1. Lecture 25: Semiconductors
ENGR-1600
Materials Science for Engineers
Lecture 25: Semiconductors

2. Electron Energy Band Structures
Pauli Exclusion Principle: no two e- in an interacting system can have exactly same energy
When N atoms are far apart, they do not interact, so electrons in a given shell in different atoms have same energy
As atoms come closer together, they do interact, perturbing electron energy levels
Electrons from each atom then have slightly different energies, producing a “band” of allowed energies

3. Band Theory for Metals and Semiconductors
@ 0 K
@ room temp
Metals:
very large n
Semiconductors:
modest n

4. Microscopic Electric Conductivity
vd = eE
 = n e e
each line between scatter events is very slightly curved under bias
vd drift velocity [m/s]
μ e- mobility [m2/Vs]
n # of free electrons
|e| charge of an e- [C]
When an electric field E is applied, e- experience a force. Hence, they accelerate.
This force is counteracted by scattering events (analogy to friction).
When the forces balance out, there is a constant mean value of e- velocity vd.
The vd is proportional to E by the factor μ, the “electron mobility”

5. Conductivity of Metals and Semiconductors
metal >> semi

6. The Silicon Age

7. image from Wikipedia

10. Charge Carriers in Semiconductors
Two types of electronic charge carriers:
negative charge in conduction band
positive charge of a vacant electron state in the valence band
1. Free Electron:
2. Hole:
Move at different speeds - drift velocities

11. p = # of holes h+ left behind
Intrinsic Semiconductors (for pure substances only)
n = # of free electrons e- Si Si Si Si
p = # of holes h+ left behind Si Si Si Si Si Si Si Si
E field
At a given temperature, intrinsic semiconductors have some electrons with enough energy to excite through the bandgap. What they leave behind is a “hole”
Both e- and h+ are charge carriers, they move in opposite directions.

12. n = p Intrinsic Semiconductors: Conductivity vs T
• Pure Silicon:
- σ increases with T
- opposite to metals
n = p
material Si Ge
GaP
CdS
GaAs
SiC
band gap Egap (eV)
1.11
0.67
2.25
2.40
1.43
2.86
Larger electronegativity difference  larger bandgap.

13. Team Problem

14. Team Problem
1. Which of ZnSe and CdTe will have the larger band gap energy Eg ?
2. Which of ZnSe and CdTe will have the higher intrinsic carrier concentration at room temperature?

15. Extrinsic Semiconductors: the role of impurity3 5
These elements have one less valence e- relative to Si
When present as impurities, they will create lots of extra holes
called “p-type”
These elements have one more valence e- relative to Si
When present as impurities, they will create lots of extra mobile e-
called “n-type” 4

16. Extrinsic Semiconductors: n-type
-- electrical behavior is determined by impurities that introduce excess electrons or holes
-- n ≠ p
• n-type Extrinsic: (n >> p)

17. Extrinsic Semiconductors: n-type

18. Extrinsic Semiconductors: p-type
• p-type Extrinsic: (p >> n)

19. Extrinsic Semiconductors: p-type

20. Intrinsic vs. Extrinsic Semiconductors
Extrinsic n-type
Extrinsic p-type
n for “negative”
p for “positive”

21. What’s the difference between intrinsic and extrinsic semiconductors?
Team Problem
What’s the difference between intrinsic and extrinsic semiconductors?
Which do you think would be more useful in modern technology?

22. T1 T2 Extrinsic Semiconductors: Conductivity vs. Temperature
T<T1: Freeze-out region, thermal energy is not high enough to excite electron from donor state to CB
T1<T<T2: Extrinsic region, thermal energy is high enough to excite electron from donor state to CB
T>T2: Intrinsic region, thermal energy is high enough to excite electron from VB to CB T1 T2

23. Mobility vs. Impurity concentration
@ room temp

24. Mobility vs. Temperature

25. So, the As is present at about 0.001 atomic %. That’s a tiny bit
Team Problem
Si is doped with As at a concentration of 1022 As atoms 1/m3.
Is this a lot or a little bit of doping?
MW [g/mol]
ρ [g/cm3]
So, the As is present at about atomic %. That’s a tiny bit

26. p-n Rectifying Junction
• Allows flow of electrons in one direction only (e.g., AC/DC).
-- No applied potential:
no net current flow.
-- Forward bias: carriers
flow through p-type and
n-type regions; holes and
electrons recombine at
p-n junction; current flows. + -
-- Reverse bias: carriers
flow away from p-n junction;
junction region depleted of carriers; little current flow. - +

27. Properties of Rectifying Junction

28. p-n-p junction Voltage amplifier

29. M.O.S.F.E.T. device
Positive electric field at the gate: drives holes out of the p-type channel
This reduces conductivity to the drain (ON/OFF, a binary communication device)
Tiny change in gate voltage = big change in conductivity across the channel