The electronic and optical properties of the lead sulphide group of semi-conductors

Abstract

Synopsis Fundamental properties Fundamental properties of a semi-conductor which determine its characteristics are width of forbidden energy gap ΔE, and mobilities of positive holes and electrons. It is necessary to know these over a wide range of temperature. Subsidiary properties are life-time of holes and electrons, existence of surface states leading to space charge barriers, properties of donor and acceptor impurities, existence of traps, etc. Methods available for determining ΔE Optical absorption; long-wave limit of photo-conductivity; measurement of Hall-constant and conductivity as a function of temperature; theory of band-structure. All four have given values for this group of semi-conductors. Methods available for determination of mobilities as above. measurement of thermo-electric power, magneto resistance, etc. For these semi-conductors only (iii) has given useful results so far. Optical methods Data given by absorption and photo-conductivity, which agree well, but require identification of long-wave limit with transition across full band. Reasons for thinking identification correct in this case. “Slope” methods The “Hall-slope” method and its limitations. Applicable only when ΔE is a linear function of T and mobility ratio b a constant. Works well for Ge and Si but has given values for PbS, PbSe, PbTe now thought to be much too high. Same difficulty found for InSb, etc. ΔE known from optical data not be a linear function of T and shall see later b may not be a constant. Analysis of Hall-constant and conductivity data using absolute values This method cannot give ΔE without further assumptions — can only give ni, number of intrinsic carriers. Can give useful information on mobility. Methods of analysis and results. Variation of mobility with temperature, T−5/2 law for electrons. T−5/2 law for holes only at low temperatures. Increase of mobility ratio b with temperature. Value of ni. Combination of electrical and optical data to obtain ΔE Variation of ΔE with temperature. Maximum value for PbS, PbSe, PbTe. “Effective-mass” ratio. Consistent with existing theoretical calculation of band structure. Methods of determining life-time Spot light method. photo-electro-magnetic effect. (Dr T. S. Moss will describe). Values for PbS, PbSe, PbTe and variation with carrier density. Photo-conductivity in single crystals and in poly-crystalline layers Photo-conductivity in single crystals appears to be a simple excitation and recombination phenomenon. In layers trapping mechanisms operate. Effect of surface traps. Preservation of carriers from recombination, leading to greater effectiveness. Time constant and life-time.