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The energy as a functional of the charge density and the charge-density susceptibility: A simple, exact, nonlocal expression for the electronic energy of a molecule

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In the p‐type quasi‐neutral and heavily doped emitter region of silicon devices at room temperature, with the aid of our accurate empirical models for the apparent band‐gap narrowing and minority‐electron lifetime, a simple accurate theory of minority‐electron (emitter) saturation current density JEO, and effective minority‐electron transit time, which are expressed as functions of the surface acceptor density Ns, the electron surface recombination velocity S, and the emitter width W, is derived and discussed. It is found that, under transparent emitter region condition, our theoretical values of JEO(Ns) for S = ∞ and 0.19 μm ≦ W ≦ 0.25 μm are in good agreement with the corresponding ones measured by Cuevas et al., with a precision of the order of 22%.

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In the n(p)-type degenerate semiconductors, our expression for the relative static dielectric constant, ε r d a , is determined by an effective Bohr model, r d a being the donor (acceptor) d(a)-radius, suggesting that, for an increasing r d a , both ε r d a and the effective Bohr radius a B r d a , due to such the impurity size effect, decrease (↘), according to the increase (↗) in: (i)the effective d(a)-ionization energy E d(a) r d a in absolutes values, (ii) the effective band gap E gn(gp) r d a , and also (iii) the critical density N CDn(CDp) r d(a) , 0.25 ≤ y ≤ 1 in the MIT, as those showed in Tables 2-4, for the n(p)-type (Si, GaAs, InP)-semiconductors, in which the empirical parameter y has been chosen as: y=0.25 and 0.271. One notes here that y=0.25 was given

Using the Green function methods, in the Feynman-path integral formulation, applied to disordered systems and developed already in four previous papers, the thermoelectric effects at low temperatures are studied from a simplified model of heavily doped semiconductors. Two typical cases concerning the relation between t,he carrier and the donor concentrations are discussed.En utilisant les mbthodes de fonctions dc Green et l'intkgrale de parcours de Feynman appliqubes a des systbmes dbsordonn&, dbjh dbvelopphes dans quatre articles prbcbdents, les effets thermoblectriques h basse temperature sont Btudibs A partir d'un modble simplifib des semiconducteurs fortement dopbs. Deux cas typiques concernant la relation entre la concentration des blectrons e t celle des impuretbs sont discutbs.