Hot-Electron Transport in Semiconductors
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The time-of-flight (ToF) technique has emerged over the last few years as the most reliable method of measuring drift velocity and longitudinal diffusion coefficient of hot carriers in semiconductors. In this respect it is worth noting that the results obtained with this technique have been supported by an accurate theoretical analysis so that, besides improving our knowledge on the transport coefficients of different materials, they can offer a good standard to validate alternative methods. The aim of this chapter is to present the principles of this technique and then to report a comprehensive survey of the results which have appeared in the literature. Section 3.1 gives a brief historical outline on the development of this technique from the pioneering experiments of Haynes and Shockley to present. Sections 3.2, 3.3 describe the principles of the traditional time-of-flight technique and of the more recent microwave-time-of-flight technique. Section 3,4 reports the measurements of the drift velocity obtained for electrons and holes in different materials. Section 3.5 illustrates the method for measuring the longitudinal diffusion coefficient and reports the data obtained for electrons and holes in different materials.
3.1 Historical Survey The basic ideas of the ToF technique as applied to the study of transport phenomena in semiconductors were first presented by Haynes and Shockley [3.1 ] in their pioneering experiments. The most important measurable quantity is the value of the transit time TR, that is, the time taken by the charge carriers to travel across a given region of the sample under the influence of a known electric field. Thus, the ToF technique is usually synonymous with transit-time measurements
[3.2]. Since the Haynes and Shockley experiment, in which minority carriers were injected through point contacts into a filamentary sample, other groups adopted this technique and several improvements were introduced. Spear [3.3,4] produced electron-hole pairs by short pulses of low energy (about 10 keV) electrons in high-resistivity materials~ thus enabling the analysis of drift velocity for carriers of each type to be carried out in the same sample. By adopting the Spear's method, Ruth and Kino [3.5], and Sigmon and Gibbons [3.6] improved the technique in order to obtain the measurement of the
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longitudinal diffusion coefficient. Neukermans and Kino [3.7] succeeded in coupling the T o F technique with an external uniaxiat pressure. The M o d e n a group [3.8-16] completed a systematic analysis o f drift and diffusion primarily in the elemental semiconductors of group four. Evans and Robson [3,17], by modulating the ionizing source at a microwave frequency (microwave-time-offlight technique), obtained drift velocity measurements on very thin samples (2 to I 0 ~ m ) , and for very high electric fields near the breakdown region.
3.2 Time-of-Flight Technique 3.2.1 Principles of the Method The schematic principle of T o F is illustrated in Fig. 3.1. An ionizing radiation of sufficient
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