Evolution of Physics and Chemistry of Surfaces and Interfaces: A Perspective of the
Last 40 Years
David K. Ferry
Citation: Journal of Vacuum Science & Technology B 31, 048501 (2013); doi: 10.1116/1.4806761
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Evolution of Physics and Chemistry of Surfaces and Interfaces:
A Perspective of the Last 40 Years
David K. Ferrya)
School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287

(Received 25 March 2013; accepted 29 April 2013; published 17 May 2013)
The Physics and Chemistry of Surfaces and Interfaces conference has maintained a focus on the
interfacial and surface properties of materials since its initiation in 1974. The conference continues
to be a major force in this field, bringing together scientists from a variety of disciplines to focus
upon the science of interfaces and surfaces. Here, a historical view of the development of the
conference and a discussion of some of the themes that have been focal points for many years are
C 2013 American Vacuum Society. [http://dx.doi.org/10.1116/1.4806761]
presented. V
I. INTRODUCTION
In the early Fall of 1973, Horst Wittman and I were discussing the lack of a forum for addressing the scientific
issues concerning the physics of surfaces and interfaces in
the III-V compounds. As has been rumored, these discussions took place in a bar at the Los Angeles airport while
awaiting flights back to the east coast. At the time, Horst
was with the Army Research Office, while I was with the
Office of Naval Research. So, we both had considerable
exposure to researchers working in this important area; at
least the area was important to our programs on future electronics. The result of these discussions was a plan to create a
workshop which would bring together a number of the leading people in the field to discuss germane questions, providing of course that we could draw them to the meeting.
Upon returning to the east coast, the concept was discussed with Larry Cooper, also with the Office of Naval
Research, and the consensus was to give the workshop a try.
The first workshop would be organized by Carl Wilmsen and
Jim Sites, and held at Colorado State University in January
1974. The resulting success of this first workshop led to a
continuation of the idea on an annual basis. This has become
the series of Physics and Chemistry of Surfaces and
Interfaces (PCSI) workshops.
The name has evolved over the years, as the scope of the
workshop has evolved. The first series of workshops were
titled Physics of Compound Semiconductor Interfaces, and
the sites of this first series are shown in Table I. Following
the 1981 workshop, it was decided to broaden the scope to
incorporate studies, which could be classified as more chemistry related. This led to a change in the title to Physics and
Chemistry of Semiconductor Interfaces. The sites for this second series of workshops are shown in Table II. Finally, in
2008, the scope was broadened once again to expand beyond
semiconductors and include a broader range of materials with
electronic applications. Beginning with the 2009 conference,
this third series of meetings was for Physics and Chemistry of
Surfaces and Interfaces, with the sites listed in Table III.
The strength of the PCSI conference has always lay with
an active program committee, whose commitment to it has

a)

guaranteed the presence of invited talks at the forefront of
the field. Often the set of invited talks will include both sides
of a contentious issue, in order to bring to light the underlying disagreements and views that exist in the field. As
mentioned, some of these themes were centerpieces of the
conference for a great many years, as the scientific questions
were not quickly resolved. It should be remarked that
another quite popular part of the conference is to connect
short presentations to each poster as well as to encourage
even the invited speakers to put up a poster on their talk.
This has always stimulated far more discussion for the posters as well as for the oral talks.
In the next few sections, some of these themes, for which
PCSI has been an important factor, are described. A number
of theoretical and experimental contributions are mentioned
as they highlighted the evolution of thinking about each of
the problems. But, the list is a personal choice of problems,
and is not intended to be a complete discussion of the advances since the first conference.
II. SOME DEBATE IN THE EARLY YEARS
The first PCSI was focused mainly upon Schottky barriers
and oxides on the III-V materials. It was not recognized at
the time that the behavior was governed by the same defect
structure, as this latter insight came later. There have been
several themes that have flowed through a series of workshops. It is impossible to cover them all, but I will focus upon
a few whose impact has been felt throughout the community.
A. Schottky barriers and defects

At the beginning, it was clear to all involved that the
surfaces and interfaces of the compound semiconductor
TABLE I. First PCSI series.
1974
1975
1976
1977
1978
1979
1980
1981

Fort Collins, Co
UCLA
San Diego, CA
Princeton, NJ
Los Angeles, CA
Asilomar, CA
Estes Park, CO
Williamsburg, VA

Electronic mail: ferry@asu.edu

048501-1 J. Vac. Sci. Technol. B 31(4), Jul/Aug 2013

2166-2746/2013/31(4)/048501/6/$30.00

C 2013 American Vacuum Society
V

048501-1

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048501-2 David K. Ferry: Evolution of PCSI: A Perspective of the Last 40 Years
TABLE II. Series 2 PCSI.
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008

Asilomar, CA
Sante Fe, NM
Pinehurst, NC
Tempe, AZ
Pasadena, CA
Salt Lake City, UT
Asilomar, CA
Bozeman, MT
Clearwater Beach, FL
Long Beach, CA
Death Valley, CA
Williamsburg, VA
New Paltz, NY
Scottsdale, AZ
La Jolla, CA
Research Triangle, NC
Salt Lake City, UT
San Diego, CA
Salt Lake City, UT
Orlando, FL
Sante Fe, NM
Salt Lake City, UT
Kailua-Kona, HI
Bozeman, MT
Cocoa Beach, FL
Salt Lake City, UT
Sante Fe, NM

materials were significantly different than those of the elemental semiconductors. Yet, the surface/interface structure
itself was not clearly known for any of these materials,
although there were already a number of groups addressing
the problems. At the time of the first meeting, it was supposed that the presence of surface states on, e.g., GaAs was a
result of specific surface atoms.1 It was felt that this was
especially true for the intrinsic, or clean, surface, as much
less work had been done on the over-layers such as metals,
although Spicer’s group was well known for this latter
endeavor, and particularly for their studies in photoemission
spectroscopy.
Others, however, particularly the Princeton group, performed surface studies of cleaved surfaces of these materials.
They felt that the states at the surface were intrinsic surface
states, perhaps arising from relaxation or reconstruction of a
cleaved surface, when it was a nonpolar surface.2 This view
was supported by, e.g., IBM, and clear indications of dangling bond surface states in GaAs were found.3,4
However, the situation was clouded by the claim of dominance of metal-induced gap states. These were first discussed

048501-2

by Heine,5 but significant importance was attached to them
after theoretical calculations at Berkeley.6 These latter calculations suggested that the gap states were bulk-like within
the metal, and they decayed rapidly into the semiconductor.
Nevertheless, they induced occupation of these states in the
Schottky barrier by semiconductor carriers. Later, Tersoff7
pointed out that these were both conduction and valence like
in nature, and the latter should be occupied. This suggested
that the Fermi level should lie near the crossover between
these two types of states. However, as we will see below, the
idea of induced states was losing traction, and this latter idea
went on to prominence in heterostructures. The way in which
the various models fit to the wealth of experimental data has
been carefully reviewed by M€onch.8
The problem of Schottky barriers was deeper than just the
question of the source of the Fermi energy pinning. A part of
this question had to do with whether or not the metal overlayer reacted with the semiconductor, and what the nature of
this interaction could be.9 The statement that the result of the
creation of the Schottky barrier was simply pinning by an
intrinsic surface state or by the properties of an overlayer
atom is too simplistic at first thought, as the metallurgy
might well be much more complex and this could well have
an important effect. Indeed, the question over whether or not
there was an interfacial layer which played a crucial role in
the determination of the Schottky barrier height was of considerable interest through the years.10,11 The question was
heightened by Williams, who showed that the presence of an
interfacial oxide or chlorine affected the electronic structure
of the semiconductor, but made little effect on the magnitude
of the Schottky barrier.12,13 He also questioned the S parameter that had been earlier suggested as a characteristic of
Schottky barriers.14
Almost separately, other groups worried about the nature
of the oxides that were put on the compound semiconductors.3 It was known that trying to make a MOS structure on
GaAs was quite difficult, and these devices just did not seem
to have a future. But, putting an oxide on InP gave a situation with a much lower density of surface states.15 But, at
the beginning, it was not appreciated that these studies might
well be connected to those of the Schottky barrier.
Nevertheless, as time went by, the views of these distinct
surfaces began to merge quite rapidly. By the time of
Asilomar 2 (1982), the commonality was established, and it
was now believed that Fermi level pinning did not depend
upon what was put on the surface, but it did depend upon
what the cation was. Thus, Ga compounds seem to be
doomed to a pinned Fermi level, but In compounds had a
much lower density of defect levels and could be used for
MOS transistors.

TABLE III. Series 3 PCSI.

B. Heterojunction band alignments
2009
2010
2011
2012
2013

Santa Barbara, CA
Sante Fe, NM
San Diego, CA
Sante Fe, NM
Waikoloa, HI

The question of the alignment of the bands of two distinct
semiconductors when they were joined to form a heterostructure also was a key issue at the first PCSI. As Kroemer
expressed it:16 “All of these devices depend to a varying
degree on the details of the band structure of the

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048501-3 David K. Ferry: Evolution of PCSI: A Perspective of the Last 40 Years

heterojunctions, especially on the way in which the total
energy gap discontinuity
DeG ¼ eG2  eG1 ¼ DeC þ DeV

(1)

of an (abrupt) heterojunction is divided into a conduction
band discontinuity DeC and a valence band discontinuity
DeV ,….” This became a central issue which propagated
through the conference for a great many years. To begin,
Kroemer considered the so-called electron-affinity rule and
found it very unsatisfying. In short, this rule aligns the bands
of the two materials such that the conduction bands each lie
the proper distance from the vacuum level that corresponds
to their electron affinity. One problem pointed out is that this
quantity is a surface quantity and not really relevant to a buried interface.
At the second conference, Ray Dingle presented the
results of optical studies of an array of heterojunction quantum wells.17 By studying the electron-hole transitions, they
were able to infer that 88% of the band discontinuity lay in
the conduction band. While the measurements were very
nice, the number which they inferred came under attack
almost immediately, with a smaller value ultimately being
determined. But, it was also determined that the use of the
square wells did not allow a unique determination of the
band offset.18 The problem was that as one moved the band
offset from the conduction band to the valence band, the
electron quantum well levels would move to lower energies,
and at the same time, the hole levels would also move, in the
same absolute direction. Since these levels moved like
1/L2, it was exceedingly difficult to pin down the proper
band offset. In the end, the best estimate came from single
band measurements utilizing internal photoemission.19
These measurements suggested that the conduction band offset was closer to 62% of the band offset, a number that is
still considered to be believable today.
But, the question remained: “How does one predict the
band offset in the heterostructures?” Or, if the electron affinity rule was not going to work, what would? This has led to
a long history of suggestions. One of the first was the common-anion rule.20 It was noted that in semi-empirical tightbinding calculations of the semiconductor band structure,21
the valence band maximum was invariably given by the
anion p-state wave functions. It was then obvious that, for a
material like GaAlAs/GaAs, there should be no discontinuity
in the valence band, and nearly all of the discontinuity
should be in the conduction band, in keeping with the earlier
optical measurements. But, this approach was not very
successful for GaAlAs/GaAs, much less for many other
heterostructures.
Kroemer set out to see if bulk band structures could be
used to predict the discontinuity in the heterostructure
bands.22 The problem lay in trying to predict just which
point in the Brillouin zone should be used to try to create the
cross interface boundary. It was suggested that an average
potential might be the route forward. But, what the bulk calculations missed is the inevitable interface dipole. That is,
there is a break in the local bonding structure as one crosses

048501-3

the interface, and charge penetration from one side to the
other leads to an interface dipole.23 Such dipoles lead to
potential shifts between the two sides of the interface. One
needed to be able to determine this dipole in order to predict
the band lineup of the heterostructure. However, the concept
of the total energy bands suggested to many that by measuring the core levels of the various constituent atoms, one
could estimate the band shifts, and therefore determine the
band offsets.
By 1981, results of experiments on measuring the core
level shifts across the heterointerface were beginning to
appear, and the results were not pretty. To be sure, it is a difficult experiment since photoemission requires the generated
electrons to be close enough to the surface to be emitted and
measured. Thus, the heterointerface needs to be close to the
surface and therefore requires quite thin epitaxial layers.
With this in mind, the results began to arrive. As an example,
one study showed that growth of AlAs on top of GaAs led to
a valence band discontinuity (average) of 0.4 eV, but growth
of a GaAs layer on top of AlAs gave a valence band discontinuity of only 0.15 eV.24 Now, it was known to be possible
to grow atomically sharp interfaces when AlAs was grown
on GaAs, but the reverse order produced rougher interfaces.
It was obvious that this led to a different interfacial dipole.
Finding the “right” band offsets was not going to be easy,
and the results were likely going to depend upon how the
material was grown.
It was also suggested that one could use the presence of
deep levels to infer how the bands should be aligned in the
heterostructure. It was proposed that, in cases where the
interface was atomically abrupt, bulk properties might well
be usable to predict the band lineups, and that an appropriate
bulk level would arise from the transition-metal impurities.25
These impurities are known to form deep levels within most
semiconductors. But, since these levels do not seem to be
associated with either the conduction band or the valence
band, they should provide a good reference level for alignment of the bands in heterostructures. This argument predicts
a valence band offset in AlAs/GaAs of about 0.34 eV, which
is close to the 0.35 predicted by Frensley and Kroemer,26
and not far from that found from the photoemission above,
even though this predicted number ignores their calculated
charge transfer dipole.
In subsequent calculations, it was pointed out that a dangling bond level associated with the transition-metal atoms
played the role of the “neutrality” level, and led to the correlation found from using these atoms to predict band lineups.27 Earlier, it was noted that the average hybrid energy,
determined from tight-binding calculations, played a role not
unlike the neutrality level discussed above for Schottky barriers.28 Indeed, the connection between Schottky barriers
and the band lineup for various oxides on Si was again discussed by Robertson in connection with the advent of high-j
dielectrics.29
In some sense, a closure was arising, but it always seemed
like good agreement was obtained after the measurements
were made, and that the theories were not sufficiently predictive in nature. Perhaps, the status was (and is) best described

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048501-4 David K. Ferry: Evolution of PCSI: A Perspective of the Last 40 Years

by a statement from Charley Duke. I believe it was at the
first Sante Fe conference (1983), when Duke was chairing a
theory session. A young Asian scientist ran into some difficulty with questions. At this point, the chair cut off debate
by stating what I now call Duke’s Law:
“All theory is wrong; it is just a matter of degree.”
Needless to say, there is always a corollary, in this case
coming from Wolf Porod:
“All experiment is correct; it is just a matter of what is
measured.”
C. Contacts

Contacts on III-V materials have always been a problem,
and there has been interest at PCSI since the beginning. In
Si, for example, “good” electrical contacts are made by doping the material beneath the contact metal to a very high
level. This makes an extremely thin Schottky depletion
layer, and electrons readily tunnel through this layer. But,
most of the III-V materials cannot be doped to such high levels, and therein lies the problem. Putting the metal down just
creates a Schottky barrier which impedes the motion of carriers to the semiconductor. In fact, many felt that this problem would not be solved until the Schottky barrier was fully
understood.
Secondarily, there was a problem with the fact that the
actual tunneling coefficient that was calculated did not agree
well with any measurements (usually too low a value of
calculated tunneling). At first, it was suggested that one
needed to use a more sophisticated multiband model with a
dynamic dielectric function and properly account for image
charge and trapped negative charge.30 But, it was shortly
realized that, with the small effective mass in these materials, one had to account for the discrete nature of the doping,
and use the exact positions of the impurities in the solving of
Poisson’s equation.31 The random nature of the dopant
caused some impurities to be closer to the metal, and this
then led to as much as half an order of magnitude increase in
tunneling. This was a harbinger of important effects soon to
be crucial to the device industry.
Keyes had first suggested that the small number of dopant
atoms in small transistors would lead to fluctuations in current that could not be ignored.32 The statistical fluctuations
that would arise from a small number of impurities would
dramatically affect the device performance. The above variation in contact resistance was a signal of the arrival of this
problem.31 Then, Joshi considered the random impurities in
bulk GaAs and showed that each electron was, on average,
interacting with three impurities at any one time,33 which
heralded the importance of multiple-scattering. Soon afterward, Wong and Taur presented the results of this random
impurity distribution on MOSFETs,34 clearly demonstrating
that it was important in future generation of devices. Our
own group demonstrated the importance in III-V devices.35
The importance of interface roughness at the oxidesemiconductor interface had earlier been emphasized.36 Now,
line-edge roughness,37 which led to fluctuations in channel
length, and even interface roughness between the gate metal

048501-4

and the oxide were shown to produce important effects in
devices.38 It was clear that fluctuations arising from randomness in the device structure were going to be an important
problem within the short term future.
Relief of the contact problem came with the introduction
of the alloyed AuGeNi contact formulation. It was discovered that a number of intermetallic compounds were formed,
if the alloying was done at the proper temperature.39,40 In the
intervening years, many other intermetallic compounds have
been used to create acceptable contacts.41
Until this point, I have not addressed the fact that most
people do not consider contacts to be important aspects of
their research. This is a mistake, as contacts may be the most
critical part of an experimental structure. Bad aspects can
include injection of carriers and current limiting behavior,
just to name two contrary effects. We generally hear about
the problem of injection of carriers, but most are not familiar
with current limiting behavior.42 But, a simple example illustrates this very efficiently. Over the past decade or so, there
has been interest in transport in GaN, and its heterostructure
with AlGaN. Yet, measurements of the velocity-field curve
gave current/velocity values much below those expected
from theory. It was only when the titanium rich Ti:Au metallurgy was developed that these ohmic contacts allowed sufficient current for the samples to demonstrate their very high
velocities.43,44 Thus, the understanding of the role that contacts play in the experiment is crucial as one addresses new
materials, especially for electronic applications.
III. FAST FORWARD
Through the years, PCSI has had a history of creating
focus sessions, in which a new or evolving “effect” is
brought to the attention of the attendees. Quite often, this
arises through a special session, with multiple papers so that
various sides of the scientific debate can be brought together
to give a fuller view of the issues. Among the topics in recent
years has been graphene, two-dimensional electron (or hole)
gasses at the interface of two normal insulating oxides, and
recently topological insulators. I will focus here only upon
the last two of these topics, because there are some practical
issues involved in these particular fields.
A. Oxide interfaces

In normal HEMTs, the two-dimensional electron gas is
derived from dopants, usually placed within the “insulating”
layer. That is, in GaAs HEMTs, the dopants are placed in the
AlGaAs layer via what is known as modulation doping.45
This approach is used in nearly all III-V based HEMTs.
However, wurtzite materials such as GaN and AlGaN possess a spontaneous polarization. Naturally, the amplitudes of
the polarization are different in these two materials, and an
interface will see the discontinuity in this polarization. As a
result, a two-dimensional electron (or hole) gas will form at
the interface to provide the charge required to balance this
polarization discontinuity.46
But, polar imbalance has been discovered in nonsemiconductor materials. Recently, two oxide insulators have revealed

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048501-5 David K. Ferry: Evolution of PCSI: A Perspective of the Last 40 Years

the existence of a quasi-two-dimensional electron gas at the
interface between them, when one is grown on the other by
molecular-beam epitaxy.47 In this case, both oxides are wide
bandgap insulating perovskites, yet they produce this semiconductor behavior when the heterointerface is formed.
SrTiO3 is a typical ABO3 material, in which the structure can
be considered as alternate layers of BO2 and AO. Both of
these layers are charge neutral, so there is nothing immediately weird at this point. However, the similar LaAlO3 has
sheets that are charged by 6e/2, and this changes the net
behavior. The growth by molecular-beam epitaxy allows one
to form the structure basically layer by layer. When the interface was (AlO2)(SrO)0, a hole layer was expected, but the
interface remained insulating. On the other hand, when the
interface was (LaO)þ(TiO2)0, an electron gas was pulled into
the interface. The electrons exhibited a very high mobility
and quantum behavior at low temperatures.
In this latter situation, as in the HEMTs above and
MOSFETs, the electrons in the interfacial inversion layer are
drawn into the structure from the contacts, if there is no
intrinsic source. Presumably, there are traps which absorb
the holes in the first situation. The presence of the electrons
at the interface is symbolic of the fact that nature prefers
charge neutrality. Even in transistor structures, where space
regions are engineered, global charge neutrality is maintained. If this did not occur, it would be shocking indeed.
The above interpretation is nice, but there are many problems existing before a full understanding can be obtained.
Not the least of the problems, is the fact that Hall measurements on the above structure leads one to believe that there
is an incredibly large electron density in the inversion
layer.47 And, there is the role of strain in these layers.48 It
appears that the carriers have strong correlation, which can
lead to superconductivity49 and magnetism,50 which, unusually, can coexist.51 This is even before we consider that other
oxides can be used for these effects. It is clear that this is a
new and exciting field, which may well have an important
impact in electronics.
B. Topological insulators

Topological insulators have been all the rage the past few
years, so it is natural that they have come to PCSI. A reasonably recent review of the subject can be found in Ref. 52. Of
key interest for electronic properties is that these materials often possess a Dirac-like band structure, which is topologically
stabilized at a surface or interface. One prototypical material
is a heterostructure between the negative band gap material
HgTe and the positive band gap HgCdTe or CdTe. In HgTe,
the energy state that composes the normal top of the valence
band and the one that normally is the bottom of the conduction band are inverted. When crossing the interface between
the two materials, this band ordering must reverse itself, and
this can lead to the Dirac-like band structure at the interface,
especially with the large spin-orbit interaction in HgTe. For
the discussion here, it is not the presence of a topological
state in this heterostructure, but the question as to why this
property was not discovered much earlier.

048501-5

The nature of bands in the HgTe/CdTe superlattice was
being discussed at PCSI at least as early as 1979.53,54 So, the
nature of the energy structure in the interface between the two
materials must have been known, especially as the spin-orbit
interaction was specifically included. But, there may well
have been two reasons that the interesting interfacial properties were not appreciated. First, the concepts of topology were
not in the mainstream of condensed matter and materials
physics at the time. Second, the intriguing ideas of Dirac-like
bands in semiconductors were not appreciated at the time.
In one sense, topology crept into the field with Laughlin’s
introduction of a structure and phase rigidity to explain the
accuracy of the quantum Hall effect.55 It became stronger
with the discussion of fractionally charged quasiparticles in
the fractional quantum Hall effect. In the latter, the filling
factor for various Hall states is the ratio of the number of
electrons to the number of flux quanta in the structure. Thus,
in the  ¼ 1/3 state, there are three flux quantum for each
electron. When the magnetic field is exactly at this filling
factor, all the states in this level are completely full. If we
now add a single flux quantum, then the unoccupied state
must hold a quasihole with a charge of 1/3 to fit the statistics,56,57 a fact that has been verified with experiment.58 It is
generally believed that these statistics are best described by
a Chern–Simons gauge theory,59 and this leads to a connection to quantum computing.60 The interaction between two
fractional states has shown the phase interference that would
be necessary for this purpose.61 So, topology and topological
computing came to the forefront with these fractional charge
states, and the genie was out of the bottle.
Appreciation of the Dirac-like band structure came later.
The details of this band structure have been known for decades.62 But, it was only with the isolation of single layers of
graphene63 that experiments could begin to establish the
unique properties of this band structure. And, studies of the
quantum Hall effect quickly illustrated that these bands had
different properties than normal semiconductors.64
So, by 2005 or so, there was a reasonable appreciation of
the role of topology in condensed matter physics, and there
was demonstrated different behavior in Dirac-like bands. At
this point, the stage was set for someone to suggest a more
general view of topological insulators (although the idea of a
topological superconductor is older65), and the ideas on topological changes were widespread and growing a few years
earlier. For example, the topological transition between a correlated insulator and a band insulator was discussed about
this time.66 In spite of this nice argument, the phrase
“topological insulator” actually seems to have originated in
biology,67 but burst into condensed matter theory at about the
same time.68,69 Today, the focus is more directed at materials
(and structures) which have insulating bulk properties, but
exhibit metallic surfaces.52 One hopes that we will continue
to hear more about these at future PCSI conferences.
IV. SUMMARY
PCSI has continued to be an important, and interesting,
conference over the past 40 years. This is best exemplified

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048501-6 David K. Ferry: Evolution of PCSI: A Perspective of the Last 40 Years

by the continued strong presence. Perhaps more importantly,
the conference continues to draw a sizable number of young
(student) attendees, which points to the strong environment
for discussion and interaction which the conference provides. Thus, it appears to have the necessary requisites to
continue for another 40 years.
ACKNOWLEDGMENTS
The author would like to especially thank Rudy Ludeke
for his aide in recalling the early years of PCSI, particularly
with respect to the publications and some important people.
However, the neglect of some important contributions is
entirely my own failure.
1

W. E. Spicer and P. E. Gregory, CRC CR Solid State Sci. 5, 231 (1975).
P. Mark, S. C. Chang, W. F. Creighton, and B. W. Lee, CRC CR Solid
State Sci. 5, 189 (1975).
3
R. Ludeke and A. Koma, CRC CR Solid State Sci. 5, 259 (1975).
4
J. L. Freeouf and D. E. Eastman, CRC CR Solid State Sci. 5, 245 (1975).
5
V. Heine, Phys. Rev. 138, A1689 (1965).
6
S. G. Louie, J. R. Chelikowsky, and M. L. Cohen, J. Vac. Sci. Technol.
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