Unit 1: PN Junction - Subjective Questions

Depletion Region:

The depletion region is the region around the PN junction that is depleted of free charge carriers (electrons and holes).

Formation:

• When a P-type and N-type semiconductor are joined, majority carriers diffuse across the junction.
• Electrons from the N-side diffuse to the P-side and recombine with holes; holes from the P-side diffuse to the N-side.
• This leaves behind immobile ionized donor atoms (positive) on the N-side and acceptor atoms (negative) on the P-side.
• These uncovered charges create an electric field and a built-in potential barrier () that opposes further diffusion.

Factors affecting width:

• Doping concentration: Higher doping narrower depletion region.
• Applied bias: Forward bias reduces width; Reverse bias increases width.
• Temperature: Affects carrier concentration and hence the width.

The built-in potential is given by:

Junction Capacitance:

A PN junction exhibits capacitance because charge is stored across the junction. There are two types:

1. Transition (Depletion) Capacitance ():

• Dominant under reverse bias.
• Arises due to the immobile charges in the depletion region acting like a parallel plate capacitor.
• Given by:
  
  where = junction area, = depletion width, = permittivity.
• As reverse bias increases, increases and decreases.

2. Diffusion (Storage) Capacitance ():

• Dominant under forward bias.
• Arises due to the storage of minority charge carriers near the junction.
• Given by:
  
  where = mean lifetime of carriers, = forward current, = thermal voltage.

Key Difference:

• dominates in reverse bias; dominates in forward bias.
• is generally much larger than .

Diode Current Equation (Shockley Equation):

The current through a PN junction diode is given by:

Derivation outline:

• Under forward bias , the potential barrier reduces, allowing minority carrier injection.
• The excess minority carrier concentration at the edge of the depletion region is proportional to .
• The diffusion current due to injected minority carriers gives:
  

Explanation of terms:

• = diode current.
• = reverse saturation current (leakage current due to minority carriers).
• = applied voltage across the diode.
• = ideality factor ( for Ge, for Si).
• = thermal voltage ( mV at room temperature).

Cases:

• Forward bias (): exponential term dominates, .
• Reverse bias (): (small saturation current).

Effect of Temperature on Reverse Saturation Current ():

• The reverse saturation current arises due to minority carriers, which are thermally generated.
• As temperature increases, more electron-hole pairs are generated, increasing .

Rule of Thumb:

• approximately doubles for every rise in temperature.

This is expressed as:

Consequences:

• Increased leakage current in reverse bias.
• The diode's forward voltage drop decreases by about .
• Can lead to thermal runaway if not controlled.

Temperature dependence of is also related to intrinsic carrier concentration:

where is the band gap energy.

Construction:

• A PN junction diode is formed by joining a P-type semiconductor (rich in holes) with an N-type semiconductor (rich in electrons).
• Metallic contacts are provided at both ends to connect to external circuits — the P-side terminal is the anode and the N-side is the cathode.
• Common materials: Silicon (Si) and Germanium (Ge).

Working:

1. No Bias (Equilibrium):

• A depletion region forms with a built-in potential barrier.

2. Forward Bias:

• P connected to positive, N to negative terminal.
• The barrier potential is reduced, depletion width decreases.
• Majority carriers cross the junction large forward current flows.
• Conducts once applied voltage exceeds the knee/cut-in voltage (V for Si, V for Ge).

3. Reverse Bias:

• P connected to negative, N to positive terminal.
• Barrier potential increases, depletion width widens.
• Only a small reverse saturation current flows due to minority carriers.
• The diode acts as an open switch.

Thus, the diode allows current in one direction only (unidirectional conduction).

V-I Characteristics of PN Junction Diode:

Forward Bias Region:

• Initially, for small voltage (below cut-in voltage), current is negligible.
• Cut-in / Knee voltage: V for Si, V for Ge.
• Beyond the knee voltage, current increases exponentially with voltage.
• The relationship follows the Shockley equation:
  

Reverse Bias Region:

• Only a very small reverse saturation current () flows.
• Current remains almost constant with increasing reverse voltage.
• At the breakdown voltage (), current increases sharply due to avalanche/Zener breakdown.

Graph Description:

    I (mA)
      |        /
      |       /  (Forward)
      |      /

----------+-----/---------- V
/| 0.7V
(Reverse)|
V_BR |

Key Points:

• Forward: low resistance, large current.
• Reverse: high resistance, negligible current until breakdown.

Junction Diode Rectifier:

A rectifier is a circuit that converts alternating current (AC) into direct current (DC) using the unidirectional conduction property of a PN junction diode.

Working Principle:

• A diode conducts only when forward biased and blocks when reverse biased.
• This property is used to allow current in only one direction, producing a pulsating DC output.

Need for Rectification:

• Most electronic devices (radios, TVs, computers) require DC supply.
• The power supplied by mains is AC.
• Rectifiers are essential in power supplies, battery chargers, and DC power adapters.

Types of Rectifiers:

• Half-wave rectifier — uses one diode, rectifies one half cycle.
• Full-wave rectifier — uses two diodes (center-tap) or four diodes (bridge), rectifies both half cycles.

The output is usually filtered to obtain smooth DC.

Half-Wave Rectifier:

Construction: Uses a single diode in series with a load resistor , connected to the secondary of a transformer.

Working:

• Positive half cycle: Diode is forward biased conducts current flows through .
• Negative half cycle: Diode is reverse biased blocks no current flows.
• Output is a pulsating DC consisting of only positive half cycles.

Key Parameters:

• Ripple factor
• PIV

Efficiency Derivation:

Substituting and :

Assuming :

Maximum efficiency = 40.6%

Full-Wave Center-Tapped Rectifier:

Construction:

• Uses a center-tapped transformer and two diodes ( and ).
• The center tap is grounded and serves as the reference point.

Working:

• Positive half cycle: is forward biased and conducts; is reverse biased. Current flows through .
• Negative half cycle: is forward biased and conducts; is reverse biased. Current again flows through in the same direction.
• Both half cycles produce output output frequency is twice the input frequency.

Key Parameters:

• Ripple factor
• Maximum efficiency
• PIV (disadvantage)

Advantages:

• Higher efficiency than half-wave.
• Lower ripple.

Disadvantages:

• Requires center-tapped transformer.
• High PIV rating diodes needed.

Bridge Rectifier:

Construction:

• Uses four diodes (, , , ) arranged in a bridge configuration.
• Does not require a center-tapped transformer.

Working:

• Positive half cycle: Diodes and conduct; and are OFF. Current flows through .
• Negative half cycle: Diodes and conduct; and are OFF. Current flows through in the same direction.

Key Parameters:

• Maximum efficiency
• Ripple factor
• PIV

Advantages over Center-Tapped Rectifier:

• No center-tapped transformer required cheaper and smaller.
• Lower PIV ( vs ) cheaper diodes.
• Better transformer utilization factor (TUF).

Disadvantages:

• Requires four diodes.
• Two diode voltage drops in the conduction path.

Comparison of Rectifiers:

Conclusion:

• Bridge rectifier is most widely used due to high efficiency, low PIV, and no center-tap requirement.
• Half-wave is simplest but least efficient with high ripple.

Ripple Factor ():

A measure of the AC content present in the rectified DC output.

Since :

Rectifier Efficiency ():

The ratio of DC output power to AC input power:

Ripple Factor Derivation for Full-Wave Rectifier:

For a full-wave rectifier:

Therefore:

Ripple factor for full-wave rectifier = 0.482

Zener Diode:

A Zener diode is a specially doped PN junction diode designed to operate in the reverse breakdown region without being damaged.

Construction:

• Heavily doped PN junction (both P and N regions), resulting in a narrow depletion region.
• Designed to have a precise, sharp breakdown voltage ().

Working:

• In forward bias, it behaves like an ordinary diode.
• In reverse bias, when voltage reaches (Zener voltage), it breaks down and conducts heavily.
• The voltage across it remains nearly constant at even as current varies.
• This makes it ideal for voltage regulation.

Breakdown Mechanisms:

• Zener breakdown: Dominant for V (strong electric field breaks covalent bonds).
• Avalanche breakdown: Dominant for V (carriers accelerated cause impact ionization).

Difference from Ordinary Diode:

Zener Diode as Voltage Regulator:

A voltage regulator maintains a constant output voltage despite variations in input voltage or load current.

Circuit:

• A Zener diode is connected in reverse bias across the load .
• A series resistor limits the current.

         GND

Working:

• The Zener operates in the breakdown region, maintaining .

1. Line Regulation (input voltage varies):

• If increases, current through Zener increases, but stays constant.
• Excess voltage drops across .

2. Load Regulation (load varies):

• If load current increases, Zener current decreases to keep total current constant.
• Output voltage remains at .

Key Equations:

Condition: The Zener must always carry a minimum current () to stay in regulation.

Zener Breakdown vs Avalanche Breakdown:

Explanation:

• Zener breakdown: In heavily doped junctions, the depletion region is very thin. A high electric field ( V/m) pulls electrons out of covalent bonds directly, generating carriers.
• Avalanche breakdown: In lightly doped junctions, minority carriers gain enough energy from the field to knock out other electrons, causing a cumulative multiplication (avalanche) of carriers.

Note: For between 5–6V, both mechanisms occur, and the temperature coefficient is nearly zero.

Given:

• Peak current mA A
• Load resistance k

1. DC Current ():

2. RMS Current ():

3. DC Output Power ():

Results:

• mA
• mA
• W

Peak Inverse Voltage (PIV):

PIV is the maximum reverse voltage that a diode must withstand when it is reverse biased (non-conducting) during rectifier operation. Choosing a diode with adequate PIV rating is critical to prevent breakdown.

1. Half-Wave Rectifier:

• During the negative half cycle, the diode is reverse biased.
• The full peak secondary voltage appears across the diode.
  

2. Center-Tapped Full-Wave Rectifier:

• When one diode conducts, the non-conducting diode experiences the sum of the peak voltage across it and the load.
  
• This is a major disadvantage — requires high voltage rated diodes.

3. Bridge Rectifier:

• Two diodes conduct in series; the reverse-biased diodes share the load.
  
• This is an advantage — lower voltage rating diodes can be used.

Summary Table:

Static (DC) Resistance ():

It is the ratio of the DC voltage to DC current at a particular operating point:

• It represents the resistance to DC and depends on the operating point.

Dynamic (AC) Resistance ():

It is the ratio of a small change in voltage to the corresponding small change in current:

Derivation:

From the diode equation (neglecting in forward bias):

Differentiating with respect to :

Therefore, dynamic resistance:

At room temperature ( mV, ):

Example: For mA, .

Effect of Biasing on the PN Junction:

1. Forward Bias:

• P-side connected to positive, N-side to negative terminal.
• The applied voltage opposes the built-in barrier potential.
• Barrier potential decreases:
• Depletion width decreases (majority carriers pushed toward junction).
• Majority carriers can now cross the junction large forward current flows.

2. Reverse Bias:

• P-side connected to negative, N-side to positive terminal.
• The applied voltage aids the built-in barrier potential.
• Barrier potential increases:
• Depletion width increases (majority carriers pulled away from junction).
• Only a small reverse saturation current flows due to minority carriers.

Summary Table:

Note: The depletion region width is proportional to .

Full-Wave Rectifier Analysis:

The output of a full-wave rectifier consists of both half cycles rectified. Let the input be .

1. DC (Average) Voltage:

Over one half cycle (repeated), the average value:

2. RMS Voltage:

3. Efficiency Derivation:

With and :

Assuming :

Maximum efficiency of full-wave rectifier = 81.2% (twice that of half-wave).