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Title: Negative and oscillatory magnetoresistance in lead sulphide
Author: Mathewson, Alastair G.
Awarding Body: University of Aberdeen
Current Institution: University of Aberdeen
Date of Award: 1967
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In the first two chapters we introduce the concept of constant energy surfaces in semiconductors and show how the conduction electrons behave in electric and magnetic fields. We summarize the low field galvanomagnetic theory but detail the work of Toyozawa in his explanation of negative magnetoresistance. The third chapter deals with the experimental details involved in the selection of the PbS samples and the electrical measuring apparatus. The fourth chapter presents the experimental results obtained. From these results we conclude that the negative magnetoresistance in n-type PbS observed at temperatures below 30K is due to an interaction between the conduction electrons and a number of localized magnetic moments isolated at impurity sites. The origin of this localized magnetic moment was discussed and also a quantitative explanation of the concentration dependence of the negative magnetoresistance was given. The true saturating negative magnetoresistance component was separated from the observed and the concentration dependence of this saturating com- ponent was obtained and found to vary as n-0.75. The literature pertaining to negative magnetoresistance in semiconductors was reviewed and other effects giving rise to negative magnetoresistance were discussed. The second section of this thesis deals with quantum effects in semiconductors. The fifth chapter deals with the theory of these effects and in particular details the theory of the Shubnikov-de Haas Effect as developed by Argyres. Expressions are obtained for the number of conduction electrons per valley as a function of the period of the Shubnikov-de Haas magnetoresistance oscillations. With a knowledge of the total carrier concentration obtained from Hall Effect measurements we show how to arrive at the appropriate multi-valley model. The remainder of the chapter describes the cryostat, crystal holders, superconducting magnet and the electrical measuring apparatus. In the sixth chapter we describe a check on the working of the apparatus using a bismuth sample. The results for thirteen samples of n-type PbS are presented and from one sample with a large amplitude of oscillation a value of 4.5K for the non- thermal broadening temperature T' was obtained. The theoretical calculations and other experimental results of the band structure of PbS were reviewed. The experimental results appeared to conflict in that measurements on low concentration samples yielded either a (100) model or a nearly spherical surface at k = 0, whereas the results obtained from high concentration crystals indicated that a (111) zone boundary model was appropriate. From our results we concluded that the number of electrons per valley we obtained from the oscillatory period was in excess of that required to fill eight ellipsoids at (111) zone boundaries. This indicated that there was more than one section of the Fermi surface although only one oscillatory period had been observed. On the basis of these results we proposed the following two interpretations:- (a) The observed oscillatory period is due to carriers in (ill) valleys at the zone boundary and there exists elsewhere a second band to hold the excess electrons and whose cross section was not observed. (b) The observed single period is due to a spherical surface at k = 0 whose cross seotion is equivalent to an nv of between xi n and in addition there are several nearly spherical ellipsoids whose cross seotion were again not observed.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available