NCERT Solutions for Class 12 Physics Chapter 14 Semiconductor Electronic Material Devices and Simple Circuits

• Semiconductors are the basic materials used in the present solid state electronic devices like diode, transistor, ICs, etc.

• Lattice structure and the atomic structure of constituent elements decide whether a particular material will be insulator. Metal or semiconductor. 

• Metals have low resistivity  (10-2 to 10-8$\Omega$m),     insulators have very high resistivity (>108$\Omega$m-1), while semiconductors have intermediate values of resistivity.

• Semiconductors are elemental (Si, Ge) as well as compound (GaAs, CdS, etc.). 

• Pure semiconductors are called ‘intrinsic semiconductors’. The presence of charge carriers (electrons and holes) is an ‘intrinsic’ property of the material and these are obtained as a result of thermal excitation. The number of electrons (ne ) is equal to the number of holes (nh) in intrinsic conductors. Holes are essentially electron vacancies with an effective positive charge.

• The number of charge carriers can be changed by ‘doping’ of a suitable impurity in pure semiconductors. Such semiconductors are known as extrinsic semiconductors. These are of two types (n-type and p-type). 

• In n-type semiconductors, ne >> nh while in p-type semiconductors nh >> ne.

• n-type semiconducting Si or Ge is obtained by doping with pentavalent atoms (donors) like As, Sb, P, etc., while p-type Si or Ge can be obtained by doping with trivalent atom (acceptors) like B, Al, in etc. 

• nenh=n2t in all cases. Further, the material possesses an overall change neutrality

• There are two distinct band of energies (called valence band and conduction band) in which the electrons in a material lie. Valence band energies are low as compared to conduction band energies. All energy levels in the valence band are filled while energy levels in the conduction band may be fully empty or partially filled. The electrons in the conduction band are free to move in a solid and are responsible for the conductivity. The extent of conductivity depends upon the energy gap (Eg ) between the top of valence band (EV ) and the bottom of the conduction band EC. The electrons from valence band can be excited by heat, light or electrical energy to the conduction band and thus, produce a change in the current flowing in a semiconductor. 

• For insulators Eg > 3eV, for semiconductors Eg is 0.2 eV to 3 eV, while for metals Eg ≈ 0.

• p-n junction is the ‘key’ to all semiconductor devices. When such a junction is made, a ‘depletion layer’ is formed consisting of immobile ion-cores devoid of their electrons or holes. This is responsible for a junction potential barrier. 

• By changing the external applied voltage, junction barriers can be changed. In forward bias (n-side is connected to negative terminal of the battery and p-side is connected to the positive), the barrier is decreased while the barrier increases in reverse bias. Hence, forward bias current is more (mA) while it is very small (µA) in a p-n junction diode. 

• Diodes can be used for rectifying an ac voltage (restricting the ac voltage to one direction). With the help of a capacitor or a suitable filter, a dc voltage can be obtained. 

• p-n junctions have also been used to obtain many photonic or optoelectronic devices where one of the participating entity is ‘photon’:

1. Photodiodes in which photon excitation results in a change of reverse saturation current which helps us to measure light intensity:

2. Solar cells which convert photon energy into electricity: 

3. light Emitting Diode and Diode laser in which electron excitation by a bias voltage result in the generation of light.  

• There are some special circuits which handle the digital date consisting of 0 and 1 levels. This forms the subject of Digital Electronics.  

• The important digital circuits performing special logic operations are called logic gates. These are: OR, AND, NOT, NAND, and NOR gates.

• In modern day circuit, many logical gates or circuits are integrated in one single ‘Chip’. These are known as integrated circuits (IC). 

1. In an n-type silicon, which of the following statements is true:

1. Electrons are majority carriers and trivalent atoms are the dopants.

2. Electrons are minority carriers and pentavalent atoms are the dopants.

3. Holes are minority carriers and pentavalent atoms are the dopants.

4. Holes are majority carriers and trivalent atoms are the dopants.

Ans: c) Electrons are majority carriers whereas holes are minority carriers in an n-type silicon atom.

When pentavalent atoms such as Phosphorus are doped in Silicon atoms, an n-type semiconductor is formed.

2. In an p-type silicon, which of the following statements is true:

1. Electrons are majority carriers and trivalent atoms are the dopants.

2. Electrons are minority carriers and pentavalent atoms are the dopants.

3. Holes are minority carriers and pentavalent atoms are the dopants.

4. Holes are majority carriers and trivalent atoms are the dopants.

Ans: d) Electrons are minority carriers whereas holes are majority carriers in an p-type silicon atom. 

When trivalent atoms such as Aluminum are doped in Silicon atoms, an p-type semiconductor is formed.

3. Carbon, silicon and germanium have four valence electrons each. These are characterized by valence and conduction bands separated by energy band gap respectively equal to ${{({{E}_{g}})}_{C}}$, ${{({{E}_{g}})}_{Si}}$ and ${{({{E}_{g}})}_{Ge}}$ . Which of the following statements is true?

1. \[{{({{E}_{g}})}_{Si}}<{{({{E}_{g}})}_{Ge}}<{{({{E}_{g}})}_{C}}\]

2. \[{{({{E}_{g}})}_{C}}<{{({{E}_{g}})}_{Ge}}<{{({{E}_{g}})}_{Si}}\]

3. \[{{({{E}_{g}})}_{C}}>{{({{E}_{g}})}_{Si}}>{{({{E}_{g}})}_{Ge}}\]

4. \[{{({{E}_{g}})}_{C}}={{({{E}_{g}})}_{Si}}={{({{E}_{g}})}_{Ge}}\]

Ans: c) The energy band gap of Carbon is maximum and Germanium is minimum.

\[{{({{E}_{g}})}_{C}}>{{({{E}_{g}})}_{Si}}>{{({{E}_{g}})}_{Ge}}\]  is the energy band gap order of Carbon, Silicon and Germanium.

4. In an unbiased p-n junction, holes diffuse from the p-region to n-region because 

1. Free electrons in the n-region attract them.

2. They move across the junction by the potential difference. 

3. Hole concentration in p-region is more as compared to n-region.

4. All the above

Ans: c) The concentration of holes is more in the p-type region than that of n-type region. 

Diffusion of charge carriers takes place from the region of higher concentration to the region of lower concentration across a junction.

Therefore, in an unbiased p-n junction, holes diffuse from the p-type region to the n-type region.

5.When a forward bias is applied to a p-n junction, it 

1. Raises the potential barrier. 

2. Reduce the majority carrier current to zero. 

3. Lower the potential barrier. 

4. None of the above.

Ans: c) In forward bias of a p-n junction, the potential barrier is opposed by the applied voltage.

So, when forward bias is applied to a p-n junction, the potential barrier is lowered. 

Therefore, the potential barrier across the junction decreases.

6. For transistor action, which of the following statements are correct.

1. Base, emitter and collector regions should have similar size and doping concentrations. 

2. The base region must be very thin and lightly doped. 

3. The emitter junction is forward biased and collector junction is reverse biased. 

4. Both the emitter junction as well as the collector junction are forward biased.

Ans: (b) and (c) are correct statements.

The base region is lightly doped so that it is very thin whereas the emitter junction is forward biased and the collector junction is reverse biased for proper transistor action. 

7. For a transistor amplifier, the voltage gain 

1. Remains constant for all frequencies. 

2. Is high at high and low frequencies and constant in the middle frequency range. 

3. Is low at high and low frequencies and constant at mid frequencies.

4. None of the above.

Ans: c) In a transistor amplifier, the voltage gain is constant at the middle frequencies and low at both low and high frequencies.

8. In a half-wave rectifier, find the output frequency if the input frequency is \[~\mathbf{50Hz}\]. Also, find the output frequency of a full-wave rectifier for the same input frequency?

Ans: It is provided that,

Input frequency of rectifier$=50Hz$

It is known that,

The input frequency of a half-wave rectifier is equal to the output frequency.

$\Rightarrow $Output frequency$=50Hz$

The output frequency of a full-wave rectifier is twice the input frequency.

$\Rightarrow $Output frequency$=2\times 50=100Hz$

Therefore, the output frequency of a half-wave and full-wave rectifier with input frequency $50Hz$ is equal to $50Hz$and $100Hz$respectively.

9. For a CE-transistor amplifier, the audio signal voltage across the collector resistance of \[\mathbf{2}k\Omega \] is \[\mathbf{2}V\]Suppose the current amplification factor of the transistor is $100$, find the input signal voltage and base current, if the base resistance is \[1k\Omega \].

Ans: It is known that,

Voltage amplification, \[\frac{V}{{{V}_{i}}}=\beta \frac{{{R}_{c}}}{{{R}_{B}}}\]

Base resistance, ${{R}_{B}}=\frac{{{V}_{i}}}{{{V}_{B}}}$

It is given that for a CE-transistor amplifier,

Collector resistance, ${{R}_{c}}=2k\Omega =2000\Omega $

Audio signal voltage across the collector resistance, $V=2V$

Current amplification factor of the transistor, $\beta =100$$\Rightarrow $

Base resistance, \[{{R}_{b}}=1k\Omega =1000\Omega \]

Input signal voltage, ${{V}_{i}}=?$

Base current, ${{V}_{B}}=?$

From amplification relation: \[\frac{V}{{{V}_{i}}}=\beta \frac{{{R}_{c}}}{{{R}_{B}}}\]

$\Rightarrow \frac{2}{{{V}_{i}}}=100\times \frac{2000}{1000}$

$\Rightarrow \frac{2\times 1000}{100\times 2000}={{V}_{i}}$

$\Rightarrow {{V}_{i}}=\frac{1}{100}V$

$\Rightarrow {{V}_{i}}=0.01V$

From base resistance relation: ${{R}_{B}}=\frac{{{V}_{i}}}{{{V}_{B}}}$

$\Rightarrow {{R}_{B}}=\frac{0.01}{1000}$

$\Rightarrow {{R}_{B}}={{10}^{-6}}A=1\mu A$

Clearly, input signal voltage is $0.01V$and base current is $10\mu A$ for the given CE-transistor amplifier.

10. Two amplifiers are connected one after the other in series (cascaded). The first amplifier has a voltage gain of $10$ and the second has a voltage gain of $20$. If the input signal is $0.01$ volt, calculate the output ac signal.

Ans: It is given that,

Voltage gain of the first amplifier, ${{V}_{1}}=10$

Voltage gain of the second amplifier, ${{V}_{2}}=20$

Input signal voltage, ${{V}_{i}}=0.01V$

Output signal voltage, ${{V}_{o}}=?$

When two amplifiers are connected one after another is series (cascaded) the total voltage gain is the product of voltage gains of both amplifiers.

$\Rightarrow V={{V}_{1}}\times {{V}_{2}}$

$\Rightarrow V=10\times 20$

$\Rightarrow V=200$

Voltage amplification, $V=\frac{{{V}_{o}}}{{{V}_{i}}}$

$\Rightarrow 200=\frac{{{V}_{o}}}{0.01}$

$\Rightarrow {{V}_{o}}=200\times 0.01$

$\Rightarrow {{V}_{o}}=2V$

Thus, the output AC signal for the given amplifier is $2V$.

11. A p-n photodiode is fabricated from a semiconductor with a band gap of \[\mathbf{2}.\mathbf{8}\text{ }\mathbf{eV}\]. Can it detect a wavelength of \[\mathbf{6000}\text{ }\mathbf{nm}\]?

Ans: It is provided that,

Band gap of the p-n photodiode$=2.8eV$

Wavelength, $\lambda =6000nm=6\times {{10}^{-6}}m$

It is known that,

Energy of a signal, $E=\frac{hc}{\lambda }$

where,

$h$ is the Planck’s constant, $h=6.626\times {{10}^{-34}}Js$

$c$ is the speed of light, $c=3\times {{10}^{8}}m{{s}^{-1}}$

$\Rightarrow E=\frac{6.626\times {{10}^{-34}}\times 3\times {{10}^{8}}}{6\times {{10}^{-6}}}$

$\Rightarrow E=3.313\times {{10}^{-34+8+6}}$

$\Rightarrow E=3.313\times {{10}^{-20}}J$

It is known that, $1.6\times {{10}^{-19}}J=1eV$

$\Rightarrow E=\frac{3.313\times {{10}^{-20}}}{1.6\times {{10}^{-19}}}eV$

$\Rightarrow E=0.207eV$

Energy of the signal with wavelength $6000nm$is $0.207eV$.

As the energy of the signal is less than $2.8eV$(energy band gap of p-n photodiodes) the signal can’t be detected.

Therefore, the photodiode cannot detect the signal.

12. The number of silicon atoms per ${{m}^{3}}$ is $5\times {{10}^{28}}$. This is doped simultaneously with $5\times {{10}^{22}}$ atoms per ${{m}^{3}}$ of Arsenic and $5\times {{10}^{20}}$ per ${{m}^{3}}$ atoms of indium. Calculate the number of electrons and holes. Given that${{n}_{i}}=1.5\times {{10}^{16}}{{m}^{-3}}$. Is the material n-type or p-type?

Ans: It is provided that,

Number of silicon atoms, $N=5\times {{10}^{28}}atoms/{{m}^{3}}$

Number of arsenic atoms, ${{n}_{As}}=5\times {{10}^{22}}atoms/{{m}^{3}}$

Number of indium atoms, ${{n}_{In}}=5\times {{10}^{20}}atoms/{{m}^{3}}$

Number of thermally-generated electrons, ${{n}_{i}}=1.5\times {{10}^{16}}electrons/{{m}^{3}}$

Total number of electrons, ${{n}_{e}}={{n}_{As}}-{{n}_{i}}$

$\Rightarrow {{n}_{e}}=5\times {{10}^{22}}-1.5\times {{10}^{16}}$

$\Rightarrow {{n}_{e}}=(5-1.5\times {{10}^{-6}})\times {{10}^{22}}$

$\Rightarrow {{n}_{e}}\approx 4.99\times {{10}^{22}}electrons/{{m}^{3}}$

Number of holes, ${{n}_{h}}=?$

The concentration of electrons and holes in a semiconductor in thermal equilibrium is ${{n}_{e}}{{n}_{h}}={{n}_{i}}^{2}$

$\Rightarrow {{n}_{h}}=\frac{{{n}_{i}}^{2}}{{{n}_{e}}}$

$\Rightarrow {{n}_{h}}=\frac{{{(1.5\times {{10}^{16}})}^{2}}}{4.99\times {{10}^{22}}}$

$\Rightarrow {{n}_{h}}\approx 4.51\times {{10}^{9}}electrons/{{m}^{3}}$

Hence, the number of electrons is approximately equal to $4.99\times {{10}^{22}}$ electrons per ${{m}^{3}}$ and the number of holes is approximately equal to $4.51\times {{10}^{9}}$ electrons per ${{m}^{3}}$.

As the number of electrons is greater than the number of holes, the material is n-type semiconductor.

13. In an intrinsic semiconductor the energy gap ${{E}_{g}}$ is \[1.2\text{ }eV\]. Its hole mobility is much smaller than electron mobility and independent of temperature. What is the ratio between conductivity at \[600K\] and that at $300K$? Assume that the temperature dependence of intrinsic carrier concentration ${{n}_{i}}$ is given by ${{n}_{i}}={{n}_{o}}\exp \left( -\frac{{{E}_{g}}}{2{{k}_{B}}T} \right)$.

Ans: It is provided that,

Energy gap of the intrinsic semiconductor, ${{E}_{g}}=1.2eV$

Initial temperature, ${{T}_{1}}=300K$

Final temperature, ${{T}_{2}}=600K$

It is known that,

The temperature dependence of intrinsic carrier-concentration is:${{n}_{i}}={{n}_{o}}\exp \left( -\frac{{{E}_{g}}}{2{{k}_{B}}T} \right)$

Where,

${{k}_{B}}$ is the Boltzmann constant, ${{k}_{B}}=8.62\times {{10}^{-5}}eV/K$

$T$ is the Temperature

${{n}_{o}}$ is the constant

The intrinsic carrier-concentration at temperature ${{T}_{1}}=300K$: ${{n}_{i1}}={{n}_{o}}\exp \left( -\frac{{{E}_{g}}}{2{{k}_{B}}\times 300} \right)$

The intrinsic carrier-concentration at temperature ${{T}_{2}}=600K$:${{n}_{i2}}={{n}_{o}}\exp \left( -\frac{{{E}_{g}}}{2{{k}_{B}}\times 600} \right)$

Ratio between conductivities at $600K$ and $300K$is equal to the ratio between their respective intrinsic carrier- concentrations.

\[\Rightarrow \frac{{{n}_{i2}}}{{{n}_{i1}}}=\frac{{{n}_{o}}\exp \left( -\frac{{{E}_{g}}}{2{{k}_{B}}\times 600} \right)}{{{n}_{o}}\exp \left( -\frac{{{E}_{g}}}{2{{k}_{B}}\times 100} \right)}\]

$\Rightarrow \frac{{{n}_{i1}}}{{{n}_{i2}}}=\exp \frac{{{E}_{g}}}{2{{k}_{B}}}\left( \frac{1}{300}-\frac{1}{600} \right)$

$\Rightarrow \frac{{{n}_{i1}}}{{{n}_{i2}}}=\exp \frac{1.2}{2\times 8.62\times {{10}^{-5}}}\left( \frac{2-1}{600} \right)$

$\Rightarrow \frac{{{n}_{i1}}}{{{n}_{i2}}}=\exp (11.6)$

$\Rightarrow \frac{{{n}_{i1}}}{{{n}_{i2}}}=1.09\times {{10}^{5}}$

Thus, the ratio between the conductivities at $600K$ and $300K$ is $1.09\times {{10}^{5}}$.

14. In a p-n junction diode, the current $I$ can be expressed as $I={{I}_{0}}\exp \left( \left( \frac{eV}{{{k}_{B}}T} \right)-1 \right)$ where ${{I}_{0}}$ is called the reverse saturation current, $V$ is the voltage across the diode and is positive for forward bias and negative bias, and $I$ is the current through the diode, ${{k}_{B}}$ is the Boltzmann constant $(8.62\times {{10}^{-5}}eV/K)$ and $T$ is the absolute temperature. If for a given diode ${{I}_{0}}=5\times {{10}^{-12}}A$and\[\mathbf{T}\text{ }=\mathbf{300}\text{ }\mathbf{K}\], then 

(a) What will be the forward current at a forward voltage of \[\mathbf{0}.\mathbf{6}\text{ }\mathbf{V}\]? 

Ans: It is provided that,

Forward voltage, $V=0.6V$

Reverse saturation current, ${{I}_{0}}=5\times {{10}^{-12}}A$

Absolute temperature, $T=300K$

Boltzmann constant, ${{k}_{B}}=8.62\times {{10}^{-5}}eV/K$

It is known that,

Current in p-n junction diode is $I={{I}_{0}}\exp \left( \left( \frac{eV}{{{k}_{B}}T} \right)-1 \right)$

$\Rightarrow I=5\times {{10}^{-12}}\exp \left( \left( \frac{0.6}{8.62\times {{10}^{-5}}\times 300} \right)-1 \right)$

$\Rightarrow I=5\times {{10}^{-12}}\times \exp (22.36)$

$\Rightarrow I=0.0256A$

Therefore, the forward current is $0.0256A$.

(b)What will be the increase in the current if the voltage across the diode is increased to \[\mathbf{0}.\mathbf{7}\text{ }\mathbf{V}\]?

Ans: It is provided that,

Forward voltage, $V=0.7V$

Current in p-n junction diode is $I={{I}_{0}}\exp \left( \left( \frac{eV}{{{k}_{B}}T} \right)-1 \right)$

$\Rightarrow I=5\times {{10}^{-12}}\exp \left( \left( \frac{0.7}{8.62\times {{10}^{-5}}\times 300} \right)-1 \right)$

$\Rightarrow I=5\times {{10}^{-12}}\times \exp (26.25)$

$\Rightarrow I=1.257A$

Increase in current, $\Delta I=1.2757-0.0256$

$\Rightarrow \Delta I=1.23A$

Therefore, the increase in current $\Delta I=1.23A$

(C) What is dynamic resistance?

Ans: It is known that,

Dynamic resistance$=\frac{Change\text{ }in\text{ }voltage}{Change\text{ }in\text{ }current}$

$\Rightarrow \frac{(0.7-0.6)}{2.972}=0.0336/\Omega $

Therefore, the dynamic resistance is$0.0336/\Omega $.

(d) What will be the current if reverse bias voltage changes from \[\mathbf{1V}\] to \[2\mathbf{V}\]?

Ans: When reverse bias voltage changes from $1V$ to $2V$, the current$(I)$ remains almost equal to ${{I}_{0}}$ in both the cases. Change in current becomes equal to zero giving dynamic resistance an infinite value.

Hence, the dynamic resistance in the reverse bias would be infinite.

15. You are given the two circuits as shown in figure. Show that current 

1. acts as OR gate

Ans: Inputs are A and B and Outputs are Y for the given circuit.

The first half of the figure represents NOR Gate and the right half represents NOT Gate.

From the figure, the output of the NOR gate is $\overline{A+B}$. This becomes the input of the NOT gate and its output becomes $\overline{\overline{A+B}}=A+B$.

The output of the system $Y=A+B$.

Therefore, the circuit functions as an OR gate.

(b) acts as AND gate

Ans: Inputs are A and B and output is Y for the given circuit.

The first half of the figure contains two NOT gates and the right half represents NOR Gate.

From the figure, the output of the circuit can be written as:

$Y=\overline{\overline{A}+\overline{B}}=\overline{\overline{A}}.\overline{\overline{B}}=A.B$

Therefore, the circuit functions as an AND gate.

16. Write the truth table for a NAND Gate connected as given in figure. 

Hence identify the exact logic operation carried out by this circuit.

Ans: The input of the NAND gate is A and output is Y.

The output can be written as:

$Y=\overline{A.A}=\overline{A}+\overline{A}=\overline{A}$

Truth table for the given combination:

The symbol of the circuit:

17. You are given two circuits as shown in figure, which consist of NAND gates. Identify the logic operation carried out by the two circuits.

Ans: In the given circuit, inputs are A and B and output is Y.

The output of the left NAND gate is $\overline{A.B}$.

The output of the combination can be written as:

\[Y=\overline{(\overline{A.B}).(\overline{A.B})}=\overline{\overline{AB}}+\overline{\overline{AB}}=AB\]

Therefore, the circuit functions as an AND gate.

b)

Ans: In the given circuits, inputs are A and B and output is Y.

$\overline{A}$ is the output of the upper left NAND gate and $\overline{B}$ is the output of the lower left NAND gate.

The output of the combination can be written as:

$Y=\overline{A}.\overline{B}=\overline{\overline{A}}+\overline{\overline{B}}=A+B$

Therefore, the circuit acts as an OR gate.

18. Write the truth table for circuit given in figure below consisting of NOR gates and identify the logic operation (OR, AND, NOT) which this circuit is performing.

(Hint:$A=0$, $B=1$ then A and B inputs of second NOR gate will be 0 and hence $Y=1$. Similarly work out the values of Y for other combinations of A and B. Compare with the truth table of OR, AND, NOT gates and find the correct one.)

Ans: The inputs of the AND gate are A and B.

The output of the first NOR gate is $\overline{A+B}$.

The output of the combination can be written as:

\[Y=\overline{\overline{A+B}+\overline{A+B}}\]

$\Rightarrow Y==\overline{\overline{A}.\overline{B}}+\overline{\overline{A}.\overline{B}}$

$\Rightarrow Y=\overline{\overline{A}.\overline{B}}=\overline{\overline{A}}+\overline{\overline{B}}$

$\Rightarrow Y=A+B$

Truth table for the given combination:

Therefore, the circuit acts as an OR gate.

19. Write the truth table for the circuits given in the figure consisting of NOR gates only. Identify the logic operations (OR, AND, NOT) performed by the two circuits.

a)

Ans: A is the input for the NOR gate and Y is the output.

The output can be written as, $Y=\overline{A+A}=\overline{A}$

Truth table for the given combination:

Therefore, the circuit functions as NOT gate.

b)

Ans: For the given circuit, A and B are the inputs and Y is the output.

From the result of the first case, we can conclude that the output of the first two NOT gates is $\overline{A}$ and $\overline{B}$.

The output for the combination can be written as:

$Y=\overline{\overline{A}+\overline{B}}$

$\Rightarrow Y=\overline{\overline{A}}.\overline{\overline{B}}=A.B$

Truth table for the given combination:

Therefore, the circuit acts as an AND gate.

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NCERT Solutions of Physics Class 12 Chapter 14: Semiconductor

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The key topics covered in this chapter include energy bands in conductors, semiconductors and insulators, semiconductor diodes- I-V- characteristics in reverse and forward bias, special purpose p-n junction diodes, diode as a rectifier, photodiode, LED, and solar cell. A few of the topics are also covered in the syllabus for CBSE Term 2 Class 12 Physics practical examination. So it is highly recommended that students must have a very clear understanding of each concept covered in Class 12 Ch-14 Semiconductor Electronics: Materials, Devices, and Simple Circuits to secure good marks in their 12th Boards Physics exam.

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