Modeling of an interface
between two solids
Ashcroft and Mermin Ch. 18
Sze Ch.3
1987 Review Chapter by Tersoff
The Work Function of a Metal
A. If there are no interface dipoles
• Negative value of Ef reflects the attractive
force of the positive ions
The Work Function of a Metal
B. Surface dipole – additional component due
to dipole field
Evaluation of a Single Monolayer
Maximum Dipole Energy in GaAs
a
a  0.56nm
d  0.14nm
qns
qns d
V Q/C 

0 d
0
ns  2 / a 2  2 / (5.6 108 ) 2  6.4 1014 cm2
1.6 1019  6.4 1014 1.4 108 cm
V
 16V
14
8.8 10 F / cm
Two metals
• Same chemical potential after contact is
established – if electrons are free, by the
definition of chemical potential.
q(V1  V2 )  W1  W2
W1
W2
Measurement of the Contact
Potential by the Kelvin Probe Method
d  d0 sin(t )
W1
W2
A
VDC
i  i0 cos(t )
Ideal Insulator ε=1
• No charge redistribution due to an electric
field – no dipole at the interface. Afinity rule
exact
The Neutrality Level Concept
• Surface neutrality level – Bardeen 1947
Cowley and Sze 1965
• Bulk neutrality layer - Tejedor and Flores 1977,
Tersoff 1984
Cowley and Sze’s analysis
Qss  qDit ( EFm  E0 )
E0
Cowley and Sze’s analysis
E0
Silicon Barrier with Metals
Other Semiconductors
Summary
The bulk neutrality level
• Epitaxial interfaces are almost defect free
• Yet, the affinity rule is not obeyed
• The bulk neutrality level plays a role analogous
to the Fermi level in metals
• No Charge transfer if both neutrality layers
coincide
The bulk
neutrality
level -Tersoff
limits
metal
Ideal
insulator
Evaluation of α – consider bulk
material- Tersoff’s thought
experiment
EC
EV
freeze all charges - introduce dipole –
E 0  En0  EC0  EV0
ΔE 0
EC
EV
relax charges (not the fixed dipole) fixed dipole is screened like in a plate
capacitor
E  En  EC  EV
ΔE =ΔE 0 /ε
EC
EV
Compare to previous definitions
hence
ΔE =ΔE 0 /ε
EC
EV
Conclusion: in semiconductors
neutrality levels are almost aligned
Microscopic origin of the dipole
(the homogenous material thought
experiment)
• States induced by tunneling – empty states
are positively charged, filled states negatively
charged.
The sum rule – the integrated
density of states at any location is a
constant
A fraction of the states
that tunneled from the
right originate from the
conduction band – DOS
below Fermi level
increased
Ef
A fraction of the states that
tunneled from the left
originate from the valence
band - DOS below Fermi level
decreased
A heterojunction aligned at the neutrality levels - total DOS bellow
Fermi level remains unchanged
A fraction of the states
that tunneled from the
left originate from the
conduction band
Ef
A fraction of the states
that tunneled from the
left originate from the
valence band
Microscopic or macroscopic α ?
• Tersoff – 1     r
• but charge is located at bond distance
• Tejedor and Flores calculate   2.5
Calculation of neutrality level at 1D
(Tersoff)
Eb is a natural division between the valence
and conduction bands
Calculation of neutrality level at
3D- Tersoff
Calculation of the neutrality level
by Tersoff and comparison with
barrier height
2011 comments by Tersoff
Q. I am accustomed to the way of thinking which relates band
alignment between semiconductors as well as Schottky barriers to
the properties of the interface. Thinking of bulk properties in this
context is unusual to me, and I was intrigued to find out how your
ideas have evolved over the years.
A. I can't really say that my ideas have evolved much since then,
since I moved on to other things. I don't remember what is in
that chapter, but strictly speaking, both the interfacial properties
and the bulk properties do matter. A metal-metal interface is
the ideal example where bulk properties totally screen out
interfacial effects. The smaller the dielectric constant,
the more the interfacial details matter. The interface could
also dominate if it is too non-bulk-like, e.g. non-stochiometric,
or high density of defects.
2011 comments by Tersoff
Just from my very out-of-date memories, I don't remember silicides
behaving any differently than other metals -- i.e. Schottky barriers
roughly consistent with calculated neutrality levels, with small shifts
reflecting the different metal workfunctions.
There is much more opportunity for complications at III-V interfaces,
especially for polar orientations like 001 and 111, because the
chemistry might lead to a dipole at the interface, just as for polar surfaces.
It's intriguing that such effects usually don't seem important -different metals on (001) surfaces of III-V's show the trends expected
from simple bulk arguments. This is convenient, but it isn't really
understood.