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. Which of these statements is/are correct ?
2. the sum of electron and hole currents.
3. the difference between electron and hole current.
1 and 2
The two currents add, even though the carriers move in opposite directions — so statements 1 and 2 are correct, option 2.
Why opposite motion still gives addition. Conventional current is the direction of flow of positive charge. Holes are positive and drift along the field; electrons are negative and drift against it — but a negative charge moving one way constitutes a conventional current the other way. The two motions therefore produce currents in the same direction, and the total drift current density is
\(J=q\left(n\mu_{n}+p\mu_{p}\right)E\)
The plus sign is the whole point of the question: two sign reversals — charge and direction — cancel. Statement 3 makes the natural but wrong inference that opposite motion means subtraction.
| Carrier | Charge | Drift direction | Conventional current |
|---|---|---|---|
| Hole | +q | With E | With E |
| Electron | −q | Against E | With E |
Statement 1 is true as well, and states the other half of the picture. Both carrier types contribute; in an n-type bar the electrons are the majority carriers, so they dominate the total. Just how completely, the mass-action law shows:
\(np=n_{i}^{2}\)
For silicon doped to \(N_{D}=10^{16}\ \text{cm}^{-3}\) with \(n_{i}=1.5\times10^{10}\),
\(p=\dfrac{\left(1.5\times10^{10}\right)^{2}}{10^{16}}=2.25\times10^{4}\ \text{cm}^{-3}\)
— twelve orders of magnitude fewer holes than electrons. The hole current is thus utterly negligible in practice, but it is not zero, which is why statement 1 is correctly worded as "both… with electrons as majority carriers".
Where the minority carriers do matter : in the reverse saturation current of a diode, in the base of a bipolar transistor, and in every device that works by injection rather than by drift — because there the minority population is raised far above its equilibrium value and the mass-action balance no longer applies.
Hence, statements 1 and 2 are correct.
Similar Questions
Consider the following :
1. In semiconductors, the mobility of electrons is more than that of holes.
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.Which of the following statements 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 $1350 \text{ cm}^2/V-s$
