1
ECSE-2210 Microelectronics Technology
Homework 4
Reading list: Chapter 5 (pages 195 - 223. Ignore section 5.2.5).
1. (Problem 5.4 in text) A Si step junction under equilibrium at 300 K has a p-side doping of
NA = 2 × 1015 cm-3 and n-side doping of ND = 1015 cm-3.
Calculate:
(a) The contact potential (also called built-in voltage).
(b) The depletion layer width at the p-side and n-sides, and the total depletion layer width.
(c) The electric field at the metallurgical junction.
(d) The potential at the metallurgical junction.
(e) Make sketches of the charge density, electric field and electrostatic potential as a
function of position, that are roughly to scale
2. (Problem 5.5 in text) Repeat problem 1 taking NA = 1017cm3 to be the p-side doping. Briefly
compare the results here with those obtained in problem 1.
3. (Problem 5.10 in text). A p-n junction diode has the doping profile sketched below. Make the
assumption that xn > x0 for all applied bias of interest. Answer the following:
a. What is the built-in voltage across the junction? Justify your answer.
b. Sketch the charge density
ρ
versus x inside the diode
c. Sketch the expected electric field as a function of x inside the diode.
4. The p-i-n diode shown above is a three-region device with the middle region that is intrinsic
and relatively narrow. Assuming the p- and n-regions to be uniformly doped and ND-NA = 0
in the i-region:
a. Roughly sketch the expected charge density, electric field, and electrostatic potential
inside the device. Also, draw the energy band diagram for the device under thermal
equilibrium conditions.
b. What is the built-in voltage drop between the p- and n-regions? Show how you arrived
with your answer.
N
D-
N
A
N
D
N
D/2
x
0
N
A
0 xi
p i n
NA ND
W