1)The difference b/n intrinsic and extrinsic semiconductors 2) how to calculate mobility (electron and hole) of intrinsic semiconductors 3) how to calculate electron and hole concentration for intrinsic semiconductor 4) kp – Theory and intrinsic semiconductors
The Correct Answer and Explanation is :
1) Difference Between Intrinsic and Extrinsic Semiconductors:
- Intrinsic Semiconductor: These are pure semiconductors made of a single material, typically silicon (Si) or germanium (Ge), without any intentional impurities. In an intrinsic semiconductor, the number of electrons in the conduction band equals the number of holes in the valence band.
- Extrinsic Semiconductor: These semiconductors are doped with impurities to modify their electrical properties. The doping adds extra charge carriers (electrons or holes). There are two types of extrinsic semiconductors:
- n-type: Doped with elements that have more valence electrons (e.g., phosphorus in silicon). This increases the number of electrons in the conduction band.
- p-type: Doped with elements that have fewer valence electrons (e.g., boron in silicon), which creates holes in the valence band, increasing hole concentration.
2) How to Calculate Mobility (Electron and Hole) of Intrinsic Semiconductors:
Mobility (µ) of charge carriers refers to how quickly an electron or hole can move through a semiconductor when subjected to an electric field. The mobility of electrons (( \mu_e )) and holes (( \mu_h )) in intrinsic semiconductors can be calculated experimentally, typically using the formula:
[
J = qn \mu E
]
Where:
- ( J ) is the current density,
- ( q ) is the charge of the electron,
- ( n ) is the carrier concentration,
- ( \mu ) is the mobility,
- ( E ) is the electric field.
By measuring the current density ( J ) and the applied electric field ( E ), the mobility of electrons and holes can be derived.
3) How to Calculate Electron and Hole Concentration for Intrinsic Semiconductor:
In an intrinsic semiconductor, the number of electrons in the conduction band ( n ) is equal to the number of holes in the valence band ( p ), and both are determined by the intrinsic carrier concentration ( n_i ). The concentration can be expressed using the equation:
[
n_i = \sqrt{N_c N_v} \exp\left(\frac{-E_g}{2kT}\right)
]
Where:
- ( n_i ) is the intrinsic carrier concentration,
- ( N_c ) and ( N_v ) are the effective density of states in the conduction and valence bands, respectively,
- ( E_g ) is the energy gap,
- ( k ) is Boltzmann’s constant,
- ( T ) is the absolute temperature in Kelvin.
At equilibrium, for intrinsic semiconductors, ( n = p = n_i ).
4) Kp – Theory and Intrinsic Semiconductors:
The term ( K_p ) refers to the product of the electron concentration ( n ) and hole concentration ( p ), which is constant for a given material and temperature in intrinsic semiconductors. This is often expressed as:
[
K_p = n \cdot p = n_i^2
]
In an intrinsic semiconductor, because the number of electrons equals the number of holes (( n = p = n_i )), the product of electron and hole concentrations is constant and equal to ( n_i^2 ). This is an important principle because it defines the behavior of intrinsic semiconductors, where the carrier concentration is solely dependent on the temperature and the material’s properties (such as bandgap).