Masters Theses


"The narrowing of donor electron spin resonance spectra with increasing donor concentration ND and increasing temperature T has been observed in semiconductors in the past. One proposed explanation for this phenomenon has been narrowing due to electron motion caused by phonon-induced tunneling (hopping) between donor sites. According to the Anderson narrowing theory, the line width of the narrowed line can be expressed in terms of the average square spread of the non-narrowed spectrum, < H²>ave, and the average frequency of electron motion, ωn. Previous work has been done on narrowing by hopping, but rigorous expressions for ωn or < H²>ave have never been derived. In addition, the past treatment has omitted several important concepts from the problem which have a direct bearing on the theoretical results.

To rigorously examine if the hopping process was producing the spectrum, it was first necessary to derive expressions for ωn and < H²>ave. To find the average hopping frequency, a previous derivation of the transition rate for hopping was averaged over the electron ensemble and the donor and acceptor impurity ensemble with methods derived in the hopping theory for electrical conductivity in a semiconductor containing impurities. These methods had not been applied to narrowing in the past. A major portion of this derivation was the discussion and calculation of the Fermi energy for electrons in donor ground states, ζg, based, in part, on a previous treatment of this quantity. To complete the calculation, analytical and numerical solutions for ωn and ζg were derived. The resulting ωn was found to be a function of ND and T. It was also found to be a function of the compensation K, the ratio of the acceptor concentration to the donor concentration. This K dependence had not been previously predicted, and the ND and T dependences were in disagreement with what earlier treatments had supposed. To calculate < H²>ave, a mathematical distribution function describing the shape of the non-narrowed donor ESR spectrum was deduced and the square of the spread of the spectrum was subsequently averaged over that distribution. This result also disagreed with previous expressions for < H²>ave.

The new narrowing theory was then compared with existing published data. It was found that hopping could not predict the observed ND dependence of the line width and could not predict all of observed T dependence. Thus it was concluded that hopping is not the only mechanism causing narrowing and is, in fact, not the dominant mechanism. Complete rejection of phonon-induced tunneling as a contributing mechanism was not possible, however. This was due partly to the lack of data on the direct K dependence of the line width and partly to the lack of data on the influence of compensation on the temperature dependence of the line width. Thus, an experiment was proposed to obtain the necessary data on the K and T dependences to decide conclusively whether or not hopping contributes to donor ESR spectral narrowing"--Abstract, pages ii-iii.


Hale, Edward Boyd

Committee Member(s)

Higgins, James J.
Parks, William F.



Degree Name

M.S. in Physics


United States. Department of Health, Education, and Welfare
United States. Air Force. Office of Scientific Research
University of Missouri--Rolla. Department of Physics
United States. Air Force. Reserve Officer Training Corps
Phelps County Memorial Hospital


University of Missouri--Rolla

Publication Date



ix, 136 pages

Note about bibliography

Includes bibliographical references (pages 119-120).


© 1973 David Lawrence Meier, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Tunneling (Physics)
Electron paramagnetic resonance

Thesis Number

T 2863

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Electronic OCLC #


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Physics Commons