Module PHY6002 Inorganic Semiconductor Nanostructures Lectur.docx

Module PHY6002 Inorganic Semiconductor Nanostructures
Lectures 7, 8, 9 and 10
1
Lecture 7 – The fabrication of semiconductor
nanostructures I
Introduction
In this lecture we will look at the techniques used to fabricate
semiconductor
nanostructures. The well-established epitaxial methods used to
produce
quantum wells will be described. The main techniques applied
to produce
quantum wires and quantum dots will be discussed, with a
comparison of their
relative advantages and disadvantages. In the next lecture we
will look in
detail at the most successful technique used to produce quantum
dots, self-
organisation.
Epitaxial techniques
There are two well established epitaxial growth techniques used
to produce
high quality quantum wells: molecular beam epitaxy (MBE) and
metal organic
vapour phase epitaxy (MOVPE).
The following figure shows the main components of an MBE
reactor.

The reactor consists of an ultra-high vacuum chamber with a
number of
effusion cells, each containing a different element. Each cell
has a mechanical
shutter placed in front of its opening. In operation the cells are
heated to a
temperature where the elements start to evaporate, producing a
beam of
atoms which leave the cells. These beams are aimed at a heated
substrate
which consists of a thin wafer of a suitable bulk semiconductor.
The incident
beams combine at the surface of the substrate and a
semiconductor is
deposited atomic-layer by atomic-layer. The substrate is rotated
to ensure
even growth over its surface. By opening the mechanical
shutters in front of
certain cells it is possible to control which semiconductor is
deposited. For
example opening the shutters in front of the Ga and As cells
results in the
growth of GaAs. Shutting the Ga cell and opening the Al cell
switches to the
growth of AlAs. Because the shutters can be operated very
rapidly in
comparison to the rate at which material is deposited, it is
possible to grow
An MBE reactor

2
very thin layers with very sharp interfaces between layers. The
following figure
shows a transmission electron microscope image of a quantum
well sample
containing five wells of different thicknesses. The thinnest well
has a
thickness of only 1nm. Other cells in the MBE reactor may
contain elements
used to dope the semiconductor and it is possible to monitor the
growth as it
proceeds by observing the electron diffraction pattern produced
by the
surface.
The second epitaxial growth technique is metal organic vapour
phase epitaxy
(MOVPE). In this technique the required elements are carried,
as a
component of gaseous compounds, to a suitable chamber where
they mix as
the gases flow over the surface of a heated substrate. The
compounds
breakdown to deposit the semiconductor on the surface of the
substrate with
the remaining waste gases being removed from the chamber.
Valves in the
gas lines leading to the chamber allow the gases flowing into
the reactor to be
switched on and off. A suitable switching sequence allows
layered structures
to be deposited. Because it is difficult to switch a gas flow

quickly, and
because the growth rate with MOVPE is faster than for MBE,
the latter
technique is generally capable of growing thinner layers with
more abrupt
interfaces. However the faster growth rate of MOVPE has
advantages in
commercial production where it is necessary to deposit the
material as quickly
as possible. MOVPE has a number of safety implications as the
gases are
highly toxic. The following figure shows a schematic diagram
of the main
components of a MOVPE system.
A cross sectional transmission electron microscopy (TEM)
image of an InGaAs-
InP quantum well structure containing five wells of different
thicknesses.
Main components of a MOVPE system (From Davies)
3
Requirements for semiconductor nanostructures
Before we look at the various techniques that have been used to
produce
quantum wires and dots, it is useful to consider what properties
ideal

structures should exhibit. This will help in analysing the
relative advantages
and disadvantages of each technique.
The main requirements of a semiconductor nanostructure can be
summarised
as follows
• Size. For many applications we require all the electrons and
holes to be in
their lowest energy state, implying negligible thermal excitation
to higher
states. The amount of thermal excitation is controlled by the
ratio of the
energy spacing between the confined states and the thermal
energy, given
by kT. At room temperature the thermal energy is 25meV and a
rule of
thumb is that the level separation should be at least three times
this value
(~75meV). As the spacing between the states is controlled by
the size of
the structure (see lecture 5 for the case of a quantum well) this
places
requirements on the size of the nanostructure.
• Quality. Defects may increase the probability of carriers
recombining non-
radiatively. Structures with a large number of defects may be
very
inefficient light producers. For optical applications
nanostructures with low
defect numbers are required.
• Uniformity. Devices generally contain a large number of
nanostructures.
Ideally all the nanostructures should be identical otherwise they

will all emit
light at slightly different energies.
• Density. It should be possible to produce dense arrays of
nanostructures.
• Growth compatibility. Industry uses MBE and MOVPE
extensively.
Nanostructures will find more applications if they can be
produced using
either or both of these techniques.
• Confinement potential. The depth of the potential wells which
confine the
electrons and holes must be relatively deep. If this is not case
then at room
temperature carriers will be thermally excited out of the
nanostructure.
• Electron and/or hole confinement. For electrical applications
it is
generally only necessary for either electrons or holes to be
trapped
(confined) within the nanostructure. For electro-optical
applications it is
necessary for both types of carrier to be confined.
• p-i-n structures. Many applications require the electrical
injection of
carriers into the nanostructure or the transfer of carriers,
initially created in
a nanostructure, to an external electrical circuit. This can be
achieved if the
nanostructure can be incorporated within the intrinsic region of
a p-i-n
structure.

Fabrication of semiconductor quantum wires and quantum dots
Lithography and etching
This starts with an epitaxially grown two dimensional system to
provide
confinement along the growth direction. Lithography (etch
resist, optical
lithography with a mask or electron beam lithography) is then
used to define a
pattern on the surface consisting of either wires or dots. These
are
subsequently etched using a plasma, resulting in free standing
dots or wires.
The structure can subsequently be returned to a growth reactor
to be
4
overgrown and incorporated in a p-i-n device. The main stages
of this
technique are shown in the following figure. The main
disadvantage of this
technique is that the surface is damaged during the etching
stage. The
resultant defects produce an optically dead layer where non-
radiative
recombination is the dominant electron-hole recombination
process. This

dead layer has an almost constant width so becomes
increasingly important
as the size of the structure decreases. For the small sizes
required for
practical nanostructures the dead layer occupies all of the
structure which is
consequently optically dead.
Cleaved edge overgrowth
A quantum well is initially grown and then the sample is
cleaved in the growth
reactor along a plane parallel to the growth direction. The
sample is then
rotated through 90° and a second quantum well followed by a
barrier is grown.
The growth sequence is shown in the following figure.
The two quantum wells form a T-shaped structure. At the
intersection of the
two wells the effective well width is slightly larger. Because the
confined
energy levels depend on the inverse of well width squared (see
Lecture 5) the
intersection region has a slightly lower potential and hence
electrons and
holes become trapped there – a quantum wire is formed. If
during the initial
growth multiple wells are grown then the overgrowth of the
final well results in
a linear array of wires. A second cleave followed by a further
overgrowth can
be used to produce quantum dots.
The surfaces produced by cleaving are clean, in contrast to the
dirty surface

formed by etching. Hence cleaved edge overgrowth dots and
wires have a
(a) (b) (c) (d)(a) (b) (c) (d)
The main stages in forming lithographically defined dots. (a)
growth of a 2D quantum
well. (b) surface coating with etch resist. (c) exposure of resist
to form pattern (d)
etching to form dot or wire.
(a) (b) (c) (d)(a) (b) (c) (d)
The steps involved in the cleaved edge overgrowth of a quantum
wire. (a) initial
quantum well growth (b) cleavage to form a perfect surface (c)
rotation (d) growth
of the second quantum well.
5
high optical quality. Their main disadvantage is that the
potential at the
intersection of the wells is not much smaller than in the wells.
The carriers are
only weakly confined in the intersection region and at room
temperature their
thermal energy is sufficient to allow them to escape. These
structures are

therefore generally suitable for studying physics at low
temperatures but not
for device applications, which need to work at room
temperature. In addition
the cleaving step is a difficult, non-standard process.
Growth on Vicinal Substrates
Semiconductors are crystalline materials with a periodic
structure. Only when
a semiconductor crystal is cut in certain directions will it have a
flat surface.
For other directions the surface will consists of a series of steps
(think about a
brick wall). Epitaxial growth is usually performed on flat
surfaces. However the
use of stepped surfaces (so-called vicinal surfaces) can be used
to produce
quantum wires. The size of the steps is determined by the
direction along
which the surface is formed but are typically ~20nm or less.
The above figure shows the main steps in the growth of vicinal
quantum
wires. Starting with the stepped surface (a) the wire
semiconductor is initially
deposited epitaxially (b). Growth tends to occur in the corner of
the steps as it
here that the highest density of atomic bonds occurs. As the
growth proceeds
the semiconductor spreads out from the initial corner. When
approximately
half of the step width has been covered growth is switched to
the barrier
material (c) which is used to cover the remainder of the step.
Growth can then

be switched back to the wire semiconductor to increase the
height of the wire
(d). This growth cycle is repeated until the desired vertical
height is obtained.
Finally the wire is overgrown with a thick layer of the barrier
material (e).
Although very thin wires can be produced using this technique
the growth has
to be very well controlled so that exactly the same fraction of
the step is
covered during each cycle. In addition the coverage on different
steps varies
and it is difficult to ensure that the original steps are uniform.
The resultant
wires tend not to exhibit good uniformity.
Growth on patterned substrates
This starts with a flat semiconductor substrate which is coated
with an etch
resist and then exposed using either optical or electron beam
lithography to
produce an array of parallel stripes. The regions between the
stripes are then
etched in a suitable acid. Because the acid etches different
crystal directions
at different rates, a v-shaped groove is obtained. The patterned
substrate is
then cleaned and transferred to a growth reactor.
(a) (b) (c) (d) (e)(a) (b) (c) (d) (e)
The main steps in the growth of vicinal quantum wires (a)
original stepped surface
(b) growth occurs in corners of steps, sufficient material
deposited to cover ~1/2
of step (c) remainder of step filled in with first material (d)
more wire material

deposited to increase thickness of wire (e) final over growth of
wire.
6
Quantum wires are usually formed from GaAs, with AlGaAs as
the barrier
material. Initially the AlGaAs barrier is deposited. This grows
uniformly over
the whole structure and may sharpen the bottom of the groove
which, after
the etching, has a rounded profile. Next a thin layer of GaAs is
deposited.
Although this again grows over the whole surface, the growth
rate at the
bottom of the groove is faster than that on the sides of the
grooves due to the
different crystal surfaces. A quantum well is formed with a
spatial modulation
of its thickness, being thicker at the bottom of the groove. In a
similar manner
to cleaved edge overgrowth, this thicker region results in a
potential minimum
forming a quantum wire. A second AlGaAs barrier layer can
now be grown;
this re-sharpens the groove after the formation of the wire, after
which further
wires can be grown. The main steps of this technique, resulting
in v-groove
quantum wires, are shown in the above figure.

The following figure shows a cross sectional transmission
electron
microscope image of a multiple v-groove quantum wire
structure. The wires
have a crescent cross section.
(a) (b) (c) (d)
The main steps in the formation of v-groove quantum wires (a)
original patterned
substrate, (b) growth of barrier semiconductor (c) growth of
wire semiconductor,
greater growth at bottom of groove (d) growth of second barrier,
re-sharpening of
groove.
A cross sectional transmission electron micrograph of three v-
groove quantum
wires. The wires have a maximum thickness of approximately
8nm.
7
Because the quantum wire is not next to the original etched
surface, v-groove
quantum wires exhibit good optical efficiencies. However it is
difficult to
control the inplane size of the wires as this is mainly
determined by the shape

of the groove. The uniformity of the wire along its length is
also influenced by
the original groove quality. For achievable wire sizes the energy
level
spacings are typically 20~30meV, some what less than required
for room
temperature operating devices. However in some cases careful
control of the
groove cross-section has lead to slightly larger level spacings.
A further
disadvantage of v-groove quantum wires is their complicated
structure. In
addition to the wire there are quantum wells formed on the sides
of the groove
(side wall wells) and on the region between the grooves (top
wells). These
wells may capture carriers, reducing the fraction which
recombine in the wire
and also producing additional features in the emission spectra.
Although the
top wells and some of the side wells can be removed by etching
after growth
this requires a further fabrication step and the structure may
need to be
returned to the reactor to complete the growth of a p-i-n
structure.
By initially patterning the substrate not with a single array of
stripes but with
two perpendicular arrays to give a two dimensional array of
squares, the
subsequent etching forms an array of pyramidal shaped pits.
Epitaxial growth
now results in the formation of quantum dots at the bottom of
each pit.
Strain induced dots and wires

If a semiconductor is subjected to strain its band structure is
modified. In
particular by applying the correct sign of strain the band gap
may be reduced.
If strain is only applied to a small region of the semiconductor
then a local
reduction of the band gap may occur, resulting in the formation
of a wire or
dot. In practise a local strain is produced by depositing a thin
layer of a
different material (e.g. carbon) on the surface of the
semiconductor. This will
have a very different atomic spacing to the semiconductor so to
fit together
both the atomic positions in the carbon layer and the surface
region of the
semiconductor will alter. This alteration constitutes a strain. If
the carbon layer
is patterned by lithography and then etched to leave only stripes
or dots, the
local strain field produces a wire or dot in the underlying
semiconductor. The
remaining isolated pieces of carbon are known as stressors. It is
necessary to
place a quantum well near to the surface of the semiconductor
to provide
confinement along the growth direction. The steps in the
production of strain
induced dots and wires are shown in the following figure.
(a) (b) (c)(a) (b) (c)
Steps in the formation of strain induced nanostructures (a)
initial quantum well (b)
deposition of carbon layer (c) formation of stressors by

lithography and etching.
The resultant, localised strain field (dashed lines) forms a wire
or dot in the
quantum well.
8
Although this technique involves an etching step, only the
carbon layer is
etched, the etching is kept away from the optically active
quantum well. Hence
defect formation is not a problem as is the case for the etched
dots and wires
described above. However the strain fields only produce a weak
modulation of
the band gap and so the confinement potential is relatively
small. At room
temperature carriers are thermally excited from the dots or
wires.
Electrostatically induced dots and wires
If a thin metal layer is deposited on the surface of a
semiconductor (a
Schottky contact) then a voltage can be applied between the
metal and the
semiconductor. This voltage has the effect of either raising or
lowering the
energies of the conduction and valence bands near the surface,
with respect
to their energies deeper in the semiconductor. If the bands are

raised then a
potential minimum is created for holes near to the surface.
Alternatively if the
bands are lowered a potential minimum for electrons is created.
This is shown
in the following figure.
If the metal layer used to make the Schottky contact is patterned
using
lithography and etching, then the resultant shapes can be used to
locally
modulate the conduction and valence bands, forming quantum
wires or
quantum dots. An added sophistication is to form two slightly
separated metal
strips on the semiconductor surface, a so-called split gate. By
applying
appropriate voltages a potential minimum is created in the
region between the
gates, the width of which is determined by the size of the
applied voltage.
Hence a wire of variable width is created.
Electrostatically induced nanostructures form clean systems as
only the metal
needs to be etched, not the semiconductor. However the
potential minima are
not very deep and the spacing between the energy levels is
small, they are
hence only suitable for low temperature operation. Their main
limitation
however is that only electrons or holes are confined in a given
structure, they
are hence not suitable for optical applications.
V

V
The effect of applying a voltage to a Schottky contacted
semiconductor
9
Quantum well width fluctuations
The width of a quantum well is not constant but exhibits a
spatial fluctuation
(see the following figure). Because the confined energy levels
depend upon
the well width, potential minima are formed for electrons and
holes at points
where the well width is above its average value. These
fluctuations confine
the carriers within the plane of the dot (the well provides
confinement along
the growth direction) to give a quantum dot. Although these
dots have good
optical properties their confining potential is very small, as are
the spacings
between the confined levels. The inplane size of the dots is
virtually
impossible to control (the well width fluctuations are essentially
random) and
the spread of dot sizes is very large. These dots have no device
prospects.

Thermally annealed quantum wells
A GaAs-AlGaAs well is grown using standard epitaxial
techniques. A very
finely focussed laser beam is then used to locally heat the
surface. This
produces a diffusion of Al from the AlGaAs into the GaAs well,
causing an
increase in the band gap. By scanning the beam round the edges
of a square
a potential barrier is produced surrounding the unilluminated
centre of the
square. Carriers optically excited within this square are
confined by the
potential barrier and the quantum well, forming a quantum dot.
Quantum wires
can also be formed by scanning the laser beam along the edges
of a
rectangle. Because the minimum size of the focussed laser beam
is ~1µm the
minimum size of the dots is fairly large (~100nm). This results
in very closely
spaced energy levels and, in addition, the annealing processes
can affect the
optical quality of the semiconductor. This technique also
requires specialised,
non-standard equipment.
Semiconductor nanocrystals
Very small semiconductor particles, which act as quantum dots,
can be
formed in a glass matrix by heating the glass with a small
percentage of a
suitable semiconductor. Dots with radii between 1~40nm are
formed, the
radius being a function of the temperature and heating time. The

main
limitation of these dots is that, because they are formed in an
insulating glass
matrix, the electrical injection of carriers is not possible.
Quantum well width fluctuations. The electrons and holes are
localised in
regions where the well width is above its average value (blue
dashed line).
10
Colloidal quantum dots
These are formed by injecting organometal reagents into a hot
solvent.
Nanoscale crystallites grown in the solution with sizes in the
range 1~10nm.
Subsequent chemical and physical processing can be used to
select a subset
of the crystallites with good size uniformity. The dots are
formed from II-IV
semiconductors, including CdS, CdSe and CdTe. The dots
exhibit good
optical properties but as they are free standing the electrical
injection of
carriers is not possible.
Summary and conclusions
In this lecture we have looked briefly at the two established

epitaxial
techniques (MBE and MOVPE) used to grow two dimensional
quantum wells.
We then considered the main requirements for the properties of
semiconductor nanostructures, before discussing the various
techniques
which have been developed to produce quantum wires and
quantum dots. Of
the techniques used to produce wires the most important are the
v-groove
and electrostatic induced ones. Only the former technique has
been applied to
room temperature device applications (mainly lasers) although
it still has a
number of disadvantages. For quantum dots, growth on
patterned substrates,
strain induced structures, electrostatic induced structures,
quantum well width
fluctuations, quantum well thermal annealing and colloidal dots
have all been
used to study physics in zero-dimensional systems (generally at
very low
temperatures). However none of these techniques has so far
been suitable for
room temperature device applications. We will see in the next
lecture that self-
organised techniques come the closest to producing ideal dots.
Further reading
The epitaxial techniques of MBE and MOVPE are discussed in
Davies ‘The
Physics of Low-Dimensional semiconductors’. Bimberg,
Grundmann and
Ledentsov ‘Quantum Dot Heterostructures’ discuss some of the
requirements
for semiconductor nanostructures. Some of the numerous

fabrication
techniques developed to produce wires and dots are described in
the
previously mention books and in the book by Weisbuch and
Vinter ‘Quantum
Semiconductor Structures’
More information can be obtained from a number of research
papers.
Suggestions are
• A close look on single quantum dots, A Zrenner, Journal of
Chemical
Physics Volume 112 page 7790 (2000). Provides an overview of
many of
the techniques used to prepare quantum dots. Many useful
references.
• Photoluminescence from a single GaAs/AlGaAs quantum dot,
K Brunner
et al Physical Review Letters Volume 69 Page 3216 (1992).
Thermally
annealed dots.
• Quantum size effect in semiconductor microcrystals, A
Ekimov et al Solid
State Communications Volume 56 Page 921 (1985).
Semiconductor
nanocrystals.
• Luminescence from excited states in strain induced InGaAs
quantum dots,
H Lipsanen et al, Physical Review B Volume 51 page 13868
(1995). Strain
induced dots.

11
• One-dimensional conduction in the two-dimensional electron
gas in a
GaAs-AlGaAs heterojunction, T J Thornton et al, Physical
Review Letters
Volume 56 Page 1198 (1986). Electrostatically induced wires.
• Synthesis and characterisation of nearly monodispersive CdE
(E=S, Se,
Te) semiconductor nanocrystallites, C B Murray et al, Journal
of the
Americal Chemical Society Volume 115 Page 8706 (1993).
Colloidal
quantum dots.
• Formation of a high quality two-dimensional electron gas on
cleaved
GaAs, L N Pfeiffer et al, Applied Physics Letters Volume 56
Page 1697
(1990). Cleaved edge overgrowth of quantum wires.
• Patterned quantum well heterostructures grown by OMCVD on
non-planar
substrates - applications to extremely narrow SQW lasers, R
Bhat et al
Journal of Crystal Growth Volume 93 Page 850 (1988). V-
groove quantum
wires.
• Molecular beam epitaxy growth of tilted GaAs AlAs

superlattices by
deposition of fractional monolayers on vicinal (001) substrates,
J M Gaines
et al, Journal of Vacuum Science and Technology B Volume 6
Page 1381
(1988). Growth of quantum wires on vicinal surfaces.
• Self-limiting growth of quantum dot heterostructures on
nonplanar {111}B
substrates, A Hartmann et al Applied Physics Letters Volume 71
Page
1314 (1997). Growth of quantum dots on patterned substrates.
• Homogeneous linewidths in the optical spectrum of a single
gallium
arsenide quantum dot, D Gammon et al, Science Volume 273
Page 87
(1996). Dots formed from quantum well width fluctuations.
12
Lecture 8 – The fabrication of semiconductor
nanostructures II
Introduction
In this lecture we will look at the most successful technique
developed so-far
to fabricate semiconductor quantum dots – self-assembly. The
use of this

technique will be described and some of the properties of
resultant dots will
be discussed.
The growth of strained semiconductor layers
Generally when growing quantum wells it is arranged that the
well, barrier and
substrate semiconductors have the same atomic spacing (lattice
constant).
For example GaAs and AlGaAs have almost identical lattice
constants. GaAs
quantum wells with AlGaAs barriers can therefore be grown on
GaAs
substrates. If we try to grow a semiconductor which has a very
different lattice
constant to that of the substrate, then initially it adjusts its
lattice constant to fit
that of the substrate and the semiconductor will be strained.
However to strain
a material requires energy. Hence as the thickness of the
semiconductor
increases energy will build up. Eventually there is sufficient
energy to break
the atomic bonds of the semiconductor and dislocations (a
discontinuity of the
crystal lattice) form. Beyond this point the semiconductor can
grow with its
own lattice constant, strain energy no longer builds up. The
thickness of
semiconductor which can be grown before dislocations form is
known as the
critical thickness. The critical thickness is a function of the
semiconductor
being grown and also the degree of lattice mismatch between
this
semiconductor and the underlying semiconductor or substrate.

Dislocations provide a very efficient mechanism for non-
radiative carrier
recombination. Hence a structure which contains dislocations
will, in general,
have a very poor optical efficiency. When growing strained
semiconductor
layers it is therefore important not to exceed the critical
thickness.
A good example of a strained semiconductor system is InxGa1-
xAs-GaAs.
When growing quantum wells InxGa1-xAs forms the wells, as it
has the smaller
band gap, with GaAs forming the barriers. As the In
composition of InxGa1-xAs
increases the lattice mismatch between InxGa1-xAs and GaAs
also increases.
Because InxGa1-xAs-GaAs quantum wells are generally grown
on a GaAs
substrate the InxGa1-xAs wells are strained to fit the GaAs
lattice constant.
For low In compositions (x~0.2) it is possible to grow quantum
wells with
thicknesses up to a few 10s nm before the critical thickness is
reached.
However for higher x the critical thickness decreases rapidly.
Self-assembled growth of quantum dots
The lattice mismatch between InAs and GaAs is very large (7%)
and the
critical thickness for the growth of an InAs layer on GaAs is
expected to be
very small (of the order of a few atomic layers). When InAs is
first deposited
on GaAs it grows as a highly strained, flat layer (two
dimensional growth).
However for certain growth conditions before dislocations start

to form the
growth changes to three dimensions in the form of small
islands. These
islands form the quantum dots and sit on the original two
dimensional layer,
which is known as the wetting layer.
13
This behaviour in which the growth transforms from two to
three dimensional
is known as the Stranski-Krastanow growth mode. It is caused
by a trade off
between elastic and surface energy. All surfaces have an
associated energy
because of their incomplete atomic bonds. The surface energy is
directly
proportional to the area of the surface. Hence the surface after
the islands
start to form has a greater energy than the original flat surface.
However
within the islands the lattice constant of the semiconductor can
start to shift
back to its bulk value, hence reducing the elastic energy (note
this shift is
gradually and increases with distance along the growth
direction, there are no
dislocations formed - see following figure). Because the
reduction in elastic
energy is greater than the increase in surface energy the
transformation to

three dimensional growth represents the lowest energy, and
hence most
favourable, state. Following the growth of the dots they are
generally
overgrown by the barrier semiconductor GaAs. The following
figure shows the
main steps in the formation of self-assembled quantum dots.
InAs
GaAs
(a)
(b)
(c)
(d)
InAs
GaAs
(a)
(b)
(c)
(d)
LHS - change in the lattice spacing for atoms in a self-
assembled quantum dot.
RHS the main stages in the formation of a self assembled dot:

(a) GaAs substrate
(with buffer layer), (b) initial 2D growth of InAs (c)
transformation above critical
thickness to 3D island-like growth (d) over growth of dots with
GaAs.
14
The Physical Properties of Self-Assembled Dots
The physical properties of self assembled dots (e.g. size, shape
and density)
depend to some extent on the conditions used to growth them
(e.g.
temperature and growth rate). Typically they have a base size
between
10~30nm, a height of 5~20nm and a density of
1x1010~1x1012cm-2. However
values outside this range may be possible by carefully
controlling the growth
conditions. Because of their small size the energy separation
between their
confined levels is relatively large (40~70meV). They contain no
dislocations
and so exhibit excellent optical properties. They have a high
two dimensional
density and multiple layers can be grown (see below). They are
grown entirely
by an epitaxial process and can easily be incorporated within
the intrinsic
region of a p-i-n structure. Their confinement potential is
relatively deep (100-

300meV) and both electrons and holes are confined. Uniformity
is reasonable
but could be better (see below). The following figure shows a
cross-sectional
transmission electron microscope (TEM) image of a typical
quantum dot. This
is a bare dot which has not been over grown with GaAs (it is
difficult to obtain
similar images of over grown dots as there is very little contrast
between InAs
and GaAs in the TEM images).
The following figure shows an AFM image of quantum dot
sample. Again the
dots have not been overgrown with GaAs.
A cross-sectional TEM image of an InAs quantum dot grown on
GaAs. The base of
the dot is approximately 18nm.
An AFM image of a quantum dot sample. Note the
exaggerated vertical scale.
15
The shape and composition of self assembled quantum dots
Although extensively studied there is still considerable
uncertainty as to the

precise shape of self assembled quantum dots. Various shapes
have been
claimed including pyramids, truncated pyramids, cones and
lenses (part of a
sphere). One problem in determining the shape is that it is
difficult to study
dots which have been overgrown. Although bare dots can be
studied using
AFM and related surface techniques, there is some evidence that
the dot
shape may change when they are overgrown. It may be that the
shape of self
assembled quantum dots depends upon the precise growth
conditions.
A further complication is the composition of the dots. The dots
can either be
grown using pure InAs or the alloy InGaAs. However even when
grown with
InAs there is evidence that the dots consist of InGaAs
indicating the diffusion
of Ga into the dots from the surrounding GaAs. The Ga
composition in the
dots is unlikely to be uniform leading to a highly complicated
system which is
difficult to model theoretically (see below).
Multiple quantum dot layers
Once one layer of dots has been deposited and overgrown with
GaAs a flat
surface is formed upon which a second layer can be deposited.
It is hence
possible to grow multiple layers of dots. When the first dot
layer is deposited
the positions of the dots are reasonably random. As the InAs in
the dots
gradually returns to its bulk lattice constant as the dot height

increases, the
initial GaAs deposited on top of the dot will be slightly
strained. A strain field
will be produced in the GaAs above each dot, although this will
gradually
decrease to zero as the thickness of the GaAs is increased.
However if, when
the next dot layer is deposited, these strain fields are still
present (only a thin
GaAs layer has been grown) they may act as nucleation sites for
the next
layer of dots. In this case the dots are vertically aligned and
stacks of aligned
dots may be formed with 10 or more dots in a stack. This
alignment only
occurs when successive dot layers are separated by very thin
GaAs layers
(<10nm). For thicker GaAs layers the strain field is essentially
zero when the
next layer is deposited and the dots form at random positions.
The following
figure shows a cross sectional transmission electron microscope
image of a
sample containing 10 dot layers with each layer separated by
9nm of GaAs.
The vertical alignment of the dots into stacks can be clearly
seem. This
alignment may be important for the electronic and optical
properties as it is
possible that electrons and holes may be able to move between
the dots in a
stack.
A cross sectional TEM image of vertically aligned quantum
dots.

16
Dot uniformity
The growth of self assembled dots is a semi-random process.
Dots at different
positions on the surface will start to form at slightly different
times as the
amount of InAs deposited will not be totally uniform. This
results in the final
shape and size (and possibly composition) varying slightly from
dot to dot. As
the energies of the confined energy states are a function of the
dot size,
shape and composition these will also vary from dot to dot.
The emission from a single dot will consist of a very sharp line
(similar to the
emission from an atom). However most experiments on self
assembled
quantum dots probe a large number of dots. For example a
typical
photoluminescence experiment will use a laser beam focussed to
a diameter
of 250µm. If the dot density is 1x1011cm-2 the area of the laser
beam will
contain ~50 million dots, each of which will contribute to the
measured
spectrum. As each dot will emit light at a slightly different
energy the sharp
emission from each dot will merge into a broad, featureless
emission. This is

known as inhomogeneous broadening. Only if the number of
dots probed can
be reduced significantly (e.g. by reducing the diameter of the
laser beam - see
later lectures) will the individual sharp emission lines be
observed.
The non-uniformity of self-assembled quantum dots and the
resultant
inhomogeneous broadening of the optical spectra is a
disadvantage for a
number of potential device applications. For example the
absorption is spread
out over a wide energy range instead of being concentrated at a
single
energy. The inhomogeneous broadening also complicates
fundamental
physics studies; as will be discussed in later lectures. However
there are
some applications (e.g. optical memories) which make use of
the
inhomogeneous broadening. The following figure shows
photoluminescence
spectra of different numbers of quantum dots. This is achieved
by evaporating
an opaque metal mask on the sample surface in which holes of
different sizes
are formed. By shining the laser beam through these different
size holes,
different numbers of dots can be probed.
Photoluminescence spectra of different numbers of quantum
dots.
From Gammon MRS Bulletin Feb. 1998 Page 44

17
Theoretical modelling of self-assembled quantum dots
Self assembled quantum dots have a high degree of strain and
this strain is
non-uniform. In addition they have a complicated shape. This
makes the
calculation of the confined energy levels very difficult. The
following figures
show the distribution of strain, calculated for pyramidal shaped
dots, and the
shapes of the wavefunctions for the lowest energy electron and
hole states.
As we will see in later lectures the optical spectra of the
quantum dots are
very complicated and difficult to interpret. Hence it is still not
possible to test
the predictions of the various available theoretical models. In
addition many of
the input parameters required for the models (e.g. the exact dot
size, shape
and composition) are still not well known.
The strain distribution in self assembled quantum dots: (a)
through the wetting
layer, (b) through the dot. From Stier et al PRB 59, 5688
(1999).

Electron and hole wavefunctions for the lowest energy confined
quantum dot
states. From Stier et al ibid.
18
Different self assembled quantum dot systems
The most commonly studied self assembled system consists of
InAs or
InGaAs dots grown within a GaAs matrix. The band gap of bulk
InAs is 0.4eV
but quantum confinement and strain increase this to between
0.95 and 1.4eV,
the precise value being dependent on the shape and size of the
dots. This
energy range correspond to wavelengths 1300~900nm, which is
in the near
infrared region of the electromagnetic spectrum.
The emission energy can be increased if InAs or InGaAs dots
are grown in an
AlGaAs matrix. This allows energies up to ~1.8eV (≡690nm) to
be obtained. Al
can also be added to the dots to increase their emission energy
(AlInAs-
AlGaAs dots).
Self assembled dots have also been fabricated from other
semiconductor
combinations where there is sufficient lattice mismatch.
Examples include InP

dots in GaInP (emission energy ~1.6-1.9eV [~775-650nm]), Ge
dots in Si and
InSb, GaSb or AlSb dots in GaAs (emission energy ~1.0-1.3eV
[~1200-
950nm]). More recently there have been attempts to grow dots
in the wide
band gap nitride semiconductors GaN, InN and AlN.
Summary and Conclusions
In this lecture we have looked at the most promising method for
producing
quantum dots suitable for electro-optical applications. The main
properties of
quantum dots prepared using the self-assembly technique are
compared with
other types of dots and wires in the following table. Self-
assembled dots
satisfy the majority of requirements for device applications,
possibly with the
exception of uniformity. As we will see in later lectures, a
number of devices
based on self assembled quantum dots have now been
demonstrated.
Further reading
'Quantum Dot Heterostructures' by Bimberg et al provides a
comprehensive
overview of the self-assembly technique including a discussion
of optical,
electrical and structural studies and devices based on these
quantum dots.

19
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20
Lecture 9 – Modulation doping and transport
phenomena in semiconductor nanostructures
Introduction
Using a technique known as modulation doping it is possible to
obtain
extremely high carrier mobilities in semiconductor
nanostructures. This has a
number of practical applications and also leads to the
observation of a
number of highly novel transport related phenomena.
Modulation Doping
We saw in Lecture 2 that in a bulk semiconductor the carrier
mobility is limited
by phonon scattering at high temperatures and scattering from
charged
impurity atoms at low temperatures. The temperature
dependence of the
electrical mobility hence has the following form.
Although the low temperature mobility can be increased by
reducing the
impurity density this lowers the electrical conductivity as it is
these impurities
which provide the free carriers (doping).
In a semiconductor nanostructure however it is possible to
spatially separate
the dopant atoms and the resultant free carriers, significantly
reducing this
scattering mechanism. This leads to very high low temperature
carrier

mobilities. This arrangement, which is known as remote or
modulation doping,
is shown schematically for n-type doping of a quantum well in
the following
figure. In this case the donor atoms are placed only in the wider
band gap
barrier material, the quantum well is undoped1. However the
electrons
released by the donor atoms in the barrier transfer into the
lower energy well
states, resulting in a spatial separation of the free electrons and
the charged
donor atoms. The confined electrons in the quantum well are
said to form a
two-dimensional electron gas (2DEG); a two-dimensional hole
gas can
similarly be formed by doping the barriers p-type. The non-zero
charge
1 This is simply achieved during MBE growth by only opening
the shutter in front of the cell
containing the dopant atoms during growth of the barriers. In
MOVPE the gas carrying the dopant
atoms is similarly switched.
M
ob
ili
ty
Temperature
Phonon
scattering

Impurity
scattering
M
ob
ili
ty
Temperature
Phonon
scattering
Impurity
scattering
Temperature dependence of electrical mobility for a
semiconductor
21
present in both the barriers and the well2 adds an electrostatic
potential
energy which results in a bending of the band edges, as
indicated in figure
(b). This band bending allows the formation of a modulation
doping induced
2DEG at a single interface (a single heterojunction) between
two different

semiconductors, as shown in figure (c). Here the combined
effects of the
conduction band offset and the band bending result in the
formation of a
triangular shaped potential well which restricts the motion of
the electrons to
two dimensions.
In a modulation doped structure the barrier region immediately
adjacent to the
well is generally undoped, forming a spacer layer, which further
separates the
charged dopant atoms and the free carriers. By optimising both
the width of
this spacer layer and the structural uniformity of the interface,
and by
2 The total charge of the structure remains zero but there are
equal and opposite charges in the well and
barriers.
(a) (b) (c)
Donor atom Free electron
(a) process of n-type modulation doping in a quantum well, (b)
as (a) but also showing the
effects on the band edges of the non-zero space charges, (c)
modulation doping of a single
heterostructure.
0.1 1 10 100
1

10
100
1000
1980
1982
1989
GaAs-AlGaAs
single heterojunctions
Clean bulk GaAs
Bulk GaAs
El
ec
tro
n
M
ob
ili
ty
(c
m
2 V

-1
s-1
)
Temperature (K)
Temperature dependence of the mobility of bulk GaAs (standard
and clean) and three GaAs-
AlGaAs single heterostructures (numbers give the
corresponding years). Data taken from
Stanley et al (Appl. Phys. Lett. 58, 478 (1991)) and Pfeiffer et
al (ibid 55, 1888 (1989))
22
minimising unintentional background impurities, it is possible
to achieve
extremely high low temperature mobilities. The previous figure
compares the
temperature variation of the electron mobility of standard bulk
GaAs, a very
clean bulk specimen of GaAs and a series of GaAs-AlGaAs
single
heterojunctions. At high temperatures, where mobility is limited
by phonon
scattering, the mobilities of the different structures are very
similar. At low
temperatures the mobility of bulk GaAs is increased in the
cleaner material

where a lower impurity density reduces the charged impurity
scattering.
However the absence of doping results in a low carrier density
and, as a
consequence, a low electrical conductivity. It is therefore not
possible to
achieve both a high conductivity and high mobility in a bulk
semiconductor.
Modulation doping however results in both high free carrier
densities and low
temperature mobilities more than two orders of magnitude
larger than those of
clean bulk GaAs and almost four orders of magnitude larger
than ‘standard’
bulk GaAs. The data for the different heterojunctions presented
in the figure
demonstrates how the low temperature mobility of a single
heterojunction has
increased over time, reflecting optimisation of the structure, the
use of purer
source materials and cleaner MBE growth reactors. The ability
to produce
2DEGs of extremely high mobility has allowed the observation
of a range of
interesting physical processes, a number of which will be
discussed later in
this lecture and the following lecture.
Modulation doping is now used extensively to provide the
channel of field
effect transistors (FETs), particularly for high frequency
applications. Such
devices are known as high electron mobility transistors
(HEMTs) or
modulation doped field effect transistors (MODFETs). Although
the use of
modulation doping provides negligible enhancement of the room

temperature
carrier mobility, the free carriers are confined to a two
dimensional sheet in
contrast to a layer of non-zero thickness for conventional
doping. This precise
positioning of the carriers results in devices exhibiting more
linear
characteristics and, for still unclear reasons, these devices also
exhibit lower
noise. III-V semiconductor HEMTs or MODFETs operating up
to ~300GHz are
achievable with applications including mobile communications
and satellite
signal reception.
The Hall effect in bulk semiconductors
The following figure shows the geometry used to study the Hall
effect. A
current Ix flows along a semiconductor bar to give a current
density Jx (=Ix/wh).
A magnetic field B applied normal to the axis of the bar
produces a magnetic
force on each moving charge carrier given by qvB, where q is
the charge and
v the carrier drift velocity. This force causes the carrier motion
to be deflected
in a direction perpendicular to both the field and the original
motion as shown
in the figure. As a consequence of this deflection there is a
build up of the
charge carriers, and hence a non-zero space charge, along the
side of the
bar, which results in the creation of an electric field along the
y-axis, Ey. This
so-called Hall field produces an electrostatic force (qEy) on the
charge carriers

which opposes the magnetic force. Equilibrium is quickly
reached where the
two forces balance to give a zero net force.
/( ) / 1/( )y y x y x HqE qvB E vB J B nq or E J B nq R= ⇒ = =
= =
23
where the last step follows from the relationship Jx=nqv (see
Lecture 2). The
ratio Ey/(JxB) is known as the Hall coefficient and has a value
1/(nq). As Ey
produces a voltage between the sides of the bar, given by
Vy=wEy, all three
quantities Ey, Jx and B are easily determined allowing RH and
hence the
product nq to be found. A Hall measurement of a bulk
semiconductor hence
allows the carrier density n to be determined as well as the
majority carrier
type (electrons or holes) from the sign of RH.
The Quantum Hall Effect
The Hall effect can also be observed in a nanostructure
containing a 2DEG.
Experimentally the electric field along the sample, Ex, can also
be determined

by measuring Vx as shown in the previous figure. This allows
two resistivities
to be determined, defined as:
ρ ρxx
x
x
xy
y
x
E
J
E
J
= =
Because RH=Ey/(BJx), for a bulk semiconductor ρxy=RHB,
which increases
linearly with increasing magnetic field, with ρxx remaining
constant. However
for a two-dimensional system a very different behaviour is
observed, as
shown in the following figure. In this case although ρxy
increase with
increasing field, it does so in a step-like manner. In addition
ρxx oscillates
between zero and non-zero values, with zeros occurring at fields

where ρxy
forms a plateau. This surprising behaviour of a two-dimensional
system is
known as the Quantum Hall effect and was discovered in 1980
by Klaus von
Klitzing, for which he was awarded the 1985 Nobel Physics
Prize. The
Quantum Hall effect arises as a result of the form of the density
of states of a
two-dimensional system in a magnetic field. This corresponds to
that of a fully
quantised system, with quantisation in one direction resulting
from the
physical structure of the sample and quantisation in the
remaining two
directions provided by the magnetic field. Diagram (a) of the
following figure
shows the discrete energy levels for a perfect system. However
in any real
system the levels are broadened by carrier scattering events and
the energy
levels have the form given by the right hand diagrams. These
‘bands’ of states
VXVY
IX
JX
B
w
h Ex
Ey

The geometry of the Hall effect
0 1 2 3 4 5 6 7 8 9
0
2000
4000
6000
8000
10000
12000
14000
ρ
XY resistance (h/e
2)
1/7
1/6
1/5
1/4
1/3
1/2
(x60)ρxx

ρ
xy
R
es
is
ta
nc
e
(Ω
)
Magnetic Field (T)
An example of the integer quantum Hall
effect. Data taken from Paalanen et al,
Phys. Rev. B. 25, 5566 (1982)
24
have similarities with the energy bands in a solid (see Lecture
1) and as in
that case the electronic properties are a very sensitive function
of how the
charge carriers occupy the bands. Each band formed by the

magnetic field is
known as a Landau level and it can be shown that the
degeneracy of each
Landau level is given by
eB
h
Hence as the field is increased the degeneracy of each level also
increases.
Therefore for a given carrier density in the structure the number
of occupied
levels decreases with increasing field. In (c) the Landau level
degeneracy is
such that only the lowest two levels are occupied. This
corresponds to the
case of an insulator with completely filled bands followed by
completely empty
bands. In this case the structure has a zero conductivity
(σxx=0). In (b) the
field has been increased so that now the second Landau level is
only half
filled. Conductivity is possible for the electrons in this level
and hence σxx≠0.
Under conditions of high magnetic field the following
relationships relate the
conductivity and resistivity components
2
1xx
xx xy H

xy xy
R B
σ
ρ ρ
σ σ
≈ ≈ =
The first relationship shows that the zero conductivity values
obtained when
exactly an integer number of Landau levels are occupied results
in a zero
value for ρxx.
The plateau values of ρxy can be found by noting that if exactly
j Landau levels
are fully occupied then
S
eB
N j
h
=
where NS is the two dimensional carrier density. From the
above definition of
ρxy
(a) (b) (c)
Quantised energy levels of a two dimensional system placed in a

magnetic field (a) case of
zero level broadening (b) and (c) with level broadening and for
different occupations of the
levels up to the dashed line.
25
2
1 25812.8
xy H
S
B h
R B
N e j e j
ρ = = = = Ω
The plateau values of ρxy are sample independent and are
related to the
fundamental constants h and e. Values for ρxy can be measured
to very high
accuracy and are now used as the basis for the resistance
standard and also
to calculate the fine structure constant α=µ0ce2/2h, where the
permeability of
free space, µ0, and the speed of light, c, are defined quantities.

The parameter j is known as the filling factor The quantum Hall
effect
discussed previously occurs for integer values of j and is
therefore known as
the integer quantum Hall effect. However, in samples with very
high carrier
mobilities, plateaus in ρxy and minima in ρxx are also observed
for fractional
values of j, giving rise to the fractional quantum Hall effect.
The discovery and
theoretical interpretation of the fractional quantum Hall effect,
which results
from the free carriers behaving collectively rather than as single
particles, lead
to the award of the 1998 Nobel Physics prize to Stormer, Tsui
and Laughlin.
An example of the fractional quantum Hall effect is given in the
above figure
which was recorded at very low temperatures for a very high
mobility GaAs-
AlGaAs single heterostructure. In addition to minima in ρxx and
plateaus in ρxy
for integer values of the filling factor, similar features are also
observed for
non-integer values, for example 3/5, 2/3, 3/7 etc.
Ballistic Carrier Transport
The carrier transport considered so far is controlled by a series
of random
scattering events (see Lecture 2). However the high carrier
mobilities which
can be obtained by the use of modulation doping correspond to
very long path
lengths between successive scattering events, lengths that can
significantly

An example of the fractional quantum Hall effect which where
the filling factor j has non
integer values. The integer quantum Hall effect is still observed
at low fields. Figure from
R Willet et al Phys. Rev. Lett. 59, 1776 (1987).
26
exceed the dimensions of a nanostructure. In this case a carrier
can pass
through the structure without experiencing a scattering event, a
process
known as ballistic transport. Ballistic transport conserves the
phase of the
charge carriers and leads to a number of novel phenomena, two
of which will
now be discussed.
When carriers travel ballistically along a quantum wire there is
no dependence
of the resultant current on the energy of the carriers. This
results from a
cancellation between the energy dependence of their velocity
(v=(2E/m*)1/2)
and the density of states, which in one dimension varies as E-
1/2 (see Lecture
6). For each subband occupied by carriers, a conductance equal
to 2e2/h is
obtained, a behaviour known as quantised conductance. If the
number of
occupied subbands is varied then the conductance of the wire

will exhibit a
step-like behaviour, with each step corresponding to a
conductance change of
2e2/h. Quantum conductance is most easily observed in
electrostatically
induced quantum wires (see Lecture 7). The gate voltage
determines the
width of the wire, which in turn controls the energy spacing
between the
subbands. For a given carrier density, reducing the subband
spacing results
in the population of a greater number of subbands and hence an
increased
conductance. The following figure shows quantum conductance
in a 400nm
long electrostatically induced quantum wire. These
measurements are
generally performed at very low temperatures to obtain the very
high
mobilities required for ballistic transport conditions. In contrast
to the plateau
values observed for ρxy in the quantum Hall effect, which are
independent of
the structure and quality of the device, the quantised
conductance values of a
quantum wire are very sensitive to any potential fluctuations
which result in
scattering events. This sensitivity prevents the use of quantum
conductance
as a resistance standard.
The inset to the above figure shows a structure in which a
quantum wire splits
into two wires which subsequently rejoin after having enclosed
an area A.
Under ballistic transport conditions the wavefunction of an
electron incident on

the loop will split into two components which, upon
recombining at the far side
-1.6 -1.4 -1.2 -1.0 -0.8 -0.6
0
2
4
6
8
10
12 Split gate
2D EG
O hmic co ntacts
Split gate
2D EG
O hmic co ntacts
C
on
du
ct
an
ce

(u
ni
ts
2
e2
/h
)
Split Gate Bias Voltage (V)
Example of quantum conductance in a
quantum wire defined electrostatically
from a 2DEG. The inset shows the
sample geometry. Data from Hamilton et
al, Appl. Phys. Lett. 60, 2782 (1992).
0 10 20 30 40 50 60 70 80
50
100
150
200
250
300
AA

R
es
is
ta
nc
e
(Ω
)
Magnetic Field (mT)
An example of the Aharonov-Bohm effect in
an electrostatically defined quantum ring.
The inset shows the sample geometry. Data
from Timp et al, Phys. Rev. B. 39, 6227
(1989).
27
of the loop, will interfere. If a magnetic field is now applied
normal to the plane
of the loop an additional phase difference is acquired or lost by
the
wavefunctions, depending upon the sense in which they traverse
the loop.
The phase difference increases by 2π when the magnetic flux
through the

loop, given by the area multiplied by the field (BA), changes by
h/e. Hence as
the magnetic field is increased the system will oscillate between
conditions of
constructive interference (corresponding to a high conductance)
and
destructive interference (corresponding to low conductance).
The change in
field (∆B) between two successive maxima (or minima) is given
by the
condition ∆BA=h/e, resulting in the conductance of the system
oscillating
periodically with increasing field. An example of this
behaviour, known as the
Aharonov-Bohm effect is shown in the previous figure for a
loop of diameter
1.8µm formed from the 2DEG of a GaAs-AlGaAs single
heterostructure by
patterning the surface with metal gates defined by electron
beam lithography.
In this lecture we have shown how modulation doping allows
the attainment of
very high carrier mobilities at low temperatures. This allows the
observation of
a number of novel effects including the integer and fractional
quantum Hall
effects. The high mobilities correspond to long average
distances between
scattering events and carriers may be able to pass through a
nanostructure
ballistically without undergoing a single scattering event. In
this case
processes which include quantised conductance and the
Aharonov-Bohm

effect are observable.
Further reading
The paper by Pfeiffer et al (Appl. Phys. Lett. 55, 1888 (1989))
describes the
optimisation of the MBE technique to give very high electron
mobilities.
Carrier scattering processes are discussed in detail in ‘The
Physics of Low
Dimensional Semiconductors’ by J H Davies. The discussion of
the integer
quantum Hall effect give in this lecture is relatively non-
mathematical. A more
detailed treatment which includes the importance of disorder is
given in ‘Band
theory and Electronic Properties of Solids’ by J Singleton
(OUP).
28
Lecture 10 Tunnelling and related processes in
semiconductor nanostructures
Introduction
Quantum mechanical tunnelling, in which a particle passes
through a
classically forbidden region, is the mechanism by which α
particles escape
from the nucleus during α decay and electrons escape from a
solid in

thermionic emission. Tunnelling can also be observed in
semiconductor
nanostructures where the ability to deposit very thin layers
permits the easy
production of tunnelling barriers. Tunnelling can be observed
either through a
single barrier or through two barriers separated by a quantum
well or quantum
dot. A range of novel physical processes are observed with a
number of
practical applications.
Tunnelling through a single square barrier
Consider the single square barrier of potential height V0 and
thickness a as
shown in the following figure. Such a structure can be easily
fabricated by
depositing a thin layer of a wide band gap semiconductor
between thicker
layers of a narrower band gap semiconductor. Away from the
barrier, and on
both sides, would normally be doped regions to provide a
reservoir of carriers.
By fabricating a suitable device an applied voltage can be used
to vary the
energy of the carriers and their ability to pass through the
barrier is indicated
by the magnitude of current flowing through the device.
The following figure shows the calculated transmission
probability for an
electron of energy E incident on a barrier of height 0.3eV and
thickness 10nm.
The classical result has a value of zero when the electron energy
is less than
the barrier height and one otherwise. In contrast the quantum

mechanical
result is non-zero for energies below that of the barrier height
indicating that
the electron can quantum mechanically tunnel through the
barrier, a region
where classically it would have negative kinetic energy. The
oscillations of the
probability for energies which exceed the barrier height are a
result of the
interference between waves which are reflected from the two
sides of the
barrier.
For electron energies less than the barrier height the
transmission probability
T can be approximated to
Vo
a
E
Schematic diagram of a single barrier tunnelling structure.
29
*
0

2
0
2 ( )16
exp( 2 )
m V EE
T a where
V
κ κ
−
≈ − =
Because of the exponential function the transmission probability
is very
sensitive to both the energy of the electron and the width and
height of the
barrier.
Double barrier resonant tunnelling structures
Of greater practical interest than a single barrier tunnelling
structure is the
case of two barriers separated by a thin quantum well, known as
a double
barrier resonant tunnelling structure (DBRTS). A schematic
diagram of a
DBRTS is shown in the following figure. Quantised energy
levels are formed
in the quantum well as described in Lecture 5.

Calculated transmission coefficient as a function of electron
energy for a single barrier of height
0.3eV. taken from J H Davies ‘The Physics of Low-dimensional
semiconductors’ CUP
I
V
I
I
V
V
(a)
(b)
(d)
(c)
A double barrier resonant tunnelling structure.
30

The previous figure also shows a DBRTS for various applied
voltages. For the
sign of voltage shown electrons travel from left to right.
Electrons are first
incident on the left most barrier through which they must
tunnel. However at
low applied voltages their energy when they have tunnelled into
the well is
below that of the lowest confined state and the two barriers plus
the well
therefore behave as one effectively thick barrier; the tunnelling
probability and
hence the current is very low. As the voltage is increased the
energy of the
electrons tunnelling through the first barrier comes into
resonance with the
lowest state in the well. The effective barrier width is now
reduced and it
becomes much easier for the electrons to pass through the
structure. As a
result the current increases significantly. For further increase in
voltage the
resonance condition is lost and the current decreases. However
additional
resonances may be observed with higher energy confined states.
The figure
also shows the expected current-voltage characteristic of a
DBRTS indicating
the relationship between specific points on the characteristic
and the different
voltage conditions.
The previous figure shows experimental results obtained for a
DBRTS
consisting of a 20nm GaAs quantum well confined between

8.5nm AlGaAs
barriers. Resonances with five confined quantum well states are
observed.
Beyond each resonance a DBRTS exhibits a negative
differential resistance,
a region where the current decreases as the applied voltage is
increased.
Such a characteristic has a number of applications including the
generation
and mixing of microwave signals. Very high frequencies are
possible because
of the rapid transit time of the electrons through the structure.
DBRTS can also exhibit hysteresis in their current-voltage
characteristics,
particularly when the thicknesses of the two barriers are
asymmetrical. A
thinner first barrier allows carriers to tunnel easily into the well
but a thicker
second barrier impedes escape, resulting in charge build up in
the well. This
charge build up modifies the voltage dropped across the initial
part of the
structure and maintains the resonance condition to higher
voltages than would
0
10
20
30
40
50

60
0 1 2 3
0
10
20
30
40
x35
E4
E3
E2
E1
C
ur
re
nt
(m
A
)

Bias Voltage (V)
x100
C
ur
re
nt
(m
A
)
Bias Voltage (V)
Measured current voltage characteristics of a double barrier
resonant tunnelling
structure. Data supplied by P Buckle and W Tagg (University of
Sheffield).
31
occur in the case of an empty well. This broadened resonance is
only
observed as the voltage is increased allowing charge to

accumulate in the
well. If the voltage is taken above the resonance condition the
well empties
and decreasing the voltage results in a narrower resonance as
there is now
no charge accumulation. For such a structure the current follows
a different
path depending upon the direction in which the voltage is
varied; the current-
voltage characteristics exhibit a hysteresis. The inset to the
previous figure
shows the characteristics of an asymmetrical DBRTS with 8.5
and 13nm thick
Al0.33Ga0.67As barriers and a 7.5nm In0.11Ga0.89As quantum
well.
Two important figures of merit for a resonant tunnelling
structure are the
widths of the resonance and the ratio of the current at the peak
of the
resonance to that immediately after the resonance, the peak-to-
valley-ratio.
Once resonance has been reached with the lowest energy
confined quantum
well state it might be expected that current would continue to
flow for higher
voltages because of the continuum of states which exist as a
result of inplane
motion (see Lecture 5). However when an electron tunnels
through the first
barrier not only must energy be conserved but also the two
components of the
inplane momentum or wavevectors kx and ky. Conservation of
kx and ky
prevents tunnelling into higher continuum states as these
correspond to high
values of kx and ky whereas the tunnelling electrons will

generally have
relatively small inplane wavevectors. In fact the electrons to the
left of the first
barrier will have a range of initial energies, a result of their
density and the
Pauli exclusion principle, and hence a range of kx and ky
values. This range of
inplane wavevectors contributes to the width of the resonance.
That the current immediately after a resonance does not fall to
zero indicates
that additional non-resonant tunnelling is occurring. The precise
nature of
these additional processes is still unclear but may include
tunnelling via
impurity states in the barriers or phonon scattering which allows
electrons of
an initially incorrect energy to tunnel via the quantum well
states. In general
the peak-to-valley-ratio decreases as the device temperature is
increased.
Tunnelling via quantum dots – Coulomb blockade
The quantum well of a double barrier resonant tunnelling
structure can be
replaced by a quantum dot. In addition to the modification of
the energy level
structure the small size of a typical quantum dot results in a
new effect. A
small quantum dot will posses a relatively large capacitance. If
a quantum dot
already contains one or more electrons then a significant energy
is required to
add an additional electron as a result of the work that must be
done against
the repulsive electrostatic force between like charges. This
charging energy,

given by e2/2C where C is the dot capacitance, modifies the
energies of the
confined dot states which would occur for an uncharged system.
Charging
effects are most easily understood by referring to a structure of
the form
shown in the inset to the following figure, which consists of a
quantum dot
placed close to a reservoir of free electrons. Applying a voltage
to the metal
gate on the surface of the structure allows the energy of the dot
to be varied
with respect to the reservoir. If a given energy level in the dot
is below the
energy of the reservoir then electrons will tunnel from the
reservoir into the dot
level. Alternatively if the energy level is above the reservoir
then the level will
be unoccupied. Hence by varying the gate voltage the dot states
can be
sequentially filled with electrons. This filling can be monitored
by measuring
32
the capacitance of the
device which will exhibit a
characteristic feature each
time an additional electron
is added to the dot.
The main part of the

previous figure shows the
capacitance trace recorded
for a device containing an
ensemble of self assembled
quantum dots. These dots
have two confined electron
levels; the lowest (ground
state) able to hold two
electrons (degeneracy of
two) with the excited level
able to hold four electrons
(degeneracy of four). In the
absence of charging effects
only two features would be
observed in the capacitance
trace, one at the voltage
corresponding to the filling of the ground state, the other when
the voltage
reaches the value required for electrons to tunnel into the
excited state.
However once one electron has been loaded into the ground
state charging
effects result in an additional energy, and a higher voltage,
being required to
add the second electron. This leads to two distinct capacitance
features
corresponding to the filling of the ground state. Similarly four
distinct features
are expected as electrons are loaded into the excited state
although in the
present case inhomogeneous broadening prevents these being
individually
resolved. This charging behaviour is known as Coulomb
blockade and is
observed experimentally when the charging energy exceeds the

thermal
energy, kT.
Coulomb blockade effects can also be observed in transport
processes where
carriers tunnel through a quantum dot. Suitable dots may be
formed
electrostatically using split gates to define the dot and to
provide tunnelling
barriers between the dot and the surrounding 2DEG which forms
a reservoir
of carriers. An additional gate electrode allows the energy of
the dot to be
varied with respect to the carrier reservoirs. The relatively large
dot size
results in Coulomb charging energies that are much larger than
the
confinement energies. The former therefore dominate the
energetics of the
system. The inset to the following figure shows a schematic
diagram of the
structure where a small bias voltage has been applied between
the left and
right two-dimensional carrier reservoirs. The dot initially
contains N electrons
resulting in an energy indicated by the lower horizontal line. An
additional
electron can tunnel into the dot from the left hand reservoir but
this increases
the dot energy by the charging energy. Hence this process is
only
energetically possible if the energy of the dot with N+1
electrons lies below
the maximum energy of the electrons in the left hand reservoir.
Tunnelling of
this additional electron into the right hand reservoir may
subsequently occur

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
2.10
2.12
2.14
2.16
2.18
2.20
2.22
2.24
f r e e e l e c t r o n s
q u a n t u m d o t
b l o c k in g b a r r ie r
g a te
Excited state
Ground state
C
ap
ac

ita
nc
e
(n
F)
Voltage (V)
Structure and results from a device in which a
controllable number of electrons can be loaded on to
a quantum dot. Figure redrawn from Fricke et al
Europhysics Lett. 36, 197 (1996).
33
but only if the N+1 dot energy
lies above the maximum
energy of this reservoir. If
these two conditions are
satisfied, requiring that the
N+1 dot energy lie between
the energy maxima of the two
reservoirs, a sequential flow
of single electrons through
the structure occurs; the
system exhibits a non-zero
conductance. As the gate
voltage is used to vary the
dot energy, the condition for
sequential tunnelling will be

satisfied for different values
of N and a series of
conductance peaks will be
observed, an example is
shown in the above figure for
a dot of radius 300nm. This
large dot size results in a
large capacitance and a correspondingly small charging energy
(0.6meV for
the present example). Hence measurements must be performed
at very low
temperatures in order to satisfy the condition e2/2C>>kT. Two
practical
applications of Coulomb blockade will be described in a later
lecture.
In this lecture we have seen that it is possible to fabricate
tunnelling structures
based on semiconductor nanostructures. Double barrier resonant
tunnelling
structures give very non-linear current-voltage characteristics
and display
negative differential resistance. Because the transit time of
carriers through
such a structure is very short they have a number of applications
including
high frequency microwave oscillators and mixers. Tunnelling
structures
containing a quantum dot display an added complication due to
the charge of
the carriers; the Coulomb blockade effect.
Further reading
For a fuller, mathematical treatment of Coulomb blockade the

following
articles may be useful, ‘Artificial Atoms’ by M A Kastner,
Physics Today 24
January 1993 and ‘Single electron charging effects in
semiconductor quantum
dots’ by L P Kouenhoven et al Zeitschrift für Physik B
Condensed Matter 85,
367 (1991).
The generally mathematics of quantum mechanical tunnelling is
described in
quantum mechanics text books and also with respect to the
present subject in
‘The Physics of Low-Dimensional semiconductors’ by J H
Davies CUP. Finally
‘Low-Dimensional Semiconductors materials, physics,
technology, devices’ by
M J Kelly OUP discusses applications of resonant tunnelling
structures.
-0.60 -0.58 -0.56 -0.54 -0.52 -0.50
0.0
0.5
1.0
N
N+1
eV
C
on

du
ct
an
ce
(e
2 /h
)
Gate Voltage (V)
Coulomb blockade effect observed for tunnelling
through an electrostatically defined quantum dot.
The measurement temperature is 10mK. The inset
shows the carrier tunnelling steps and the energy
levels of the system. Data redrawn from L P
Kouwenhoven, et al Z. Phys. B. 85, 367 (1991).
Financial Management • Autumn 2004 • pages 5 - 37
Why Has IPO Underpricing
Changed Over Time?
Tim Loughran and Jay Ritter*
In the 1980s, the average first-day return on initial public
offerings (IPOs) was 7%. The
average first-day return doubled to almost 15% during 1990-
1998, before jumping to 65%

during the internet bubble years of 1999-2000 and then
reverting to 12% during 2001-2003.
We attribute much of the higher underpricing during the bubble
period to a changing issuer
objective function. We argue that in the later periods there was
less focus on maximizing IPO
proceeds due to an increased emphasis on research coverage.
Furthermore, allocations of
hot IPOs to the personal brokerage accounts of issuing firm
executives created an incentive
to seek rather than avoid underwriters with a reputation for
severe underpricing.
What explains the severe underpricing of initial public offerings
in 1999-2000, when the average
first-day return of 65% exceeded any level previously seen
before? In this article, we address
this and the related question of why IPO underpricing doubled
from 7% during 1980-1989 to
almost 15% during 1990-1998 before reverting to 12% during
the post-bubble period of 2001-
2003. Our goal is to explain low-frequency movements in
underpricing (or first-day returns) that
occur less often than hot and cold issue markets.
We examine three hypotheses for the change in underpricing: 1)
the changing risk composition
hypothesis, 2) the realignment of incentives hypothesis, and 3) a
new hypothesis, the changing
issuer objective function hypothesis. The changing issuer
objective function hypothesis has
two components, the spinning hypothesis and the analyst lust
hypothesis.
The changing risk composition hypothesis, introduced by Ritter
(1984), assumes that riskier

IPOs will be underpriced by more than less-risky IPOs. This
prediction follows from models
where underpricing arises as an equilibrium condition to induce
investors to participate in the
IPO market. If the proportion of IPOs that represent risky stocks
increases, there should be
greater average underpricing. Risk can reflect either
technological or valuation uncertainty.
Although there have been some changes in the characteristics of
firms going public, these
changes are found to be too minor to explain much of the
variation in underpricing over time if
there is a stationary risk-return relation.
The realignment of incentives and the changing issuer objective
function hypotheses both
We thank Hsuan-Chi Chen, Harry DeAngelo, Craig Dunbar,
Todd Houge, Josh Lerner, Lemma Senbet and James
Seward (the Editors), Toshio Serita, Ivo Welch, Ayako Yasuda,
and Donghang Zhang; seminar participants at the
2002 Chicago NBER behavioral finance meetings, the 2002
Tokyo PACAP/APFA/FMA meetings, the 2003 AFA
meetings, Boston College, Cornell, Gothenburg, Indiana,
Michigan State, Penn State, Stanford, the Stockholm
School of Economics, Vanderbilt, NYU, SMU, TCU, and the
Universities of Alabama, California (Berkeley), Colorado,
Houston, Illinois, Iowa, Notre Dame, and Pennsylvania, and
several anonymous referees; and especially Alexander
Ljungqvist for useful comments. Chris Barry, Laura Field, Paul
Gompers, Josh Lerner, Alexander Ljungqvist, Scott
Smart, Li-Anne Woo, and Chad Zutter generously provided IPO
data. Bruce Foerster assisted us in ranking underwriters.
Underwriter ranks are available online at
http://bear.cba.ufl.edu/ritter/rank.htm. Donghang Zhang
supplied useful

research assistance.
*Tim Loughran is a Professor of Finance at the University of
Notre Dame. Jay Ritter is the Cordell Professor of
Finance at the University of Florida.
Financial Management • Autumn 2004 6
posit changes over time in the willingness of issuing firms to
accept underpricing. Both
hypotheses assume that underwriters benefit from rent-seeking
behavior that occurs when
there is excessive underpricing.
The realignment of incentives hypothesis, introduced by
Ljungqvist and Wilhelm (2003),
argues that the managers of issuing firms acquiesced in leaving
money on the table during
the 1999-2000 bubble period. (Money on the table is the change
between the offer price and
the first closing market price, multiplied by the number of
shares sold.) The hypothesized
reasons for the increased acquiescence are reduced chief
executive officer (CEO) ownership,
fewer IPOs containing secondary shares, increased ownership
fragmentation, and an
increased frequency and size of “friends and family” share
allocations. These changes made
issuing firm decision-makers less motivated to bargain for a
higher offer price.
The realignment of incentives hypothesis is similar to the
changing risk composition
hypothesis in that it is changes in the characteristics of

ownership, rather than any
nonstationarities in the pricing relations, that are associated
with changes in average
underpricing. It differs from the changing risk composition
hypothesis, however, in that
underpricing is not determined solely by the investor demand
side of the market.
In our empirical work, we find little support for the realignment
of incentives hypothesis as
an explanation for substantial changes in underpricing. We find
no relation between the
inclusion of secondary shares in an IPO and underpricing. And
although CEO fractional
ownership was lower during the internet bubble period, the CEO
dollar ownership (the market
value of the CEO’s holdings) was substantially higher, resulting
in increased incentives to
avoid underpricing. Furthermore, it is possible that changes in
the characteristics of
ownership may be partly a response to higher underpricing as
well as a cause. Ljungqvist
and Wilhelm (2003) do not provide an explanation for why
these changes occurred.
The changing issuer objective function hypothesis argues that,
holding constant the
level of managerial ownership and other characteristics, issuing
firms became more willing to
accept underpricing. We hypothesize that, during our sample
period, there are two reasons
for why issuers became more willing to leave money on the
table. The first reason is an
increased emphasis on analyst coverage. As issuers placed more
importance on hiring a lead
underwriter with a highly ranked analyst to cover the firm, they

became less concerned
about avoiding underwriters with a reputation for excessive
underpricing. We call this desire
to hire an underwriter with an influential but bullish analyst the
analyst lust hypothesis.
This results in each issuer facing a local oligopoly of
underwriters, no matter how many
competing underwriters there are in total, because there are
typically only five Institutional
Investor all-star analysts covering any industry. As Hoberg
(2003) shows, the more market
power that underwriters have, the more underpricing there will
be in equilibrium.
The second reason for a greater willingness to leave money on
the table by issuers is the
co-opting of decision-makers through side payments. Beginning
in the 1990s, underwriters
set up personal brokerage accounts for venture capitalists and
the executives of issuing
firms in order to allocate hot IPOs to them. By the end of the
decade, this practice, known as
spinning, had become commonplace. The purpose of these side
payments is to influence the
issuer’s choice of lead underwriter. These payments create an
incentive to seek, rather than
avoid, underwriters with a reputation for severe underpricing.
We call this the spinning
hypothesis. In the post-bubble period, increased regulatory
scrutiny reduced spinning
dramatically. This is one of several explanations why
underpricing dropped back to an average
of 12%. The reduction in spinning removed the incentive for
issuers to choose investment
bankers who underprice. Investment bankers responded by
underpricing less in the post-

bubble period.
Loughran & Ritter • Why Has IPO Underpricing Changed Over
Time? 7
The contributions of our research are three-fold. First, we
develop the changing issuer
objective function hypothesis for the increased underpricing of
IPOs during the 1990s and
the bubble periods. Second, we document many patterns
regarding the evolution of the US
IPO market during the last two decades. Much of the data has
been or will be posted on a
website for other researchers to use. Many, although not all, of
these patterns have been
previously documented, especially for the first two subperiods.
Third, we formally test the
ability of the changing risk composition, realignment of
incentives, and changing issuer
objective function hypotheses to explain the changes in
underpricing from 1980-1989 (“the
1980s”) to 1990-1998 (“the 1990s”), 1999-2000 (“the internet
bubble”), and 2001-2003 (“the
post-bubble period”).
Much of the increased underpricing in the bubble period is
consistent with the predictions
of the changing issuer objective function hypothesis. In multiple
regression tests, the
changing risk composition and the realignment of incentives
hypotheses have little success
at explaining the increase in first-day returns from the 1980s to
the 1990s, to the bubble
period, or to the post-bubble period. The regression results

show that only part of the
increase in the bubble period is attributable to the increased
fraction of tech and internet
stocks going public. Consistent with the changing issuer
objective function hypothesis,
underpricing became much more severe when there was a top-
tier lead underwriter in the
latter time periods. These conclusions are not substantially
altered after controlling for the
endogeneity of underwriter choice.
The rest of this article is as follows. In Section I, we present
our changing issuer objective
function hypothesis. In Section II, we describe our data. In
Section III, we report year-by-
year mean and median first-day returns and valuations. In
Section IV, we report average first-
day returns for various univariate sorts. In Section V, we report
multiple regression results
with first-day returns as the dependent variable. Section VI
discusses alternative explanations
for the high underpricing of IPOs during the internet bubble
period. Section VII presents our
conclusions. Four appendices provide detailed descriptions of
our data on founding dates,
post-issue shares outstanding, underwriter rankings, and
internet IPO identification.
I. Causes of a Changing Issuer Objective Function
Most models of IPO underpricing are based on asymmetric
information. There are two
agency explanations of underpricing in the IPO literature. Baron
(1982) presents a model of
underpricing where issuers delegate the pricing decision to
underwriters. Investment bankers

find it less costly to market an IPO that is underpriced.
Loughran and Ritter (2002) instead
emphasize the quid pro quos that underwriters receive from
buy-side clients in return for
allocating underpriced IPOs to them. The managers of issuing
firms care less about
underpricing if they are simultaneously receiving good news
about their personal wealth
increasing. This argument, however, does not explain why
issuers hire underwriters who will
ex post exploit issuers’ psychology. Neither does the
realignment of incentives hypothesis.
One can view issuers as seeking to maximize a weighted
average of IPO proceeds, the
proceeds from future sales (both insider sales and follow-on
offerings), and side payments
from underwriters to the people who will choose the lead
underwriter:
α
1
IPO Proceeds + α
2
Proceeds from Future Sales + (1 - α
1
- α
2
)Side Payments (1)

The changing issuer objective function hypothesis states that
issuers choosing an
underwriter in some periods put less weight on IPO proceeds
and more weight on the proceeds
from future sales and side payments.
In Equation (1), IPO proceeds are a function of the choice of
underwriter and underwriting
contract (auction or bookbuilding) at the start of the process
and, several months later, the
bargaining at the pricing meeting for IPOs when bookbuilding is
used. Loughran and Ritter
(2002) provide a prospect theory analysis of the bargaining at
the pricing meeting. The
Ljungqvist and Wilhelm (2003) realignment of incentives
hypothesis can also be viewed as
a theory of the bargaining at the pricing meeting. Neither of
these theories, though, explains
why an issuing firm would choose an underwriter that would, at
the pricing meeting, propose
an offer price that leaves more money on the table than
necessary. In contrast, the changing
issuer objective function hypothesis does provide a theory for
the choice of underwriter at
the start of the process. Before discussing the analyst lust and
spinning hypotheses in more
detail, we explain why underwriters want to underprice.
A. Why Underwriters Want to Underprice IPOs
Underwriters, as intermediaries, advise the issuer on pricing the
issue, both at the time of
issuing a preliminary prospectus that includes a file price range,
and at the pricing meeting
when the final offer price is set. If underwriters receive

compensation from both the issuer
(the gross spread) and investors, they have an incentive to
recommend a lower offer price
than if the compensation was merely the gross spread.
Bookbuilding is the mechanism used to price and allocate IPOs
for 99.9% of our sample,
with auctions used for the other 0.1%. In the case of
bookbuilding, underwriters can decide
to whom to allocate shares if there is excess demand.
Benveniste and Wilhelm (1997) and
Sherman and Titman (2002) emphasize that underwriter
discretion can be used to the benefit
of issuing firms. Underwriters can reduce the average amount of
underpricing, thereby
increasing the expected proceeds to issuers, by favoring regular
investors who provide
information about their demand that is useful in pricing an IPO.
Shares can be allocated to
those who are likely to be buy-and-hold investors, minimizing
any costs associated with
price support.
Underwriter discretion can completely eliminate the winner’s
curse problem if underwriters
allocate shares in hot issues only to those investors who are
willing to buy other IPOs. As
Ritter and Welch (2002) note, if underwriters used their
discretion to bundle IPOs, problems
caused by asymmetric information could be nearly eliminated.
The resulting average level of
underpricing should then be no more than several percent. Thus,
given the use of
bookbuilding, the joint hypothesis that issuers desire to
maximize their proceeds and that
underwriters act in the best interests of issuers can be rejected

whenever average
underpricing exceeds several percent.
Although underwriter discretion in allocating IPOs can be
desirable for issuing firms, it
can also be disadvantageous if conflict of interest problems are
not controlled. Underwriters
acknowledge that in the late 1990s IPOs were allocated to
investors largely on the basis of
past and future commission business on other trades. In 1998-
2000, for example, Robertson
Stephens allocated IPOs to institutional clients almost
exclusively on the basis of the amount
of commission business generated during the prior 18 months,
according to its January 9,
2003 settlement with the NASD and SEC. Credit Suisse First
Boston (CSFB) received
commission business equal to as much as 65% of the profits that
some investors received
Loughran & Ritter • Why Has IPO Underpricing Changed Over
Time? 9
from certain hot IPOs, such as the December 1999 IPO of VA
Linux.1 The VA Linux IPO was
priced at $30 per share, with a 7% gross spread equal to $2.10
per share. For an investor who
was allocated shares at $30, and who then sold at the closing
market price of $239.25, the
capital gains would have amounted to $209.25 per share. If the
investor then traded shares to
generate commissions of one-half of this profit, the total
underwriter compensation per
share was $2.10 plus $104.625, or $106.725.

The receipt of commissions by underwriting firms in return for
hot IPO allocations violates
NASD Rule 2110 on “Free Riding and Withholding.” Because
the underwriter has an economic
interest (a share of the profits) in the IPO after it has been
allocated, there is not a “full
distribution” of the security. This is economically equivalent to
withholding shares and
selling them at a price higher than the offer price, in violation
of Rule 2110. But if the NASD
(a self-regulatory organization) did not enforce its rules,
underwriters might find it optimal to
violate the rules. Evidence consistent with commission business
affecting IPO allocations is
contained in Reuter (2004).
The willingness of buy-side clients to generate commissions by
sending trades to integrated
securities firms depends on the amount of money left on the
table in IPOs. Underwriters have an
incentive to underprice IPOs if they receive commission
business in return for leaving money on
the table. But the incentive to underprice presumably would
have been as great in the 1980s as
during the internet bubble period, unless there was a “supply”
shift in the willingness of firms to
hire underwriters with a history of underpricing. We argue that
such a shift did indeed occur,
resulting in increased underpricing.
B. The Analyst Lust Explanation of Underpricing
We hypothesize that issuing firms have increasingly chosen
their lead underwriter largely
on the basis of expected analyst coverage. Providing research

coverage is expensive for
investment bankers; the largest brokerage firms each spent close
to $1 billion per year on
equity research during the bubble (Rynecki, 2002). These costs
are covered partly by charging
issuers of securities explicit (gross spread) and implicit
(underpricing) fees. The more that
issuing firms see analyst coverage as important, the more they
are willing to pay these costs.
There are several reasons for our opinion that analyst lust was
more important during the
1990s and bubble period than in the 1980s. First, the investment
bankers and venture
capitalists we have talked to are unanimous in their agreement.
Supporting this, in the early
1970s Morgan Stanley had “no research business to speak of,”
even though it was a major
IPO underwriter (Schack, 2002). As we will show, the number
of managing underwriters in
1See the January 22, 2002 SEC litigation release 17327 and
news release (available on the SEC website at
http://www.sec.gov), and the NASD Regulation news release
(available at http://www.nasdr.com). The NASD
Regulation news release states that “For example, after a CSFB
customer obtained an allocation of 13,500 shares
in the VA Linux IPO, the customer sold two million shares of
Compaq and paid CSFB $.50 a share—or $1
million—as a purported brokerage commission. The customer
immediately repurchased the shares through other
firms at normal commission rates of $.06 per share at a loss of
$1.2 million on the Compaq sale and repurchase
because of the $1 million paid to CSFB. On that same day,
however, the customer sold the VA Linux IPO shares,
making a one-day profit of $3.3 million.”

According to paragraphs 48 and 49 of the SEC complaint, for
the July 20, 1999 IPO of Gadzoox, which CSFB
lead managed, “at least 261,025 shares were allocated to
customers that were willing to funnel a portion of their
IPO profits to CSFB.” CSFB distributed approximately 3.4
million of the 4.025 million offer, which went from
an offer price of $21 to a closing price of $74.8125, up 256%.
The following day, July 21, 1999, CSFB was the
lead manager on MP3, which was priced at $28 and closed at
$63.3125, up 126%. “CSFB distributed 7.2 million
of the 10.35 million MP3 shares offered through underwriters.
Of the 7.2 million MP3 shares distributed by
CSFB, at least 520,170 shares were allocated to customers that
were willing to funnel a portion of their trading
profits to CSFB.”
IPO syndicates has increased over time. Investment bankers
note that co-managers are
included in a syndicate almost exclusively to provide research
coverage. Indeed, by 2000 co-
managers were generally not even invited to participate in road
shows and the pricing meeting
at which the final offer price is determined.
Second, as valuations have increased, changes in growth rates
perceived in the financial
markets represent more dollars. Firm value can be decomposed
into the value of existing
assets in place plus the net present value of growth
opportunities. As the value of growth
opportunities increases relative to the value of assets in place,
issuing firms come to place

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