Date of Award
Doctor of Engineering Science in Electrical Engineering
R. E. McMillan
Roy H. Cornely
The purpose of this study is to demonstrate the feasibility of obtaining the electrical conductivity of band gap semiconductors, by considering the absorption of radiation in the visible region. The experimental evidence confirmed predictions that the conductivities of the silicon samples are related to the horizontal displacement of energy in the absorption curves. The material used in this study was p-doped silicon, although the approach should be valid in general for either elemental or compound semiconductors.
The absorption coefficient for silicon was measured in the radiation region between 2.0 and 3.0 ev. This region above the indirect band gap (= 1.1 ev) is where the absorption coefficient is significant (order of 105 cm-1), consequently, a reflectance method was considered most appropriate to measure the absorption. Measurements were made on p-doped silicon wafers differing by four orders of magnitude. The nominal values of the resistivities as determined by four point probe measurements were from 0.005 ohm-cm to 50 ohm-cm.
Maxwell's equations are applied for a plane electromagnetic wave propagating in an absorbing, homogeneous, linear medium. The resulting solutions lead to expressions for the real refractive index, nr, and the extinction coefficient, k. The amount of absorption of radiation in the medium is defined in terms of the absorption coefficient, α, which is directly proportional to k and inversely proportional to the wavelength, λ.
The value for k as a function of wavelength was measured using a non-normal incidence reflectance method in which the pseudo-polar izing angle was measured. A Bausch and Lomb Grating Monochromator and a Tungsten light source was used for the monochromatic source (±1Å at the 50% intensity points). The incident monochromatic light beam was collimated, chopped mechanically by a chopper wheel to produce 3600 HZ, and then reflected from a silicon wafer. The wafer was mounted on a turn-table designed so that the reflected and incident angles were equal to better then five minutes of arc. The reflected light which was elliptically polarized was measured by a photomultiplier assembly. The amplitude of the reflected components in and normal to the plane of incidence was determined by a good grade of polarizer mounted before the photomultiplier entrace slit. Expressions are given which show that only the polarizing angle, θp, and the amplitude ratio of reflected components, are necessary to determine k and nr.
Two theoretical models were assumed in an effort to fit the experimental data. The first attempt was on a semi-classical model in which the charge carriers were considered to be bound elastically with damping to account for dissipation due to collisions. The model, through a proper choice of the damping constants is found to be a reasonable fit to the absorption curve, but only for the region from 2.0 to 2.5 ev.
The quantum mechanical approach was, as expected, by far the better of the two models chosen. The experimental absorption coefficient curve had the same general shape as the ideal quantum mechanical curve, but higher by an order of magnitude. This discrepancy is explained by the presence of a surface oxide layer and the fact that the quantum mechanical curve was based on an ideal semiconductor.
The absorption coefficient is found to vary as the square of the radiation energy in excess of the indirect band gap, for the entire region between 2.0 and 3.0 ev. There was no evidence that the absorption process was due to direct transitions, even for energies near 3.0 ev. Expressions are derived which indicate that the ratio of two low frequency electrical conductivities are dependent on the effective band shrinkage due to doping and the Fermi level shift. The conductivity σ2 can be determined by comparing its absorption curve with that of a known al. This is realized by using the horizontal energy displacement between the two curves, ΔEd, in the derived expression.
Further data taken on clean (etched surfaces) silicon wafers did indicate that direct transitions occurred consistently at 2.48 ev.
Russo, Onofrio Louis, "An investigation of the optical absorption properties of silicon as related to its electrical conductivity" (1975). Dissertations. 1302.