Homework #2 - due Thursday, 24 February 2005, in class

1. A piece of silicon is uniformly doped with 1.2E16 atoms cm^-3 of boron acceptors.  Assume that all the atoms are ionized at 300 K, (a) determine the position of the Fermi level, and (b) plot the electron and hole concentration as a function of energy in the respective bands.

2.  Calculate the displacement of the intrinsic Fermi level E_i from the center of the band gap in the case of (a) GaAs, and (b) InSb.  Hint, for InSb,  m_e/m_o = 0.013, and m_h/m_o = 0.18.

3.  Phosphorus in Si has a donor level 0.045 eV below E_C.  Using Eqn (1.1.7) in MKC, (a) calculate the effective mass of the electron bound to the donor.  Using Eqn (1.1.2), (b) calculate the Bohr radius r_o, using Z = 1, and n = 1, with the effective mass from (a) above instead of m_o, and the full permittivity (e_re_o) in place of e_o.  It is observed that the ionization energy of phosphorus becomes zero at a dopant concentration of  3E18 atoms cm^-3  .  (c) Calculate the average separation between impurity atoms at this doping, and compare it with r_o.

4.  Assuming all the impurities to be ionized, determine how many grams of boron should, be added to 1 Kg of Ge to obtain a resistivity of 0.2 Ohm-cm.  Use a hole mobility m_p = 1250 cm²V^-1sec^-1.

5.  The hole diffusion coefficient in a Si sample is 12 cm²sec^-1.  Determine the mean free path and the carrier drift velocity in a filed of 200 V/cm.  Also calculate the energy gained by the carrier in a mean free path.  Assume T =300 K.
 
 

  Homework assignments will appear on the web at: http://www.ece.udel.edu/~kolodzey/courses/eleg646s05.html
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