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 ?
(a) and (c) are correct.
To solve the given problem, we need to understand the properties of semiconductors, particularly the relationship between majority and minority carrier concentrations in non-degenerate semiconductors.
For non-degenerate semiconductors, the product of the majority carrier concentration (electrons \(n\) in n-type or holes \(p\) in p-type) and the minority carrier concentration (holes \(p\) in n-type or electrons \(n\) in p-type) is given by the intrinsic carrier concentration squared, \(n_i^2\). This is a fundamental principle in semiconductor physics known as the mass action law.
So, the correct expression for the carrier concentration product is:
\(np = n_i ^ {2}\)
The intrinsic carrier concentration \(n_i\) is a measure of electron concentration in the conduction band and hole concentration in the valence band when no doping is present. Therefore, option (a) is correct.
Let's examine the other options:
- Option (b) \(N_cN_v\exp\left(\dfrac{E_g}{kT}\right)\) is incorrect because the exponential term in the equation has a positive exponent, which is not consistent with the standard expression for intrinsic carrier concentration.
- Option (c) \(N_cN_v\exp\left(-\dfrac{E_g}{kT}\right)\) is correct. This form is derived from the Boltzmann approximation and represents the product of the effective density of states in the conduction band (\(N_c\)) and valence band (\(N_v\)) with the correct exponential factor showing the dependence on the bandgap energy (\(E_g\)), temperature (\(T\)), and Boltzmann's constant (\(k\)).
- Option (d) \(N_v\exp\left(-\dfrac{E_g}{kT}\right)\) is incorrect as it only accounts for part of the equation and does not represent the entire relationship for non-degenerate semiconductors.
Therefore, the correct answer is: (a) and (c) are correct.
In conclusion, understanding the mass action law and the derivation of carrier concentrations in semiconductors helps us identify that options (a) and (c) are correct expressions for the product of the majority and minority carrier concentrations in non-degenerate semiconductors.
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 :
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
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 $1350 \text{ cm}^2/V-s$
