Advertisements
Advertisements
प्रश्न
A semiconducting material has a band gap of 1 eV. Acceptor impurities are doped into it which create acceptor levels 1 meV above the valence band. Assume that the transition from one energy level to the other is almost forbidden if kT is less than 1/50 of the energy gap. Also if kT is more than twice the gap, the upper levels have maximum population. The temperature of the semiconductor is increased from 0 K. The concentration of the holes increases with temperature and after a certain temperature it becomes approximately constant. As the temperature is further increased, the hole concentration again starts increasing at a certain temperature. Find the order of the temperature range in which the hole concentration remains approximately constant.
(Use Planck constant h = 4.14 × 10-15 eV-s, Boltzmann constant k = 8·62 × 10-5 eV/K.)
उत्तर
Given:
Band gap = 1 eV
After doping,
Position of acceptor levels = 1 meV above the valence band
Net band gap after doping = (1 − 10−3) eV = 0.999 eV
According to the question,
Any transition from one energy level to the other is almost forbidden if kT is less than 1/50 of the energy gap.
\[\Rightarrow k T_1 = \frac{0 . 999}{50}\]
\[ \Rightarrow T_1 = \frac{0 . 999}{50 \times 8 . 62 \times {10}^{- 5}}\]
\[ \Rightarrow T_1 = 231 . 78 \approx 232 . 8 \] K
\[T_1\] is the temperature below which no transition is possible.
If kT is more than twice the gap, the upper levels have maximum population; that is, no more transitions are possible.
For the maximum limit,
\[\text{ K T}_2 = 2 \times {10}^{- 3} \]
\[ \Rightarrow T_2 = \frac{2 \times {10}^{- 3}}{8 . 62 \times {10}^{- 5}}\]
\[ \Rightarrow T_2 = \frac{2}{8 . 62} \times {10}^2 = 23 . 2 \] K
\[T_2\] is the temperature above which no transition is possible.
∴ Temperature range = 23.2−231.8
APPEARS IN
संबंधित प्रश्न
Distinguish between a metal and an insulator on the basis of energy band diagrams ?
Write two characteristic features to distinguish between n-type and p-type semiconductors ?
How many 1s energy states are present in one mole of sodium vapour? Are they all filled in normal conditions? How many 3s energy states are present in one mole of sodium vapour? Are they all filled in normal conditions?
When an electron goes from the valence band to the conduction band in silicon, its energy is increased by 1.1 eV. The average energy exchanged in a thermal collision is of the order of kT which is only 0.026 eV at room temperature. How is a thermal collision able to take some to the electrons from the valence band to the conduction band?
Let np and ne be the number of holes and conduction electrons in an intrinsic semiconductor.
When an impurity is doped into an intrinsic semiconductor, the conductivity of the semiconductor
An incomplete sentence about transistors is given below:
The emitter−..... junction is __ and the collector−..... junction is __. The appropriate words for the dotted empty positions are, respectively,
In a pure semiconductor, the number of conduction election 6 × 1019 per cubic metre. How many holes are there in a sample of size 1 cm × 1 mm?
When a semiconducting material is doped with an impurity, new acceptor levels are created. In a particular thermal collision, a valence electron receives an energy equal to 2kT and just reaches one of the acceptor levels. Assuming that the energy of the electron was at the top edge of the valence band and that the temperature T is equal to 300 K, find the energy of the acceptor levels above the valence band.
Find the maximum wavelength of electromagnetic radiation which can create a hole-electron pair in germanium. The band gap in germanium is 0.65 eV.
(Use Planck constant h = 4.14 × 10-15 eV-s, Boltzmann constant k = 8·62 × 10-5 eV/K.)
Estimate the proportion of boron impurity which will increase the conductivity of a pure silicon sample by a factor of 100. Assume that each boron atom creates a hole and the concentration of holes in pure silicon at the same temperature is 7 × 1015 holes per cubic metre. Density of silicon 5 × 1028 atoms per cubic metre.
The conductivity of an intrinsic semiconductor depends on temperature as σ = σ0e−ΔE/2kT, where σ0 is a constant. Find the temperature at which the conductivity of an intrinsic germanium semiconductor will be double of its value at T = 300 K. Assume that the gap for germanium is 0.650 eV and remains constant as the temperature is increased.
(Use Planck constant h = 4.14 × 10-15 eV-s, Boltzmann constant k = 8·62 × 10-5 eV/K.)
With reference to Semiconductor Physics,
Draw a labelled energy band diagram for a semiconductor.
What is forbidden band?
For germanium crystal, the forbidden gas energy gap
A semiconductor is cooled from T.K to T2K its resistance will
The valance of an impurity added to germanium crystal in order to convert it into p-type semiconductor is
Which one of the following elements will require the highest energy to take out an electron from them?
Pb, Ge, C and Si
With reference to semiconductor physics, answer the following question.
What is meant by “Forbidden band" of energy levels?
