Problem 3.36 (Sedra/Smith)
In a phosphorus doped silicon layer with impurity concentration of 1016/cm3 find the hole and electron concentration at 300K and 400K. Use ni = 1010 cm-3 at 300K.
Upon completion of this laboratory students should be able to understand the physical meaning of the parameters and to calculate the electron and hole concentration using the applet.
Pre-lab (Hand Calculation)
a) Find the electron and hole concentration (per cm3) for
different temperatures. To do so,
b) Substitute these values into the formula ni= BT3 exp(-Eg/kT) obtain the intrinsic concentration ni=( )/cm3
c) Now calculate the hole concentration using pno=(ni2/Nd), Where Nd is the impurity concentration given in the problem.
d) So the values of the hole and electron concentrations are respectively
pno=( )/ cm3
and nno=( )/ cm3
Procedure using applets in the lab:
1) Visit the virtual lab at the URL: http://jas.eng.buffalo.edu/education/semicon/fermi/heavyVSmoderate
2) This applet lets you visualize the various parameters for different values of the Fermi levels and the absolute temperature.
3) Use the “MB” button to hide the MB portion of data.
4) Fill in the textbox (at the bottom of the applet) 300K. You can also do it by clicking on the arrow knobs of the field below the temperature field.
5) Make sure that the material of the device is set to silicon.
6) The Fermi levels (Ef) can be set using the arrow keys at the top of the applet.
7) Move the Ef value until n is equal to the Phosphorus (Donor) doping level (Nd). Then read the electron (n) and hole (p) concentrations from the applet. This is the answer for T=300K.
8) Now, set the Temperature to 400K. Repeat the steps 6) and 7). The n and p values are the majority and minority carrier concentrations at 400K. The solution is complete here.
9) The buttons Ef , FD, MB ,Relconc and delta can be used to watch the
Fermi level, FD and MB refer to the Fermi Dirac and Maxwell Boltzmann resp.
These buttons are used to see the values on the applet screen.
10) You can view the values of Eg and kT from the applet.