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EECS 130 Fall 1997 Integrated Circuit Devices Professor King
Midterm Examination # October 2, 1997 Time allotted: 80 minutes. Problem 1. [15 points] The doping profiles for 2 ideal silicon long-base p-n junction diodes maintained at 300k are picture below.
The minority carrier lifetimes in the quasi-neutral regions ( , ) are the same for these 2 diodes. Answer the following questions (circle the correct choice): a) The magnitude of the built-in potential in Diode A is [larger than, equal to, smaller than] the magnitude of the built-in potential in Diode B. b) The saturation current of Diode A is
[larger than, equal to, smaller than] the saturation current of Diode B. c) The reverse breakdown voltage of Diode A is [larger than, equal to, smaller than] the reverse breakdown voltage of Diode B. d) The minority carrier diffusion length on the n-type side is [larger, equal, smaller] in Diode A as compared with Diode B. e) For a given forward bias (V (^) a >0), the excess hole density at the edge of the depletion region on the n-type side p' (^) n (x (^) n), will be
[larger, equal, smaller] in Diode A as compared with Diode B. Problem 2 (20 points) Consider a silicon sample maintained at 300k under equilibrium conditions, doped with the following impurities: Phosphorous: 110^16 cm^(-3) Boron : 210^16 cm^(-3)
Problem 3 [25 points] Consider an ideal long-base P+ - n step-junction diode with cross-sectional area A which is uniformly illuminated with light, resulting in a photogeneration rare of G (^) l electron-hole pairs per cm^3-sec. Assume that steady-state and low-level injection conditions prevail.
a) what is the excess hole concentration on the n-type side a large distance (x->infinity) from the metallurgical junction? b) Derive an expression for the excess hole distribution, p'n (x), on the n-type side.
(Hint: solve the minority carrier diffusion equation, and use the boundary condition established in part (a). Also, assume that the excess hole concentration at the edge of the depletion region, p' (^) n (x (^) n), is not significantly affected by the photogenertation, i.e. use the standard depletion-edge boundary condition). c) From your answer in part (b), derive an expression for I-V characterisitc of the P+-n diode under the stated conditions of illumination. Assume that no recombination-generation (including photogeneration) occurs in the depletion region. Answers to Problems 3 a) P'n(x->infinity): [5 pts] b) p'n(x)= [10 pts] c) I= [10 pts]
Problem 4 (40 points) Given the following electric field distribution in a reverse-biased silicon p-n-n+ junction diode maintained at 300K:
Note: It is common to assume that the Fermi level (E (^) f) coincides with E (^) c in n+ (degenerately doped n-type) semiconductor and with E (^) v in p+ (degenerately doped p-type) semiconductor.
a) Sketch the doping profile of this p-n-n+ junction between x=-1 um and x=1 um. Indicate the numerical values of the doping concentrations in the p and n regions. b) Sketch the energy band diagram for this device at zero bias (between x=-1 um to x=2 um). Include E (^) c , E (^) v , and E (^) f on your diagram, and indicate energy (difference between these energy levels in each region of the device. (Numerical values are required).
c) What is the built-in potential of this p-n junction? d) What is the bias voltage applied across this p-n junction (in the Figure above)? e) What is the junction capacitance at this bias? f) What is the punch-through voltage of this device, i,e, what is the minimum (reverse) bias which will ensure that the depletion width on the n-type is 1.0 um?
Answers to Problem 4 a) Doping Profile b) Equilibrium Energy Band Diagram c) d) V (^) a =
e) Cj =
f) V punch-through=
