1. Tutorial #4 – selected problems
Problem 1 (Problem 3.7 Streetman)
Given mn* and mp* from Table 3-1 p 65, calculate
the effective densities of states Nc and Nv for GaAs
at 300K (assume mn* and mp* do not vary with
temperature). Calculate the intrinsic carrier
concentration.
Answer:
mn*=0.067m mp*=0.48m T=300K
The effective densities of states are given by:

2. The intrinsic carrier concentration is given by
Eg=1.43eV
ni=1.87 x 106 cm-3

3. Problem 2
For silicon doped to 1014 donors/cm3:
Calculate the temperature where the total electron
carrier density in this semiconductor is equal to
twice the donor concentration. (This gives a good
estimate of where the sample changes from
“extrinsic” to “intrinsic” behavior.)
Answer:
If the material is to remain electrostatically neutral,
the sum of the positive charges (holes and ionized
donor atoms) must balance the sum of the negative

4. charges (electrons and ionized acceptor atoms):
p0 + Nd+ = n0 + Na-
Nd+ = 1014 cm Na- = 0 cm-3
n0 = 2 Nd+ cm-3
p0 = n0 – Nd+ = 1014 (2-1) = 1014 cm-3
ni2 = n0p0

5. where h=6.63 x J·s
k=1.38 x J/K = 8.62 x 10-5 eV/K
mn*= 1.1·(9.11 x kg)
mp*=0.56·(9.11 x kg)
Eg = 1.11eV
So,
We can solve for T in various ways.
One way is to let a calculator solve the equation.

6. Another way is to solve for T using Excel or Quattro Pro.
T Tpower3/2 exp( /T) (Tpower3/2) * exp( /T)
E E-06 E E E E E E

7. You can start with e.g. T = 300 K. Check last
column to see how close you are to
Repeat for 400 K and 500 K.
Increase to 510 K, and then 515 K.
Decrease to 514 K.
Fine tune by trying K. This value gives a
product close to
Therefore,
T=513.9K.

8. 3. Show that for acceptor doping concentration NA
the equilibrium hole concentration p0 is
Solution: =0
n0p0= ni2

9. negative root not realistic