Using these numbers, calculate and plot the fraction of ionized donors as a function of temperature. (b) Assuming that the conduction electrons behave like an ordinary ideal gas (with two spin states per particle), write their chemical potential in terms of the number of conduction electrons per unit volume, $N_$ atoms per cubic centimeter. Express your formula in terms of the temperature, the ionization energy $I$, and the chemical potential of the "gas" of ionized electrons. Do not neglect the fact that the electron, if present, can have two independent spin states. (a) Write down a formula for the probability of a single donor atom being ionized. If you are author or own the copyright of this book, please report to us by using this DMCA report form. This document was uploaded by user and they confirmed that they have the permission to share it. This system is analogous to the hydrogen atom considered in the previous two problems except that the ionization energy is much less, mainly due to the screening of the ionic charge by the dielectric behavior of the medium. Download An Introduction To Thermal Physics - Daniel Schroeder. The ionized electron is called a conduction electron, because it is free to move through the material the impurity atom is called a donor, because it can "donate" a conduction electron. The extra electron is then easily removed, leaving behind a positively charged ion. Suppose that the impurity atom has one "extra" electron compared to the neighboring atoms, as would a phosphorus atom occupying a lattice site inĪ silicon crystal. Consider a system consisting of a single impurity atom/ion in a semiconductor.
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