The quantized Hall effect

Abstract

tory since one may come to the conclusion that such a complicated system like a semiconuctor is not useful for very fundamental discoveries. Indeed, most of the experimental data in solid state physics are analyzed on the basis of simplified theories, and very often the properties of a semiconductor device is described by empirical formulas since the microscopic details are too complicated. Up to 1980 nobody expected that there exists an effect like the Quantized Hall Effect, which depends exclusively on fundamental constants and is not affected by irregularitie s in the semiconductor like impurities or interface effects. The discovery of the Quantized Hall Effect (QHE) was the result of systematic measurements on silicon field effect transistors-the most important device in microelectron ics. Such devices are not only important for applications but also for basic research. The pioneering work by Fowler, Fang, Howard and Stiles [l] has shown that new quantum phenomena become visible if the electrons of a conductor are confined within a typical length of 10 nm. Their discoveries opened the field of two-dimension al electron systems which since 1975 is the subject of a conference series [2]. It has been demonstrated that this field is important for the description of nearly all optical and electrical properties of microelectron ic devices. A two-dimensiona l electron gas is absolutely necessary for the observation of the Quantized Hall Effect, and the realization and properties of such a system will be discussed in section 2. In addition to the quantum phenomena connected with the confinement of electrons within a two-dimensional layer, another quantization - the Landau quantization of the electron motion in a strong magnetic field - is essential for the interpretation of the Quantized Hall Effect (section 3). Some experimental results will be summarized in section 4 and the application of the QHE in metrology is the subject of section 5.