1. ECE 875: Electronic Devices
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University

2. Lecture 21, 26 Feb 14
Chp. 03: metal-semiconductor junction: Schottky barrier
Ideal barrier
Effective barrier
VM Ayres, ECE875, S14

3. Example from Exam:
For the equilibrium condition:

4. E (x) Junction metal n0= 1017 cm-3 Depletion region W ~ WDn
Equilibrium: metal contact to n-type Si when work functions qFm > qFs
Junction
metal
n0= 1017 cm-3
Although the charges are balanced, the layer on the metal side is very thin: similar to p+: ionized acceptors
qybi EC EF EF
- -
P+ P+ P P P P P P P Ei EV
Neutral region
n-side
E (x)
Depletion region W ~ WDn

5. --Nd+ Nd+ n --Nd+ Nd+ Answer: (a) qV0 = (b) Band-bending diagram:
q FB = 4.0 eV – 3.8 eV = 0.2 eV
q ybi =qV0 = eV
W = 0.14 mm

6. Ideal Schottky barrier:
q ybi = eV
q fBn0 = 0.2 eV EC
ECm = EF EF
- -
P+ P+
W ≈ WDn = 0.14 mm
More accurately to scale:
q ybi = eV EC
q fBn0 = 0.2 eV
ECm = EF EF
- -
P+ P+
W ≈ WDn = 0.14 mm

7. Ideal Schottky barrier:
q ybi = eV EC
q fBn0 = 0.2 eV
q fn
ECm = EF EF
- -
ND+ ND+
W ≈ WDn = 0.14 mm
EC – EF = q fn : Chp. 01:
NC = effective DOS at the conduction band edge (eq’n (18)).
Practical: use Appendix G
n ≈ ND assumes fully fully ionized donors in saturation Temp range

8. qfBn0 = height of ideal Schottky barrier as seen from the metal
= qybi + [qfn = (EC - EF)]

9. n-type semiconductor
qfn = EC - EF
p-type semiconductor
qfp = EF - EV

10. Assume:
300 K
Equilibrium condition

11. Draw band-diagrams with the following values marked on it:
Barrier height on metal side: qfBn0 = 0.8 eV = given
Barrier height on semiconductor side: qybi
Barrier width W: primarily on n-side: WDn

12. Draw band-diagrams with the following values marked on it:
Barrier height on metal side: qfBn0 = 0.8 eV = given
Barrier height on semiconductor side: qybi
Barrier width W: primarily on n-side: WDn

14. Fixed:
r.t.
Two factors change as a function of doping concentration
Competing effects

15. q ybi = ? EC
q fBn0 = 0.8 eV
q fn
ECm = EF EF
- -
ND+ ND+
W ≈ WDn = ?
EC – EF = q fn : Chp. 01:

18. Lecture 21, 26 Feb 14
Chp. 03: metal-semiconductor junction: Schottky barrier
Ideal Schottky barrier
Effective Schottky barrier
VM Ayres, ECE875, S14

19. During a C-V voltage sweep, real current is flowing.
Current flowing lowers the ideal barrier height
Lowered barrier height is called the effective barrier height
Any active measurement will give you the effective barrier height not the ideal one

21. Same as abrupt junction
Pr. 02, Chp. 02
Intercept  ybi
Slope  N
Pr. 8(a), Chp. 03:
VR to VF is plotted right to left
Not left to right
You take a C-V curve data in F/V.
But Units in eqn’s and Fig 30 are C = es/WD in F/cm2
The extra factor 1012 or 13 came from normalizing to a contact area to get the F/cm2 unit.

22. Current flowing lowers the ideal barrier height
Why:
During a C-V voltage sweep, real current is flowing.
Current flowing lowers the ideal barrier height
Lowered barrier height is called the effective barrier height
Any active measurement will give you the effective barrier height not the ideal one

23. Consider an e- in a current reaching a previously established Schottky barrier as shown:
--Nd+ Nd+ n
--Nd+ Nd+ e-

24. The e- is leaving the metal.-- e-

25. An e- that leaves a metal induces a re-arrangement of charge in the metal. Keep in mind that metallic electrons can rearrange very easily. The real re-arrangements of e- and + that develops can be described as an image charge.
Mathematical equivalent
REAL -- + e- ++ e-

26. The image charge field also does work on the e-, independent of anything the depletion region field E is doing.
e0 => es as the e- is really transporting into a semiconductor.

27. Combined potential energy of an e- entering the semiconductor from image charge field AND depletion region field :
e0 => es as the e- is really transporting into a semiconductor.

28. Lowered barrier height is called the effective barrier height qfBn
During a C-V voltage sweep, real current is flowing.
Current flowing lowers the ideal barrier height and shifts the max to xm
Lowered barrier height is called the effective barrier height qfBn
Any active measurement will give you the effective barrier height not the ideal one