Electronic Devices and Circuits : Formation of PN Junction

1. Semiconductor Diode (p-n junction diode)

Majority carrier electrons in the n-region will begin diffusing into the p-region and majority carrier holes in the p-region will be diffusing into the n-region. If we assume there are no external excitation to the semiconductor, then this diffusion process cannot continue indefinitely. As electrons diffuse from the n-region, positively charged donor atoms are left behind. Similarly, as holes diffuse from the p-region, they uncover negatively charged acceptor atoms. The un-neutralized ions in the neighbourhood of the junction are referred to as uncovered charges. The general shape of the charge density ‘ρ’ depends upon how the diode is doped. Since the region of the junction is depleted of mobile charges, it is called depletion region, the space-charge region, or the transition region.

The net positive and negative charges in ‘n’ and ‘p’ regions induce an electric fields in the region near the metallurgical junction, in the direction from the positive to the negative charge, or from the n to the p region.

Density gradients still exist in the exist in the majority carrier concentrations at each edge of the space charge region and producing a “diffusion force” that acts on the majority carriers as shown in Figure 1. The electric field in the space charge region produces another force on the electrons and holes which in the opposite direction to the diffusion force for each type of particle. In thermal equilibrium, the diffusion force and the field force exactly balance each other.

2. I-V Characteristics of a p-n Junction Diode: 

Below figure indicates the characteristic curve consisting of three distinct regions:

NOTE:

When PN junction is reverse biased, the reverse voltage must be always less than breakdown voltage of device, otherwise the normal diode will be damaged.

3. Contact Potential or Built-in potential

Let the PN junction is kept either open circuit condition or unbiased condition.

Mathematically,

V₀ = V_bi

NOTE:

• Contact Potential, V₀ is a function of temperature.
• Contact Potential, V₀ decreases with the temperature.
• For 1⁰C rise in temperature, V₀ decreases by 2.5 mV.

4. Biasing of a Diode

The electric field across the junction has a fixed polarity called barrier potential or height of the barrier. A popular semiconductor device is formed using a p-n junction called p-n junction diode.

4.1 No Applied Bias (V_D = 0V): 

In the absence of an applied bias voltage, the net flow of charge in anyone direction for a semiconductor diode is zero.

4.2 Forward Bias (V_D > 0V):

R_s = Current Limiting Resistance

V_D = Forward Voltage across diode

By KVL we get:

V = V_R + V_D

V = I_f R_s + I_f R_f

R_f = Forward resistance of diode

The General formula of forward current, if (diode current) is:

Also

A = Cross Sectional Area of Junction

4.3 Reverse Bias (V_D < 0V):

                                                  Figure 4

When PN junction is reverse biased, the width of the depletion layer increases.

NOTE:

When PN junction is reverse biased the majority carries of P & N region will move away from the junction and this increases the region of IMMOBILE CHARGES i.e. the width of the depletion layer is increased.

5. Reverse Bias Breakdown in Diode 

We have found that a p-n junction biased in the reverse direction exhibits a small, essentially voltage-independent saturation current. This is true until a critical reverse bias is reached, for which reverse breakdown occurs [Fig. (18)]. At this critical voltage (V_Br) the reverse current through the diode increases sharply, and relatively large currents can flow with little further increase in voltage. The existence of a critical breakdown voltage introduces almost a right-angle appearance to the reverse characteristic of most diodes.

6. Static and Dynamic Resistance

The static resistance of a diode is defined as the ratio V/I of the voltage to the current. At any point on the volt-ampere characteristic of the diode the resistance R_f is equal to the reciprocal of the scope of a line joining the operating point to the origin.

For small-signal operation the dynamic, or incremental, resistance r is defined as the reciprocal of the slope of the volt-ampere characteristic. R º dV/dI. For a semiconductor diode, we find from equation that the dynamic conductance where I is forward current.

NOTE:

• The dynamic resistance of Ge diode with a forward current of 26 mA is 1 Ω
• Dynamic resistance in Si diode is more than in Ge diode.

Example:

Find the voltage drop across each of the Silicon junction diodes shown in the figure below at room temperature. Assume that reverse saturation current flows in the circuit and the magnitude of the reverse breakdown voltage is greater than 5 Volts.

Solution:

7. Transition and Diffusion Capacitance

7.1 Transition or depletion layer capacitance:

A = Cross Sectional Area Of junction

W = Width of Depletion Region

C_T ∝ A

C_T ∝ 1/W

For better performance of diode or BJT, the value of C_T must be as small as possible.

In a reverse biased PN junction, the transition capacitance, C_T

C_T ∝ V^-n

where

V = reverse Biased Voltage

n = constant

n = grading coefficient

n = 1/2; for Step graded diode (abrupt PN Junction diode)

   = 1/3; for Linear graded diode

7.2 Diffusion Capacitance:

For a forward bias p-n junction a capacitance which is much larger than the transition capacitance C, comes into picture. The origin of this larger capacitance lies in the injected charge stored near the junction outside the transition region. It is convenient to introduce an incremental capacitance defined as the rate of charge of injected charge with voltage, called the diffusion or storage capacitance C_D.

Where η is a constant dependent upon semiconductor, and V_T is volt equivalent temperature and τ is the mean life-time of minority carriers.

NOTE

• For a reverse bias junction C_D may be neglected compared with C_T (transition capacitance).
• For a forward bias junction C_D is usually much larger than C_T
• Diffusion capacitance C_D is proportional to the current I.

8. Shockley diodes

• A Shockley diode is formed by bonding a metal, such as platinum, to an n-type silicon.
• This type of diodes has no depletion layer and can switch faster than ordinary diodes.
• The most important application of Shockley diodes is in digital computers
• Since a Shockley diode has a cut-in voltage of 0.25 V, they are frequently used in low-voltage rectifiers.

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