Revision Notes: Class 12 | Physics | Chapter 14 | Semiconductor Electronics: Materials

Ruhul Amin Alig

A quick revision of all the important concepts

SEMICONDUCTOR ELECTRONICS: MATERIALS, DEVICES AND SIMPLE CIRCUITS

Energy Band structure in solids
Metal: There are two cases in metals.
Case1: the conduction band partially filled and the valence band partially empty, in this case, the electrons from the lower level go to a higher level making the conduction possible.
Case2: the valence band and conduction band overlapping, where electrons from the valence band easily move into the conduction band giving rise to electric conduction.
Hence, metals have high conductivity and low resistivity.

Insulator: Insulators have a large bandgap

E_{g}

so electrons cannot be excited from the valence band to the conduction band. Since the conduction band has no electrons, so electric conduction is not possible. Hence, insulators have high resistivity and very low conductivity.

Semiconductor: Here a small bandgap exists. At room temperature, some electrons from the valence band acquire enough energy to cross the band gap and enter the conduction band. Semiconductors have resistivity and conductivity intermediate to metals and insulators.

Intrinsic Semiconductor:

An intrinsic semiconductor is a pure semiconductor without any significant dopant species present. In intrinsic semiconductors,

n_{e} = n_{h} = n_{i}

, where

n_{i}

is the intrinsic carrier concentration.

Extrinsic Semiconductor:

These are a.k.a. impurity semiconductors or doped semiconductors. The process of adding impurities deliberately is termed doping and the atoms that are used as an impurity are termed as dopants.

n-type semiconductor: doped with electron donor atoms, $n_{e} > > n_{h}$
p-type semiconductor: doped with electron acceptor atoms, $n_{e} < < n_{h}$

Formation of P-N junction:

The diffusion of holes ( $p \to n$ ) and electrons ( $n \to p$ ) gives rise to diffusion current across the junction.
As the holes continue to diffuse, a layer of negative charge on the $p - s i d e$ of the junction is developed. This space-charge region on either side of the junction together is known as thedepletion region.
Due to the positive space-charge region on the n-side and negative on $p - s i d e$ of the junction, an electric field from positive charge towards negative charge develops.
Due to this electric field, electrons and holes start to move in the opposite direction of the diffusion current giving rise to drift current.

5. Diffusion process continues, increasing the drift current. This process continues until the diffusion current equals the drift current. Thus a

p - n

junction is formed.
6. Fig. b shows the

p - n

junction at equilibrium and the potential across the junction. Since this potential tends to prevent the movement of electrons from the

n

region into the

p

region, it is often called a barrier potential.

Semiconductor Diode:

A semiconductor diode is basically a

p - n

junction with metallic contacts provided at the ends for the application of an external voltage. It's one of the basic electronic devices used extensively in circuits.

P-N Junction under forward-bias:

The direction of the applied voltage ( $V$ ) is opposite to the built-in potential $V_{o}$ .
Hence, the depletion layer width decreases, and the barrier height is reduced. The effective barrier height under forward bias is ( $V_{o} - V$ ).
If we increase the applied voltage significantly, the barrier height will be reduced and more carriers will have the required energy. Thus, the current goes on increasing.
Due to the applied voltage, electrons move $n \to p$ side and holes move $p \to n$ side crossing the depletion region. This process under forward bias is known as minority carrier injection.
The total diode forward current is the sum of hole diffusion current and conventional current due to electron diffusion. The magnitude of this current is usually in mA.

P-N Junction in Reverse bias:

The direction of the applied voltage is the same as the direction of barrier potential. So, barrier height increases, and the depletion region widens due to the change in the electric field.
The effective barrier height under reverse bias is ( $V_{o} + V$ ).
When electrons on the $p - s i d e$ or holes on the $n - s i d e$ move in random motion, and come close to the junction, then they get swept to their majority zone, giving rise to electric current.
The current under reverse bias is essentially voltage-independent up to a critical reverse bias voltage, known as breakdown voltage ( $V_{b r}$ ). When $V = V_{b r}$ , the diode reverse current increases sharply.

V-I characteristics of a diode

The battery is connected to a diode through a potentiometer so that the applied voltage can be changed.
We use a milliammeter for forward bias and a micrometer for reverse bias to measure the current.
For different values of voltages, the value of the current is noted. A graph between $V$ and $I$ is obtained as in fig. c

4. In forward bias, the diode current increases (exponentially), even for a very small increase in the diode bias voltage. This voltage is called the threshold voltage or cut-in voltage.
5. Dynamic resistance:

R_{d} = \frac{Δ V}{Δ I}

P-N Junction diode as Half-wave Rectifier:

The property to rectify alternating voltages is used in Rectifiers.
If an alternating voltage is applied across a diode in series with a load, a pulsating voltage will appear across the load only during the half cycles of the ac input during which the diode is forward biased. Such a rectifier circuit is called a half-wave rectifier.
The secondary transformer supplies the desired ac voltage across terminals $A$ and $B$ .
When the voltage at A is positive: forward biased and it conducts. When voltage at $A$ is negative: reverse-biased and it does not conduct.

P-N Junction as Full-Wave Rectifier:

The $p - s i d e$ is connected to the ends of the secondary transformer. The n-side is connected together and the output is taken between this common point of diodes and the midpoint of the secondary of the transformer.
Fig. $(c)$ shows the voltage rectified by each diode is only half the total secondary voltage. Each diode rectifies only for half the cycle, but the two do so for alternate cycles.
Thus, the output between their common terminals and the centre-tap of the transformer becomes a full-wave rectifier output.
Diode $D_{1}$ is forward biased and conducts , while $D_{2}$ is reverse biased and does not conduct. Hence, during this positive half cycle we get an output current as shown in fig. $(c)$ .
When the voltage at $A$ becomes negative with respect to centre tap, the voltage at $B$ would be positive.

A Full-wave Rectifier using Capacitor circuit:

To get steady dc output from the pulsating voltage, a capacitor is connected across the output terminals as in fig. $(a)$ .
These additional circuits filter out the ac ripple and give a pure dc voltage, so they are called filters.
When the voltage across the capacitor is rising, it gets charged. If there is no external load, it remains charged to the peak voltage of the rectified output. When there is a load, it gets discharged through the load and the voltage across it begins to fall.
In the next half-cycle of rectified output it again gets charged to the peak value as in fig.b.
The rate of fall of the voltage across the capacitor depends inversely upon the product of capacitance $C$ and the effective resistance $R_{L}$ and is called the time constant.

Zener diode as Voltage Regulator:

The unregulated dc voltage is connected to the Zener diode through a series resistance $R_{s}$
The Zener diode is reverse biased.
Any increase/ decrease in the input voltage results in, increase/ decrease of the voltage drop across $R_{s}$ without any change in voltage across the Zener diode.
Thus the Zener diode acts as a voltage regulator.

Photodiode:

When the photodiode is illuminated with light (photons) with energy ( $h ν$ ) greater than the energy gap ( $E_{g}$ ) of the semiconductor, then electron-hole pairs are generated due to the absorption of photons.
Due to the electric field of the junction, electrons and holes are separated before they recombine.
The direction of the electric field is such that electrons reach n-side and holes reach p-side giving rise to an emf. When an external load is connected, current flows.
Photodiodes can be used as a photodetector to detect optical signals.

Light Emitting Diode:

An LED is a special purpose heavily doped

p - n

junction which emits spontaneous radiation under forward bias. The emission of radiation occurs due to recombination of excess minority carriers with majority carriers near the junction.

This transition of electron from conduction band (high energy) to valence band (low energy) happens.
A loss of its energy in the form of photons take place.
For visible LEDs, the band gap of the semiconductors used must be such that the released photon has a frequency lying in the visible spectrum range: 0.4 $μ$ m to 0.7 $μ$ m, i.e., from about 3 eV to 1.8 eV.

Solar Cell:

It is a

p - n

junction which generates emf when solar radiation falls on the

p - n

junction. The generation of emf by a solar cell is due to the following three basic processes

-

generation of $e - h$ pairs due to light (with $h v > E_{g}$ ) close to the junction;
separation of electrons and holes due to the electric field of the depletion region. Electrons are swept to $n - s i d e$ and holes to $p - s i d e$ ;
The electrons reaching $n - s i d e$ are collected by the front contact and holes reaching $p - s i d e$ are collected by the back contact giving rise to photovoltage.

Transistor and its types:

A transistor has three doped regions forming two

p - n

junctions between them. There are two types of transistors

$n - p - n$ transistor: two segments of $n - t y p e$ (emitter and collector) are separated by a segment of $p - t y p e$ semiconductor (base).
$p - n - p$ transistor: two segments of $p - t y p e$ (emitter and collector) are separated by a segment of $n - t y p e$ semiconductor (base).

Emitter :

moderate size and heavily doped.
supplies a large number of majority carriers for the current flow through the transistor.

Base:

central segment
very thin and lightly doped.

Collector:

collects a most of the majority carriers supplied by the emitter.
moderately doped and larger in size as compared to the emitter.

Common emitter transistor characteristics:

Transistor is used in $C E$ configuration,

The input is between the B and E.

The output is between the C and E.

The variation of the base current $I_{B}$ with the base-emitter voltage $V_{B E}$ is called the input characteristic.

The variation of the collector current

I_{C}

with the collector-emitter voltage

V_{C E}

is called the output characteristic.

Input resistance(

r_{i}

r_{i} = (\frac{Δ V _{B E}}{Δ I _{B}})_{V_{C E}}

Output resistance(

r_{o}

r_{o} = (\frac{Δ V _{C E}}{Δ I _{C}})_{I_{B}}

Current amplification factor (

β

β_{a c} = (\frac{Δ I _{C}}{Δ I _{B}})_{V_{C E}}

Transistor as a device

(i) As a Switch:

When the transistor is not conducting it is said to be switched off and when it is driven into saturation it is said to be switched on.
We can say that low inputs switch the transistor off and high inputs switch it on.
The switching circuits are designed in such a way that the transistor does not remain in active state.

(ii) As an Amplifier:

To operate the transistor as an amplifier, it is necessary to fix its operating point somewhere in the middle of its active region.
The operating values of $V_{C E}$ and $I_{B}$ determine the operating point of the amplifier

v_{i} = 0

then

V_{C C} = V_{C E} + I_{C} R_{L}

and

V_{B B} = V_{B E} + I_{B} R_{B}

V_{B B} + v_{i} = V_{B E} + I_{B} R_{B} + Δ I_{B} (R_{B} + r_{i})

where

r_{i}

is the input resistance
Hence,

v_{i} = Δ I_{B} (R_{B} + r_{i}) = r Δ I_{B}

Then the ac current gain is,

β_{a c} = \frac{δ I _{C}}{Δ I _{B}} = \frac{i _{c}}{i _{b}}

The change in

V_{C E}

is the output voltage;

v_{o} = Δ V_{C E} = - β_{a c} R_{L} Δ I_{B}

the voltage gain of the amplifier is,

A_{v} = \frac{v _{o}}{v _{i}} = \frac{V _{C E}}{r Δ I _{B}} = \frac{- β _{a c} R _{L}}{r}

Logic Gates:

NOT gate

It has one input and one output. It produces a '

1

' output if the input is '

0

' and vice-versa, it is also known as an inverter.

OR Gate

O R

gate has two or more inputs with one output. The output

Y

1

when either input

A

or input

B

or both are

1

AND Gate

A N D

gate has two or more inputs and one output. The output

Y

A N D

gate is

1

only when input

A

and input

B

are both

1

NAND Gate:

This is an

A N D

gate followed by a

N O T

gate. If inputs

A

and

B

either one is '

0

the output

Y

is '

1

NOR Gate

It has two or more inputs and one output. Its output

Y

is '

1

' only when both inputs

A

and

B

are '

0

'.

Integrated Circuits: The concept of fabricating an entire circuit on a small single block (or chip) of a semiconductor is known as Integrated Circuit (

I C

). Depending on nature of input signals,

I C^{'} s

can be grouped in two categories: (a) linear

I C^{'} s

- The linear

I C^{'} s

process analogue signals. The output varies linearly with the input. One of the most useful linear IC's is the operational amplifier. (b) digital

I C^{'} s

- The digital

I C^{'} s

process signals that have only two values. They contain circuits such as logic gates.

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Revision Notes: Class 12 | Physics | Chapter 14 | Semiconductor Electronics: Materials

Intrinsic Semiconductor:

Extrinsic Semiconductor:

Formation of P-N junction:

Semiconductor Diode:

P-N Junction under forward-bias:

P-N Junction in Reverse bias:

V-I characteristics of a diode

Logic Gates:

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Revision Notes: Class 12 | Physics | Chapter 14 | Semiconductor Electronics: Materials

Intrinsic Semiconductor:

Extrinsic Semiconductor:

Formation of P-N junction:

Semiconductor Diode:

P-N Junction under forward-bias:

P-N Junction in Reverse bias:

V-I characteristics of a diode

Logic Gates:

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