Class 12 Physics Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits

Key Concept:Advanced Calculation, Real-world Application

b) 1.5 mA
[Solution Description]
In a common emitter configuration, the relationship between the base current ($$I_B$$) and the collector current ($$I_C$$) can be expressed using the current gain $$\beta$$:

$$
I_C = \beta \times I_B
$$

Substituting the given values:

$$
I_C = 150 \times 10\times10^{-6}
= 1500\times10^{-6}
= 1.5\times10^{-3}\ A
= 1.5\ mA
$$

Thus, the expected change in the collector current is $$1.5\ mA$$.

Key Concept: Conductivity Range

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

[Solution Description]

Key Concept: Capacitor Filter

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

[Solution Description]

A capacitor in a rectifier circuit is essential for smoothing out the pulsating DC voltage, which results from the rectification process. It does this by charging during the peaks of the pulsating waveform and discharging to fill the gaps when the waveform dips, thus providing a more steady DC voltage output.

The time constant $$\tau$$, given by the product of capacitance $$C$$ and resistance $$R_L$$ ($$\tau = C \times R_L$$), plays a crucial role in determining how quickly the capacitor can charge or discharge. A larger time constant indicates slower charge/discharge, leading to less voltage ripple and smoother output.

Both the assertion and the reason are true. While the reason contributes to the understanding of the functionality of a capacitor in smoothing out voltage, it is not the direct explanation of why a capacitor is used in rectifiers.

Key Concept: Dynamic Resistance

b) 10 , \Omega
[Solution Description]
The dynamic resistance $$r_d$$ can be calculated using the formula:
$$
r_d = \frac{\Delta V}{\Delta I}
$$
Where $$\Delta V = 0.8 \, \text{V} – 0.7 \, \text{V} = 0.1 \, \text{V}$$ and $$\Delta I = 15 \, \text{mA} – 5 \, \text{mA} = 10 \, \text{mA}$$. Let’s convert 10 mA to amperes: $$10 \, \text{mA} = 0.01 \, \text{A}$$. Now substitute these values into the formula:
$$
r_d = \frac{0.1}{0.01} = 10 \, \Omega
$$
Therefore, the dynamic resistance is $$10 \, \Omega$$.

Key Concept: Carrier Concentration Calculation, Doping Effects

c) $$10^{16}$$ cm$$^{-3}$$
[Solution Description] With doping, the number of electrons contributed by each donor atom equals the number of donor atoms since they are fully ionized. Thus, the number of free electrons becomes equal to the number of dopant atoms, which is $$10^{16}$$ cm$$^{-3}$$. Since it’s n-type, holes can be found using mass action law: $$n_e \cdot n_h = n_i^2$$, where $$n_e$$ is the number of electrons. Plugging values: $$n_h = n_i^2 / n_e = (2.5 \times 10^{13})^2 / 10^{16} = 6.25 \times 10^{10}$$ cm$$^{-3}$$. However, the primary focus is on electrons here.

Key Concept: Barrier Height Changes, Reverse Bias Drift Current

b) $$V_0 + V_r$$
[Solution Description] The effective barrier height in a reverse-biased diode is increased by the amount of the applied reverse bias. It can be calculated as the sum of the built-in potential ($$V_0$$) and the reverse bias voltage ($$V_r$$). Therefore, the effective barrier height is given by:

$$
\text{Effective Barrier Height} = V_0 + V_r
$$

This increase results in minimal current flow due to drift currents mainly influenced by minority carriers.

Key Concept: Doping Elements

b) Phosphorus
[Solution Description]
To create an n-type semiconductor, pentavalent elements such as phosphorus are added, which donate extra electrons and make electrons the majority carriers.

Key Concept: Device Comparison

b) Semiconductors are more reliable and smaller in size.
[Solution Description] Semiconductor devices are compact and consume less power compared to vacuum tubes. They also offer greater reliability, making them more suitable for modern electronic applications.

Key Concept: Compound Semiconductors

c) Si

[Solution Description] Compound semiconductors include materials such as CdS, GaAs, CdSe, and InP. These compounds often consist of two or more elements combined in specific stoichiometric ratios. Si is an elemental semiconductor, not a compound semiconductor, whereas all others listed here—CdS, GaAs, and InP—are compound semiconductors.

Key Concept: Potential Difference

c) It balances diffusion and drift currents to maintain equilibrium.
[Solution Description]
The built-in potential difference across a p-n junction at equilibrium serves to balance the diffusion and drift currents. This potential barrier prevents further movement of charge carriers across the junction, thus maintaining equilibrium with zero net current flow.

Key Concept: Depletion Region

c) The depletion region widens

[Solution Description]

In reverse bias, the applied voltage increases the barrier potential, causing the electric field across the junction to widen the depletion region. This increase in width reduces the number of majority carriers that can cross the junction, thus decreasing the current flow through the diode.

Key Concept: Dynamic Resistance, Circuit Analysis

b) 100 k$$\Omega$$

[Solution Description] Dynamic resistance $$r_d$$ can be calculated using the formula $$r_d = \Delta V / \Delta I$$. Here, $$\Delta V = 1\,V$$ and $$\Delta I = 10\,\mu A = 10 \times 10^{-6}\,A$$. Substituting these into the formula gives:

$$r_d = \frac{1}{10\times 10^{-6}} = 100000\,\Omega = 100\,k\Omega$$

So, the dynamic resistance is 100 kΩ.

Key Concept: Advanced Logic Design, Real-World Application

b) 0 0 0, 0 1 1, 1 0 1, 1 1 0
[Solution Description]
The behavior described is typical of an XOR gate, where the output is true if only one of the two inputs is true. Therefore, construct a truth table for XOR functionality:

\[
\begin{array}{|c|c|c|}
\hline
M & D & L \\
\hline
0 & 0 & 0 \\
0 & 1 & 1 \\
1 & 0 & 1 \\
1 & 1 & 0 \\
\hline
\end{array}
\]

Choose the option that matches this configuration.

Key Concept: Material Composition

c) The energy gap of the semiconductor material.
[Solution Description] The color of light emitted by an LED is primarily determined by the energy gap (bandgap) between the valence band and the conduction band of the semiconductor material. Different semiconductor materials have different bandgaps, resulting in the emission of different colors. For example, Gallium Nitride (GaN) emits blue or green light due to its specific bandgap.

Key Concept: Full-wave Rectifier

b) Two diodes
[Solution Description] A full-wave rectifier with a center-tap transformer uses two diodes. One diode conducts during the positive half-cycle, while the other conducts during the negative half-cycle, thereby allowing current to be rectified in both directions of the AC input.

Key Concept: Function Identification

b) To split the input voltage into two equal parts with opposite polarity.
[Solution Description] In a full-wave rectifier, the center-tap transformer splits the secondary voltage into two equal voltages with opposite phases. This allows each half of the winding to supply power to the circuit during alternate half cycles of the input AC signal, enabling both halves of the waveform to be used for rectification.

Key Concept: Energy Gap

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

[Solution Description]

At absolute zero temperature (\$0\,K\$), semiconductors have a completely filled valence band and an empty conduction band similar to insulators. However, as the temperature increases, thermal energy allows electrons to jump across the smaller energy gap typical of semiconductors. This is why semiconductors can conduct electricity under specific conditions like increased temperature or applied voltage. While both Assertion and Reason are true, the Reason does not correctly explain the Assertion since it simply describes the behavior at absolute zero, not why the smaller energy gap enables conduction.

Key Concept: Application Areas

b) Optical communication
[Solution Description] Optoelectronic devices are widely used in optical communication systems where they play crucial roles in detecting and emitting light signals, which forms the backbone of modern telecommunications.

Key Concept: LED Characteristics

d) Low power consumption
[Solution Description] LEDs are known for their low power consumption, small size, and long lifespan which makes them energy-efficient compared to traditional lighting solutions like incandescent bulbs.

Key Concept: Doping Effects

c) Increases the number of holes
[Solution Description]
Doping a pure silicon semiconductor with a trivalent impurity such as boron introduces holes in the material, creating a p-type semiconductor. This is because the trivalent dopant has one less electron than needed to complete the covalent bond with silicon atoms, resulting in a hole that acts as a positive charge carrier. Thus, the number of holes increases significantly.

Key Concept: Recombination Process

b) Electrons recombine with holes
[Solution Description] During the recombination process in semiconductors, free electrons lose energy and fall into a hole in the valence band, effectively causing the disappearance of both the electron and the hole. This is a critical process in maintaining equilibrium in semiconductors.

Key Concept: Classification

d) Metals
[Solution Description] Based on conductivity, materials are classified as metals, semiconductors, or insulators. Metals have high conductivity due to their free electrons that allow for easy flow of electric current.

Key Concept: Voltage Regulation

b) Its sharp breakdown voltage
[Solution Description]
A Zener diode has a sharp breakdown voltage known as the Zener voltage, which allows it to maintain a constant output voltage even with variations in the input voltage, making it suitable for voltage regulation purposes.

Key Concept: Depletion Region

c) The width increases as the external voltage widens the potential barrier.
[Solution Description] When a p-n junction diode is reverse biased, the external voltage increases the barrier potential, thus widening the depletion region. The increased voltage further separates the majority charge carriers (holes in the p-type and electrons in the n-type), thereby increasing the width of the depletion zone as the mobile charges are drawn away from the junction.

Key Concept: Expression Evaluation

a) 0
[Solution Description] Substituting the given values into the expression: $$A’ + B.C$$. Since $$A=1$$, $$A’=0$$. Also, $$B.C=0.1=0$$. Therefore, $$A’ + B.C = 0 + 0 = 0$$.

Key Concept: Simple Advantage

c) Lower power consumption
[Solution Description] A direct advantage of miniaturized integrated circuits is lower power consumption, which is beneficial for portable devices and energy efficiency.

Key Concept: Semiconductor Basics

b) Intrinsic Semiconductor

[Solution Description] Intrinsic semiconductors are pure materials that have no impurities added, thus they have equal concentrations of electrons and holes.

Key Concept: Junction Behavior

d) Barrier increases
[Solution Description]
In reverse bias, the external voltage increases the potential barrier at the p-n junction, widening the depletion region and inhibiting the flow of charge carriers across the junction.

Key Concept: Reverse Bias Characteristics

b) Current decreases significantly
[Solution Description] Under reverse bias, the external voltage increases the potential barrier, making it difficult for the majority carriers to move across the junction. Consequently, the current is limited to the minority carrier flow, which is significantly smaller, resulting in very low current.

Key Concept: Intrinsic vs Extrinsic

b) Level of impurity concentration
[Solution Description] Intrinsic semiconductors are pure forms of semiconductor materials that have their electrical properties solely determined by the element itself without any added impurities. On the other hand, extrinsic semiconductors are those that have been intentionally doped with impurities to modify their conductivity. The doping process introduces additional charge carriers, either electrons or holes, thereby enhancing conductivity.

Key Concept: Current Flow

b) Minority carriers
[Solution Description]
In a reverse-biased p-n junction, the majority carriers are pushed away from the junction, increasing the width of the depletion region. However, the minority carriers can still drift through the junction due to the increased electric field. Therefore, the current that flows in a reverse-biased diode is primarily due to the movement of these minority carriers. Although the magnitude of this current is generally very small compared to the forward current, it represents the predominant current mechanism under reverse bias.

Key Concept: Circuit Integration

c) Integrate the LDR in series with a resistor to form a voltage divider controlling a transistor that powers the lamp.
[Solution Description] To automatically turn on a lamp when it gets dark using an LDR, you can connect the LDR in series with a transistor. As darkness increases the LDR’s resistance, less current flows through it, triggering the transistor to switch on the lamp by completing the circuit.

Key Concept: Analog vs Digital Signals

b) Both Assertion and Reason are true, but Reason is NOT the correct explanation of Assertion.

[Solution Description]

Both the Assertion and Reason statements are true. The susceptibility of analog signals to noise is because they can take any value in a continuous range, making them more affected by variations, such as noise or interference. In contrast, digital signals, which are represented using discrete steps and often in binary form, are inherently more robust against such issues. However, the reason does not directly explain why analog signals are susceptible to noise; rather, it explains why digital signals are less affected. Therefore, although both statements are true, the Reason is not the direct explanation for the Assertion.

Key Concept: Analog and Digital IC Distinction

c) Analog ICs deal with continuous signals, digital ICs handle discrete signals.
[Solution Description] Analog ICs process continuous signals, while digital ICs handle discrete signals. Amplifiers are examples of analog ICs, whereas logic gates are examples of digital ICs.

Key Concept: Recombination Process

c) Minority carrier concentration decreases

[Solution Description]

Recombination is the process by which electrons and holes combine, reducing the number of free charge carriers. In a p-type semiconductor, the recombination mainly reduces the minority carrier concentration, which are electrons. Thus, the number of minority carriers decreases.

Key Concept: Complex Charge Interactions, Semiconductor Device Comparison

a) Minority carrier injection increases exponentially with increased voltage.
[Solution Description] In a p-n junction diode under forward bias, applying a voltage reduces the barrier potential, allowing for greater minority carrier injection from the n-side to the p-side and vice versa. When the applied voltage exceeds the built-in potential, it significantly lowers the energy barrier, causing an exponential increase in minority carrier injection. This is because the reduction of the potential barrier allows more electrons from the n-region and holes from the p-region to cross over, thereby enhancing the diffusion process.

Key Concept: Doping Effects

d) Creating acceptor energy levels above the valence band
[Solution Description]
Doping silicon with a trivalent element like boron creates acceptor energy levels just above the valence band. These acceptor levels can capture electrons from the valence band, leaving behind holes.

Hence, doping with boron results in:
$$
\text{Creation of acceptor energy levels just above the valence band.}
$$

This change allows for increased hole concentration due to the available acceptor states.

Therefore, the correct answer is: Creation of acceptor energy levels just above the valence band.

Key Concept: Truth Table Basics

a) Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

[Solution Description] The assertion that a NOR gate outputs high only when all inputs are low is correct according to its definition: $$Y = \overline{A + B}$$. This means the output is true if and only if both inputs, $$A$$ and $$B$$, are false. The reason provided states that the truth table of a NOR gate is indeed the complement of the OR gate’s truth table, as the OR gate outputs high if any input is high, while NOR outputs low in such cases. Both statements are true, and the reason correctly explains why the assertion is true.

Key Concept: Semiconductor Doping Effects

c) Increases the number of charge carriers
[Solution Description] Doping a semiconductor involves adding impurity atoms to increase its electrical conductivity. When doped with donor atoms (n-type), the number of electrons increases. When doped with acceptor atoms (p-type), the number of holes increases. Thus, doping increases the number of charge carriers in the semiconductor.

Key Concept: Time Constant Calculation

b) 1 second
[Solution Description] The time constant ($$\tau$$) of an RC circuit is calculated using the formula $$\tau = R \times C$$. Here, $$R = 2 \text{k}\Omega = 2000 \Omega$$ and $$C = 500 \mu F = 500 \times 10^{-6} F$$. Hence,

$$
\tau = 2000 \times 500 \times 10^{-6} = 1 \text{s}
$$

Therefore, the time constant of this RC circuit is 1 second.

Key Concept: Majority and Minority Carriers

c) Holes are the majority carriers
[Solution Description] In a p-type semiconductor, trivalent impurities add acceptor energy levels close to the valence band, increasing the number of holes. At equilibrium, holes are the majority carriers due to these additional acceptor atoms, while electrons are the minority carriers. Charge neutrality must still be maintained, so the overall concentration of positive charge (holes) equals the negative charges (electrons plus ionized acceptors). The correct statement is that holes are the majority carriers and electrons are the minority carriers.

Key Concept: Basic Concepts

a) Vacuum tubes
[Solution Description] Before semiconductors, vacuum tubes were the primary devices used in electronic circuits. Vacuum tubes could amplify electrical signals and were used in radios, televisions, and early computers. However, despite their usefulness, they had limitations such as being bulky and consuming a lot of power.

Key Concept: Gain Analysis

b) Common Emitter (CE)
[Solution Description] The Common Emitter (CE) configuration is recognized for its high voltage gain compared to other configurations. It provides a significant amplification of input signals, which makes it suitable for general-purpose amplification.

Key Concept: Advanced Band Theory, Carrier Concentration

c) Increase
[Solution Description] As the temperature increases, the energy band gap $$E_g$$ decreases, making it easier for electrons to move from the valence band to the conduction band. For intrinsic semiconductors, the intrinsic carrier concentration $$n_i$$ can be estimated using the relation:

$$
n_i = A T^{3/2} e^{-E_g/(2kT)}
$$

Here, $$A$$ is a constant, $$T$$ is the absolute temperature, $$k$$ is the Boltzmann constant, and $$e$$ represents the exponential function. As $$E_g$$ decreases, the exponential term becomes less negative, leading to an increase in $$n_i$$. Therefore, as temperature rises and $$E_g$$ decreases, $$n_i$$ increases significantly.

Key Concept: Application Identification

b) Voltage regulation
[Solution Description] One of the most common applications of Zener diodes is in voltage regulation circuits where they stabilize and control voltages.

Key Concept: Diode Biasing

c) During the positive half-cycle of AC
[Solution Description] In a half-wave rectifier, the diode is forward-biased during the positive half-cycle of the AC input. During this time, the diode conducts electricity allowing current to pass through and converting the AC input into DC output.

Key Concept: Basic Concepts

b) To convert AC to DC
[Solution Description] A diode in a rectifier circuit primarily functions to allow current to flow in only one direction, converting alternating current (AC) into direct current (DC). This unidirectional flow helps in rectification.

Key Concept: Half-wave Rectifier

b) Positive half-cycle
[Solution Description] In a half-wave rectifier, the diode conducts during the positive half-cycle of the input AC signal. During this period, the diode is forward-biased, allowing current to pass through, resulting in a pulsating DC output.

Key Concept: Time Constant Analysis, Circuit Design

b) The output voltage will have large ripples due to fast capacitor discharging.
[Solution Description] The time constant $$\tau = RC$$ determines how quickly the capacitor charges and discharges in response to the incoming rectified voltage. If $$\tau$$ is small, the capacitor will discharge quickly between cycles, leading to increased ripple in the output voltage. This means the DC output will not be smooth, as the capacitor cannot hold its charge for long enough to maintain a steady output during the periods when the input AC signal falls to zero.

Key Concept: Binary Error Detection, Binary System Applications

c) 1101101
[Solution Description] In a system using odd parity, the total number of 1s must be odd. Initially, $$1101001$$ has three 1s, so it already meets odd parity. If one bit was flipped due to an error, the corrected data should still allow for an odd number of 1s:

Possible data corrections include:
– Changing any ‘0’ to ‘1’ or vice versa.

Evaluate each option:
– Option a) $$1101011$$: This has four 1s, providing even parity, thus incorrect.
– Option b) $$1101000$$: This has two 1s, also even parity, thus incorrect.
– Option c) $$1101101$$: This has five 1s, maintaining odd parity, potentially correct.
– Option d) $$1111001$$: This has six 1s, giving even parity, hence incorrect.

Thus, the correctly received data could be $$1101101$$.

Key Concept: Intrinsic Semiconductor Properties

c) Number of free electrons is equal to the number of holes
[Solution Description] An intrinsic semiconductor is a pure form of semiconductor without any significant dopants. As per the syllabus, the number of free electrons ($$n_e$$) is equal to the number of holes ($$n_h$$) in an intrinsic semiconductor, denoted by $$n_i$$, which represents the intrinsic carrier concentration.

Key Concept: Temperature Effect

b) Increases
[Solution Description] At absolute zero (0 K), intrinsic semiconductors behave like insulators with no electrons in the conduction band. As the temperature increases above 0 K, thermal energy excites some electrons from the valence band to the conduction band, thereby increasing their number in the conduction band.

Device Characteristics

b) Converts light to electricity
[Solution Description] A photodiode is a semiconductor device that converts light into an electrical current. It operates by generating electron-hole pairs when photons are absorbed, which causes a flow of current. This functionality makes it ideal for light detection in circuits.