Photoconductivity in Lead Selenide: Theory of the Dependence of Sensitivity on Film Thickness and Absorption Coefficients

Recently developed theoretical expressions for the responsivity Rₛ and noise of photoconductive films are examined. Assuming that the time constant is independent of film thickness we express Rₛ and signal/noise (S/N) in terms of the absorption coefficient α and thickness d. Using a curve of α vs λ for lead selenide obtained by Avery from crystal measurements, we calculate Rₛ vs λ for films of different thicknesses. These curves indicate that the photoconductive knee should lie near 5{μ} for PbSe films of all thicknesses. Experimentally, however, the position of the knee is observed to be a function of film thickness, being near 3.3{μ} in thin films and 5{μ} in thick films.It is then shown from the theory that in very thin films the responsivity is a direct measure of α. Accordingly the wavelength dependence of α is calculated from responsivity data for thin films; the magnitude is determined from the crystal absorption data at 5{μ}. Curves of responsivity vs λ for various film thicknesses are computed, using the α vs λ curve derived from responsivity data on thin films. These curves agree with the observed responsivity data; they show the shift of the knee from 3.3 to 5{μ} with increased film thickness, and show that no increase in responsivity can be obtained at any wavelength by increasing the film thickness.The dependence of signal/noise on λ and d is calculated, using the same α vs λ curve, and found to be in qualitative agreement with experiment. The curves show that for any given wavelength the signal/noise is a maximum at a certain value of film thickness. The maximum occurs at greater thicknesses for longer wavelengths. The dependence of S/N on d and α is given for any material fitting the same general photoconductive model. The same conclusion, that there is an optimum thickness for any particular absorption coefficient, holds in this general case.Finally, the derived α vs λ curve is shown to be consistent with recent theories of indirect optical transitions.