Comparison between optical and electrophysical data on free electron concentration in tellurium doped n-GaAs

Abstract

A theoretical model has been developed for determining free electron concentration in n-GaAs from characteristic points in the far infrared region of reflection spectra. We show that when determining free electron concentration one should take into account the pasmon–phonon coupling, otherwise free electron concentration will be overestimated. We have calculated electron concentration Nopt as a function of characteristic wave number ν+ which is described by a second order polynomial. Twenty-five tellurium doped gallium arsenide specimens have been tested for electron concentration using two methods, i.e., the conventional four-probe method (Van der Pau) and the optical method developed by us (the measurements have been carried out at room temperature). We have used the experimental results to plot the dependence of electron concentration based on the Hall data (NHall) on electron concentration based on the optical data (Nopt). This dependence is described by a linear function. We show that the data of optical and electrophysical measurements agree if the electron concentration is Neq = 1.07 · 1018 cm-3. At lower Hall electron concentrations, NHall < Nopt, whereas at higher ones, NHall > Nopt. We have suggested a qualitative model describing these results. We assume that tellurium atoms associate into complexes with arsenic vacancies thus reducing the concentration of electrons. The concentration of arsenic vacancies is lower on the crystal surface, hence the Nopt > NHall condition should be met. With an increase in doping level, more and more tellurium atoms remain electrically active, so the bulk concentration of electrons starts to prevail over the surface one. However with further increase in doping level the NHall/Nopt ratio starts to decrease again and tends to unity. This seems to originate from the fact that the decomposition intensity of the tellurium atom + arsenic vacancy complexes decreases with an increase in doping level.

Comparison between results of optical and electrical measurements of free electron concentration in n-InAs specimens

“…As noted above the result was different for n-GaAs: N Hall could be lower or higher than N opt . The concentrations measured by the two methods were equal at N eq = 1.07 • 10 18 cm -3 [1]. For the low-doped material this ratio was < 1 but with an increase in the tellurium concentration the relation became > 1.…”

“…We show that the plasmon-phonon coupling being disregarded, N opt proves to be overestimated but this difference near the edge of the Tensor-27 Fourier spectrometer operation range is within 10% and decreases further with an increase in n. Note that the respective differences are 20% for n-GaAs [1] and 30% for n-InSb [22]. Since the absolute random error of n + is only controlled by spectral instrument resolution and is within ±2 cm -1 , the relative random error of N opt is within ±0.6 %.…”

“…More detailed information on N opt determination from the reflection spectrum was reported earlier for n-GaAs [1] and for n-InSb [22]. When plotting the N opt = f 2 (n) calibration curve for n-InAs the non-parabolic shape of the conduction band of InAs was taken into account.…”

“…By analogy with the cited work [1] in which tellurium-doped gallium arsenide specimens were studied we present below the optical and electrical measurement data for sulfur-and tin-doped n-InAs specimens.…”

“…For this reason data obtained with these methods may differ. It was shown [1] that the free electron concentrations in n-GaAs calculated on the basis of Hall effect (N Hall ) may be either lower or higher than those determined from far IR reflection spectra (N opt ).…”