## Hall Effect (Electronics devices and circuits)

in this post we will discuss about Hall Effect , this topic is very important for many competitive exams. if you have any doubt regarding this post then comment below, for video lectures on electronics devices and circuit subscribe our you tube channel, all links given below.

# Hall effect

here are the important points for which hall effect is used

•  To find the type of semiconductor specimen whether semiconductor is P-type or N-type
•  To find the charge concentration
•  To find the mobility of charge carrier

# What is Hall Effect

Whenever a current carrying semiconductor is subjected to a magnetic field, there will be an induced electric field in the perpendicular direction of the plane consist of I & B, which intern exert a force over the carrier is known ass hall effect.

In above shown figure the direction of current is considers towards X-direction and direction of magnetic field is in Z-direction so induced electric field will have Y-direction because of Lorentz force

# working

we can easily find the types of semiconductor specimen whether it is P-type or N-type by hall effect. if the consider specimen is N-type then electron will be accumulated to the lower surface of the bar which makes hall voltage ${ V }_{ H }$ positive, similarly if the consider specimen is P-type then holes will be accumulated to the lower surface of the semiconductor bar which makes hall voltage ${ V }_{ H }$ negative.

NOTE – in any case (either P-type or N-type) the direction of exerted force over the charge carrier is negative Y-direction.

# Hall Voltage

${ V }_{ H }\quad =\quad \frac { BI }{ \rho W }$    —————(1)

# Hall coefficient

It is defined as the reciprocal of charge density (ρ)

${ R }_{ H }\quad =\quad \frac { 1 }{ \rho }$

by equation (1)

${ R }_{ H }\quad =\quad \frac { W.{ V }_{ H } }{ BI }$

# Application of Hall Effect

•  To determine type of extrinsic semiconductor (using polarity of ${ V }_{ H }$)
•  To determine carrier concentration (n)
•  Used in magnetic field meter
•  As a hall effect multiplier
•  To calculate mobility

NOTE – Hall effect is very less effective in case of metal because in metal n is very large

${ V }_{ H }$ will be very small in order of micro volts.

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## Effect of temperatures on semiconductor parameter

in this post we will discuss about effect of temperatures over different types of semiconductor parameters, this topic is very important for many competitive exams. if you have any doubt regarding this post then comment below, for video lectures on electronics devices and circuit subscribe our you tube channel, all links given below.

# Effect of temperatures over different types of semiconductor parameters

In this topic we will discuss effect of temperature on different parameters of semiconductor, such as

1.   Effect of temperature on intrinsic concentration (ni)
2.   Mobility (μ)
3.   Conductivity (σ)

## effect of temperature on intrinsic concentration (${ n }_{ i }$)

${ n }_{ i }=\sqrt { { A }_{ 0 } } \quad { T }^{ \frac { 3 }{ 2 } }\quad { e }^{ -\frac { { E }_{ GO } }{ 2KT } }$

Where,  $\sqrt { { A }_{ 0 } }$  is  constant that depends on material

T is temperature

${ E }_{ GO }$ is energy gap

NOTE –  Energy gap ${ E }_{ GO }$ at 0k = 1.21 ev for Si

= 0.785 ev for Ge

K = Boltzmann constant = $1.38\times { 10 }^{ -23 }\quad j/kelvin$

Having seen above relation we have come to know that intrinsic concentration is heavily depends upon the temperature. that means if we increase temperature then intrinsic concentration also increased and  if we decrease temperature then intrinsic concentration also decreased.

## Energy Gap

$Energy\quad gap\quad =\quad { E }_{ GO }-\beta T$

Where,

β is constant and very small

NOTE- Energy gap decreases with respect to temperature

## Mobility

$\mu =\frac { V }{ E }$

where,

V = drift velocity

E = Electric Field

NOTE – mobility is inversely proportional to temperature i.e. when temperature increase then mobility decreases and vice versa also valid, because drift velocity in certain direction decreases when temperature increases.

# Conductivity

## (1) for intrinsic semiconductor

${ \sigma }_{ i }={ n }_{ i }q({ \mu }_{ e }+{ \mu }_{ h })$

As we already discuss intrinsic concentration is directly proportional to temperature and mobility is inversely proportional to temperature that means if we increases temperature then intrinsic concentration will increase and mobility will decrease, but the rate of decrement  is very small comparison to increment, so when temperature increase then conductivity of intrinsic semiconductor is also increases.

so we can say conductivity of intrinsic semiconductor is directly proportional to temperature.

## For extrinsic semiconductor

### P-type   ${ \sigma }_{ p }={ n }q{ \mu }_{ h }$

NOTE – there is a little impact of the temperature over the majority charge carrier but in extrinsic semiconductor the mobility of charge carrier decreases heavily, hence we see that conductivity of extrinsic semiconductor decreases with respect to temperature.

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# Semiconductors

## N-Type semiconductors

n (majority carrier concentration in no of electron in CB/volume)

p (minority carrier concentration in no of holes in VB/volume)

${ N }_{ D }$ (donor concentration per unit volume)

## P-Type semiconductors

p (majority carrier concentration in no of holes in VB/volume)

n (minority carrier concentration in no of electrons in CB/volume)

${ N }_{ A }$ (donor concentration per unit volume)

NOTE –  CB (conduction band)

VB (valance band)

## Mass Action Law

Mass action law states that Under thermal equilibrium the product of the free electron concentration and the free hole concentration is equal to a constant equal to the square of intrinsic carrier concentration.

It is also known as low of conservation of charges

so mass action law is $n.p={ n }_{ i }^{ 2 }$  —————(1)

## Charge Neutrality Equation

Charge neutrality occurs when all the charge in a volume adds to zero, it is neutral, neither positive or negative.

no of +ve charge = no of -ve charge

$n+{ N }_{ A }=p+{ N }_{ D }$   —————(2)

Using mass action law and charge neutrality equation we can find the minority charge carrier concentration

### For n-type semiconductor (n>>p)

so using (2) equation   $n\quad \simeq \quad { N }_{ D }$

${ N }_{ A }=0$

Now by using mass action law

$p\simeq \frac { { n }_{ i }^{ 2 } }{ { N }_{ D } }$

### For p-type semiconductor (p>>n)

so using (2) equation $p\quad \simeq \quad { N }_{ A }$

${ N }_{ D}=0$

Now by using mass action law

$n\simeq \frac { { n }_{ i }^{ 2 } }{ { N }_{ A} }$

## Current component in semiconductor

Basically there are two types of current component in semiconductors

1.  Drift current density
2.  Diffusion current density

### Drift current density

• Drift current density is due to free charges or potential gradient

$E=-\frac { { dv } }{ dx }$

• It is also known as conduction current density

### Diffusion current density

• Diffusion current density is due to presence of concentration gradient
• It is not present in metal or conductors
• It is only present in semiconductors

we will continue this topic on our upcoming post keep visiting

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