*Applet Worksheet*

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

1)

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) n_{i}= ( )/cm^{3}@ 200Kb) n_{i}= ( )/cm^{3}@ 300Kc) n_{i}= ( )/cm^{3}@ 400K

Useful Si Formulas: n_{i}^{2}= B T^{3}exp(-E_{g}/kT) where B=2.4x10^{31}[1/cm^{6}K^{3}], and k=8.62x10^{-5}[eV/K], E_{g}(T)= 1.17 – 4.73x10^{-4}T^{2}/ (T+636) [eV]

3) For Si doped with As (donor) impurities to N_{d}=1x10^{17}/cm^{3},
**calculate**
the electron concentration and hole concentration at 300 K. Note
that `n*p=n _{i}^{2} (Mass-Action Law)` under thermal
equilibrium.

4) Calculate En = ( )/cm^{3}p = ( )/cm^{3}

E

E

**Procedure**: *Energy 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 **N _{d}=0**, Acceptor
concentration

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 ?

n4)_{i}= ___________ cm^{-3}@ 200 K

n_{i}= ___________ cm^{-3}@ 300 K

n_{i}= ___________ cm^{-3}@ 400 K

Click the

5) Extrinsic Si with **both Donor and Acceptor impurities** (Compensation)

Click the **“Reset”** button. Set **Nd = 2x10 ^{17}/cm^{3},
Na = 3x10^{17}/cm^{3}.** Read n and p from the
applet. From the result explain

6) **Extrinsic Si at various T**

Click the **“Reset”** button. Set **Nd = 0 **and **Na=1x10 ^{15}/cm^{3}**.
Read n and p from the applet at various temperatures and calculate or find
n

200 K: n = ( ) p = ( ) n_{i}= ( )

300 K: n = ( ) p = ( ) n_{i}= ( )

400 K: n = ( ) p = ( ) n_{i}= ( )

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 = 10 ^{17}/cm^{3}**and

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=10 ^{16}/cm^{3}**.

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: