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IN RECENT years, we have become familiar with the idea of materials
that behave as superconductors at reasonably high temperatures (between
77 and 90 K). The discovery of these new materials is exciting because they
revive a dream that engineers have had for many years – the ability to make
materials with no resistance at room temperature.

Strangely, although this prospect is not yet in our grasp, we have been
using devices and materials that behave as if they have negative resistance
– even when heated well above room temperature – for many years. Devices
with negative resistance have become a vital part of many microwave systems,
in applications from radar and radio communications to instruments for making
environmental or astronomical measurements. Recent developments in our ability
to manufacture very small semiconductor structures may lead to a new generation
of improved devices, such as oscillators, that make use of the properties
of a negative resistance .

To anyone familiar with normal electronics, negative resistance seems,
at first glance, impossible. Can an applied voltage cause current to flow
the ‘wrong’ way? It seems as absurd as the possibility of water flowing
uphill. In order to understand negative resistance, we can start by thinking
about the behaviour of normal conducting materials.

When we place an object in an electric field, we exert a force on any
charged particles that the object contains. In a solid, the atoms are normally
held tightly together and will not move unless we apply very large forces.
However, some of the electrons orbiting each atom may require only a small
force to detach them. These electrons can move around relatively freely
within the material and are, therefore, called ‘free’ electrons.

If a material contains free electrons, they will move in response to
an electric field, carrying their charges with them. They cause a current
to flow. Each charged particle is continuously accelerated by the field.
But as the electron moves through the material it will occasionally collide
with an atom or another electron, losing some momentum. Each moving charge
is in a situation similar to that of someone trying to run through a crowd
of dancers. It is impossible not to keep bumping into people and bouncing
off them. It is these collisions that constitute the electrical resistance
of a material.

When we measure a current, we are observing the overall effect of millions
of charges moving in response to the applied field. The size of the current
will depend upon the density of free charge carriers and upon how often
they bump into something. It also depends upon the size of the applied electric
field. This is the basis of Ohm’s law: the current we observe increases
in proportion with the applied potential difference and decreases in proportion
to the resistance.

Materials that have enough free charges to give a measurable current
are called conductors. Those that have almost no free carriers are called
insulators. A semiconductor, as its name implies, has a modest number of
charge carriers so it conducts, but not as effectively as a good conductor
such as a metal. The distinction between conductors and insulators is, in
practice, one of convenience. Under many circumstances, an applied field
will produce a current through an insulator, although it is usually so small
as to be practically unmeasurable.

Ohm’s law works very well for low voltages and currents. If we apply
a very big field, however, and try to produce large currents, things begin
to change. For example, when we apply a field and set up a current flow
through a piece of material, we find that the material tends to warm up.
As the free carriers accelerate, they gain kinetic energy. When they collide
with an atom, they pass on some of this energy. As a result, the current
flow transfers kinetic energy to the atoms and their dance hots up. The
power that heats up the sample is simply equal to the applied potential
difference multiplied by the current.

Changes in the temperature of the material will alter the density of
free electrons and the probability of the collisions that hold up the flow.
Thus, when we observe how the current varies with the size of the applied
field, we may find that Ohm’s law works well only if we keep the field and
current small. Higher fields will change the temperature of the sample,
causing noticeably more (or less) current to flow than we would expect from
Ohm’s law.

Exceptions to Ohm’s law

At very large fields, ionisation also begins to take place. This is
where the free electrons are accelerated so much that they gain sufficient
energy to strike an atom hard enough to knock another electron out of its
grasp. As a result, extra electrons are freed and can be accelerated, releasing
yet more new charge carriers when they collide with other atoms. This process
causes an ‘avalanche’ of free charge carriers. Under these circumstances,
a steady applied field produces a rapidly increasing current and, unless
the avalanche is limited in some way, the process may well destroy the material.
Although the required electric fields are high, ionisation avalanches are
common. For instance, air is a fairly good insulator until a high field
is applied. When this happens, the result is an ionisation avalanche in
the form of a lightning discharge.

Ionisation avalanches are a good example of how the conduction properties
of a material can be very different from the simple proportional relationship
between current and applied as predicted by Ohm’s law. Unfortunately, avalanches
are difficult to control and may lead to unwanted results. Fortunately,
some materials show other forms of ‘nonlinear’ conduction at levels of electric
field below those that produce ionisation. One of the most interesting of
these is the Gunn effect, named after its discoverer, JB Gunn.

To understand what this effect is, we need to look at how electrons
behave in solid materials. The electrons orbiting a single isolated atom
must have energies that obey certain rules. These rules are generally defined
by the theory of quantum mechanics, which ‘forbids’ orbiting electrons to
have any energy other than a series of well-defined values. When we bring
a number of atoms together to form a solid they affect one another. The
electromagnetic fields from each atom and its electrons tend to change the
energy levels of neighbouring atoms slightly. The result is that electrons
within the solid material have energies that are confined to ‘bands’ of
energies rather than specific levels. Electrons with relatively low energies
stay close to a single atom and contribute to the forces that bind the atoms
of a solid together. The energy bands that these electrons occupy are called
valence bands. At higher energies where the electrons can move, the band
is called a conduction band.

Generally, the free electrons are almost all in one conduction band
– the one with the lowest energy that is not a valence band. Under the right
circumstances, however, we can give some free electrons enough energy to
let them reach another conduction band with a higher energy, which is usually
empty. In some materials – notably, semiconductors such as gallium arsenide
(GaAs) or indium phosphide (InP) – electrons in this higher band find it
much harder to move.

If we start to apply an increasing voltage across a piece of one of
these materials, we find that at first, the current increases in proportion
with the voltage. Eventually, we reach a voltage high enough to ‘excite’
electrons to move into another band. Now the current stops rising and begins
to fall as we continue to increase the voltage. This is because we are transferring
more and more electrons into the higher band, where they cannot move as
easily. If we increase the voltage still further, we will finally reach
the point where all the moving charges have been transferred. Once this
has happened, any extra increase in voltage will cause the current to rise
once more as the charges are forced to move more swiftly in the higher band.

Figure 1 compares the variation of current with applied voltage – the
resistance – for a material showing the Gunn effect with that for a material
obeying Ohm’s law. Now, we have a choice of how we wish to measure the electrical
resistance of something. The simplest way is to apply a known voltage, V,
measure the current, I, it produces, and use Ohm’s law to say that the resistance,
R, will be equal to V/I, the voltage divided by the current. A resistance
measured in this way is called a static resistance because it tells us the
relationship between a fixed voltage and the steady current that it produces.

An alternative method for determining the resistance is to draw a graph
showing how the current we have obtained varies with the applied voltage.
The slope of this graph can be used as a measure of how the current depends
upon the voltage. A resistance determined from the slope in this way is
called the dynamic resistance because it tells us how much the current changes
if we alter the voltage. For a material that obeys Ohm’s law, the graph
of current against voltage is a straight line, which passes through the
origin. When we measure the slope of its graph at a chosen voltage, V, we
discover that it equals I/V in other words, its value is identical to 1/R,
so this method gives the same result as the static measurement.

For anything that fails to follow Ohm’s law – as is the case when the
Gunn effect comes into play – the variation of current with voltage follows
some other sort of curve. If we choose a point on this curve and determine
both the static and dynamic resistances, we find that they are usually different.

In particular, we find for an electronic device exploiting the Gunn
effect that, although the static resistance is always positive, the dynamic
resistance is negative over the range of voltages where charge carriers
are being excited into the higher energy band. The precise range of voltages
where this happens depends on the material. We can, however, be confident
that this region of negative dynamic resistance cannot include zero volts.
This is because a given level of applied electric field is required in order
to provide the moving charges with enough energy to become excited into
the higher energy band.

Alternatively, we can say that this result is a consequence of the law
of energy conservation. It is possible to use the negative dynamic resistance
to make an oscillating source of electrical power . This power must come
from somewhere. In practice, we must apply a given steady ‘bias’ voltage,
V, and current, I, to reach the region of negative resistance. This steady
bias provides an input power, some of which can re-emerge as an oscillation
back and forth about this steady average value.

A type of electronic oscillator based upon the Gunn effect, called the
Gunn device, has come into widespread use, as a source in many applications
using microwaves. More recently, people have been interested in building
new systems that operate at higher frequencies extending into the millimetre-wave
range, in other words, at frequencies around 100 gigahertz, or more, where
the equivalent wavelength is just a few millimetres. Unfortunately, a number
of practical problems crop up as we try to make oscillators at ever higher
frequencies.

One basic problem with a negative resistance based upon the Gunn effect
is that it takes a finite period of time to persuade free charges to transfer
from one energy band to another. To make an oscillation take place, the
carriers must transfer back and forth between the two energy bands during
each cycle.

First, we must wait while the applied voltage accelerates the moving
charges until they gain sufficient energy to reach the higher band. Then
we must wait again, once the voltage has fallen, until the moving charges
collide with atoms in the material, lose some energy, and drop back into
the lower band. One cycle of oscillation at 100 gigahertz takes only 100
000 millionth of a second. So we must switch charge carriers from band to
band in less than half this time if a Gunn oscillator is to work at this
high frequency.

Most ordinary electronic devices make use of silicon semiconductors.
But for microwave applications, engineers usually use gallium arsenide because
this material’s free charges respond more swiftly to changes in the applied
field. Unfortunately, because of the time delays already mentioned, it becomes
increasingly difficult to persuade a Gunn device made from gallium arsenide
to operate a frequencies above about 60 gigahertz.

We can employ various ‘tricks’ to obtain higher frequencies. We can,
for example, persuade a Gunn device to produce a ‘distorted’ waveform at
50 gigahertz. The waveform that it generates will then contain some power
at harmonics of the basic frequency, and we can arrange to collect the signal
it produces at, say, 100 gigahertz. With some ingenuity, therefore, we can
extend the operating frequency of such an oscillator, but the scope for
advance is limited by a reluctance of the material to respond as swiftly
as we would like. The amount of power that is produced falls rapidly as
we try to increase the output frequency.

Indium phosphide is an alternative semiconductor, whose free charges
can respond about twice as swiftly as those in gallium arsenide. We can
produce oscillators using this material at frequencies up to about 120 gigahertz
(or perhaps 240 gigahertz if we can make a harmonic oscillator). In order
to reach still higher frequencies we need either an even better material
or a different approach.

Quantum electronic devices

During the past couple of years, engineers have made some new forms
of semiconductor device exploiting the quantum effects that appear in very
small electronic structures. These devices are similar to ordinary diodes
in that their behaviour comes from joining together materials with different
energy levels. As a charge approaches the boundary between two materials,
it will experience a force that changes the velocity of the charge. When
the charge moves into a material with lower energy bands, this force is
attractive and the moving charge speeds up. If moving towards a material
with bands of higher energy, the force repels the charge, slowing it down.

For a charge that crosses from one material to another, the change in
kinetic energy is just equal, and opposite, to the difference in energy-band
levels. If the increase in band energy is large, we may find that it is
more than the available kinetic energy. When this is the case the moving
charge cannot cross the boundary. Instead, the repulsive force ‘reflects’
the moving charge just as if it were a ball bearing bouncing off a metal
plate.

Although it is useful to think of electrons as if they were very small
ball bearings, we must take care. Electrons are extremely small, and their
behaviour is better described using quantum mechanics. In reality, we cannot
measure precisely both the position and the movement of an individual electron
– this is Heisenberg’s uncertainty principle. All we can do is map out some
kind of wave that describes how likely it is than an electron will be in
any one place and be moving in a certain way.

Consider now what happens if we take a piece of semiconductor and place
inside it a very thin layer of material whose energy bands are higher. The
layer acts as a barrier to the free movement of carriers. If the electrons
behaved like classical ball bearings, those whose kinetic energy is less
than the difference in band energies would never be able to get through
this barrier. A real electron, however, has a ‘blurred’ position and kinetic
energy. If the barrier is thinner than the uncertainty in the position of
the electron, it may be able to ‘tunnel’ through the barrier. This is because
when the electron moves close to one side of the barrier, its range of possible
locations extends far enough to include the other side of the barrier.

An alternative way of looking at this is to regard the electron’s energy
as fluctuating enough, over a brief period, to give it a boost to surmount
the barrier. As a result, some electrons can ‘leak’ through a thin layer
of material even though they would not have enough energy to enter a thicker
piece.

Researchers can analyse the detailed behaviour of an electron as it
approaches a thin barrier and is either transmitted or reflected by regarding
the electron as a sort of wave. The behaviour of such a barrier is interesting
to physicists because it provides a way of checking our understanding of
quantum mechanics. If we place two thin barriers really close together,
things get much more interesting. This is because the wave representing
a moving electron has a phase and wavelength just like any other kind of
wave. In fact, the presence of two barriers allows us to produce interference
effects with the electron waves.

A double-barrier diode is an electronic device made by growing a piece
of semiconductor that contains two thin, barriers with high-energy bands.
The barriers are closer together than the uncertainty in an electron’s position.
Engineers make electrical contacts to the ends of the diode so that they
can measure how the current produced varies with an applied electric field.

If we draw a graph of how the current passing through a double-barrier
diode varies with the applied voltage we find that there are one or more
regions of negative resistance, produced by interference of the electron
waves inside the diode . Hence this form of diode can be used as the basis
of a negative resistance oscillator.

It is only in the past few years that electronic engineers have made
and tested devices designed to work at millimetre-wave frequencies. So far,
they have made simple double-barrier diodes, with two identical barriers,
to oscillate at frequencies around 400 gigahertz. Although there is still
a heated debate over their theoretical limitations there is evidence that
higher frequencies – possibly up to 600 gigahertz and above – will be produced.

Now that engineers have evolved the techniques that make such tiny semiconductor
barriers possible, we should be able to make a wide range of exciting new
structures. For example, we can start to think of making devices containing
a number of layers, each with an individually chosen thickness. These devices
would have differing barrier energy levels, and spacing between adjacent
layers. Devices of this sort are often referred to as multiple-barrier diodes.

We can even consider structures that contain other shapes, such as small
rectangles of material embedded in a regular pattern inside a semiconductor.
Regular patterns of tiny barriers, rectangles, and so on, have the effect
of modifying the electronic properties of the lump of semiconductor. It
is almost as if we can create new, ‘artificial’ crystal lattices whose electronic
properties can be chosen for the required application. In general, these
sorts of devices are called quantum-well or low-dimensional devices.

One group working on millimetre wavelengths at the University of St
Andrew’s is interested in developing solid-state oscillators for frequencies
above 100 gigahertz. We are working on devices manufactured by Martin Chamberlain
and Paul Steenson at the University of Nottingham.

Semiconductor devices are widely used in optics as well as electronics.
People have used diodes for many years as lasers and light detectors. This
new range of solid state structures promise to extend our ability to build
new optical devices and systems. Indeed, as we begin to consider new structures
that can oscillate or detect light at higher millimetre-wave frequencies,
we find that similar devices are interesting to optical scientists for making
lasers and light detectors that extend further into the infrared than was
previously possible. In fact, although engineers working with laser and
millimetre wavelengths tend to approach their understanding of these devices
in different ways, the physical processes that they are exploiting are the
same. It may be that these devices will ultimately bridge the gap between
optics and electronics.

* * *

The ups and downs of an electronic circuit

ONE of the most common uses of a negative resistance is as the basis
of very high frequency oscillators. Figure 2 shows a typical electronic
resonant circuit, made from a capacitor, inductor and a resistor connected
together in a loop.

We can cause a current to start flowing in the loop by, for example,
arranging that the capacitor we use should be charged before it is connected.
The initial voltage on the capacitor will cause a current to flow through
the inductor and resistor. This current, however, will not stop once the
capacitor has lost its charge. The reason is that a current flowing through
an inductor tends to keep going by virtue of the magnetic field that it
produces. The current continues to flow, recharging the capacitor, but with
the opposite polarity.

The growing charge on the capacitor will oppose the current flow, eventually
bringing it to a halt. Now the situation is similar to that in which we
started. The capacitor is charged and there is no current flow. So the process
repeats itself. Because the charge on the capacitor has been reversed, the
current flows back through the inductor and continues until the capacitor
is recharged again and the current flow stops once more.

This process repeats itself over and over again. The result is an oscillating
current around the loop. If the resistance in the loop were zero, then none
of the energy initially stored in the charged capacitor would ever be lost
and the oscillation would continue forever, or at least until the loop was
broken. A careful analysis of the behaviour of this type of circuit shows
that the current varies sinusoidally and has a frequency that depends upon
the values of the inductance and capacitance chosen for the circuit.

Some researchers have experimented with resonant circuits made of superconducting
materials operating at low temperatures. Just as predicted by theory, any
oscillating current, once started, persists indefinitely without getting
any smaller.

Unfortunately, in most practical situations we cannot make circuits
that are completely free of resistance. The current flowing in a circuit
must lose some power in passing through the resistance. As a consequence,
the electrical energy is dissipated and the size of the oscillating current
falls exponentially to nothing.

A negative resistance behaves in the opposite way. Any current passing
through a negative resistance is ‘encouraged’ rather than being ‘resisted’.
If we place a negative resistance in a resonant loop, we discover that the
oscillatory current grows instead of getting smaller. Thus, the combinations
of a resonant circuit and a negative resistance can be used as a source
of oscillating signals. Unlike a normal resistance, which dissipates electronic
energy, a negative resis tance can produce electronic energy.

Happily, neither a positive nor a negative resistance has to violate
the law of energy conservation in order to work. The electronic energy ‘lost’
by a resistor is converted into an equal amount of some other form of energy,
usually heat. (It can be lost in other ways, an example being the light
produced by the resistive filament in a light bulb.) In a similar way, the
oscillatory electronic energy produced by a negative resistance has to be
initially supplied in some other form.

Electronics engineers have devised negative-resistance oscillators that
operate at frequencies up to and above 100 gigahertz enabling them to function
in microwave and millimetre-wave applications. Some of the newer forms of
device may well work at still higher frequencies.

* * *

Double barriers to interfering electrons

THE wavelength of an electron depends upon its kinetic energy. The faster
the electron, the shorter its wavelength. When we apply a low electric field
to a double barrier diode, the moving charges travel fairly slowly and have
a wavelength that is much greater than the distance between the barriers.
Under these circumstances, the reflected waves produced by the barriers
share almost the same phase and they add up, increasing the chance that
the charge will be reflected. Hence the double barrier behaves as a large
resistance to current when the applied electric field is low.

If we steadily increase the applied field, we speed up the charges,
reducing their wavelength. Eventually, we reach the point where the distance
covered by that portion of the wave that travels to the far barrier and
back is a half-wavelength longer than that reflected from the nearer barrier.

Now the reflected waves are out of phase and tend to cancel each other
out. As a result, when the applied field is high enough, the double barrier
provides only a modest resistance to the current flow (see Figure 3).

In principle, as we continue to increase the applied field, reducing
the wavelength still further, the reflected waves will swing alternately
in and out of phase, causing the resistance to rise and fall. Unless we
apply a very high field, the rest of the semiconductor, away from the barriers,
will show a fairly steady resistance which is in series with that of the
barriers. Combining the barriers and the rest of the device we find that
the current-voltage variation will look something like Figure 4. The resistance
is generally positive, but becomes negative in a series of voltage regions.

When we apply a very large electric field the moving charges can gain
sufficient energy to enter the barriers, so they no longer have to ‘tunnel’
through them. Once this happens, the swings in resistance stop. In practice,
therefore, most double-barrier diodes show only a few regions of negative
resistance.

Jim Lesurf is a lecturer in the department of physics and astronomy
at the University of St Andrews. He has been designing and building millimetre-wave
optical circuits for more than 10 years.

Further reading James Lesurf, Millimetre Wave Optics, Devices and Systems,
Adam Hilger, 1990.