Semiconductor Electronics: Materials, Devices and Simple Circuits - Comprehensive Study Guide

Fundamental Principles of Electronic Devices

• Electronic Control and Building Blocks: Devices capable of yielding a controlled flow of electrons serve as the basic building blocks of all modern electronic circuits.
• Historical Evolution:
  • Vacuum Tubes: Historically, electron flow was achieved using vacuum tubes operating on the principle of thermionic emission.
  • Solid-State Semiconductors: In modern electronics, solid-state semiconductor devices have completely replaced bulky, fragile vacuum tubes due to superior efficiency, compactness, and reliability.

Atomic Energy Levels and Energy Band Theory

• Isolated Atom Energy Levels: According to electronic configuration theory, electrons residing in an isolated atom possess definite, discrete energy amounts corresponding to specific shells and sub-shells. Thus, isolated atoms exhibit well-defined, discrete energy levels.
• Formation of Energy Bands in Solids:
  • In a crystalline solid, a massive number of atoms are brought into close proximity, causing interatomic interactions.
  • These interactions modify the energy levels of the outer valence electrons.
  • Consequently, discrete valence energy levels spread out into a collection of an extraordinarily large number of closely spaced energy levels known as an energy band.
• Valence Band: The energy band formed by a series of energy levels containing valence electrons.
• Fermi Level: The highest energy level occupied by an electron in the valence band at absolute zero temperature ($0\,\text{K}$).
• Conduction Band: The lowest unfilled energy band positioned directly above the valence band in a solid. Electrons within this band act as free charge carriers and contribute directly to electrical conductivity.
• Forbidden Band Gap ($E_g$): The energy separation existing between the top of the valence band and the bottom of the conduction band where no electron energy states can exist.

Classification of Solids: Conductors, Insulators, and Semiconductors

• Conductors (Metals):
  • Band Structure: The conduction band and valence band overlap, resulting in zero forbidden band gap ($E_g = 0$).
  • Carriers: A vast number of electrons are readily available in the conduction band at all temperatures.
  • Resistivity Range: Very low resistivity, ranging from $10^{-2}\,\Omega\,\text{m}$ to $10^{-8}\,\Omega\,\text{m}$.
  • Conductivity Range: High electrical conductivity, ranging from $10^2\,\text{S}\,text{m}^{-1}$ to $10^8\,\text{S}\,\text{m}^{-1}$.
• Insulators:
  • Band Structure: The valence band is completely filled, while the conduction band is completely empty, separated by a large band gap ($E_g > 3\,\text{eV}$).
  • Carriers: No electrons possess sufficient thermal energy to jump across the wide forbidden gap into the conduction band.
  • Examples: Glass, rubber, wood, plastic, and diamond/carbon ($E_g = 5.4\,\text{eV}$).
  • Resistivity Range: Extremely high resistivity, varying from $10^{11}\,\Omega\,\text{m}$ to $10^{19}\,\Omega\,\text{m}$ or higher.
  • Conductivity Range: Extremely low conductivity, lying between $10^{-11}\,\text{S}\,\text{m}^{-1}$ and $10^{-19}\,\text{S}\,\text{m}^{-1}$.
• Semiconductors:
  • Band Structure: Band structure resembles that of insulators, but with a comparatively small energy band gap ($E_g < 3\,\text{eV}$).
  • Temperature Dependence:
  • At absolute zero ($0\,\text{K}$), semiconductors act as $100\%$ perfect insulators.
  • At non-zero temperatures, thermal excitation enables some electrons to cross the small energy gap into the conduction band, producing finite electrical conduction.
  • Resistivity Range: At room temperature, resistivity ranges from $10^{-5}\,\Omega\,\text{m}$ to $10^6\,\text{m}$.
  • Conductivity Range: At room temperature, conductivity ranges from $10^5\,\text{S}\,\text{m}^{-1}$ to $10^{-6}\,\text{S}\,\text{m}^{-1}$.
  • Mathematical Model for Electron Thermal Excitation: The number of electrons $n$ jumping from the valence band to the conduction band at absolute temperature $T\,\text{K}$ is given by:

$n = C e^{-\frac{E_g}{2 k_B T}}$

    where $C$ is a material constant, $E_g$ is the forbidden energy band gap, and $k_B$ is Boltzmann's constant. Electrical conductivity increases when energy gap $E_g$ is small and temperature $T$ is high.

Intrinsic Semiconductors

• Definition: Pure semiconducting materials containing no added impurities or dopants are known as intrinsic semiconductors.
• Elemental Semiconductors:
  • Silicon (Si): $E_g = 1.1\,\text{eV}$; valence electrons reside in the 3rd orbit.
  • Germanium (Ge): $E_g = 0.72\,\text{eV}$; valence electrons reside in outer orbits requiring less ionization energy.
• Compound & Advanced Semiconductors:
  • Inorganic Compounds: Cadmium Sulfide ($\text{CdS}$), Gallium Arsenide ($\text{GaAs}$), Indium Phosphide ($\text{InP}$), Aluminium Phosphide ($\text{AlP}$), Cadmium Selenide ($\text{CdSe}$).
  • Organic Compounds and Polymers: Certain organic molecules and conjugated polymers also exhibit semiconducting properties.
• Crystal Structure & Charge Generation:
  • Silicon and Germanium are tetravalent (4 valence electrons in outermost shell).
  • In a crystal lattice, each atom shares its 4 valence electrons with 4 neighboring atoms to form strong covalent bonds, fulfilling an octet configuration.
  • At $0\,\text{K}$, all covalent bonds remain intact, so the material behaves as a complete insulator.
  • At finite temperatures ($T > 0\,\text{K}$), thermal energy breaks covalent bonds, liberating free electrons and creating vacant electron sites with effective positive charge called holes.
  • Free electrons and holes are generated in equal numbers:

$n_e = n_h = n_i$

    where $n_e$ is electron concentration, $n_h$ is hole concentration, and $n_i$ is intrinsic carrier concentration.

• Conduction Mechanism:
  • Upon applying an external electric field, free electrons migrate toward the positive potential terminal, while holes effectively move toward the negative potential terminal.
  • Total conduction current $I$ is the sum of electron current $I_e$ and hole current $I_h$:

$I = I_e + I_h$

• Conductivity Determinants: Electrical conductivity of an intrinsic semiconductor is purely a function of temperature and increases monotonically with temperature.

Extrinsic Semiconductors and Doping Mechanisms

• Doping Definition: Doping is the deliberate addition of a controlled, microscopic amount of specific impurity atoms (typically $1\,\text{part in } 10^6$ or $0.0001\%$) to a pure semiconductor to substantially enhance its conductivity.
• Extrinsic Semiconductor Definition: A semiconductor whose electrical properties are governed by added trivalent or pentavalent impurity atoms.
• Mass Action Law: In any semiconductor in thermal equilibrium, whether $n$-type or $p$-type, the product of electron density $n_e$ and hole density $n_h$ satisfies:

$n_e \cdot n_h = n_i^2$

• Overall Electrical Neutrality: Every semiconductor ($n$-type or $p$-type) remains overall electrically neutral because the charge of mobile carriers is balanced by the stationary charge of ionized donor or acceptor core ions in the lattice.
• $n$-Type Semiconductors:
  • Dopants: Pentavalent impurities such as Phosphorus ($\text{P}$), Arsenic ($\text{As}$), or Antimony ($\text{Sb}$).
  • Mechanism: Each pentavalent atom shares 4 electrons in covalent bonding with adjacent tetravalent atoms and donates its 5th electron to the conduction band (donor atom).
  • Carrier Dominance: Electrons serve as majority charge carriers, while holes are minority carriers ($n_e \gg n_h$).
  • Energy Level: Donor impurity atoms introduce a donor energy level $E_D$ located just below the conduction band ($\approx 0.01\,\text{eV}$ below $E_c$ in Ge/Si).
  • Conductivity Comparison: $n$-type semiconductors possess higher electrical conductivity than $p$-type semiconductors at identical doping levels because electron mobility exceeds hole mobility.

• $p$-Type Semiconductors:
  • Dopants: Trivalent impurities such as Boron ($\text{B}$), Aluminium ($\text{Al}$), Gallium ($\text{Ga}$), or Indium ($\text{In}$).
  • Mechanism: Each trivalent atom forms covalent bonds with 3 neighboring tetravalent atoms, leaving one bond incomplete and generating an electron vacancy or hole (acceptor atom).
  • Carrier Dominance: Holes serve as majority charge carriers, while electrons are minority carriers ($n_h \gg n_e$).
  • Energy Level: Acceptor impurity atoms introduce an acceptor energy level $E_A$ located just above the valence band ($\approx 0.01 - 0.05\,\text{eV}$ above $E_v$).

Physics of the $p-n$ Junction

• Fabrication Techniques: Simply pressing two separate $p$ and $n$ slabs together cannot form a junction because surface roughness at microscopic scales (much larger than crystal interatomic spacing) prevents atomic-level contact. Junctions are fabricated via:
  • Alloying
  • Diffusion
  • Vapour deposition
  • Rate-grown junction techniques

• Junction Formation Processes:
  • Diffusion: Due to concentration gradients, majority holes diffuse from $p$-side to $n$-side, and majority electrons diffuse from $n$-side to $p$-side.
  • Diffusion of an electron leaves behind an immobile, positively charged donor ion core on the $n$-side.
  • Diffusion of a hole leaves behind an immobile, negatively charged acceptor ion core on the $p$-side.
  • Depletion Layer: The space-charge region created on both sides of the junction consisting of fixed, immobile ion cores completely devoid of mobile charge carriers.
  • Internal Electric Field and Drift: Space charge generates an internal electric field across the junction directed from $n$-side to $p$-side.
  • This field forces minority electrons to drift from $p$ to $n$ and minority holes to drift from $n$ to $p$, creating a drift current.
  • Equilibrium: Equilibrium is attained when the magnitude of the drift current equals that of the diffusion current, resulting in zero net junction current.
• Barrier Potential ($V_B$):
  • The buildup of positive charge on the $n$-side and negative charge on the $p$-side produces a potential difference across the depletion layer that opposes further majority carrier diffusion.
  • Direct Voltmeter Measurement: Barrier potential cannot be measured directly using a conventional voltmeter because the junction depletion layer presents nearly infinite internal resistance, preventing current flow through the meter.
  • Effect of Doping: Increasing the doping concentration narrows the depletion layer width.

Biasing Modes of $p-n$ Junction Diodes

• Forward Biasing:
  • Connection: $p$-side connected to positive terminal; $n$-side connected to negative terminal of voltage supply.
  • Junction Effects: Depletion layer width decreases, potential barrier is lowered, and junction resistance drops dramatically.
  • Current Behavior: Below the knee/threshold voltage, forward current $I_F$ increases slowly. Above threshold, current rises exponentially.
  • Threshold Voltages: $\approx 0.2\,\text{V}$ for Germanium diodes; $\approx 0.7\,\text{V}$ for Silicon diodes.
• Reverse Biasing:
  • Connection: $p$-side connected to negative terminal; $n$-side connected to positive terminal of voltage supply.
  • Junction Effects: Depletion layer width widens, potential barrier increases, and junction resistance becomes extremely high.
  • Current Behavior: A tiny leakage current (reverse saturation current $I_R$) flows due to minority charge carriers. This current remains nearly constant up to a critical breakdown voltage.
  • Breakdown Voltage (Zener Voltage): At high reverse voltage, the intense junction electric field pulls electrons out of valence bonds (field ionization/tunneling), resulting in a sharp spike in reverse current.
  • Zener Diode: A specialized semiconductor diode engineered to operate safely in the reverse breakdown region to function as a voltage regulator.

Applications: Rectifiers and Filter Circuits

• Rectification: The conversion of alternating current (a.c.) input signals into unidirectional direct current (d.c.) signals using the selective one-way conduction property of $p-n$ junctions.

• Half-Wave Rectifier:
  • Uses a single $p-n$ junction diode connected in series with a load resistor $R_L$
  • Conducts current only during the positive half-cycle of the a.c. input signal; blocks the negative half-cycle.
  • Output is unidirectional, intermittent, pulsating, and has an output frequency equal to input frequency ($ u$).

• Full-Wave Rectifier:
  • Uses a center-tapped transformer and two $p-n$ junction diodes ($D_1, D_2$) operating in complementary cycles.
  • During positive input half-cycles, $D_1$ is forward-biased and conducts; $D_2$ is reverse-biased.
  • During negative input half-cycles, $D_2$ is forward-biased and conducts; $D_1$ is reverse-biased.
  • Output current flows through load resistor $R_L$ continuously in a single direction throughout the entire a.c. cycle.
  • Output signal frequency is double the input signal frequency ($2\nu$).

• Capacitor Filter Circuits:
  • The raw output of a full-wave rectifier is pulsating d.c. containing a.c. ripple components.
  • A filter capacitor $C$ of high capacitance is connected in parallel with load resistor R_L$.\n - The capacitor charges to peak voltage during input peaks and slowly discharges through R_L during voltage drops.\n - Because C provides a low-impedance path to high-frequency a.c. ripples, ripples are bypassed, smoothing the output into a steady d.c. voltage.\n\n# Temperature Dependence of Resistivity\n\n\n\n- **Mathematical Model of Resistivity**:\n\n\rho = \frac{m}{n e^2 \tau}\n\n  where m$is electron mass,$n$is electron number density,$e$is elementary electronic charge, and$\tau is relaxation time between collisions.\n- **Conductors**:\n - As temperature increases, carrier density n remains essentially constant.\n - Thermal vibration amplitudes of lattice ions increase, raising collision frequency and reducing relaxation time \tau\n - Consequently, resistivity \rho increases monotonically with temperature.\n- **Semiconductors**:\n - As temperature increases, thermal energy breaks covalent bonds rapidly, causing carrier density n to increase exponentially.\n - The exponential rise in n$far outweighs the minor reduction in relaxation time$\tau\n - Consequently, resistivity \rho decreases rapidly with rising temperature.\n\n# Very Short Answer Questions and Solutions\n\n- **Q1**: Carbon and silicon both have four valence electrons each. How then are they distinguished?\n - **Solution**: Valence electrons in carbon reside in the 2nd orbit, whereas in silicon they reside in the 3rd orbit. The energy required to extract a valence electron from carbon is E_g = 5.4\,\text{eV}$, making carbon an insulator. For silicon,$E_g = 1.1\,\text{eV}, making it a semiconductor.\n- **Q2**: What is a hole?\n - **Solution**: A hole is a vacant electron site acting as a seat of effective positive charge, created when an electron breaks away from a covalent bond in a semiconductor.\n- **Q3**: What is an intrinsic semiconductor?\n - **Solution**: A pure semiconductor crystal free from any added impurities or doping.\n- **Q4**: Give the ratio of the number of holes and the number of conduction electrons in an intrinsic semiconductor.\n - **Solution**: The ratio is 1$, since$n_h = n_e = n_i\n- **Q5**: At what temperature would an intrinsic semiconductor behave like a perfect insulator?\n - **Solution**: At absolute zero temperature (0\,\text{K}).\n- **Q6**: Name two factors on which electrical conductivity of a pure semiconductor at a given temperature depends.\n - **Solution**: (i) Energy band gap (E_g) between valence and conduction bands, and (ii) temperature.\n- **Q7**: What is doping?\n - **Solution**: The process of adding controlled, small quantities of trivalent or pentavalent impurities into a pure semiconductor.\n- **Q8**: What is an extrinsic semiconductor?\n - **Solution**: A pure semiconductor doped with controlled quantities of trivalent or pentavalent impurity atoms.\n- **Q9**: What is the difference between an n$-type and a$p-type semiconductor? [Delhi 2012 C]\n - **Solution**: In n$-type semiconductors, pentavalent dopants are used and electrons are majority carriers. In$p-type semiconductors, trivalent dopants are used and holes are majority carriers.\n- **Q10**: Draw energy band diagram for a p-type extrinsic semiconductor.\n - **Solution**: Refer to Fig. 14.09.\n- **Q11**: Why is the conductivity of n$-type semiconductor greater than that of$p-type semiconductor even when both have the same level of doping?\n - **Solution**: Electron mobility is higher than hole mobility.\n- **Q12**: Draw energy band diagram for an n-type extrinsic semiconductor.\n - **Solution**: Refer to Fig. 14.10.\n- **Q13**: Why can't we take one slab of p$-type semiconductor and physically join it to another slab of$n$-type semiconductor to get a$p-n junction? [A.I. 2010]\n - **Solution**: Any physical semiconductor surface has microscopic roughness far exceeding interatomic lattice spacing, preventing continuous atomic-level contact. The contact interface would act as a structural discontinuity.\n- **Q14**: What is depletion region in a p-n junction?\n - **Solution**: A thin layer surrounding the junction interface devoid of mobile charge carriers (electrons and holes), containing fixed immobile ion cores.\n- **Q15**: What happens to the width of depletion layer of a p-n junction when it is (i) forward biased, (ii) reverse biased? [A.I. 2011, Delhi 2012]\n - **Solution**: (i) Decreases in forward bias; (ii) increases in reverse bias.\n- **Q16**: Name the type of biasing of a p-n junction diode so that the junction offers very high resistance.\n - **Solution**: Reverse bias.\n- **Q17**: What is the cause of a small leakage current in reverse bias arrangement of a p-n junction?\n - **Solution**: Drift of minority charge carriers across the junction driven by the internal junction electric field.\n- **Q18**: In Fig. 14.11 (10\,\text{V}$applied to resistor$R$connected to anode of diode$D$grounded at cathode), is diode$D forward or reverse biased?\n - **Solution**: Forward biased.\n- **Q19**: In Fig. 14.12 (cathode connected to 5\,\text{V}, anode grounded), is the diode forward or reverse biased? [A.I. 2017]\n - **Solution**: Reverse biased.\n- **Q20**: Draw output signal across a p-n$junction diode when a square input signal of$\pm 5\,\text{V} is applied. [A.I. 2019]\n - **Solution**: The diode conducts during positive half-cycle (+5\,\text{V}$output) and cuts off during negative half-cycle ($0\,\text{V}$output), yielding a square wave between$+5\,\text{V}$and$0\,\text{V} (Fig. 14.14).\n- **Q21**: Can the potential barrier across a p-n junction be measured by simply connecting a voltmeter across the junction? [NCERT Exemplar]\n - **Solution**: No, because the depletion region has extremely high resistance, preventing current from flowing through the voltmeter.\n\n# Short Answer Questions - Type I and Solutions\n\n- **Q1**: If antimony is added to a pure silicon crystal, what type of extrinsic semiconductor is obtained? Draw its energy band diagram. [CBSE Sample Paper]\n - **Solution**: Antimony (\text{Sb}$) is pentavalent, producing an$n-type extrinsic semiconductor. Energy band diagram corresponds to Fig. 14.15.\n- **Q2**: Distinguish between 'intrinsic' and 'extrinsic' semiconductors. [Delhi 2015]\n - **Solution**:\n - *Intrinsic*: Pure material without added impurities (n_e = n_h = n_i); conductivity is small and depends strictly on temperature.\n - *Extrinsic*: Prepared by doping trivalent or pentavalent impurities (n_e eq n_h$,$n_e \cdot n_h = n_i^2); conductivity is higher and governed primarily by doping level.\n- **Q3**: Distinguish between n$-type and$p-type semiconductors based on energy band diagrams.\n - **Solution**:\n - *n$-type*: Pentavalent dopants create a donor energy level$E_D$slightly below the conduction band$E_c; conduction occurs predominantly via electrons in conduction band.\n - *p$-type*: Trivalent dopants create an acceptor energy level$E_A$slightly above the valence band$E_v; conduction occurs predominantly via holes in valence band.\n- **Q4**: What is meant by doping? How does it affect conductivity?\n - **Solution**: Doping is the deliberate addition of controlled impurities (\approx 1\,\text{part in } 10^6). It increases electrical conductivity multi-fold compared to pure semiconductors.\n- **Q5**: Why is a p$-type semiconductor electrically neutral although$n_h \gg n_e?\n - **Solution**: The positive charge of majority holes is exactly balanced by the equal and opposite negative charge of stationary ionized acceptor cores in the crystal lattice.\n- **Q6**: Explain formation of depletion layer and barrier potential in a p-n junction.\n - **Solution**: Electron diffusion from n\rightarrow p$leaves positive donor ions on the$n$-side; hole diffusion from$p\rightarrow n$leaves negative acceptor ions on the$p$-side. These immobile charges create a space charge depletion layer and an internal junction potential$V_B opposing further diffusion.\n- **Q7**: How do (i) doping concentration and (ii) biasing affect depletion layer width? [A.I. 2011, 2013, 2017 C]\n - **Solution**: (i) Increased doping decreases depletion layer width; (ii) Forward biasing decreases width, while reverse biasing increases width.\n- **Q8**: Draw V-I graph for p-n junction diode in forward and reverse bias.\n - **Solution**: Refer to Fig. 14.17.\n- **Q9**: In Fig. 14.18, assuming ideal diodes D_1$and$D_2$, calculate current through$2\,\Omega resistor. [Foreign 2017]\n - **Solution**: D_1$is forward-biased (zero resistance) and$D_2$is reverse-biased (infinite resistance). No current flows through$D_2$. Total resistance =$3\,\Omega + 2\,\Omega = 5\,\Omega. Current:\n\nI = \frac{2\,\text{V}}{(3 + 2)\,\Omega} = 0.4\,\text{A}\n\n- **Q10**: Semiconductor materials X and Y are germanium doped with indium and arsenic, respectively. Connected to battery with X to positive terminal.\n - **Solution**: Indium is trivalent (X$is$p$-type); Arsenic is pentavalent ($Y$is$n$-type). Since$p-side is connected to positive terminal, the junction is forward biased.\n- **Q11**: Contrast forward biasing and reverse biasing.\n - **Solution**:\n - *Forward Bias*: Positive to p$, negative to$n; depletion layer narrows; barrier potential drops; low resistance, easy current flow.\n - *Reverse Bias*: Negative to p$, positive to$n; depletion layer widens; barrier potential rises; high resistance, minimal leakage current.\n- **Q12**: Semiconductor has n_e = n_h = 6 \times 10^8\,\text{m}^{-3}$. On doping,$n_e$increases to$9 \times 10^{12}\,\text{m}^{-3}.\n - **Solution**:\n - (i) Material becomes an n-type semiconductor.\n - (ii) Using mass action law n_e \cdot n_h = n_i^2:\n\nn_h = \frac{n_i^2}{n_e} = \frac{(6 \times 10^8)^2}{9 \times 10^{12}} = 4 \times 10^4\,\text{m}^{-3}\n\n- **Q13**: Output waveform across load resistor R$for square wave input ($\pm 5\,\text{V}).\n - **Solution**: Diode conducts during positive half-cycle (+5\,\text{V}$across$R$) and blocks during negative half-cycle ($0\,\text{V}$across$R).\n- **Q14**: Explain working of half-wave rectifier with circuit diagram. [A.I. 2013 C, 2014, 2016]\n - **Solution**: Refer to Fig. 14.22(a) and (b).\n- **Q15**: Give two differences between half-wave and full-wave rectifiers.\n - **Solution**:\n - *Half-wave*: Intermittent unidirectional output; output signal frequency equals input frequency (\nu).\n - *Full-wave*: Continuous unidirectional output; output signal frequency is double input frequency (2\nu).\n- **Q16**: Determine bias state for diodes in Fig. 14.23: [A.I. Delhi 2005]\n - **Solution**:\n - (a) V_p - V_n = 0\,\text{V} - 5\,\text{V} = -5\,\text{V}$$\rightarrow Reverse biased.\n - (b) V_p - V_n = 10\,\text{V} - 5\,\text{V} = +5\,\text{V}$$\rightarrow Forward biased.\n - (c) V_p - V_n = -10\,\text{V} - 0\,\text{V} = -10\,\text{V}$$\rightarrow Reverse biased.\n - (d) V_p - V_n = -5\,\text{V} - (-12\,\text{V}) = +7\,\text{V}$$\rightarrow Forward biased.\n\n# Short Answer Questions - Type II and Solutions\n\n- **Q1**: Explain full-wave rectifier working and waveforms. [A.I. 2011, 2012, 2017]\n - **Solution**: Employs center-tapped transformer and two diodes (D_1, D_2$). During positive input half-cycle,$D_1$conducts while$D_2$is off. During negative half-cycle,$D_2$conducts while$D_1$is off. Current through load$R_L$flows in identical direction throughout, yielding output frequency$2 u (Fig. 14.24, 14.25).\n- **Q2**: Doping intrinsic semiconductor to form p$-type and$n-type.\n - **Solution**: Doping Si with Pentavalent Phosphorus provides free electrons (n$-type, donor level$E_D$). Doping Si with Trivalent Aluminium creates electron vacancies/holes ($p$-type, acceptor level$E_A).\n- **Q3**: Processes in p-n junction formation.\n - **Solution**: Diffusion of majority carriers and Drift of minority carriers under built-in field.\n- **Q4**: Features distinguishing conductors, semiconductors, insulators via energy bands. [A.I. 2014, Delhi 2010]\n - **Solution**: Refer to Fig. 14.26 and comparative summary table.\n- **Q5**: Resistivity variation with temperature for conductor vs semiconductor. [A.I. 2019]\n - **Solution**: Using \rho = \frac{m}{n e^2 \tau}$, conductor resistivity increases because$\tau$decreases as lattice collisions increase while$n$is constant. Semiconductor resistivity decreases exponentially because carrier density$n increases sharply with thermal generation.\n- **Q6**: Explain V-I characteristics of p-n junction in forward and reverse bias. [Delhi 2011, 2017]\n - **Solution**: Forward bias exhibits exponential current growth past threshold (\approx 0.7\,\text{V}$Si). Reverse bias exhibits tiny reverse saturation current$I_R up to Zener breakdown (Fig. 14.28, 14.29).\n- **Q7**: (i) Why is reverse current independent of potential up to breakdown? (ii) Why does current increase sharply at breakdown? [A.I. 2013]\n - **Solution**: (i) Reverse current is driven purely by minority carriers whose generation rate is limited by temperature, not applied voltage. (ii) High electric field strips valence electrons, allowing band-to-band tunneling.\n- **Q8**: What is a filter? Describe capacitor filtering role.\n - **Solution**: Capacitor C$parallel to$R_L stores charge at voltage peaks and supplies current during dips, eliminating a.c. ripple (Fig. 14.30).\n- **Q9**: How to obtain steady d.c. output from pulsating full-wave rectifier voltage? [Delhi 2013 C]\n - **Solution**: Connect a large parallel filter capacitor C$across load resistor$R_L\n- **Q10**: (a) Semiconductor S$is in series with resistor$R$and ammeter$A$. If$S$is heated, how to adjust$R$to keep current constant? (b) In circuit with parallel diodes$D_1$(forward) and$D_2$(reverse) connected to bulbs$B_1, B_2, which bulb glows?\n - **Solution**:\n - (a) Heating S$decreases its resistance. To maintain constant total resistance and current, resistance$R must be increased.\n - (b) Bulb B_1$glows because$D_1$is forward-biased and conducts. Bulb$B_2$remains dark because$D_2 is reverse-biased.\n\n# Long Answer Questions and Solutions\n\n- **Q1**: Device 'X' converts alternating full input wave into all-positive full wave output. Name device 'X' and draw circuit diagram. [Delhi 2010]\n - **Solution**: Device 'X' is a full-wave rectifier. Circuit diagram is shown in Fig. 14.24 / Fig. 14.40.\n- **Q2**: (a) Role of diffusion and drift in p-n junction formation. (b) Name device used as voltage regulator. [A.I. 2012]\n - **Solution**: (a) Diffusion builds charge layers; drift balances diffusion at equilibrium forming depletion layer and potential barrier. (b) Zener diode.\n- **Q3**: How V-I characteristics of p-n junction diode are utilized in rectification. [Delhi 2014]\n - **Solution**: Diode conducts heavily under forward bias (low resistance) and blocks current under reverse bias (high resistance). This unidirectional conduction converts alternating current (a.c.) to direct current (d.c.).\n- **Q4**: A.C. signal fed into circuits X and Y produces half-wave (X) and full-wave (Y) outputs. Explain modification when capacitor is added. [Delhi 2011 C]\n - **Solution**: Circuit X is a half-wave rectifier; Circuit Y is a full-wave rectifier. Connecting a capacitor across load resistor R_L$$ in parallel eliminates the ripple factor, smoothing the output signal into steady direct current.