ELE-330
Homework 4.
Due date: 02/26/2025
Total Points: 25
1. (a) For a p-type silicon in which the dopant concentration NA= 2 X 1018 cm-3.
Find the electron and hole concentration at T=300K.
(b) In a boron doped silicon layer with impurity concentration of 1017 /cm3, find
the electron and hole concentrations at 27oC. Is the result p-type or n-type.
[2 Points]
2. Find the resistivity of (a) intrinsic silicon and (b) p-type silicon with NA=
1016/cm3. Use ni = 1.5 X 1010/cm3, and assume that for intrinsic silicon μn= 1350
cm2/V.s and μp= 480 cm2/V. s, and for the doped silicon μn = 1110 cm2/V.s and
μp= 400 cm2/V.s. (Note that doping results in reduced carrier mobilities).
[3 Points]
3. Examines the end-to-end resistance of a connecting bar 10-μm long, 3-μm wide,
and 1 μm thick, made of various materials. The designer considers:(a) intrinsic
silicon (b) n-doped silicon with ND = 5×1016/cm3 (c) n-doped silicon with ND =
5×1018/cm3 (d) p-doped silicon with NA= 5×1016/cm3.
Find the resistance in each case. For intrinsic silicon, use ni = 1.5 X 1010/cm3.
Assume μn = 3μp= 1200 cm2/V.s. (Recall that R = ρL/A.).
[5 Points]
4. (a) For a silicon crystal doped with phosphorus, what must ND be if at T =300 K
the hole concentration drops below the intrinsic level by a factor of 108?
(b) Calculate the electron and hole drift velocities through a 10-μm layer of
intrinsic silicon across which a voltage of 3 V is imposed. Let μn = 1350 cm2/V.s
and μp = 480 cm2/V.s
[ 5 Points]
5. Find the current that flows in a silicon bar of 10-μm length having a 5-μm × 4μm cross-section and having free-electron and hole densities of 104/cm3 and
1016/cm3, respectively, when a 1 V is applied end-to-end. Use μn=1200 cm2/V.s
and μp= 500 cm2/V.s.
[5 Points]
6. (a) If, for a particular p-n junction, the acceptor concentration is 1017/cm3 and
the donor concentration is 1016/cm3, find the junction built-in voltage. Assume
ni = 1.5×1010/cm3. Also, find the width of the depletion region (W) and its extent
Northern Illinois University
Dr. Vinay Budhraja
ELE-330
in each of the p and n-regions when the junction terminals are left open.
Calculate the magnitude of the charge stored on either side of the junction.
Assume that the junction area is 100 μm2.
(b) Repeat part (a) If a 3-V reverse-bias voltage is applied across the junction,
find W and QJ .
[5 Points]
Northern Illinois University
Dr. Vinay Budhraja
ELE-330