Semiconductors

Crystalline solid materials whose resistivities are values between those of conductors and insulators.Good electrical characteristics and feasible fabrication technology are some reasons why silicon is by far the most important semiconductor material in use today.Compound semiconductor materials such as gallium arsenide are used in photonic and microwave applications, and germanium is used for a few special purposes.

Semiconductors

Silicon atoms join together to form a regular three dimensional structure called a crystal lattice.Pure semiconductor materials, termed intrinsic semiconductors, are neutral in total charge and are also a poor conductor of electricity. This means they have very few charge carriers.

Intrinsic Semiconductor

Doping

Process that adds a small amounts of impurities, dopants, to a semiconductor, so that it can be made to contain a desired number of either holes or free electrons.After the doping process the materials generated are termed extrinsic semiconductors. They are impure.Impurities are classified as either:

Donor.Acceptor.

Extrinsic Semiconductors

Donor impurities donate extra electrons to the silicon lattice:

Antimony, Arsenic and Phosphorus.

They have 5 electrons in their outer electron shell. Four of them will be used in the covalent bonds to the neighboring silicon atoms, but the fifth can be easily freed from their original atoms by thermal energy even at room temperatures.

N-Type Semiconductor

Semiconductor materials doped to contain excess free electrons are considered n-typesemiconductors.Even though the added impurity created excess free electrons, the material is still neutral in charge.It has been found that in n-type materials the free electron concentration is approximately equal to the donor atom doping density:

n ≈ ND

N-Type Semiconductor

Extrinsic Semiconductors

Acceptor impurities create a hole in the silicon lattice:

Boron, Gallium and Indium.

They have 3 electrons in their outer electron shell, and they are not enough to fill all the orbitals around it. This leaves a bond site empty, and this empty place is called a hole.

P-Type Semiconductor

Semiconductor materials doped to contain excess holes are considered p-typesemiconductors.Even though the added impurity created excess holes, the material is still neutral in charge.It has been found that in p-type materials the hole concentration is approximately equal to the donor atom doping density:

p ≈ NA

P-Type Semiconductor

Semiconductors

Extrinsic semiconductors can be doped with both types of impurities, and their respective concentrations determine the type material they will become:

N-type when ND > NA

Majority carriers are free electrons and minority carriers are holes.

P-type when ND < NA

Majority carriers are holes and minority carriers are free electrons.

Semiconductors

In pure, intrinsic, semiconductors free electrons and holes are created in pairs; therefore the intrinsic carrier concentration is defined as:

ni = n = pFor silicon at 300°K,

ni ≈ 1.6 X 1010 electrons/cm3

Current Conduction in Semiconductors

At temperatures above absolute zero the free carriers are in constant random motion due to their thermal energy, however their net motion in any particular direction is zero, therefore there is no net current flow.

Current Conduction in Semiconductors

There are two principle mechanisms by which charge move in a particular direction, thus creating an electric current:

Drift.Diffusion.

Drift

Applying an electric field across a semiconductor material, results in both types of carrier moving in opposite directions thus creating current flow.

Drift

The magnitude of the electric field in volts/cm is given by:

And the effective velocity of the carrier moving by the drift action of an applied electric filed is given by:

Where µn = 1350 cm2/V-s and µp = 480 cm2/V-s are the electron and hole mobility constants respectively.

LV

=E

Ennv µ= Eppv µ=

Conductivity

Property of a material.It is a measure of the material’s ability to to carry electric current.It is given by:

Measured in S/m.

( )pn pnq µµσ +=

Resistivity

Measured in Ω-m it is the reciprocal of conductivity:

The resistance of a material with constant cross section can be calculated by:

σρ 1=

ALR ρ=

Current Density

Current per unit cross-sectional area.Measured in A/cm2.Given by:

The direction of current flow vector is the same direction as the electric field vector.

EJ σ=

Diffusion

Diffusion current occurs because of the physical principle that over time particles undergoing random motion will show a movement from a region of high concentration to a region of lower concentration.

Diffusion

Current density is directly proportional to the gradient of carrier concentration.Dn and Dp are the diffusion constants for electrons and holes respectively.

⎥⎦⎤

⎢⎣⎡=dxdnqDJ nn ⎥⎦

⎤⎢⎣⎡=dxdpqDJ pp

Diodes

A two terminal electronic device which conducts current if a voltage source is applied in one direction, and refuses to conduct significant current when a voltage of opposite polarity is applied.A diode is said to be forward biased when it is conducting current, and it is said to be reversed biased when it is not conducting significant current.

Diodes

It is a non-linear device.It is represented by the following symbol, where the arrow indicates the direction of positive current flow.

Diodes

Historical perspective:Vacuum tube diode, Cat’s whisker.

Modern devices:p-n junction diode, Schottky diode, Zener diode, Tunnel diode, Varactor, etc.

P-N Junction

Created by bringing together a p-type and n-type region within the same semiconductor lattice.

P-N Junction

At the instant this junction is created free electrons and holes start diffusing from their regions of high concentration to regions of low concentration.This diffusion process is stopped very quickly due to the fact that the movement of the free electrons and holes leave behind uncovered negative and positive charges bound in the lattice (dopant atoms).

Depletion Region

This process builds up charge layers in a region, called depletion region, which is depleted of carriers.The charge layer prevents further diffusion.

Potential Barrier

The charge barrier creates a state of balance with the diffusion process, and this barrier can be represented as a voltage or potential barrier.

Potential Barrier

Note that the height of the potential barrier across the p-n junction can be modified by applying an external voltage across the junction.The diffusion of carriers across the junction is exponentially related to the barrier height:

Change in voltage incurs an exponential change in current due to carrier diffusion.

Potential Barrier

If the p-region is made more positive than the n-region then the height of barrier is reduced and more carriers can diffuse through junction. This is called forward bias.

Potential Barrier

If the p-region is made more negative than the n-region then the height of barrier is increased and very few carriers can diffuse through junction. This is called reverse bias.

Turn-on Voltage

Is arbitrarily defined by some manufacturers to be the externally applied voltage (forward bias) required to obtain 1 µA of current flow.It is designated by VF

Diode Circuit Models

Diode models that predict the relation between the dc voltage across the diode, VD , and the current through the diode, ID , are used to analyze circuits containing this non-linear device. Three models will be discussed here:

The ideal diode model;The diode equation model;The piecewise linear diode model.

Diode Circuit Models

Which model should you use?Ask yourself:

What do I know about the problem?Which is the simplest model that will give me results with accuracy I desire?

Ideal Diode

Idealized two terminal device which passes current in one direction (zero resistance) and passes no current in the opposite direction (infinite resistance).Its v-i plot, which shows the relationship of the voltage across the diode and the current flowing through it, contains a discontinuity.

Ideal Diode

If the diode is forward biased then the ideal diode conducts current as a closed switch.If the diode is reverse biased then the ideal diode will not conduct current, and it will appear as an open switch.

Ideal Diode

When analyzing circuits using this model, replace the diode with a very small test resistance, δR, and solve for the voltage across the test resistance. If the polarity of the voltage across the test resistance would forward bias the diode replace it with a closed switch otherwise replace it with an open switch.

The Diode Equation and Model

The diode equation can be derived based on the assumption that carriers move by diffusion.

ID – Current through diode.IO – Reverse saturation current.VD – Voltage across the diode.k – Boltzmann’s Constant.n – Ideality factor (n = 1 for silicon).T – Temperature in degrees Kelvin.

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 1nkT

qV

OD

D

eII

39≅kTq

The Diode Equation and Model

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 1nkT

qV

OD

D

eII

Graphical Solution

Simplify the circuit connected to the diode to a Thevenin’s equivalent circuit. Analyze two cases:

iD = 0;vD = 0.

This two points identifies the Thevenin’s circuit load line, and this lines intersects the diode plot at the operating point.

Piecewise Linear Model

The real diode can be approximated by a model which uses two connected line segments.Note that the turn on voltage, VF , marks the point where the two line segments meet.

Power Supply Circuits

Power supply circuits are used to convert ac to dc for the purpose of operating electronic circuits.Typical residential ac power distribution:

110-120 volts;220-240 volts.

Power Supply Circuits

Typical electronic system requirements:

Digital electronics:5 volts dc;

Analog electronics requires two supplies:

+15 volts dc;-15 volts dc.

Power Supply Circuits

To achieve its purpose a power supply must:

Step down the voltage supplied;Convert ac to dc by rectifying the ac.

A transformer is used to step down the magnitude of the voltages from the wall receptacle.

Transformer

A transformer consists of two coils of wire on a common iron core. The voltages on these two coils are related by the turns ratio, which is the ratio of the number of turns of wire in the secondary coil to that in the primary coil.

RMS Values

Note that the 110-120 volts and 220-240 volts are RMS values.The actual amplitude of that sinusoidal signal is a factor of √2 larger.

Rectification

Converting ac to dc is accomplished by the process of rectification.Two processes are used:

Half-wave rectification;Full-wave rectification.

Half-wave Rectification

Simplest process used to convert ac to dc.A diode is used to clip the input signal excursions of one polarity to zero.

Full-wave Rectification

The output of a full-wave rectifier is driven by both the positive and negative cycles of the sinusoidal input, unlike the half-wave rectifier which uses only one cycle.

Filtering

Process used to smooth out the output of the rectifier circuit.One of the most common filter is the RC network.

Filtering

The reduction in voltage between charging cycles is dependent on the time constant stated below:

( ) τ

τt

m

L

eVtv

CR−

=

=

Ripple Factor

Ripple is the small voltage variation from the filter’s output.Good power supplies produce as little ripple as possible.Ripple is usually specified as Ripple Factor, RF :

valuedcrippleofvaluermsRF =

Clipper Circuits

Used to limit the voltage excursions of a signal at some particular positive value, negative value or both.

Clamper Circuits

Used to generate an output waveform which appears like the input one except that the DC level has either shifted positively or negatively with respect to the input waveform.

Zener Diode

Analyzing a diode operating in the reverse bias region will show that the current through it remains essentially constant until the breakdown voltage, also called the avalanche or zener breakdown voltage, is reached. At this point the current will increase very rapidly for a small voltage change.

Voltage Regulation

This characteristic of the zener diode is very useful for voltage regulation circuits. The zener diode provides an effective way to clamp or limit the voltage at a relatively constant value thus creating a voltage regulation capability.

Photo Diodes and LEDs

Photodiodes convert incident radiation to electric current.The sun’s radiation creates electron-hole pairs in the depletion region of a large p-n diode, and the electric field in this region sweeps the carriers to the terminals thus generating current.The magnitude of the current approximately proportional to the light incidence on the diode.

Photo Diodes and LEDs

Light Emitting Diodes – LEDs are p –njunctions fabricated from special semiconductors materials, like gallium arsenide. They are useful because they allow direct recombination of electrons and holes, thus releasing energy in the form of light.