10. Appendix

Cyclotron Resonance and Structure of Conduction and Valence Band Edges 563
Cyclotron Resonance and Structure of Conduction
and Valence Band Edges in Silicon and Germanium
Charles Kittel
University of California, Berkeley, USA
A prime objective of the Berkeley solid-state physics group (consisting of
Arthur Kip and myself) from 1951 to 1953 was to observe and understand cyclotron
resonance in semiconductors. The practical problems were to gain reliable
access to liquid helium, and to obtain an adequate magnet and sufficiently
pure crystals of Ge and Si. The liquid helium was obtained from the Shell Laboratories
and later from the Giauque laboratory on campus. The magnet was
part of a very early cyclotron (from what one may call the Ernest O. Lawrence
collection), and the dc current for the magnet came from recycled US Navy
submarine batteries. The semiconductor crystals were supplied by the Sylvania
and Westinghouse Research Laboratories, and later by the Bell Telephone
Laboratories. I think the microwave gear came from war surplus at MIT Radiation
Laboratory. Evidently, very little of the equipment was purchased.
The original experiments were on Ge [1], both n-type and p-type. There
were too few carriers from thermal ionization at 4 K to give detectable signals,
but the carriers that were present were accelerated by the microwave electric
field in the cavity up to energies sufficient to produce an avalanche of carriers
by impact ionization. This was true cyclotron resonance! A good question is,
why not work at liquid hydrogen temperature, where the thermal ionization
would be adequate? Hydrogen was then, and perhaps is still now, considered
to be too hazardous (explosive) to handle in a building occupied by students.
A better question is, why not work at liquid nitrogen temperature, where
there are lots of carriers and the carrier mobilities are known to be much
higher than at the lower temperatures? Cyclotron resonance at liquid nitrogen
temperature had been tried at several other laboratories without success. The
reason for the failures is that the plasma frequencies, being mixed with the
cyclotron frequencies to produce a magnetoplasma frequency, are too high at
the higher carrier concentrations – you are not measuring a cyclotron resonance
but instead a magnetoplasma resonance [2]. Indeed, one can follow the
plasma displacement of the original cyclotron lines when the cavity is allowed
to warm up. In radio wave propagation in the ionosphere this effect is called
magneto-ionic reflection, a subject I had learnt from the lectures of E.V. Appleton
at Cambridge.
A better way to produce carriers at 4 K was suggested by the MIT group.
They irradiated the crystal with weak light sufficient to excite both electrons
and holes. With this method both electrons and holes could be excited in the
same crystal. Alternatively, one can excite a known carrier type by infrared