Consider the following : 1. In semiconductors, the mobility of electrons is more than that of holes. Which of the following statements are correct ?
2. In semiconductors, the resistivity increases with the increase in temperature.
3. Metal has positive TCR.
4. In metals, thermal conductivity is inversely proportional to electronic conductivity at a particular temperature.
1, 3, 4
1, 3, 4 — option (D), as recorded in the supplied key.
Take the four statements in turn.
| Statement | Verdict | Reason |
|---|---|---|
| 1. Electron mobility exceeds hole mobility | True | In silicon \(\mu_{n}\approx 1350\) and \(\mu_{p}\approx 480\ \text{cm}^{2}/\text{V-s}\); in germanium 3900 against 1900. Holes move by successive covalent-bond transfers and carry a larger effective mass, so they are always the slower carrier. This is why n-channel devices outperform p-channel ones and why the npn transistor is preferred for high-frequency work |
| 3. Metals have a positive temperature coefficient | True | A metal already has its full complement of free electrons, so heating adds no carriers but increases lattice vibration and hence scattering. Resistance rises with temperature — the basis of the platinum resistance thermometer |
| 4. In metals thermal conductivity is inversely proportional to electrical conductivity | False | The Wiedemann-Franz law gives the opposite: \(\dfrac{\kappa}{\sigma}=LT\) with L the Lorenz number, so at a fixed temperature the two are directly proportional. The same free electrons carry both heat and charge, which is why copper is simultaneously the best ordinary conductor of each |
| 2. Semiconductor resistivity rises with temperature | False | Semiconductors have a negative temperature coefficient. Heating promotes carriers across the gap, and the exponential rise in \(n_{i}\) overwhelms the modest fall in mobility, so resistivity falls. This is the basis of the thermistor, and the cause of thermal runaway in power devices |
The difficulty with the option set, stated plainly: statements 1 and 3 are true and statements 2 and 4 are false, so the correct response would be “1 and 3 only” — and no option offers it. Every choice contains exactly one false statement alongside the two true ones :
| Option | Contents | Flaw |
|---|---|---|
| (A) 1, 2, 3 | Both true statements plus false 2 | One error |
| (D) 1, 3, 4 | Both true statements plus false 4 | One error — the keyed choice |
| (B) 1, 2, 4 | One true, two false | Two errors |
| (C) 2, 3, 4 | One true, two false | Two errors |
Options (B) and (C) can therefore be dismissed outright, since each carries two false statements. Between (A) and (D) the key selects (D), and that is the answer stored here.
The contrast to carry away is the temperature behaviour: metals have a positive TCR, semiconductors a negative one, and the reason is simply that heating a metal adds scattering while heating a semiconductor adds carriers.
Similar Questions
Consider the following statements :
If an electric field is applied to an n-type semiconductor bar, the electrons and holes move in opposite directions due to their opposite charges. The net current is
1. due to both electrons and holes with electrons as majority carriers.
2. the sum of electron and hole currents.
3. the difference between electron and hole current.Which of these statements is/are correct ?
The Debye length is a characteristic length for semiconductor. Arrange the doping density given below in such a way that Debye length changes from maximum to minimum.
(A) N = 1015 cm–3
(B) N = 1017 cm–3
(C) N = 3 × 1015 cm–3
(D) N = 1016 cm–3
(E) N = 5 × 1016 cm–3Choose the most appropriate answer from the options given below :
Match the following :
List – I List – II a. Laplace equation i. \(q\mu_n\left(\varepsilon\cdot n+\dfrac{kT}{q}\dfrac{\partial n}{\partial x}\right)\) b. Continuity equation ii. \(G_n-\dfrac{n_p-n_{p0}}{\tau_n}+n_p\mu_n\dfrac{\partial\varepsilon}{\partial x}+\mu_n\varepsilon\dfrac{\partial n_p}{\partial x}+D_n\dfrac{\partial^{2}n_p}{\partial x^{2}}\) c. Current density equation iii. \(\dfrac{\partial^{2}\psi}{\partial x^{2}}+\dfrac{\partial^{2}\psi}{\partial y^{2}}+\dfrac{\partial^{2}\psi}{\partial z^{2}}=\dfrac{qN_D}{\epsilon}\) d. Poisson’s equation iv. \(\nabla^{2}\psi=0\) Choose the correct answer from the codes given below:
A conducting line on an IC chip is 2.8 mm long and has a rectangular cross-section of 1 μm x 4 μm.. A current of 5 mA produces a voltage drop of 100 mV across the line. If the electron mobility is 500 cm2/V-s, the electron concentration is
For non-degenerate semiconductors the product of the majority and minority carrier concentration is fixed as
(a) \(ni ^ {2}\) (b) \(N_cN_v\exp\left(\dfrac{Eg}{kT}\right)\) (c) \(N_cN_v\exp\left(-\dfrac{Eg}{kT}\right)\) (d) \(N_v\exp\left(-\dfrac{Eg}{kT}\right)\)
Which of the above are correct ?
The electron density of a n-type semiconductor is proportional to :
The ionised concentration for donors is given by :
Important Questions from Carriers in Semiconductors
The velocity with which electrons are emitted in the photoemission process
The process of adding impurities to a pure semiconductor is called
Mobility and conductivity are related by which of the following equations?
How many electrons are there in the valence shell of a pure semiconductor?
In a pure silicon, what is the time for an electron to drift $1\mu m$ in an electric field of 100 V/cm?
Assume electron mobility of $1350 \text{ cm}^2/V-s$
