Dear Venkatesh Jayanti,

The info below may be helpful:

The screening influence of the conduction electrons on the shallow donor levels in n-type GaAs

• L'. Hrivnák

Czechoslovak Journal of Physics B volume 26, pages670–676 (1976)Cite this article

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Abstract Using the approximative formula found by the author for the eigenvalues of Schrödinger equation for an electron in the screened coulombic field and the condition of the charge neutrality in partially compensated semiconductor, the ground-state and the first excited-state energy levels of shallow donors in n-type GaAs are computed for various donor concentrations and compensation ratios. The energy levels are found to be temperature dependent, which enables to explain the discrepancy between the ionization energies experimentally determined by optical methods at 4·2 K and those found by fitting the experimental temperature variation of the carrier concentration. The different values of the energies for the transition from the ground-state to the first excited-state at 4·2 K and at 15 K experimentally determined by other authors also confirm the temperature dependence of shallow donor levels which can be explained by the screening effect of conduction electrons.

Len Leonid Mizrah Sir could you please elaborate on how that happens? I thought E_A was constant at approx 45meV for Boron doped silicon?

Venkatesh Jayanti

In the commercial silicon-based microelectronics MOS structures used to be studied between approximately room and liquid nitrogen temperatures, whereas liquid helium temperature studies are rather rare. I tend to agree with the authors of the article that screening effects would change the Bohr orbits of acceptor's or donor's outer carriers. That is their ionization (activation) energy will become smaller. The second link below gives some more theoretical flavor to it.

https://en.wikipedia.org/wiki/Bohr_radius

http://web.eng.gla.ac.uk/groups/sim_centre/courses/hydrogenic/titles/hydro.gif