Homework 7 - Sonoma State University

Department of Engineering Science
Sonoma State University
ES 445
HW 7
Solutions must be written clearly and explained thoroughly.
Diagrams must be drawn with care
1. Starting with the equation for the intrinsic carrier concentration ni = (Nc
Nv)1/2 e-Eg/2KT plot a computer generated linear curve of ln(ni) vs (1000/T)
for silicon. Obtain all the needed constants from available resources. On
your diagram, mark the intrinsic carrier concentrations at temperatures:
77, 300, and 450 degrees Kelvin.
Determine the equilibrium electron and hole concentrations in a
uniformly doped silicon under the following conditions:
Room temperature T = 300 K, and NA << ND = 1 x 1015 cm-3
T = 300 K, and ND << NA = 1 x 1016 cm-3
T = 300 K, and ND = 1 x 1016 cm-3 and NA = 1 x 1015 cm-3
T = 450 K, NA = 0, ND = 1 x 1014 cm-3. In this case the concentrations
are comparable to each other and can not be ignored with respect to each
other. Use the curve of problem 1 to find the intrinsic carrier
concentration at this temperature and then use the charge neutrality
condition n + NA- = p + ND+, to determine n and p.
3. A silicon wafer has been doped uniformly with 1 x 1017 cm-3
phosphorous atoms. At room temperature:
(a) Determine the type of this material: n-type or p-type? Using the
periodic table explain why?
(b) Calculate the position of the Fermi energy EF with respect to the Fermi
energy EFi in intrinsic silicon. Draw an energy band E(x) diagram and
carefully indicate the calculated energy levels.
(c) The wafer is subsequently doped with 1 x 1013 boron atoms. Is the
material n-type or p-type? Recalculate part (b).