9780030839931, Chapter 28, Problem 5P

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Chapter 28, Problem 5P Problem Constraint on Carrier Densities in p- Type Semiconductors Describe the electronic configuration of a doped semiconductor as 0, when Na > Nd Explain why (28.35) (derived in the text when Nd Na) continues to give a correct constraint on the electron and hole densities at nonzero temperatures, when Na > Nd. Step-by-step solution Step 1 of 2 Consider an extrinsic semiconductor doped with Nd donor impurities and Na impurities per unit volume. Let us assume that the number of conduction band electrons is equal to the number of valence band holes. Consider the electronic configuration when the temperature and In the unit volume of semiconductor Nd of the Na electrons supplied by the donor impurities can drop from the donor level to the acceptor level. This process gives the ground state electronic configuration. The configuration is such that the valence band and the acceptor level are filled. So that Na Nd of the acceptor level is filled. With this, the conduction band levels are empty. The electrons will be distributed among the given levels at thermal equilibrium with some specific temperature. But the number of electrons in the conduction or donor levels must exceed its value at This is due to the fact that their total number remains the same. Now, Na Nd gives the number of empty levels. Step 2 of 2 The equation 28.35 is given by, The above equation gives the same result when the temperature is not equal to zero. This is due to the fact that the calculation is done considering the fact that the temperature is not equal to zero. The above equation hold S when > Nd and Nd > Na Also, it is assume that the number of conduction band electrons is equal to the number of valence band holes.