11.1 Band Theory of Solids 11.2 Semiconductor Theory 11.3 Semiconductor Devices 11.4 Nanotechnology

CHAPTER 11Semiconductor Theory and Devices

It is evident that many years of research by a great many people, both before and after the discovery of the transistor effect, has been required to bring our knowledge of semiconductors to its present development. We were fortunate to be involved at a particularly opportune time and to add another small step in the control of Nature for the benefit of mankind.

- John Bardeen, 1956 Nobel lecture

11.3: Semiconductor Devices

pn-junction Diodes

Here p-type and n-type semiconductors are joined together.

The principal characteristic of a pn-junction diode is that it allows current to flow easily in one direction but hardly at all in the other direction.

We call these situations forward bias and reverse bias, respectively.

Operation of a pn-junction Diode

[Note: It and Ir are electron (negative) currents, but Inet indicates positive current.]

No bias Reverse bias Forward bias

A typical I –V curve for a pn-junction diode

Formation of pn-junction

When the p and n type materials are separated,The carriers (e, h) diffuse around randomly.

p-type n-type

Hole (+)

Electron (-)

Negativeion core

Positiveion core

Formation of pn-junction : Depletion region

When the materials are joined, the carriers (e, h) cross by diffusion.The fixed ion cores that are left behind set up and electric field “Depletion E”.

Depletion region

E depleted

Negativeion core

Positiveion core

p-type n-type

Hole (+)Electron (-)

Formation of pn-junction : in EquilibriumDepletion region

E depleted

p-type n-type

Majority carriers diffuse cross the depletion region Diffusion current (idiffusion), or thermal current (it)

In equilibrium, it = ir

But, some diffused carriers come back home by E_depleted Drift current (idrift) , recombination (ir)

Negativeion core

Positiveion core

Hole (+)Electron (-)

Diode under Forward Bias

E depleted

p-type n-type

E biased

Net current flows from p-type to n-type

ir > it

Diode under Reverse Bias

E depleted

E biased

p-type n-type

No net current flows from p-type to n-type

ir < it

Operation principle of pn-junction Diodes: Explanation by Energy band concept

(a) No bias

At the pn-junction, two Fermi energies must be balanced Energy band slops occurs in depletion region No net current because (thermal electron current) = (recombination current)

EFEF EF p n

(EF at p-type) = (EF at n-type)

Operation principle of pn-junction Diodes: Explanation by Energy band concept

(b) Reverse bias

(c) Forward bias

EF

EF

(EF at p-type) = (EF at n-type) + eV

Net current = 0

(EF at p-type) = (EF at n-type) - eV

Net current > 0

The diode is an important tool in many kinds of electrical circuits. As an example, consider the bridge rectifier circuit.

The bridge rectifier is set up so that it allows current to flow in only one direction through the resistor R when an alternating current supply is placed across the bridge. The current through the resistor is then a rectified sine wave of the form

This is the first step in changing alternating current to direct current. The design of a power supply can be completed by adding capacitors and resistors in appropriate proportions. This is an important application, because direct current is needed in many devices and the current that we get from our wall sockets is alternating current.

Figure 11.14: Circuit diagram for a diode bridge rectifier.

Bridge Rectifiers

The Zener diode is made to operate under reverse bias once a sufficiently high voltage has been reached.

Notice that under reverse bias and low voltage the current assumes a low negative value, just as in a normal pn-junction diode.

But when a sufficiently large reverse bias voltage is reached, the current increases at a very high rate.

Zener Diodes

A typical I-V curve for a Zener diode

A common application of Zener diodes isin regulated voltage sources. any change (say an increase) in the supply voltage V tends to

be compensated for by a sharp increase in the current through the Zener diode.

Then the voltage across the resistor increases, which in turn tends to keep the output voltage VZ = V - IR fairly constant.

Light Emitting Diodes (LED) Another important kind of diode is the light-emitting diode (LED). Whenever an electron makes a transition from the conduction band to

the valence band (effectively recombining the electron and hole) there is a release of energy in the form of a photon.

In some materials the energy levels are spaced so that the photon is in the visible part of the spectrum. In that case, the continuous flow of current through the LED results in a continuous stream of nearly monochromatic light.

Photovoltaic (Solar) Cells Solar cell, also known as photovoltaic cell. A solar cell takes incoming light energy and turns it into electrical energy.

Solar cell is to consider the LED in reverse A pn-junction diode can absorb a photon by having an electron make

a transition from the valence band to the conduction band. In doing so, both a conducting electron and a hole have been created. The holes and electrons will move so as to create an electric current,

The most widely used and studied photovoltaic materials are silicon-based.The technology exists for making large single crystals of silicon. In silicon-based cells efficiencies of more than 20% are reached. Unfortunately, the cost of making good single crystals of silicon is prohibitive. The cost of making cells with polycrystalline and amorphous silicon is lower, but so is the efficiency of the solar cells made with these materials.

Photovoltaic (Solar) Cells

The response of various solar cells as a function of wavelength

An example of a multi-layered solar cell is Boeing’s 31% efficient solar cell

Transistors Devices that amplify voltages or As an example, npn-junction transistor The three terminals are known as the collector, emitter, and base. A good way of thinking of the operation of the npn-junction transistor is to

think of two pn-junction diodes back to back.

(Bipolar) Transistors

Voltage amplifier Current amplifier Circuit symbol

The first transistor was developed in 1948 by John Bardeen, William Shockley, and Walter Brattain (Nobel Prize, 1956)

Field Effect Transistors (FET) The three terminals of the FET are known as the drain, source, and gate,

and these correspond to the collector, emitter, and base, respectively, of a bipolar transistor.

FET schematic Circuit symbol Voltage amplifier

Field Effect Transistors (FET)

BJT의낮은임피던스는응용목적에결점이많다.• 직접이어렵고, 상대적전력소비가많다.• FET는BJT보다느리지만널리사용.

• source에서 drain으로 n형채널을통해전자들이이동

• 이때 p-n접합에역바이어스를인가하면(gate에음의전압을크게인가하면) depletion region이증가하면서전하운반체가고갈됨.

• 역방향바이어스에의해게이트회로에흐르는전류가아주작아극단적으로높은입력임피던스를얻을수있음.

BJT의수%면적

Schottky Barriers

(a) Schematic drawing of a typical Schottky-barrier FET. (Metal semicon. FET – MESFET)(b) Gain versus frequency for two different substrate materials, Si and GaAs.

Energy barrier at the direct contact boundary between a metal and a semiconductor.

If the semiconductor is n-type, electrons from it tend to migrate into the metal, leaving a depleted region within the semiconductor.

The I-V characteristics of the Schottky barrier are similar to those of the pn-junction diode.

Semiconductor Lasers In a semiconductor laser, the band gap determines the energy difference

between the excited state and the ground state Photon energy

Semiconductor lasers use injection pumping, where a large forward current is passed through a diode creating electron-hole pairs, with electrons in the conduction band and holes in the valence band.

A photon is emitted when an electron falls back to the valence band to recombine with the hole.

Since their development, semiconductor lasers have been used in a number of applications, most notably in fiber-optics communication.

One advantage of using semiconductor lasers in this application is their small size with dimensions typically on the order of 10−4 m.

Being solid-state devices, they are more robust than gas-filled tubes.

Integrated Circuits The most important use of all these semiconductor devices today is not in

discrete components, but rather in integrated circuits (chips).

Some integrated circuits contain a million or more components such as resistors, capacitors, transistors, and logic switches.

Two benefits: miniaturization and processing speed

ENIAC (Electronic Numerical Integrator and Computer), built in 1945

The Intel 4004, the first commercial microprocessor(1971)

Moore’s Law and Computing Power

Moore’s law, showing the progress in computing power over a 30-year span, illustrated here with Intel chip names. The Pentium 4 contains over 50 million transistors.

“Microchip capacity doubles roughly every 18 to 24 months”

11.4: Nanotechnology Nanotechnology is generally defined as the scientific study and

manufacture of materials on a submicron scale. These scales range from single atoms

(on the order of 0.1 nm up to 1 micron). This technology has applications in engineering, chemistry, and

the life sciences and, as such, is interdisciplinary.

At an American Physical Society meeting in 1959, Feynman gave a now-famous address entitled:

“There’s Plenty of Room at the Bottom.”

What I want to talk about is the problem of manipulating and controlling things on a small scale. . . . What I have demonstrated is that there is room—that you can decrease the size of things in a practical way. I now want to show that there is plenty of room. I will not now discuss how we are going to do it, but only what is possible now in principle. . . . We are not doing it simply because we haven’t yet gotten around to it.

Carbon Nanotubes In 1991, following the discovery of C60 buckminsterfullerenes, or “buckyballs,”

Japanese physicist Sumio Iijima discovered a new geometric arrangement of pure carbon into large molecules.

In this arrangement, known as a carbon nanotube, hexagonal arrays of carbon atoms lie along a cylindrical tube instead of a spherical ball.

The basic structure leads to two types of nanotubes. A single-walled nanotube has just the single shell of hexagons as shown. In a multi-walled nanotube, multiple layers are nested like the rings in a tree trunk.

Single-walled nanotubes tend to have fewer defects, and they are therefore stronger structurally but they are also more expensive and difficult to make.

Applications of Nanotubes Because of their strength they are used as structural reinforcements

in the manufacture of composite materials (batteries in cell-phones use nanotubes in this way)

Nanotubes have very high electrical and thermal conductivities, and as such lead to high current densities in high-temperature superconductors.

One problem in the development of truly small-scale electronic devices is that the connecting wires in any circuit need to be as small as possible, so that they do not overwhelm the nanoscale components they connect.

In addition to the nanotubes already described, semiconductor wires (for example indium phosphide) have been fabricated with diameters as small as 5 nm.

nanotransistor

Graphene A new material called graphene was first isolated in 2004. Graphene

is a single layer of hexagonal carbon, essentially the way a single plane of atoms appears in common graphite.

A. Geim and K. Novoselov received the 2010 Nobel Prize in Physics for “ground-breaking experiments.” Pure graphene conducts electrons much faster than other materials at room temperature.

Graphene transistors may one day result in faster computing.

graphene-based transistor

Quantum Dots Quantum dots are nanostructures made of semiconductor materials.

They are typically only a few nm across, containing up to 1000 atoms. Each contains an electron-hole pair confined within the dot’s boundaries Somewhat analogous to a particle confined to a potential well.

Band gap varies over a wide range and can be controlled precisely by manipulating the quantum dot’s size and shape.

Can be made with band gaps that are nearly continuous throughout the visible light range (1.8 eV ~ 3.1 eV) and beyond.

Quantum Dots Quantum dots are nanostructures made of semiconductor materials.

They are typically only a few nm across, containing up to 1000 atoms. Each contains an electron-hole pair confined within the dot’s boundaries Somewhat analogous to a particle confined to a potential well.

CdSe/ZnS quantum dot nanocrystals

2.5 nm

6.3 nm

Nanotechnology and the Life Sciences The complex molecules needed for the variety of life on Earth are

themselves examples of nanoscale design. Examples of unusual materials designed for specific purposes

include the molecules that make up claws, feathers, and even tooth enamel.

gecko’s foot Plastic fibers fashioned with electron-beam lithography, made in an attempt to reproduce the adhesive powers of the gecko’s keratin hairs.

Information Science It’s possible that current photolithographic techniques for making

computer chips could be extended into the hard-UV or soft x-ray range, with wavelengths on the order of 1 nm, to fabricate silicon-based chips on that scale.

In the 1990s physicists learned that it is possible to take advantage of quantum effects to store and process information more efficiently than a traditional computer. To date, such quantum computers have been built in prototype but not mass-produced.

All-optical switch and transistor

laser cooled atoms