Extensions of Bohrs Model

The Bohr model also remains useful in predicting the properties of "hydrogenic" electrons bound to donor impurity ions in semiconductors. This analysis explains how the carrier concentrations and electrical conductivities of industrial semiconductors are related to the intentionally introduced donor and acceptor impurity concentrations, Nd and Na, respectively. The additional ideas needed are of the relative dielectric constant of the semiconductor and the "effective mass" that an electron exhibits as it moves in a semiconductor.

The Bohr model is also useful in analyzing the optical spectra of semiconductors exposed to radiation, having energy E = he/X > Eg which produces electron-hole pairs. (Eg is the symbol for the "energy gap" of a semiconductor, which is typically about 1 eV.) It is found that such electrons and holes, attracted by the Coulomb force, momentarily orbit around each other, described by the mathematics of the Bohr model, and emit photons whose energies are predicted by the relevant Bohr model. Such states, called "excitons", are well documented in experiments measuring the spectra of fluorescent light from optically irradiated semiconductors.

A relevant topic in nanophysics is the alteration, from the exciton spectrum, of the fluorescent light emitted by a semiconductor particle as its size, L, is reduced. It is found that the correct light emission wavelengths for small sample sizes L, are obtained from the energies of electrons and holes contained in three-dimensional potentials, using the Schrodinger equation. This understanding is the basis for the behavior of "quantum dots", marketed as fluorescent markers in biological experiments, as will be described below.

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