A new approach to the many-electron atom, based on the formal equivalence between the Hartree-Fock equations and a quantum-mechanical generalization of the collisionless Boltzmann (Vlasov) equation, is presented. This equivalence casts the problem into the framework of conventional plasma theory, the Vlasov equation being merely replaced by its quantum-mechanical analog. The quantum Vlasov equation permits a straightforward expansion of the quantum-mechanical phase space distribution function in powers of h. The first step of this expansion, corresponding physically to a classical correlationless plasma obeying Fermi statistics, leads to the Thomas-Fermi model. Successive steps generate quantum and exchange corrections. The method is applied to the case of the "statistical" correlationless atom (or ion), generalized for the first time to arbitrary temperature and nonzero total orbital angular momentum, with quantum and exchange effects being included to order h 2 .1 The most recent comprehensive review articles dealing with the Thomas-Fermi model are those of P. Gombas in Handbuch der Physik, edited by S.
A theory of an n-p-p+ junction is developed, entirely based on Shockley’s depletion layer approximation. Under the further assumption of uniform doping the electrical characteristics of solar cells as a function of all relevant parameters (cell thickness, diffusion lengths, etc.) can quickly be ascertained with a minimum of computer time. Two effects contribute to the superior performance of a BSF cell (n-p-p+ junction) as compared to an ordinary solar cell (n-p junction). The sharing of the applied voltage among the two junctions (the n-p and the p-p+ junction) decreases the dark current and the reflection of minority carriers by the builtin electric field of the p-p+ junction increases the short-circuit current. The theory predicts an increase in the open-circuit voltage (VOC) with a decrease in cell thickness. Although the short-circuit current decreases at the same time, the efficiency of the cell is virtually unaltered in going from a thickness of 200 μm to a thickness of 50 μm. The importance of this fact for space missions where large power-to-weight ratios are required is obvious.
A systematic and quantitative analysis is carried out to investigate the effects of the shape (point, cube, Gaussian) and size of the generation volume, the surface recombination velocity, and the diffusion length on the electron-beam-induced current (EBIC) and its derivative (DEBIC). Thick homogeneously doped samples exhibiting diffusion lengths in the low micron and submicron range are considered. The results are presented in computed EBIC curves as a function of scanning distance and of the ratio true diffusion length/effective diffusion length. Using these curves, we show (1) a simple and yet rigorous method for the determination of the true diffusion length, taking into consideration all of the factors cited above, (2) a method for the rapid determination of the surface recombination velocity, (3) the condition under which the source shape becomes insignificant, and (4) a new value for the lower limit of the diffusion length which can be determined by the EBIC technique.
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