Division by invariant integers using multiplication by Granlund T.

By Granlund T.

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In the electric field F the electron (or the hole) is acted upon by a force f = qF . Under the action of this force, the carrier acquires an acceleration a = qF/m along the line of the field. Moving without any collisions, during the time t, the carrier will acquire a velocity in the direction of the field v = at = qF t/m. In order to calculate the average velocity acquired by the carrier under the conditions of repeated collisions, we must remember two circumstances. In the first place, as we know, after a collision the carrier can move in any direction.

Deep impurities in semiconductors play three very important roles: they act as “compensators”, centres of generation and centres of recombination. We will consider each of these roles in turn. 1 Compensation by deep levels Let us imagine that we want to obtain a semiconductor, say GaAs, with a very high resistivity. Specialists manufacturing the semiconductor devices are frequently facing such problems. Films or plates whose resistivity is very high are often used as a substrate to which very thin layers of the same semiconductor containing different doping impurities are applied.

The energy level Ed , corresponding to the donor centre, is filled up with electrons. Then the donor atoms which keep the electrons are neutral. When T is not too high, the concentration of electrons at the Ec level is defined by Eq. (7). The donor atoms which have given their electrons to the Ec level are charged positively. The concentration of those positively charged donor centres is, naturally, also defined by Eq. 7. With kT ≥ ∆Ed , the concentration of free electrons at the Ec level and the concentration of the positively charged donor centres are equal to Nd (the donor exhaustion).

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