- What is an intrinsic semiconductor? Give examples.
An intrinsic semiconductor is a pure semiconductor material with no significant impurities or defects. Its electrical conductivity arises solely from the thermal excitation of electrons from the valence band to the conduction band, creating electron-hole pairs. Examples include silicon (Si) and germanium (Ge).
- Define the terms drift and diffusion current.
- Drift Current: The movement of charge carriers (electrons or holes) in a semiconductor due to an applied electric field. It is proportional to the electric field strength and carrier mobility.
- Diffusion Current: The flow of charge carriers due to a concentration gradient, where carriers move from regions of high concentration to regions of low concentration.
- What are solar cells?
Solar cells are semiconductor devices that convert sunlight directly into electricity through the photovoltaic effect. They typically consist of a p-n junction, where photons excite electrons, generating a voltage and current.
- What is the physical significance of Fermi-Dirac distribution function?
The Fermi-Dirac distribution function, \( f(E) = \frac{1}{1 + e^{(E - E_F)/kT}} \), describes the probability of an energy state being occupied by an electron in a system of fermions at thermal equilibrium. It is significant because it determines the distribution of electrons in the conduction and valence bands of a semiconductor, influencing its electrical properties.
- Why direct bandgap semiconductors are preferred in the designing of LED?
Direct bandgap semiconductors allow efficient radiative recombination of electrons and holes, emitting photons directly. This efficiency is crucial for LEDs, unlike indirect bandgap materials where recombination is less efficient and involves phonons.
- Calculate the wavelength of radiation emitted by a LED with band gap energy of 1.5 eV.
The relationship between energy and wavelength is \( E = \frac{hc}{\lambda} \), where \( h = 6.634 \times 10^{-34} \, \text{J·s} \), \( c = 3 \times 10^8 \, \text{m/s} \) and \( 1eV = 1.602 \times 10^{-19} \text{J} \).
Rearranging for \( \lambda \):
\[
\lambda = \frac{hc}{E} = \frac{(6.634 \times 10^{-34}) \times (3 \times 10^8)}{1.5 \times 1.602×10^{-19}} \approx 8.27 \times 10^{-7} \, \text{m} = 827 \, \text{nm}
\]
So, the wavelength is approximately 827 nm.
- The \( R_H \) of a specimen is \( 3.66 \times 10^{-4} \, \text{m}^3 \text{C}^{-1} \). Its resistivity is \( 8.93 \times 10^{-3} \, \Omega\text{-m} \). Find mobility and charge carrier concentration.
- Charge carrier concentration (\( n \)): \( R_H = \frac{1}{nq} \), where \( q = 1.6 \times 10^{-19} \, \text{C} \). So, \( n = \frac{1}{R_H q} = \frac{1}{(3.66 \times 10^{-4}) \times (1.6 \times 10^{-19})} \approx 1.71 \times 10^{15} \, \text{m}^{-3} \).
- Mobility (\( \mu \)): \( \mu = \frac{1}{n q \rho} \), where \( \rho = 8.93 \times 10^{-3} \, \Omega\text{-m} \). So, \( \mu = \frac{1}{(1.71 \times 10^{15}) \times (1.6 \times 10^{-19}) \times (8.93 \times 10^{-3})} \approx 4.11 \times 10^{-2} \, \text{m}^2\text{V}^{-1}\text{s}^{-1} \).
- What is \( f(E) \) values at \( T = 0 \, \text{K} \) for the cases (i) \( E \leq E_F \) (ii) \( E > E_F \)?
At \( T = 0 \, \text{K} \), the Fermi-Dirac function simplifies:
- (i) \( E \leq E_F \): \( f(E) = 1 \) (all states below Fermi level are fully occupied).
- (ii) \( E > E_F \): \( f(E) = 0 \) (all states above Fermi level are empty).
- What is Hall effect? Mention any two applications.
The Hall effect is the generation of a voltage difference (Hall voltage) across an electrical conductor or semiconductor when a current flows through it perpendicular to an applied magnetic field. Applications include:
- Measuring magnetic fields.
- Determining carrier concentration and mobility in semiconductors.
- Distinguish intrinsic and extrinsic semiconductor.
- Intrinsic Semiconductor: Pure material, conductivity due to thermal excitation (e.g., Si, Ge).
- Extrinsic Semiconductor: Doped with impurities (e.g., P or B), conductivity enhanced by added charge carriers (n-type or p-type).
- Write any two differences between direct and indirect band gap semiconductors. Give two examples for each.
- Differences:
1. Direct bandgap allows direct electron-hole recombination with photon emission; indirect requires phonon assistance.
2. Direct bandgap materials are more efficient for LEDs/lasers; indirect are better for transistors.
- Examples:
- Direct bandgap: GaAs, InP.
- Indirect bandgap: Si, Ge.
- Calculate the wavelength of light emitted by LED with the band gap of energy 1.8 eV.
The relationship between energy and wavelength is \( E = \frac{hc}{\lambda} \), where \( h = 6.634 \times 10^{-34} \, \text{J·s} \), \( c = 3 \times 10^8 \, \text{m/s} \) and \( 1eV = 1.602 \times 10^{-19} \text{J} \).
Rearranging for \( \lambda \):
Using \[ E = \frac{hc}{\lambda} \Rightarrow \lambda = \frac{hc}{E} \]:
\[ \lambda = \frac{(6.634 \times 10^{-34}) \times (3 \times 10^8)}{1.8\times 1.602×10^{-19}} \approx 6.89 \times 10^{-7} \, \text{m} = 689 \, \text{nm} \]
So, the wavelength is approximately 689 nm.
- The Hall coefficient and conductivity of an n-type specimen are \( -1.25 \times 10^{-3} \, \text{m}^3/\text{C} \) and \( 112 \, /\Omega\text{-m} \). Find the mobility of electrons.
Mobility \( \mu = \frac{\sigma |R_H|}{n} \), but since \( R_H = \frac{1}{nq} \) and \( \sigma = nq\mu \), \( \mu = \frac{|R_H|}{\rho} \), where \( \rho = \frac{1}{\sigma} = \frac{1}{112} \approx 8.93 \times 10^{-3} \, \Omega\text{-m} \). So:
\[
\mu = \frac{1.25 \times 10^{-3}}{8.93 \times 10^{-3}} \approx 0.14 \, \text{m}^2\text{V}^{-1}\text{s}^{-1}
\]
- What is the direction of current flow in a forward biased pn junction diode?
a) From n-type to p-type b) From p-type to n-type c) No current flow d) None of the above
Answer: a) From n-type to p-type
- What are the applications of Hall effect?
- Measuring magnetic fields.
- Determining carrier type and concentration in semiconductors.
- Find the wavelength associated with an electron with energy 2000 eV.
Wavelength \( \lambda = \frac{h}{p} \), where \( p = \sqrt{2mE} \), \( m = 9.11 \times 10^{-31} \, \text{kg} \), \( E = 2000 \, \text{eV} = 3.2 \times 10^{-16} \, \text{J} \).
\[
p = \sqrt{2 \times (9.11 \times 10^{-31}) \times (3.2 \times 10^{-16})} \approx 2.42 \times 10^{-23} \, \text{kg·m/s}
\]
\[
\lambda = \frac{6.626 \times 10^{-34}}{2.42 \times 10^{-23}} \approx 2.74 \times 10^{-11} \, \text{m} = 0.0274 \, \text{nm}
\]
So, the wavelength is approximately 0.0274 nm.
- What is the difference between direct and indirect band gap semiconductors?
- Direct bandgap: Electron-hole recombination emits photons directly (e.g., GaAs).
- Indirect bandgap: Recombination involves phonons, less efficient for light emission (e.g., Si).
- The semiconductor material NOT used in LED is
a) Silicon carbide b) GaAsP c) GaAs d) Si
Answer: d) Si
- On increase of temperature, the Fermi level shifts upwards in
a) p-type semiconductor b) n-type semiconductor c) intrinsic semiconductor d)none of these
Answer: c) intrinsic semiconductor
- Define Fermi energy and Fermi level for a semiconductor.
- Fermi Energy: The energy level at which the probability of finding an electron is 50% at absolute zero.
- Fermi Level: The energy level in a semiconductor that determines the occupancy of electron states, varying with temperature and doping.
- Draw the Fermi level in intrinsic and extrinsic semiconductors.