Minority Carrier Lifetime in Iodine-Doped MBEGrown HgCdTe
Theoretical: Recombination Processes in N-Type HgCdTe
Several different recombination mechanisms determine the minority carrier lifetime in n-type
HgCdTe, i.e. Auger, Radiative and Shockley-Read mechanisms which have been discussed
extensively in literature. We have applied these mechanisms to calculate the lifetime for
minority carriers in our samples. Relevant equations which meet the low injection conditions
are outlined briefly here.
For Auger process, recombination occurs directly between bands, which involve two
electrons in the conduction band and a heavy hole in the valence band. It is believed that
Auger-1 process is the dominant Auger recombination mechanism in n-type HgCdTe. It is
based on the direct band-to-band recombination of a conduction band electron with a heavy
hole and the excitation of another electron in the conduction band. The relevant lifetime is
given by,
S1
In the case of radiative mechanism, the recombination occurs between bands too, but the
excess energy is released in the form of a photon. It involves the direct band-to-band
recombination of a conduction band electron with a heavy hole and the emission of a photon.
Absorption coefficient of the material determines the radiative lifetime through the thermal
equilibrium generation rate GR. There are different expressions used by different authors to
calculate the absorption coefficient for theoretically calculating radiative lifetime. The
radiative lifetime is given by:
S2
The defect states within the energy gap due to defects in material create Shockley-Read-Hall
(SRH) centers. In the case of SRH recombination, the minority carriers’ recombination is a
two-step process. The minority carrier is trapped by the SRH center. The captured minority
carrier then recombines with a majority carrier. When electron-hole pairs recombine, energy
is released via phonon emission. The localized trap states may be created by the deep-level
impurities or by radiation and process induced defects such as vacancies, interstitials, antisite
defects and their complexes, and dislocations. The SRH lifetime for a defect level at Et below
the conduction band can be given by a familiar expression:
S3
where τρo = (VppNt)-1 and τηo = (VnnNt)-1 . Vp,n are the thermal velocity and capture cross
section for holes and electrons, and Nt is the SRH center concentration. Also, η1 = Nc exp(Et/κBT) and ρ1 = Nv exp((-Eg + Et)/κBT), where Nc and Nv are the density of states for
conduction and valence bands, respectively. The SRH recombination parameters (Et, Nt, t
and n) are determined by fitting the lifetime data as a function of temperature. This
determines the activation energy, Et, of the SRH center, in case when the capture coefficients
(Vthermal) do not strongly depend on temperature. The SRH model presented in this paper is
for describing the nonradiative recombination process via a single deep-level recombination
center in the forbidden gap. Treatment of nonradiative recombination process via multiplelevel centers in the band gap are discussed in detail in a classical work of Sah and Shockley.
Assuming that all of the above recombination mechanisms operate independently, the total
lifetime τ is determined from:
S4
Figure S1. Photoconductive decay data and exponential fitting for Sample A as representation,
at temp. 77K.