Practice Questions

Propose a reason why the dopant atoms used for Si or Ge are chosen from the nearby third or fifth group of the periodic table.

Justify why vacuum tubes are called 'valves'.

Formulate a reason why the region near the metallurgical junction in a p-n diode is named the 'depletion region'.

Define the term 'doping' as it relates to semiconductors.

Name the majority and minority charge carriers in a p-type semiconductor.

Compare the typical range of resistivity for metals and insulators.

Recall the mathematical relationship between the number of electrons ($n_e$), holes ($n_h$), and intrinsic carrier concentration ($n_i$) in any semiconductor at thermal equilibrium.

What is the primary function of a rectifier circuit?

A p-n junction diode is connected to an external DC source. In which biasing configuration, forward or reverse, does the width of the depletion layer decrease?

Explain the fundamental difference between an intrinsic semiconductor and an extrinsic semiconductor.

A pure silicon crystal has an atom density of $5 \times 10^{28} \text{ atoms/m}^3$. It is doped with pentavalent arsenic at a concentration of 1 part per million (ppm). Given the intrinsic carrier concentration $n_i = 1.5 \times 10^{16} \text{ m}^{-3}$, calculate the number of electrons and holes in the doped semiconductor.

Compare the energy band diagrams of an n-type semiconductor and a p-type semiconductor at a temperature $T > 0 \text{ K}$.

Analyze the formation of a p-n junction. Explain the roles of diffusion current, drift current, and the creation of the depletion region and potential barrier.

Evaluate the choice of Silicon (Si) over Germanium (Ge) for manufacturing most modern semiconductor devices, justifying your answer based on their respective energy band gaps ($E_g$) and temperature sensitivity.

Explain how adding a pentavalent impurity to pure Silicon creates an n-type semiconductor.

Recall the typical range for the energy band gap ($E_g$) for a semiconductor.

Propose an experimental setup to study the V-I characteristics of a p-n junction diode. Justify the choice of ammeter (milliammeter vs. microammeter) for forward and reverse biasing conditions.

Evaluate the effectiveness of a half-wave rectifier compared to a full-wave rectifier for producing a DC voltage. Your evaluation should critique their output waveforms and justify which is superior for a power supply.

List three key differences between vacuum tubes and semiconductor devices.

Explain the formation of a depletion region in a p-n junction.

Define barrier potential and explain how its magnitude changes when a p-n junction is forward biased and reverse biased.

If the input frequency to a full-wave rectifier is $50 \text{ Hz}$, what is the output frequency of the pulsating DC?

The V-I characteristic of a diode is measured. In reverse bias, a voltage of $5 \text{ V}$ results in a current of $2 \text{ } \mu\text{A}$. In forward bias, a voltage of $0.8 \text{ V}$ results in a current of $20 \text{ mA}$. Calculate the static resistance in both cases.

Contrast the working of a half-wave rectifier and a full-wave rectifier using circuit diagrams and their respective output voltage waveforms for a sinusoidal input.

Examine why an intrinsic (pure) semiconductor has very low conductivity at room temperature and how doping improves its practical utility for electronic devices.

Justify the statement: 'Doping a pure semiconductor increases its conductivity manifold, but does not violate the principle of charge neutrality.'

Analyze the behavior of a p-n junction diode under forward bias and reverse bias. Discuss the effect on the potential barrier, depletion width, and current flow in each case, using energy band diagrams.

Examine the validity of the statement: 'An n-type semiconductor has an excess of electrons, hence it is negatively charged.'

Demonstrate the role of a capacitor filter in a full-wave rectifier circuit. Explain its working with a circuit diagram and show the input and output waveforms before and after filtering.

Carbon, silicon, and germanium belong to the same group in the periodic table and have a diamond-like crystal structure. Analyze why carbon (diamond) is an insulator, whereas silicon and germanium are intrinsic semiconductors, by comparing their energy band gaps.

A student claims that a p-n junction diode is an ohmic device in the forward bias region because the current increases with voltage. Critique this statement by evaluating the V-I characteristic curve of a typical silicon diode.

Design a logical argument to explain why Carbon (in diamond form), despite having the same valence and crystal structure as Silicon and Germanium, is an insulator. Base your argument on the energy band gap theory.

Formulate an explanation for the existence of a reverse saturation current in a p-n junction diode under reverse bias. Justify why this current is largely independent of the applied reverse voltage.

If the frequency of the AC input to a full-wave rectifier is $60 \text{ Hz}$, what is the fundamental frequency of the ripple in the output voltage?

The V-I characteristic of a silicon diode shows that when the forward bias voltage changes from $0.7 \text{ V}$ to $0.8 \text{ V}$, the current changes from $5 \text{ mA}$ to $15 \text{ mA}$. In reverse bias, a voltage of $10 \text{ V}$ produces a current of $1 \text{ } \mu\text{A}$. Calculate the dynamic resistance of the diode in both forward and reverse bias.

Evaluate the roles of diffusion and drift currents during the formation of the potential barrier in an unbiased p-n junction. Which process dominates initially and what leads to equilibrium?

A germanium crystal with an atom density of $4.4 \times 10^{28} \text{ atoms/m}^3$ is doped with a trivalent impurity (Indium) at a concentration of 1 ppm. Given that the intrinsic carrier concentration $n_i = 2.4 \times 10^{19} \text{ m}^{-3}$, calculate the concentration of majority and minority charge carriers.

A pure Si crystal has $5 \times 10^{28}$ atoms $\text{m}^{-3}$. It is doped by a 1 ppm concentration of pentavalent As. Recall the formulas to calculate the number of electrons and holes. Given that $n_{i}=1.5 \times 10^{16} \text{m}^{-3}$.

With the help of a circuit diagram, summarize the working of a full-wave rectifier and show its input and output waveforms.

Design a circuit for a full-wave rectifier using a center-tapped transformer. Propose a modification to this circuit to obtain a smoother DC output and justify the role of the added component.

A pure silicon crystal with $5 \times 10^{28}$ atoms/m$^3$ has an intrinsic carrier concentration $n_i = 1.5 \times 10^{16} \text{ m}^{-3}$. Create a scenario by doping it with a pentavalent impurity such that the number of holes is exactly $1\%$ of the number of electrons. Calculate the required doping concentration in parts per million (ppm).

Describe the behavior of a p-n junction diode under forward bias and reverse bias conditions.

In an n-type semiconductor, the concentration of electrons ($n_e$) is significantly higher than that of holes ($n_h$), i.e., $n_e \gg n_h$. Justify how the law of mass action, $n_e n_h = n_i^2$, is still valid.

A lab report states that the dynamic resistance of a silicon diode was calculated to be $1000 \Omega$ under a strong forward bias ($V > 0.7 \text{ V}$) and $10 \Omega$ under reverse bias ($V = -5 \text{ V}$). Critique this result and propose the correct expected trend.

Describe the classification of solids into metals, insulators, and semiconductors on the basis of energy band theory. Illustrate with simple energy band diagrams.