Match the following : Choose the correct answer from the codes given below: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. \(\nabla^{2}\psi=0\)
a-iv, b-ii, c-i, d-iii
Each equation can be identified from its form alone, without recalling any derivation.
a → iv. Laplace equation.
\(\nabla^{2}\psi=0\)
The defining feature is the zero on the right: it is Poisson's equation in a charge-free region. So a and d are the same equation with and without a source term, and spotting that pair settles half the question at once.
d → iii. Poisson's equation.
\(\nabla^{2}\psi=\dfrac{qN_D}{\epsilon}\)
Same Laplacian, but now driven by a space-charge density — here the ionised donors in a depletion region. Integrating it twice is how the depletion width and built-in field of a junction are obtained.
c → i. Current density equation.
\(J_n=q\mu_n n\varepsilon+qD_n\dfrac{\partial n}{\partial x}\)
Recognise the two transport mechanisms sitting side by side: a drift term proportional to the field ε and a diffusion term proportional to the concentration gradient. The factor kT/q multiplying μn is Dn written through the Einstein relation \(D_n=\dfrac{kT}{q}\mu_n\).
b → ii. Continuity equation. The long expression is the only one containing generation (Gn) and recombination terms:
\(\dfrac{\partial n_p}{\partial t}=G_n-\dfrac{n_p-n_{p0}}{\tau_n}+\ldots\)
It is the book-keeping statement that carriers in a volume can only change by being generated, recombining (with lifetime τn), drifting in or diffusing in — which is exactly why all four mechanisms appear in one line.
Identify by inspection: zero on the right → Laplace; charge on the right → Poisson; drift + diffusion only → current density; generation and lifetime present → continuity. Together these four are the standard set from which every device equation is built.
Hence, the correct matching is a-iv, b-ii, c-i, d-iii.
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 ?
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 :
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 $1350 \text{ cm}^2/V-s$
