12832) In a treatment for an arbitrary geometry, he assumes that the incremental field lines cannot cross the boundaries of the semiconductor as the current lines cannot cross the boundaries. This is not always true. For instance, if the semiconductor is surrounded by a dielectric of relatively high permittivity, a considerable component of the electric field perpendicular to the boundaries should be produced as a result of accumulation or depletion of electron^.^ Obviously, the incremental field AF is not parallel to the current lines, and thus his assumption does not always hold. The boundary condition is always very important because it affects seriously the inner electric field distributions in the semiconductor.3) Equation (9) for the three-dimensional equivalent of the onedimensional Poisson equation in the previously mentioned letter' is not a p plicable to general case. General expression of the Poisson's equation in a curvilinear system (ul, u2, u3) should be as follows.where h' = / and U is the potential. The generalized proof must be discussed by using ( 5 ) instead of equation (9) of Kroemer. Otherwise, we might be misled. For instance, in a simple example of a polar coordinate where the electric field is only a function of distance, such a conclusion as given in his letter cannot be obtained from only (5). In conclusion, his letter, though very interesting, does not necessarily describe the generalized proof of Shockley's positive conductance theorem and, thus, we are not yet sure whether a positive differential conductance would always be obtainable with a bulk effect or not. HIROSHI TATENO SHOEI KATAOKA Electrotech. Lab. Ministry Int. Trade and Industry Tanashi, Tokyo, Japan
Author's Reply3Item 1) of Tateno and Kataoka's criticism is irrelevant. The question of the movement of the crossover surface does not come up anywhere. For j = j o no crossover surface can be defined; at that current level the field is everywhere equal to Po, by definition.Item 2) is related to the neglect of diffusion, an approximation specifically stated in my proof. If one makes this approximation, then, for an isotropic mobility, the local static current density and the local static electric field must be collinear, except possibly in regions with zero carrier (and current) density. The latter exception could occur insidea surface depletion layer, which is presumably the situation Tateno and Kataoka have in mind. If the thickness of such a depletion layer did not vary as the current is increased, the depletion layer could be considered as being outside the conducting medium, and the proof would continue to hold. A changing depletion layer thickness in effect introduces a current-dependent boundputer analysis of dielectric-surface-loaded GaAs bulk element," Elecrron. L~I I . , vol. 6, S. Kataoka, H. Tatcno, M. Kawashima, and M. Morisue, "Two-dimensional com- Mar. 19,1970, pp. 169-171 (see Fig. 3).Manuscript reccivcd March 5, 1971. ary shape, and in structures whose transverse dimensions are not large, compared to depletion ...