Suresh Garg

A general theory of an intensity-modulated beam method for determination of diffusion length, diffusion constant, lifetime, surface recombination velocity and absorption coefficient in a semiconductor material

Abstract Using a modulated light (or electron) beam, some efforts, both theoretical and experimental, have been made to determine parameters such as minority carrier lifetime, τ, diffusion constant, D, and surface recombination velocity, S, in a semiconductor material. However, none of these workers considered a general space and frequency dependent response of the system. Moreover, the parameters were not determined independent of each other. Here we give a general theory of such a modulated-light (electron)-beam method. Space and frequency dependent expressions for the amplitude A(x, ω) and phase shift θ(x, ω) of modulated minority carrier concentration and current have been obtained. (These are the two basic quantities which are to be measured in a modulated beam experiment.) We have also obtained frequency dependent expressions for amplitude attenuation coefficient, α(ω) and phase shift per unit distance, ζ(ω). These can be determined experimentally from the slope of the measured space dependent amplitude and phase curves at different frequencies. It is shown that it is useful to construct quantities like 2α(ω)ζ(ω)[=σ2(ω)] and α2(ω)−ζ2(ω)(=k02) which help in directly determining carrier lifetime, diffusion constant and diffusion length, L0. The procedure for determining S and a, the optical absorption coefficient, knowing the measured values of A and θ at a certain distance, has been given. It may be pointed out that the present analysis enables us to determine all 5 parameters mentioned above simultaneously and independent of each other from the measurements in a modulated light beam experiment.

A theory for the simultaneous determination of the minority carrier lifetime, diffusion length and diffusion constant in a semiconducting medium using a modulated light beam

Abstract We report a new method for the simultaneous determination of the minority carrier lifetime, diffusion length and diffusion constant in a semiconducting medium. The method consists of a space-dependent study of the amplitude and phase of the minority carrier density (or current) induced by a sinusoidally modulated photon beam. To illustrate our method, we have solved a one-dimensional time-dependent diffusion equation using a finite Fourier transformation. The procedure is exact and can readily be extended to multidimensional systems.

The existence of equilibrium spectra in fast natural uranium assemblies. The effect of anisotropy in scattering

The calculated results of steady state, space- and angle-dependent fast neutron spectra inside various one dimensional slabs of natural uranium are reported. The effect of anisotropy in scattering on fast neutron spectra has been studied for three different orders of anisotropy, zero, first and third. It is shown that with a high energy, plane source of monoenergetic neutrons, spectral equilibrium is established in natural uranium slabs beyond 90 cm from the source plane, with an associated diffusion length of 19.9 cm. This is consistent with the lower bound for diffusion length in natural uranium. Further, the neutron flux is larger when anisotropy in scattering is included in the calculations.

A method for the determination of the material parameters τ, D, L0, S and a from measured A.C. short-circuit photocurrent

Abstract A procedure is described to determine accurately the material parameters L 0 , D , τ , S and absorption coefficient a which characterize the base region of a solar cell from measured a.c. short-circuit photocurrent (both amplitude and phase) at certain low ( ωτ ωτ >50) frequencies. The method is general in the sense that it is valid for any arbitrary value of back surface recombination velocity S and thickness of the base region X j . Earlier methods consisted in obtaining only one or two material parameters using theoretical expressions for the phase shift under different approximations, in particular, taking S → ∞ and X j / L 0 ⪢ 1. Here, we have only assumed that the back surface of the solar cell is illuminated uniformly with light of short wavelength such that aX j ⪢ 1. In order to clearly bring out the frequency dependence of amplitude and phase at both low and high frequencies, numerical results have been presented for an n + /p junction solar cell. The results have been given for two limiting values of X j and S . The method is equally valid for a p + /n junction solar cell.

Space- and angle-dependent steady-state thermal neutron spectra in finite water assemblies

Neutron spectra in four angular directions at different space points inside 10 cm thick light-water assemblies with transverse dimensions 5*5 cm2 and infinity are reported. It is found that the neutron distribution attains asymptotic conditions within 3 cm even inside the 5*5*10 cm3 water assembly. However, the asymptotic spectrum in the first angular direction is harder than a Maxwellian of moderator temperature even in an infinite slab of thickness 10 cm and further, the hardening increases as the transverse dimension is reduced.

Space- and angle-dependent steady-state thermal-neutron spectra inside small beryllium assemblies. II

Earlier calculations of steady-state space- and angle-dependent thermal-neutron spectra in small beryllium assemblies have been extended to assemblies of much greater transverse dimensions and neutron diffusion has been studied up to much greater distances from the source plane, with a view toward looking for a discrete mode of decay. It is found that in the forward direction, the neutron distribution fails to attain equilibrium inside 140-cm-thick assemblies with transverse dimensions of 150 x 150 cm/sup 2/, whereas in the backward direction, equilibrium is reached even inside an assembly of transverse dimensions of 80 x 80 cm/sup 2/. It is shown that in the forward direction, equilibrium is delayed by the presence of a penetrating beam of uncollided sub-Bragg neutrons of the source. Thus, an experimentalist can hardly hope to observe equilibrium in the forward direction. The calculated value of diffusion length is in excellent agreement with the observed as well as the theoretical values obtained by earlier workers.

A modified source term for use in solar cell theory

A modified source term for solar cells under irradiation is proposed to account for processes other than electron-hole generation.

Frequency distribution function for benzene

The frequency distribution functions of benzene are calculated using the measured value of the specific heat at constant volume (1,2). (AIP)