# hw02 - ECE 315 Homework 2 Due 12noon Sept 6 2007 in the...

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1 ECE 315 Homework 2 Due 12noon, Sept. 6, 2007 in the drop box 1. (Compensational doping) For a piece of homogeneous semiconductor under equilibrium at room temperature with n i =1.5 × 10 10 cm -3 , find the electron and hole concentrations for the semiconductor contains both N A =10 18 cm -3 and N D =10 15 cm -3 : (a) Use the charge neutrality condition and np=n i 2 to obtain the exact solution of n and p (4 pts) (b) Explain why p = N A – N D is a good approximation for the majority carrier here (4 pts) (c) Repeat (a) and (b) for N A =10 18 cm -3 and N D =10 17 cm -3 . (4 pts) (d) If you are asked to calculate the electrostatic potential for the case in (a), will you use p or N A ? What is the potential in relation to the intrinsic level? (4 pts) (e) If we build a resistor with this semiconductor, how will you compare the mobility for the compensational doping with both N A =10 18 cm -3 and N D =10 17 cm -3 and the mobility for the case with only N A =9 × 10 17 cm -3 ? Briefly explain. (4 pts) 2. (Carrier concentration in different temperatures) The intrinsic silicon has E gap = 1.1eV and n i = 1.5 × 10 10 cm -3 at 300K. If we assume E gap and the dopant (impurity that is either donor or acceptor) ionization are temperature insensitive, given that n i exp( -E gap /2kT ), (a) What will be the intrinsic concentration at 250K and 400K? (4 pts) (b) If the silicon piece is doped with N D = 10 16 cm -3 , find the electron and hole concentrations at 250K and 400K. (4 pts)

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