Download Ideal Schottky barrier - MSU Engineering

ECE 875:
Electronic Devices
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University
[email protected]
Lecture 21, 26 Feb 14
Chp. 03: metal-semiconductor junction: Schottky barrier
Ideal barrier
Effective barrier
VM Ayres, ECE875, S14
Example from Exam:
For the equilibrium condition:
Junction
Equilibrium: metal contact to n-type Si when work functions qFm > qFs
metal
n0= 1017 cm-3
Although the charges are
balanced, the layer on the
metal side is very thin: similar
to p+: ionized acceptors
EF
qybi
EC
--
P+ P+ P P P P P P P
EF
Ei
E (x)
Neutral region
n-side
Depletion region W ~ WDn
EV
Answer:
(a) qV0 =
--N + N + n
--N + N +
d
d
d
d
(b) Band-bending diagram:
q FB = 4.0 eV – 3.8 eV = 0.2 eV
W = 0.14 mm
q ybi =qV0 = 0.057 eV
Ideal Schottky barrier:
q ybi = 0.057 eV
q fBn0 = 0.2 eV
EC
ECm = EF
--
EF
P+ P+
W ≈ WDn = 0.14 mm
More accurately to scale:
q ybi = 0.057 eV
EC
q fBn0 = 0.2 eV
ECm = EF
--
P+ P+
W ≈ WDn = 0.14 mm
EF
Ideal Schottky barrier:
q ybi = 0.057 eV
EC
q fBn0 = 0.2 eV
ECm = EF
--
q fn
ND+ ND+
EF
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
qfBn0
= height of ideal Schottky barrier as seen from the metal
= qybi + [qfn = (EC - EF)]
n-type semiconductor
qfn = EC - EF
p-type semiconductor
qfp = EF - EV
Assume:
300 K
Equilibrium condition
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
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
0
Two factors change as a
function of doping
concentration
Competing effects
Fixed:
0.0259V @ r.t.
q ybi = ?
EC
q fBn0 = 0.8 eV
ECm = EF
--
q fn
ND+ ND+
W ≈ WDn = ?
EC – EF = q fn : Chp. 01:
EF
Lecture 21, 26 Feb 14
Chp. 03: metal-semiconductor junction: Schottky barrier
Ideal Schottky barrier
Effective Schottky barrier
VM Ayres, ECE875, S14
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
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.
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
Consider an e- in a current reaching a previously established Schottky
barrier as shown:
e-
--N + N + n
--N + N +
d
d
d
d
The e- is leaving the metal.
e-
---
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-
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.
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.
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