Chemistry 140a
Lecture #5Jan, 29 2002
Fermi-Level Equilibration• When placing two surfaces in contact, they will equilibrate; just
like the water level in a canal lock.
• The EF of the semi-conductor will always lower to the EF of the metal or the solution. This can be understood by looking at the density of states for each material/soln.
Initial EF
Semi-Conductor Metal/Soln.
Eq. EF Initial EF
Eq. EF
Fermi-Level Equilibration• Charge comes from the easiest thing to ionize, the dopant
atoms. This leads to a large region of (+) charges within the semi-conductor.
• In the metal all of the charge goes to the surface. (Gauss’s Law)
• The more charge transferred the more band bending. E
x
EF
EF
E
x
EF
ECB
EVBEVB
ECB
Vbi
Vbi
E
x
EF
EF
E
x
EFECB
EVB
EVB
ECB
VbiVbi
Depletion Approximation
• All donors are fully ionized to a certain distance, W, from the interface.
• W=W(ND,Vbi)
XW
ND W
Vbi W
++++++++++
-----
-----
Final Picture
E
x
EF
EF
E
x
EF
ECB
EVBEVB
ECB
Vbi
Vbi
EVacEVac
scm
Eg
-
-
- ++ +
Useful Equations
Poisson’s Eqn:
d(x)dx
E x q(x)
x q p x n x NA x ND x
d2(x)dx 2
x K0
E(x)
E(x) = Electric Field (V/cm) (x) = Electric Potential (V)
(x) = Electric Potential Energy (J)
Electric Potential (V)Integrate Poisson’s Eqn.
B.C.’s
Result:
XW
+++++++Q=qNDW
-----
-----
x)
qND
d2(x)dx 2
x K0
d(x)dx
0
x 0
x W
x W
(x) qND2K0
x W 2
-qNDW2
(2K0)
(x)
x
quadratic Vbi=
Depletion Width
• Rearranging for W:
• As expected, W increases w/ Vbi and decreases w/ ND
• If one accounts for the free carrier distribution’s tail around x=W
W 2K0VbiqND
W 2K0 Vbi
kTq
qND
Typical Values
Vbimax (V) ND (cm-3) W (m) Q (C/cm2)
1 1013 11 1010
1 1016 0.36 3*1011
Electric Potential Energy• E(x) = -q(x)
(0) = -Vbi
• qVbi = (EF,SC-EF,M)
B = Vbi + Vn
– Barrier height– Independent of doping– Vbi and Vn are doping dependent
(x)
x
E
x
EF
ECB
EVB
Vbi Be-
h+
Net = 0 @ Eq.
Vn
Electric Field (V/cm)
d(x)dx
E(x)
qNDK0
x W
W
Emax=-qNDW/(K
x
Ex)
I-V Curve
No Band Bending
Low Band Bending
High Band Bending
I
V
Review
• N-type P-typeE
x
EF
ECB
EVB
Vbi
EVac
scm
Eg
-
-
- ++ +
E
x
EF
ECB
EVB
Vbi
EVac
sc
m
Eg
+
+
+
__ -
Solution Contact• 10^17 atoms in 1mL of 1mM solution • D.O.S. argument holds• Difference in exchange current across the
interface
++++++++++++++++
A-A-A-A-A-A-
Li+Li+Li+Li+Li+Li+
5-10 Angstroms
*Significantly less than typical W ~ 10nm
Semiconductor Contacting Phase
• No longer 1-Sided Abrupt Jxn. as the semi-conductor doesn’t have infinite capacity to accept charge
• Assume ND(n-type)=NA(p-type), then Wn=Wp
e-
h+
n-type p-type
Diodedirectionalized current
Degenerate Doping
• Dope p-type degenerately• NA>>ND --> 1-sided Abrupt Jxn.
Wn Wp
P-N HomojunctionN-type
BBB
N-type P+-type
Heterojunctions
• 2 different semiconductors grown w/ the same cyrstal structure (difficult)– Ge/GaAs ao~5.65 angstroms
Normal Staggered Broken
LASERs
• 3 Pieces --> 2 Heterjunctions– p-(Al,Ga)As | GaAs | n-(Al, Ga) As
e-
h+
h
Traps electrons and holes
Fermi-Level Pinning
EF,M
1
•Ideal Case
(only works for very ionic semiconductors like TiO2 and SnO2)
Never works for Si
Fermi-Level Pinning
Sze p. 278
Slope
A-B
1
CdS
TiO2 SnO2
Si GaAs
What’s Missing?• Fermi-Level pinning hurts
– Hinders our ability to fine tune Vbi
Vbi/Ni~Vbi/Pt~Vbi/Au
• Why does this happen?
E
x
EF
ECB
EVB
EVac
B
E
x
EF
ECB
EVB
EVac
B
vs.
*Solution contact for GaAs sees Fermi-level pinning, while the barrierheight correlates well with the electro-chemical potential for solutioncontact to Si
Devious Experimenter• Given a Si sample with a
magic type of metal on the surface X
• Thus the Fermi-level will alwaysequilibrate to the Fermi-level of X
• Thin interface --> e-’s tunnel through it and no additional potential drop is observed
E
x
EF,X
ECB
EVB
E
x
EF,X
ECB
EVB
EF,X-EF,M
What is X?
• Any source or sink for charge at the interface– Dangling bonds– Surface states– etc.
Questions
• Questions– Abrupt 1-sided junction(What is it?)– Sign of Electric P.E. and Electric Potential(Are they correct? I put them as they were in
the notes, but this doesn’t seem to agree with the algebra to me)