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Applet Worksheet
(Energy Band, Fermi Level, and Doping Concentration Virtual Lab)

ObjectivesAfter this Lab, students should understand the significance of Energy Band; understand the electron and hole concentrations in an intrinsic semiconductor; understand the dependence of intrinsic concentration on temperature; be able to determine the electron and hole concentrations for materials doped with extrinsic impurities; and understand the Fermi level in the band gap as the sole measure, or the single parameter, of the equilibrium carrier concentration.

PreLab:
1) Review the definitions of Energy Band.  If you are not already familiar with it, read the Introduction page of this applet.

2) Calculate the intrinsic carrier concentration in Si at 200K, 300K, and 400K.  Use Eg(200K)=1.147eV; Eg(300K)=1.124eV; and Eg(400K)=1.097eV.

a) ni = (             )/cm3  @   200K
b) ni = (             )/cm3  @   300K
c) ni = (             )/cm3  @   400K
Useful Si Formulas: ni2 = B T3 exp(-Eg/kT) where B=2.4x1031 [1/cm6 K3], and k=8.62x10-5 [eV/K],  Eg(T)= 1.17 – 4.73x10-4 T2 / (T+636) [eV]

3) For Si doped with As (donor) impurities to Nd=1x1017/cm3, calculate the electron concentration and hole concentration at 300 K.  Note that n*p=ni2 (Mass-Action Law) under thermal equilibrium.

n = (         )/cm3
p = (         )/cm3
4) Calculate Ef relative to Ei,  or Ef-Ei, for an n-type Si doped with As impurity Nd  = 1017/cm3; and Ei-Ef for a p-type Si doped with B impurity Na = 1016/cm3 .  Assume T=300 K.
Ef-Ei = (           ) eV for an n-type Si doped with As impurity Nd = 1017/cm3
Ei-Ef = (           ) eV for a p-type Si doped with B impurity Na = 1016/cm3
Useful Formulas: kT=0.0259 eV, n=ni exp((Ef-Ei)/kT), and p=ni exp((Ei-Ef )/kT)

ProcedureEnergy Band, Fermi Level, and Doping Concentration Virtual Lab
1) Visit the applet entitled "Carrier Concentration and Fermi Level" at http://jas2.eng.buffalo.edu/applets/education/semicon/fermi/bandAndLevel/fermi.html
Before proceeding, click  the buttons “ShowParameters”, “ShowDonor” and “ShowAcceptor” in the applet.

2) Intrinsic Silicon at 0 K
Set the applet at Donor concentration Nd=0, Acceptor concentration Na=0, Si, and T=1 K.  What is the electron and hole concentrations, n and p ?  What does it mean and why such value is expected ?

3) Intrinsic Silicon at finite temperature.  Set Nd = 0 and Na = 0.
Set the temperature at T=300 K.  What are the concentrations n and p ?  Discuss where the electrons and holes come from.  Explain why it should be that n = p.
Discussion:

Read the intrinsic concentration at 200K, 300 K and 400 K and compare these values with your calculation results in the PreLab.  Do they agree ?

ni = ___________ cm-3  @ 200 K
ni = ___________  cm-3  @ 300 K
ni = ___________  cm-3  @ 400 K
4) Extrinsic Si at 300 K
Click the “Reset” button.  Set Nd = 1x1017/cm3, Na = 0.  Read n and p from the applet.   Do they agree with your calculation in the PreLab ?

5) Extrinsic Si with both Donor and Acceptor impurities (Compensation)
Click the “Reset” button.  Set Nd = 2x1017/cm3, Na = 3x1017/cm3.  Read n and p from the applet.   From the result explain how is majority carrier concentration p related to Nd and Na ?   [This result is called “compensation”] How is the minority carrier concentration n related to p and ni2 ?

6) Extrinsic Si at various T
Click the “Reset” button.  Set Nd = 0 and Na=1x1015/cm3.  Read n and p from the applet at various temperatures and calculate or find ni from the applet.

200 K:  n = (     )     p = (     )      ni = (       )
300 K:  n = (     )     p = (     )      ni = (       )
400 K:  n = (     )     p = (     )      ni = (       )
What determines the majority carrier concentration  ?

How is the minority carrier density determined ?

7) Fermi Level in n-type and p-type materials
Click the “Reset” button.  Set Nd = 1017/cm3and Na=0.
Find from applet Ef - Ei = (      )eV.  Does it agree with the value you calculated in the PreLab ?

Click the “Reset” button.  Set Nd = 0 and Na=1016/cm3.
Find from applet Ei - Ef = (      )eV.  Does it agree with the value you calculated in the PreLab ?

From the applet simulation, what can you conclude about the Fermi level position, Ef, in the upper half or the lower half of the band gap AND the electrical type (n-type or p-type) of the semiconductor ?  Also for each type, what can you say about the doping level and the relative separation of the Fermi level from the Band edge ?
Your discussion on Ef and type:

Your discussion on doping level and the separation of Ef from band edge: