1. Semiconductor Devices 22
Atsufumi Hirohata
Department of Electronics
11:00 Monday, 24/November/2014 (P/L 005)

2. Exercise 1
Find the probability of occupation of a level of 0.05 eV above the conduction band edge of a Silicon device if the Fermi level is 0.7 eV above the valence band edge.
Assume the bandgap (Eg) of Silicon is 1.1 eV and
the effective mass of electron in Silicon is  (0.91  kg).
The Boltzmann constant (kB) is 1.4  J/K,
the Planck constant is 6.6  Js and
the temperature is 300K.
Use the conversion ratio: 1 eV = 1.6  J.

3. Answer to Exercise 1 Carrier density can be defined by
Here, the effective density of states at the conduction band is defined as
where me is the effective mass of electron.

4. 22 Extrinsic Semiconductor
Doping
Donor / acceptor
Carrier density

5. Extrinsic Semiconductors
p-type band structures :
n-type band structures :
Acceptor level
Donor level
Group IV semiconductors:
Si and Ge
Acceptors: B and Al
Group III-V semiconductors:
GaAs and GaN
Acceptors: Be, Zn, Cd and Ge
Group IV semiconductors:
Si and Ge
Donors: P and As
Group III-V semiconductors:
GaAs and GaN
Donors: Se, Te, Si and Ge *

6. Atomic Structure of p-Type Semiconductors
p-type semiconductor structures :
Group IV semiconductors: Group III-V semiconductors:
Si and Ge GaAs and GaN
Acceptors: B and Al Acceptors: Be, Zn, Cd and Ge *

7. p-Type Acceptors Energy potential created by an acceptor ion :
Conduction
band
Energy bandgap
Acceptor ion
Acceptor
Acceptor level (EA)
Hole
Valence
band *

8. Atomic Structure of p-Type Semiconductors
p-type band structures : *

9. Carrier Number Density
Numbers of holes in the valence band EV should equal to
the sum of those of electrons in the conduction band EC and in the acceptor level EA :
valence band
EC (Eg) EF EA
EV (0) n nA p
Similar to the intrinsic case,
Assuming numbers of neutral acceptors are NA,
For EA - EF > kBT,

10. Carrier Number Density (Cont'd)
At low temperature, one can assume p >> n,
As nA is very small, EA > EF
valence band
EC (Eg) EA EF
EV (0) n p nA
By substituting
For T ~ 0,
At high temperature, one can assume n >> nA,
Similar to the intrinsic case, for me* = mp*,

11. Typical Band Structures
Acceptor level near the valence bands : *

12. Atomic Structure of n-Type Semiconductors
n-type semiconductor structures :
Group IV semiconductors: Group III-V semiconductors:
Si and Ge GaAs and GaN
Donors: P and As Donors: Se, Te, Si and Ge *

13. n-Type Donors Energy potential created by a donor ion : Donor ion
Conduction
electron
Conduction
band
Donor level (ED)
Energy bandgap
Valence
band *

14. Atomic Structure of n-Type Semiconductors
n-type band structures : *

15. Temperature Dependence of an Extrinsic Semiconductor
Thermal excitation
* H. Ibach and H. Lüth, Solid-State Physics (Springer, Berlin, 2003); **

16. Carrier Densities of Extrinsic Semiconductors
p-type band structure :
n-type band structure : *

17. p-n Diode A junction made by attaching p- and n-doped semiconductors :
Widely used to insulate transistors.
Common circuit to convert ac to dc in a battery charger. *

18. Exercise 2
For the Silicon material with doping, estimate the dopant concentration (ND) needed to manufacture a 1 MW resister measuring 100 mm in length and 5 mm2 in cross section.
Assume that the transport of current will be carried out by majority carriers and that for Silicon,
intrinsic carrier density: ni = 1016 m-3,
mobility of electrons: me = m2/Vs
and mobility of holes: mh = 0.05 m2/Vs.
5 mm2
100 mm