# ELECTRONICS | Variation of potential barrier | Shockley equation | Light Emitting Diode | Photodiode |Zener Diode

## Current voltage relationship of a p-n junction diode

#### Shockley equation

Let Pno is the concentration of holes in n-region. With the application of a forward bias v. The height of the potential barrier (Vb) across the junction es reduced to Vb – V .

According to Boltzmann statistics, the concentration of holes at the space charge boundary (x = 0) in the n-region

The excess concentration of holes

diffuse through the n-region according to the law,

where Lp is the diffuse constant for holes.

The hole concentration at any distance x is

Therefore, the hole current density at the junction (x =0) is

Similarly, the electron current density, at the junction

Therefore, total forward current density,

If A be the area of the junction then total forward current,

This is known as Skockley equation.

where

I0 -> reverse bias saturation current

e -> electric charge.

K -> Boltzmann constant.

T -> absolute temperature of the junction.

η -> Semiconductor constant (1 for Ge, 2 for Si)

At room temperature (T = 300 K), substituting above values,

* If V is +ve, the p-n junction is forward biased.

* If V is -ve, the  p-n junction is reverse biased.

### Draw the nature of static volt-ampere characteristics curve and resistance characteristics curve of a semiconductor diode

The plot of the current (I) versus the voltage (V) of a semiconductor diode is known as static volt – ampere characteristic curve.

The state or d.c. resistance of diode is defined as the ratio of voltage to the current i.e.

Since the diode is a non-linear device its d.c. or static resistance varies with current,

Dynamic resistance is defined as

As

For forward biased condition I >> Io , hence

### Define reverse saturation current of a p-n junction diode? Is it temperature dependent ?

When the p-n junction diode is reverse biased then the width of depletion region is increased and majority charge carrier can’t cross the junction but we get a very small current ( µA ) due to flow of minority charge carrier, opposite to the direction of forward current. This is known as reverse saturation current.

It is independent of reverse saturation current (Io) increases with increase in temperature.

## Light Emitting Diode (LED)

The light emitting diode (LED) is a special type of semiconductor device having one p-n function which can emit light under forward biased condition :

Principle :

The emission of radiation of a LED, due to recombination of holes and electrons. The principle of conservation of momentum requires that the electron and the hole which are going to recombine must-have exactly equal and opposite momentum . This requirements very stringent (law must be strictly controlled).  But in Se and Ge recombination takes place indirectly (via recombination centres). As a result the energy liberated goes to heat the crystal. Hence Si and Ge are unsuitable for the construction of LEDs.

There are some semiconductors such as Gallium Arsenide Phosphide (GaAsP), Gallium Phosphide (GaP) in which recombination takes place directly and the excess energy is emitted in the form of photons, are suitable for the construction of LEDs.

#### Circuit symbol

**LEDs fabricated from Silicon Carbide emit yellow light.

**LEDs fabricated from Gallium Phosphide emit red light.

** And LEDs fabricated from Gap + Cd emit green light.

**LEDs fabricated from GaAs emit Infrared.

#### Application of LEDs

LEDs are widely used in

1. Digital display system of calculators.

2. Digital display system of watches.

3. Digital display system of microelectronic device.

4 CD Player.

5. Optical fibre communication.

6. Indicator of the presence of power line voltage of instruments.

## Photodiode

The photo diode is a p-n junction diode in which reverse current modulated by illuminating the junction with light flux.

#### Construction :

The photodiode is constructed by enclosing p-n junction in a casing. A lens is used in a window of the unit to focus maximum light on a p-n junction.

When no light incidents on the junction a small amount of reverse saturation current flows through the reverse biased junction. This current is known as dark current. Now, if light falls on the p-n junction, additional electron-hole pairs generated and the reverse current increases.The current varies almost linearly with the incident light intensity.

#### Circuit symbol

Use :

=> In high speed reading of tapes and film sound tracks.

=> In light detection systems.

=> Light operated switches.

## Zener Diode

#### What is knee voltage?

knee voltage – It is the forward voltage at which the current through the p-n junction starts to increase rapidly.

#### What is Zener diode ?

Zener diode- A Zener diode is specially designed p-n junction diode which has a sharp breakdown voltage. It is a highly doped p-n junction having a large backward resistance and it conducts in the reverse direction at a certain fixed voltage.

#### What is Zener voltage?

Zener voltage- The value of reverse voltage at which Zener breakdown occurs is called Zener voltage.

#### Explain the mechanism of Zener breakdown :

There are two distinct mechanism of breakdown

1. Avalanche breakdown.

2. Zener breakdown.

#### Avalanche breakdown :

When the reverse bias of a p-n junction is small then we get a small current due to minority carriers. When the reverse bias is increased further, a stage reaches when the applied fields is so high that the thermally generated charge carriers acquire sufficient energy. These charge carriers when collide with an immobile ion, disrupt a covalent bond. Hence a new electron-hole pair is produced. The new carrier again picks up sufficient energy due to applied field and generate further electron-hole pair. This process is cumulative· This phenomena is known as Avalanche breakdown.

#### Zener breakdown :

When the electric field across the p-n junction is so strong that it can directly tear out a bound electron from co-valent bond, thereby generating a large number of electron-hole pairs. This increases the reverse current abruptly. This phenomena is called Zener breakdown.

### Show how a Zener diode can be used as a voltage regulator

The circuit arrangement for voltage regulation using Zener diode is shown in figure.

The Zener diode with Zener voltage Vz is connected in parallel with the Load (RL) across which constant o/p voltage is desired. A series resistance Rs is connected with the Zener diode . The Zener diode is reverse biased with the variable input voltage which have to be regulated.

It is maintained a constant o/p voltage Vo = Vz across the load until the o/p voltage (Vi) greater than Vz.

When Vi > Vz , a large current Iz will flow through the Zener diode and also through the series resistance Rs. Hence voltage drop across Rs will increase maintaining o/p voltage  Vo is constant.