The numerical simulation of infrared reflection and transmission spectra for ununifomly doped semiconductor structures (P and As in Si and Zn in GaAs) was performed. The radiation interaction with free electrons as well as phonons was taken into account. The possibility of determination ofthe carrier effective mass m* and relaxation time 'C concentration dependencies from the spectrophotometrical measurements was established.
THEORYThe problem of the dispersion dependencies calculation of the infrared radiation reflection R(X) and transmission coefficients T() in ununiformly doped semiconductor structures (the direct problem) was earlier considered in 12 and was later developed in for the reconstruction of the concentration profiles (the reverse problem). This method is nondestructive, non-contacted, sufficiently operative and thus is extremely perspective for the use in modem micro-and optoelectronics technology.The idea of this method consists in the iteration fitting of R(2), T(X) spectra, calculated on the basis of Drude-Lorentz theory and obtained from the solution of non-linear diffusion equation provided the impurity redistribution under high-temperature treatment, to experimental data. This iteration procedure is run by means of parameters variation which assign the concentration dependency of impurity diffusivities.
RESULTSThe concentration dependency of m* and -r was studied in 6,7 for Si and InSb with electron conductivity. We are discussed own results for Zn doped GaAs (hole conductivity).Typical results are presented in Fig. 1 . The intersection point of R(X), T(?) curves is corresponded to the certain wave length ? (govemed by m* and 'r values) at the vicinity of the plasma resonance frequency a,, which designs the effective mass of carrier charge (D = [C(z)e2/s Co m*]h'2. Here C(z) is impurity concentration profile, e is electron charge, c, and s are dielectric constants ofthe substrate material and vacuum respectively. RA), T() curves in Fig. 1 are calculated for certain surface impurity concentration C2x1O1 cm2 and for different impurity diffusivities corresponding to the different treatment temperatures that designs the different impurity concentration profiles C(z) from the solution ofthe non-linear diffusion equation. The same results are obtained for Si.The main distinctive feature of proposed method for the determination of the concentration dependency of m* and t from one described in 6,7 is in more accurate determination of the impurity concentration profile C(z) and thus in more real determination ofm*[C] and 'r[C] dependencies. SPIE Vol. 3687 • 0277-786X/99/$1O.OO 125 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/23/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx