My recent review on Schottky barrier height can be found
in Applied Physics Reviews 1, 011304 (2014).
I plan to update this entire tutorial in 2014. Please
e-mail me if you have suggestions or know examples of good
"tutorial" websites for me to copy. Thanks.
One of the most interesting properties of any metal-semiconductor (MS)
interface is its Schottky barrier height (SBH).
The SBH is the rectifying barrier for electrical conduction across the MS
junction and, therefore, is of vital importance to the successful
operation of any semiconductor device.
The magnitude of the SBH
reflects the mismatch in the energy position of
the majority carrier band edge of the semiconductor and the metal Fermi level
across the MS interface.
At a metal/n-type semiconductor interface, the SBH is the difference between the
conduction band minimum and the Fermi level.
And for a p-type interface, the SBH is the difference between the
valence band maximum of the semiconductor and the metal Fermi level.
The most common symbol for the SBH is
FB. Other superscripts and/or
subscripts are sometimes added to indicate the type of semiconductor
and whether the SBH pertains to the flat-band condition or the depletion
For example, the symbol FoB,n
denotes the flat-band SBH with an n-type semiconductor.
We usually see band diagrams drawn in this fashion
to illustrate the band bendings for n-type and p-type semiconductors.
(You can click on most figures in this tutorial to blow them up.)
While viewing these band diagrams, however, we should keep in mind that they
are drawn to show only the long-range variation of the bands in the
space charge region of the semiconductor.
The electronic structure and charge distribution in the immediate
vicinity (~1nm) of the MS interface have been deliberately neglected.
Therefore, these often-encountered band diagrams
are in fact only "asymptotic band diagrams",
which illustrate how the semiconductor (or metal) bands vary as the bands
approach the MS interface.
The next time you look at a band diagram like the above, it may not be a
bad idea to imagine that there is actually a small gap, or a
little black box separating the semiconductor bands
and the metallic bands, as drawn below.
The region inside this little black box
is known as the interface
specific region (ISR).
This is the transitional region between the metal and the semiconductor,
where the magnitude of the SBH is determined.
"What determines the magnitude of the SBH?" is a question which has
troubled scientists for decades.
The first-order theory of the formation of a Schottky barrier (SB) is
the view attributed to W. Schottky himself originally, and also to Sir Mott.
The Schottky-Mott theory proposes that the SBH depends sensitively on the
work function of the metal.
However, this prediction has received little support from experiment.
The SBHs measured in actual experiments often showed some dependence on
the preparation of the MS interface, which indicates that the SBH depends
more than just the work function of the metal. Despite some scatters in
the experimental data, by and large, metals with larger work functions have
been found to have systematically higher SBHs than those with lower work functions.
But the actual dependence observed is much weaker than that
predicted by the Schottky-Mott theory.
A term, "Fermi level (FL) pinning", has often been used to describe the insensitivity of
the experimental SBH to the metal work function.
Because of the poignancy of the FL pinning phenomenon, explanation of this
effect alone had occupied the attention of most SBH studies conducted before the mid 1980's.
Not surprisingly, most of the SBH theories proposed during that period of time contained some
features or assumptions, which would automatically make the SBH insensitive to the interface structure.
A well-known example is the common assumption that the distribution of interface states is a property
of only the bulk semiconductor and not the metal. Although it clearly could explain the FL
pinning effect, such an ad hoc assumption is hard to rationalize from the standpoint of
general physics and chemistry. When a metal and a semiconductor are joined to form a MS interface,
a significant redistribution of charge is expected to take place due to the overlap of wave
functions from the two sides. Old bonds are broke, and new bonds are formed.
The electronic states that accommodate the charge transfer at the interface should
be characteristic of the MS interface and not just the semiconductor. So quantum mechanically,
one expects the SBH to depend sensitively not only on the identity of the metal but also on
the interface structure, which would seem to be at odds with the experimentally observed
FL pinning phenomenon. Since the mid 1980's, a few high-quality, single-crystal, MS interfaces
were successfully fabricated and the SBH measured at these interfaces showed
a rather dramatic
dependence on the orientation/structure of the MS interface. That the SBH depended
on the interface structure was very much in line with the intuitive quantum mechanics
picture of interface dipole and bonding, although it seemed to disagree with the FL-pinning
phenomenon widely observed at polycrystalline MS interfaces. Some of the disagreement was
settled when it was pointed out a few year later that the SBHs at polycrystalline MS
interfaces were often inhomogeneous.
The electrical data from polycrystalline SBs had always contained clear signs of SBH inhomogeneity.
However, the decipher of such evidence, as it turned out, would require some knowledge on the band
bending of an inhomogeneous SB, which was lacking prior to the early 1990's. Independently,
direct evidence for SBH inhomogeneity also began to mount with the arrival of spatially-resolved
SBH techniques, most notably the ballistic electron emission microscopy (BEEM). The general
inhomogeneity in polycrystalline SBHs was in very good agreement with the structure-dependence
observed at single crystal MS interfaces. It thus appeared that a consistent view on the
formation mechanism of the SBH was emerging, but there remained one more hurdle to overcome.
One still had to answer the question "how can a SBH mechanism which depends so sensitively
on the interface structure can lead to SBHs at polycrystalline interfaces that always average
out to nearly constant values, irrespective of the metal?". In other words, how does one explain
the FL-pinning phenomenon with the bonding picture? This question was answered at the turn
of the century/millennium when the interface dipole associated with chemical bonding at
MS interfaces was modeled using established methods borrowed from molecular physics.
It was shown that FL-pinning was a natural consequence of interfacial bonding.
Furthermore, a host of experimentally observed systematics which had hitherto been attributed
to interface states could be directly derived within the bonding picture, through a
minimization of the total energy. At the present moment, it seems that the major
formation mechanism of the SBH has finally been clearly identified.
It should surprise no one that the intuitive picture of the formation of the SBH should
turn out to be the right one!