Properties of semiconductors at low temperatures

Consideration has been made of bulk differential negative resistance as a low temperature property of semiconductors. The following topics have been investigated:
criteria for the existence of a differential negative resistance;
the application of irreversible thermodynamics to spontaneous instability;
double carrier injection as a cause of negative resistance in bulk material;
impact ionisation as a cause of negative resistance of the current controlled type;
methods of procuring a voltage controlled negative resistance, together with the properties of subsequent travelling domains;
thermally induced negative resistance.
General criteria for bulk differential negative resistance have been deduced; differentiation is made between current controlled and voltage controlled types. the occurrence of instability against filament and domain formation is investigated (1); domains and filaments are shown to be symptoms of negative resistance rather than causes.
The application of irreversible thermodynamics to non-linear process and in particular to negative resistance has been examined. It has been shown that maximum (2) and minimum (3) entropy production principles as presently employed are not valid for non-linear processes. An alteration which corrects this has been made and justified from statistical mechanics. While the new stationary entropy production principle provides no solution to the domain of filament situation to first order, it is shown that it does determine the solution to the second order. A physical justification has been suggested in terms of the conservation laws.
As a first example of bulk negative resistance, double carrier injection (4) has been studied. As the current flow in a diode is increased, the injected carriers penetrate further into the crystal; if the crystal contains minority carrier traps, it has been noted that a trap saturation front can be pushed through the crystal as the current is raised. Since the carrier density for the two carrier flow in higher, negative resistance may be developed in the maturation front region. In a short specimen this may dominate the characteristic over a small range. The two carrier equations have been written in a way which is particularly suitable for computation; in this way parameters for the recombination functions have been found which lead to a bulk negative resistance. experimentally this negative resistance has been observed in overcompensated zinc-doped germanium; it has been studied as a function of specimen length, probe position, composition, temperature and magnetic field. Examination of the Hall effect for double injection has been found to demand a special interpretation, due to carrier stagnation at a blocking electrode, resulting in Hall voltage inversion.
A study of impact ionization as a cause of a current controlled negative resistance has been made. From the application of criteria from section (a), it has been found that present explanations (5), (6) are rather unsatisfactory. The analysis is confined to an examination of what conditions can and what conditions cannot give rise to a negative resistance, employing an ionization rate equation. A distinction is made between spacially localized negative resistance processes loading to filament formation and non-localizes ones.
Two methods of obtaining a voltage controlled bulk negative resistance have been treated in the literature, a bond structure effect (7) and a carrier energy dependant capture cross-section (8); a third method has been considered, a carrier energy dependant scattering rate loading to distortion of distribution function, treated in outline for a number of physical processes. it is shown that for all these processes, the existence of space-charge leads to the phenomenon of travelling domains, observed as the Cunn Effect (9). Consideration has been made of the carrier flow equations; it has been found that the discrete domain solution of P. N. Butcher (10) is a limiting case of a set of continuos waveform solutions, all of higher frequency. Thus the suppression of the discrete domains would lead to higher frequency operation.
Thermal heating has been considered as a cause of negative resistance, for hot filaments and domains in an otherwise isothermal lattice, and also for specimen heating due to film boiling at the boundaries (11). Experimental results for which the above analysis was undertaken are explained under this heading.