īringing the FET to reality would take somewhat longer. Shockley would shortly follow this with the junction transistor (diffused or grown layers of various doping). It is generally believed that the work at Bell Telephone Laboratories was attempting to make the device in Ge, but the lack of a stable oxide led them to the point contact transistor (two metallic points attached to the Ge layer), developed by Bardeen and Brattain. While the Lilienfeld patent is generally considered to be the start of the FET, it is not all that clear from the description in the patent, and it was a later patent by Heil that more clearly described the surface-oriented device. A discussion of how quantum transport differs from classical transport will be presented, followed by a discussion in the next sections. This will be followed by a discussion of just what kind of quantum effects occur and how they affect the transport.
In the following sections of this introduction, a brief history of the FET, its scaling, requirements, and modeling will be introduced. Recognizing these points, it is the 3rd level of quantum mechanics and transport mentioned above that will be discussed in this review. And perhaps, with this review, a number of the quantum effects that may be surprising, will appear to the readers to change their minds. Of course, this is no longer the case, and it may be expected that the need for quantum transport will become more important in the near future. To counter this, we need only point out that for a long part of the history of FETs, these same engineers saw no need for any modeling or simulation. īut, having said this, if one were to conduct a poll of say 100 experienced device engineers, there would be no overall demand for a study of quantum transport, as most see no need for this level of sophistication. One need look no further than the introduction of strain into the channel of the FET, which is done to modify the effective mass and electronic structure, to recognize this. But, this has changed in the past few decades, as modern versions tend to be absolutely controlled by quantum confinement and the resulting modifications to the normal classical descriptions. As a result, the FET has had no need to be described by quantum transport over most of the century for which it has existed.
Finally, it is the third level of quantum effects, such as confinement in small structures, for which quantum mechanics needs to re-enter the picture, and it is here that one has need to deal with quantum transport. Then, of course, the scattering of carriers by the quantized vibrations of the lattice, the phonons, is treated quantum mechanically, but only to the extent necessary to describe a probability for scattering that is used in classical transport equations. It is this quantum potential that is folded into the concept of effective mass. This view was reinforced by Kennard, who began with the Schrödinger equation and developed a hydrodynamic corollary, and then observed that the electrons would move just as classical particles would respond to the fields and potentials, but that there would be an additional quantum force/potential. Nevertheless, the introduction of an effective mass for the quasi-particles (the electrons and holes) freed the scientist from worrying about such things, and allowed one to proceed as if the carriers were classical objects. Yet, the wave nature of the electron, and the periodicity of the crystal lattice, are the base upon which the idea of the band structure is based. Indeed, theories of quantum mechanics were just being proposed, so Lilienfeld's ideas were, by necessity, entirely classical
A knowledgeable reader might be tempted to ask the question, 'hasn't all transport in semiconductors devices been quantum mechanical?' The answer, of course, is 'yes', but it is a qualified yes, as there are several levels in which quantum mechanics may be involved, especially if we consider that almost one century has passed since the concept of the field-effect transistor (FET) was first discussed.
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