Pn Junction Diode

Let the angle of incidence be and the angle of refraction be . We are given that: Let the angle of the prism be , the refractive index , and the minimum deviation angle be . For minimum deviation in a prism, the angle of incidence and the angle of refraction are equal. Using the following relation for minimum deviation: Since at minimum deviation , we have: The refractive index is related to the prism angle and the minimum deviation by: Substituting and solving for and , we get:

When a p-n junction diode is connected in forward bias, the positive terminal of the external voltage source is connected to the p-type semiconductor, and the negative terminal is connected to the n-type semiconductor. This causes the following: - The applied voltage reduces the width of the depletion region as the holes from the p-side and the electrons from the n-side are pushed towards the junction. - If the forward voltage exceeds the threshold voltage (typically 0.7V for silicon diodes), the barrier potential is overcome, and current begins to flow through the diode. This allows current to pass easily through the diode in the direction of the applied voltage.

A p-n junction diode consists of two semiconductor regions: a p-type (positive) region and an n-type (negative) region, which are brought into contact to form a junction. In forward bias, the p-side is connected to the positive terminal and the n-side to the negative terminal, which allows current to flow. In reverse bias, the p-side is connected to the negative terminal and the n-side to the positive terminal, which theoretically prevents current from flowing. However, for an ideal p-n junction diode in reverse bias: 1. Reverse Bias Behavior:
- In reverse bias, no current flows through the ideal diode under normal conditions.
- The ideal diode has no leakage current (i.e., no reverse saturation current) in this condition.
2. Ideal Diode:
- An ideal diode is assumed to have no internal resistance when forward biased and infinite resistance when reverse biased.
- Since no current can flow through the diode in reverse bias, the resistance of the ideal p-n junction diode is considered infinite.
Since in reverse bias for an ideal diode, the resistance is considered infinite.

Step 1: Understanding the Concept:
This problem requires analyzing a circuit containing diodes and resistors in parallel. The key is to first determine the biasing of each diode (forward or reverse) to see which branches will conduct current. Then, the circuit can be simplified to calculate the total current using Ohm's law.

Step 2: Detailed Explanation:
1. Analyze the Diode Biasing:
The circuit has a 10 V battery. The positive terminal of the battery is connected to the p-side (anode, the triangle part) of all three diodes. The negative terminal is connected (through the resistors) to the n-side (cathode, the line part) of all three diodes.
Since the p-side of each diode is at a higher potential than its n-side, all three diodes are forward-biased.
2. Simplify the Circuit:
Assuming the diodes are ideal, a forward-biased diode acts as a closed switch, meaning it behaves like a wire with zero resistance. Therefore, we can replace all three diodes with connecting wires.
After this simplification, the circuit consists of three resistors connected in parallel across the 10 V battery: \begin{itemize} \item
\item
\item
\end{itemize} 3. Calculate the Equivalent Resistance ( ):
For resistors in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances: To add these fractions, we find a common denominator, which is 6: Therefore, the equivalent resistance is: 4. Calculate the Total Current:
The current through the battery is the total current flowing through the circuit. Using Ohm's Law, :

Step 3: Final Answer:
The current through the battery is 10 A.

A p-n junction diode is formed by joining a p-type semiconductor and an n-type semiconductor. When the diode is forward biased (i.e., the p-side is connected to the positive terminal of the battery and the n-side to the negative terminal), the majority charge carriers (holes from the p-side and electrons from the n-side) move towards the junction, reducing the width of the depletion region. As the applied voltage increases, the current increases rapidly after a threshold voltage (called the forward voltage).
Circuit Diagram:
In a forward biased condition, the circuit diagram is as shown below:
The diode conducts only when the voltage exceeds a certain threshold (typically 0.7V for a silicon diode).
Characteristic Graph:
The characteristic of a p-n junction diode shows the relationship between the voltage across the diode and the current through it. The graph has the following features:
- For small forward voltages (less than 0.7V for silicon diodes), the current is almost zero (the diode does not conduct). - Once the forward voltage exceeds 0.7V, the current rises exponentially. - In reverse bias, the current is negligible until the breakdown voltage is reached, after which the current increases sharply.
Dynamic Resistance of the Diode:
The dynamic resistance of the diode in the forward biased condition is defined as the slope of the curve at any given point. It is given by:
At high currents, the dynamic resistance is very small (almost zero), as the diode behaves like a short circuit.

Reverse Bias Condition: A p-n junction diode is formed by joining a p-type semiconductor and an n-type semiconductor. In reverse bias, the positive terminal of the external battery is connected to the n-type side, and the negative terminal is connected to the p-type side. This configuration increases the width of the depletion region, which prevents current from flowing under normal conditions. The key points of its working are: 1. Reverse Bias Condition: When a p-n junction diode is reverse biased, the applied voltage causes the electrons in the n-region to be attracted to the positive terminal of the battery, while the holes in the p-region are attracted towards the negative terminal. This increases the width of the depletion region, making it difficult for current to flow. 2. Depletion Region: The depletion region acts as an insulator and prevents the current from flowing. In ideal conditions, no current flows in reverse bias, but a small reverse saturation current exists due to minority carriers. 3. Breakdown: If the reverse voltage exceeds a certain threshold (the breakdown voltage), the diode undergoes avalanche breakdown or Zener breakdown, where the depletion region is destroyed, allowing a large current to flow through the diode. This is undesirable in most applications but can be used in Zener diodes for voltage regulation.

Rectification is the process of converting alternating current (AC) to direct current (DC). In a rectifier, a diode allows current to flow in one direction, blocking it in the opposite direction. The most common type of rectifier is the p-n junction diode.
A full-wave rectifier uses both halves of the input signal to produce a continuous DC output. It uses two diodes in a bridge configuration, allowing current to flow in both halves of the AC input cycle.
The circuit diagram for a full-wave rectifier is as follows:
In the positive half-cycle of the input AC, one diode conducts and allows current to pass through the load resistor. In the negative half-cycle, the other diode conducts, allowing current to flow in the same direction through the load. This results in a full-wave rectified output.
The output waveform of a full-wave rectifier is a series of positive peaks, with the negative half of the AC signal flipped to the positive side. This gives a smoother DC output compared to a half-wave rectifier.

Step 1: Circuit Diagram for Forward Bias of p-n Junction Diode.
To obtain the characteristic curve of a p-n junction diode in forward bias, we need to connect the diode in a circuit with a variable power supply. The positive terminal of the power supply is connected to the p-type side (anode) of the diode, and the negative terminal is connected to the n-type side (cathode).
\begin{center} \includegraphics[width=0.7\linewidth]{pn_diode_forward_bias.png} % Add image of the p-n junction diode in forward bias \end{center}

Step 2: Explanation of Circuit Diagram.
- A power supply provides a varying voltage across the diode.
- The anode of the diode is connected to the positive terminal, and the cathode to the negative terminal of the power supply.
- A milliammeter is connected in series with the diode to measure the current that flows through the circuit.

Step 3: Characteristic Curve.
When the diode is forward biased, the current increases as the applied voltage increases beyond a threshold (typically around 0.7V for silicon diodes). At lower voltages, the current is almost zero, but as the voltage increases, the current increases exponentially. The characteristic curve of a p-n junction diode in forward bias shows this exponential increase.

Step 4: Effect of Forward Bias on the Depletion Region.
- In forward bias, the external voltage decreases the width of the depletion region, allowing more charge carriers to recombine at the junction.
- As the forward voltage increases, the potential barrier decreases, and more charge carriers can cross the junction, leading to an increase in current.

Final Answer: In forward bias, the depletion region becomes narrower, and the current increases exponentially with the applied voltage after a certain threshold.

Working of a Reverse Bias (p-n) Junction Diode:
A p-n junction diode works by allowing current to flow in only one direction. When the diode is reverse biased, the p-side is connected to the negative terminal, and the n-side is connected to the positive terminal of the battery. This increases the width of the depletion region, and as a result, no current flows under normal conditions.
The current through the diode in reverse bias remains negligibly small (very small leakage current), and the reverse bias voltage increases the width of the depletion region, thereby preventing the flow of majority charge carriers. The diode essentially acts as an insulator.
The reverse bias is applied in such a way that the n-type material (negative side) is connected to the positive terminal of the battery and the p-type material (positive side) is connected to the negative terminal of the battery. This results in a very small reverse current, mainly due to minority charge carriers. Avalanche Breakdown:
Avalanche breakdown occurs when the reverse bias voltage exceeds a critical value. When the reverse bias increases, the minority carriers gain more energy and collide with the atoms of the semiconductor, creating more electron-hole pairs. This process multiplies and results in a large current, which is known as avalanche breakdown. The current increases rapidly with an increase in reverse voltage after the breakdown. V-I Characteristic Graph:
The V-I characteristic graph for a reverse biased diode shows a small leakage current initially. As the reverse voltage increases, the current remains nearly constant until the breakdown voltage is reached. After this point, the current increases rapidly, representing avalanche breakdown. Explanation of the Graph:
- The current remains negligible in the reverse region until the breakdown voltage is reached.
- Once the breakdown voltage is exceeded, the current increases exponentially, signifying avalanche breakdown.

Rectifying Process:
The rectifying process refers to the conversion of alternating current (AC) into direct current (DC) by using a diode. A diode only allows current to flow in one direction (forward direction), and thus, when an alternating current is passed through it, only the positive half-cycle or negative half-cycle of the current is allowed to pass. This results in the transformation of AC to a pulsating DC. Half-Wave Rectifier:
In a half-wave rectifier, a single diode is used to allow current to flow during only one half-cycle (positive or negative) of the AC supply. The negative half-cycle of the AC supply is blocked by the diode. Thus, only the positive half of the input signal is passed to the output. In this diagram, the AC supply is connected to the anode of the p-n junction diode. The cathode is connected to the load resistor . During the positive half of the AC cycle, the diode is forward biased and allows current to pass, while during the negative half of the cycle, the diode is reverse biased and blocks current, resulting in zero current flow.
Waveform of a Half-Wave Rectifier:
The output waveform of the half-wave rectifier is a pulsating DC signal that follows the positive half of the input AC signal. The negative half-cycle is blocked. The output voltage is non-zero only during the positive half-cycle of the AC input.

Given: - Peak voltage of the a.c. source, - Load resistance, - Forward resistance of the diode, - Resistive voltage across the diode, Step 1: Calculate the total resistance in the circuit.
The total resistance in the circuit is the sum of the forward resistance of the diode and the load resistance:
Step 2: Calculate the peak current through the diode.
The peak current through the diode can be calculated using Ohm's law:
Substituting the given values:
Thus, the peak current through the diode is approximately .
Step 3: Calculate the peak voltage across the load.
The peak voltage across the load can be calculated using Ohm’s law:
Substituting the values:
Thus, the peak voltage across the load is approximately .

Difference between Conductor, Semiconductor, and Insulator:
In solids, the difference between conductors, semiconductors, and insulators can be explained based on their energy band diagrams. The energy band diagram represents the energy levels available for electrons in a solid.
1. Conductor:
- In a conductor, the conduction band and valence band overlap, allowing electrons to freely move through the material.
- There is no band gap between the conduction and valence bands.
- Examples: Metals like copper, aluminum, etc.
- Conductors have high electrical conductivity.
2. Semiconductor:
- A semiconductor has a small energy gap (band gap) between the valence band and the conduction band.
- At absolute zero, the conduction band is empty, and the valence band is full. At room temperature, some electrons gain enough energy to jump to the conduction band.
- Examples: Silicon, germanium.
- Semiconductors have moderate electrical conductivity, which increases with temperature.
3. Insulator:
- In insulators, the band gap between the conduction band and the valence band is large.
- The conduction band is empty, and the valence band is full, with no electrons able to move to the conduction band at room temperature.
- Examples: Rubber, wood, glass.
- Insulators have very low electrical conductivity.
Need of Doping in Pure Semiconductors:
Pure semiconductors, like silicon, have limited electrical conductivity. Doping introduces impurities into the semiconductor material to increase its conductivity. Doping creates either an excess of electrons (n-type doping) or a shortage of electrons (p-type doping), allowing current to flow more easily. Doping is crucial for creating practical semiconductors used in devices like diodes and transistors.
Current in Ideal Diodes and :
In the given circuit, we have two diodes and , with resistors and , respectively, connected in series with a battery.
- For an ideal diode, the current flowing through the circuit is determined by Ohm's law. An ideal diode has zero resistance in the forward bias condition and infinite resistance in the reverse bias condition.
- For , if it is forward biased, it will conduct current.
- For , if it is reverse biased, it will not conduct any current.
Assuming both diodes are ideal: - Current through the circuit, Thus, the current through the circuit is if is forward biased and is reverse biased.

Working of a Reverse Bias (p-n) Junction Diode:
A p-n junction diode works by allowing current to flow in only one direction. When the diode is reverse biased, the p-side is connected to the negative terminal, and the n-side is connected to the positive terminal of the battery. This increases the width of the depletion region, and as a result, no current flows under normal conditions.
The current through the diode in reverse bias remains negligibly small (very small leakage current), and the reverse bias voltage increases the width of the depletion region, thereby preventing the flow of majority charge carriers. The diode essentially acts as an insulator.
The reverse bias is applied in such a way that the n-type material (negative side) is connected to the positive terminal of the battery and the p-type material (positive side) is connected to the negative terminal of the battery. This results in a very small reverse current, mainly due to minority charge carriers. Avalanche Breakdown:
Avalanche breakdown occurs when the reverse bias voltage exceeds a critical value. When the reverse bias increases, the minority carriers gain more energy and collide with the atoms of the semiconductor, creating more electron-hole pairs. This process multiplies and results in a large current, which is known as avalanche breakdown. The current increases rapidly with an increase in reverse voltage after the breakdown. V-I Characteristic Graph:
The V-I characteristic graph for a reverse biased diode shows a small leakage current initially. As the reverse voltage increases, the current remains nearly constant until the breakdown voltage is reached. After this point, the current increases rapidly, representing avalanche breakdown. Explanation of the Graph:
- The current remains negligible in the reverse region until the breakdown voltage is reached.
- Once the breakdown voltage is exceeded, the current increases exponentially, signifying avalanche breakdown.

Rectifying Process:
The rectifying process refers to the conversion of alternating current (AC) into direct current (DC) by using a diode. A diode only allows current to flow in one direction (forward direction), and thus, when an alternating current is passed through it, only the positive half-cycle or negative half-cycle of the current is allowed to pass. This results in the transformation of AC to a pulsating DC. Half-Wave Rectifier:
In a half-wave rectifier, a single diode is used to allow current to flow during only one half-cycle (positive or negative) of the AC supply. The negative half-cycle of the AC supply is blocked by the diode. Thus, only the positive half of the input signal is passed to the output. In this diagram, the AC supply is connected to the anode of the p-n junction diode. The cathode is connected to the load resistor . During the positive half of the AC cycle, the diode is forward biased and allows current to pass, while during the negative half of the cycle, the diode is reverse biased and blocks current, resulting in zero current flow.
Waveform of a Half-Wave Rectifier:
The output waveform of the half-wave rectifier is a pulsating DC signal that follows the positive half of the input AC signal. The negative half-cycle is blocked. The output voltage is non-zero only during the positive half-cycle of the AC input.

Reverse Bias Condition: A p-n junction diode is formed by joining a p-type semiconductor and an n-type semiconductor. In reverse bias, the positive terminal of the external battery is connected to the n-type side, and the negative terminal is connected to the p-type side. This configuration increases the width of the depletion region, which prevents current from flowing under normal conditions. The key points of its working are: 1. Reverse Bias Condition: When a p-n junction diode is reverse biased, the applied voltage causes the electrons in the n-region to be attracted to the positive terminal of the battery, while the holes in the p-region are attracted towards the negative terminal. This increases the width of the depletion region, making it difficult for current to flow. 2. Depletion Region: The depletion region acts as an insulator and prevents the current from flowing. In ideal conditions, no current flows in reverse bias, but a small reverse saturation current exists due to minority carriers. 3. Breakdown: If the reverse voltage exceeds a certain threshold (the breakdown voltage), the diode undergoes avalanche breakdown or Zener breakdown, where the depletion region is destroyed, allowing a large current to flow through the diode. This is undesirable in most applications but can be used in Zener diodes for voltage regulation.

A p-n junction diode consists of two semiconductor regions: a p-type (positive) region and an n-type (negative) region, which are brought into contact to form a junction. In forward bias, the p-side is connected to the positive terminal and the n-side to the negative terminal, which allows current to flow. In reverse bias, the p-side is connected to the negative terminal and the n-side to the positive terminal, which theoretically prevents current from flowing. However, for an ideal p-n junction diode in reverse bias: 1. Reverse Bias Behavior:
- In reverse bias, no current flows through the ideal diode under normal conditions.
- The ideal diode has no leakage current (i.e., no reverse saturation current) in this condition.
2. Ideal Diode:
- An ideal diode is assumed to have no internal resistance when forward biased and infinite resistance when reverse biased.
- Since no current can flow through the diode in reverse bias, the resistance of the ideal p-n junction diode is considered infinite.
Since in reverse bias for an ideal diode, the resistance is considered infinite.

Step 1: Understanding the Concept:
The resistance of a p-n junction diode in forward bias mentioned here is the dynamic or AC resistance ( ). It is not the static resistance ( ), but rather the ratio of a small change in voltage across the diode to the resulting small change in the current flowing through it.

Step 2: Key Formula or Approach:
The dynamic forward resistance ( ) is defined by the relation: where is the change in forward bias voltage and is the corresponding change in forward current. We need to find .

Step 3: Detailed Explanation:
We are given the following values: \begin{itemize} \item Forward bias resistance, . \item Change in current, . We must convert this to Amperes: \end{itemize} Rearranging the formula to solve for the change in voltage : Substituting the given values:

Step 4: Final Answer:
The forward bias voltage should be changed by 0.05 Volts.

A p-n junction diode is formed by joining a p-type semiconductor and an n-type semiconductor. When the diode is forward biased (i.e., the p-side is connected to the positive terminal of the battery and the n-side to the negative terminal), the majority charge carriers (holes from the p-side and electrons from the n-side) move towards the junction, reducing the width of the depletion region. As the applied voltage increases, the current increases rapidly after a threshold voltage (called the forward voltage).
Circuit Diagram:
In a forward biased condition, the circuit diagram is as shown below:
The diode conducts only when the voltage exceeds a certain threshold (typically 0.7V for a silicon diode).
Characteristic Graph:
The characteristic of a p-n junction diode shows the relationship between the voltage across the diode and the current through it. The graph has the following features:
- For small forward voltages (less than 0.7V for silicon diodes), the current is almost zero (the diode does not conduct). - Once the forward voltage exceeds 0.7V, the current rises exponentially. - In reverse bias, the current is negligible until the breakdown voltage is reached, after which the current increases sharply.
Dynamic Resistance of the Diode:
The dynamic resistance of the diode in the forward biased condition is defined as the slope of the curve at any given point. It is given by:
At high currents, the dynamic resistance is very small (almost zero), as the diode behaves like a short circuit.