Semiconductors Apr. 9, 2007

+ Semi-conductors: carriers -- electrons and holes
Introduce impurities: p-type (filled with acceptors) and n-type (filled with donors) semi-conductors.
p-type -- acceptor volume density
n-type -- donor density

+ p-type and n-type contact separation of positive and negative charges in depletion layer
This layer determines the contact voltage, e.g. 0.6-0.7V for a diode, and the capacitor of a diode.
Example 4.1: PN junction
Example 4.2: Capacitance of a PN junction

+ Current density ; the drift velocity of charges and (note: with its sign depending on carrier) (Sect. 4.2)
If and/or ,
Ohm's law .
Conductivity --
-- mobility of holes; -- mobility of electrons

+
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HW #18 (no late homework) Due 4/12/07

1. A parallel-plate capacitor with area and separation 3mm contains three dielectrics with interfaces normal to and , as follows: layer 1 -- , mm; layer 2 -- , mm; layer 3 -- , mm. The uniform surface charge density is . Find (a) the capacitance of the capacitor, (b) the voltage between the plates, (c) magnitude of between the parallel plates, and (d) energy density in layer 2.
2. A cylindrical capacitor of length L has two concentric cylinders of radii a and d. Concentric with them and lying between them is a cylindrical shell of inner radius b and outer radius c while other regions between a and d is filled with air. If the shell is filled with dielectric material of relative permittivity and a<b<c<d. a) Determine the capacitance of this system with 2 ways: 1) use Gauss's law only and 2) consider this problem having 3 cylindrical capacitors. b) find electrostatic energy density between a and b with +Q charge at radius a and -Q charge at radius d.
3. Exercise 3.19 (page 132)
Extra-credit: Two point charges of 50nC and -20nC are located at (-3,2,4) and (1,0,5) above the conducting ground plane z=2. a) Draw the charge equivalent diagram for this problem, b) Find at (3,4,8) and c) at (1,1,1).