Quadratic Zeeman Effect of Donor Lines in Silicon and Germanium. I. Theory

Calculation of the quadratic Zeeman shift of donor lines of silicon and germanium has been undertaken in the effective mass theory framework. The energies are obtained by the perturbation method up to second order and a very small interaction between two sublevels m = 1 and m = −1 is found theoretically. The Zeeman patterns (phosphorus in silicon) for different configurations show crossing or noncrossing of the levels and sublevels, depending upon the chosen configuration. The results predict that for germanium, the p0 lines exhibit a splitting due to the anisotropic shift of these lines for some configurations. This theory can also be used for shallow impurities wherever the electron effective mass possesses ellipsoidal symmetry.

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A Unified Treatment of The Thermal Donor Hierarchies in Silicon and Germanium

MRS Proceedings ◽

10.1557/proc-59-159 ◽

1985 ◽

Vol 59 ◽

Author(s):

Jeffrey T. Borenstein ◽

James W. Corbett

Keyword(s):

Dielectric Constant ◽

Effective Mass ◽

Ground State ◽

Shallow Donor ◽

Binding Energies ◽

Electron Effective Mass ◽

Perturbation Model ◽

Thermal Donor ◽

Silicon And Germanium ◽

Oxygen Atoms

ABSTRACTThe hierarchies of thermal donor binding energies produced by annealing oxygen-containing silicon or germanium at ca. 450°C are explained by using a generalized perturbation model which involves a standard repulsion parameter for the interaction between agglomerating oxygen atoms and the shallow donor electrons. This model is capable of fitting the ground state ladders for both charge states of the thermal donors in both Si and Ge, since differences between the two ladders can–ee explained entirely by the change in the electron-effective-mass and dielectric constant of the host.

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Quadratic Zeeman Effect of Donor Lines in Silicon. II. Comparison with Experiment

Canadian Journal of Physics ◽

10.1139/p72-289 ◽

1972 ◽

Vol 50 (18) ◽

pp. 2186-2193 ◽

Cited By ~ 18

Author(s):

B. Pajot ◽

F. Merlet ◽

G. Taravella

Keyword(s):

Zeeman Effect ◽

Variational Calculation ◽

Strong Interactions ◽

Bohr Radius ◽

Comparison With Experiment ◽

Principal Axes ◽

Phosphorus In Silicon ◽

Quadratic Zeeman Effect ◽

Photoexcitation Spectrum ◽

The Magnetic Field

The Zeeman effect in the photoexcitation spectrum of phosphorus in silicon has been studied up to 64 kG in the Faraday configuration with the field parallel to the three principal axes of the crystal. In this work, we have observed a slight decrease of the transverse effective mass with the field and we found a fair agreement between theory and experiment for the 2p± and 3p± levels. Better agreement is obtained, however, if the variation of the effective Bohr radii with the magnetic field is taken into account. For the 2p0 and 3p0 levels, the variation of the effective Bohr radius [Formula: see text] alone cannot be observed experimentally in the Faraday configuration, but our results indicate a much more important decrease than for the p± levels and a variational calculation is necessary in this case. The shift of the 2p0 and 3p0 lines obeys roughly the n2(n2 − 1) relation, which should not be observed in the case of strong interactions with upper levels.

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