport effects and devices.
The transition rates for an Auger collision process in semiconductors which involves the light hole band is calculated using a quantum mechanical perturbation method. Spherical energy surfaces are assumed although non parabolic energy bands are allowed for. The temperature dependence of the lifetime of excess carriers due to this process is investigated and the results applied to InSb and InAs in the temperature rango 200 to 600 OK. The shape of the temperature dependence of this theoretical lifetime for InSb agrees well with experiment a t room temperature and above, and when estimates of overlap parameters which occur in the theory are made the absolute magnitude of the lifetime also agrees with experiment. The probability per unit time that a light hole created by a photon of energy h Y will take part in an impact ionizing transition is also given aa a function of h v. It is concluded that the transition rate for this p r o w is at least comparable to that of the more usual Auger transitions involving the heavy hole and conduction bands only.Die ttbergangsraten fur einen AugerkollisionsprozcB in Halblcitern werden unter Einbeziehung der Energiebander leichter Lijcher mit einer quantenmechanischen Stijrungsrechnung berechnet. Es werden spharische Energieflachen angenommen, obwohl auch nichtparabolische Energiebander erlaubt sind. Die Temperaturabhangigkeit der h b e n sdauer der durch diesen ProzeB erzcugten iiberschussigen Ladungstriger wird untersucht und die Ergebnigse werden anf InSb und InAs im Temperaturbereich 200 bis 500 OK angewendet. Die Temperaturabhiingigkeit dieser theoretischcn Lebensdaucr stimmt fur InSb bei Zimmertemperatur und daruber gut mit dern Expcriment uberein. Wenn die Vberleppungsparameter der benutzten Theorie abgeschiitzt werden, stimmt die absolute GroBe der Lebensdauer ebenfalls rnit dem Experiment uberein. Die Wahrscheinlichkeit pro Zeiteinheit, da6 ein leichtes Loch, durch cin Photon dcr Energie h v erzeugt, an einem StoRionisationsBbergang teilnimmt, wird als Funktion von h v gegeben. Es wird geschlossen, daB dio Ubergangsrate fur dieaen ProzeB mindestens verglcichbar ist mit dem gebrauchlicheren Augeriibergang, an dem nur das Band der schweren Locher und das Leitungsband beteiligt sind.
A direct measurement of carrier recombination, far from equilibrium, in Hg0.795Cd0.205Te (Nd−Na=3.3×1014 cm−3) has been made on a picosecond time scale with a pump–probe technique using a free-electron laser. Over the range of carrier densities (5×1016–3×1017 cm−3) and at the temperatures (50–300 K) studied experimentally, contributions to the recombination from Auger, Shockley–Read–Hall, and radiative mechanisms were calculated using an analytic approximation, with carrier degeneracy included, Auger-1 (CCCH) recombination rates were calculated, which also gave the Auger-7 (CHHL) rates via a simple relationship. Excellent agreement was obtained, with Auger-1 dominant at all temperatures and, significantly, for T>225 K when the sample is intrinsic, the Auger-7 contribution was found to be important.
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