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ECSE-2210 Microelectronics Technology
Homework 3
Reading Assignment: Pages 74-104
1. A silicon sample maintained at 300 K under thermal equilibrium has a non-uniform doping
concentration profile, such that the electron concentration, n, varies linearly from 1×1012 cm-3
to 5 × 1017 cm-3 while going from point x1 to point x2 (see figure below). Assume that the
mobility is constant at 1000 cm2/Vs throughout the sample. Answer the following.
n
5 × 1017 cm-3
1 × 1012 cm-3
x1 x2
(a) Calculate the diffusion coefficient, Dn (in cm2/s) for the electrons.
(b) Explain why the electrons do not diffuse everywhere such that the concentration is
uniform throughout.
(c) Plot the diffusion current density (A/cm2) for the electrons as a function of x. Mark the
numerical value on the graph. (Hint: What is the equation for diffusion current density?)
(d) Plot the drift current density for electrons as a function of x (Hint: What should be the
total current? Then, obtain answer to this from part c).
(e) Plot the energy band diagram as a function of x. (Hint: Plot the band diagram for
x < x1 and for x > x2 and then plot qualitatively between x1 and x2).
(f) What is the potential difference (give a numerical value) between the two ends of the
sample? (Hint: Read it off from the band diagram!)
(g) Plot a graph of the electric field versus x. (Hint: You can get this from part d and from the
equation for the electron drift current density).
2. A 5-Ω resistor is to be made from a bar-shaped piece of n-type Si. The bar has a cross-
sectional area of 10-2 cm2. The silicon is doped with ND = 5 × 1017cm-3 and
NA = 4 × 1017 cm-3. Determine the length of the silicon bar.
10
µ
m
Linearly
varying