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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 of the electrons from the valence band to the conduction band?
When a semiconducting material is doped with an impurity, new acceptor levels are created. In a particular thermal collision, a valence electron revives an energy equal to 2kT and just reaches one of the acceptor levels. Assuming that the energy of the electron was at the topo 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.
The band gap between the valence and the conduction bands in zinc oxide (ZnO) is 3.2 eV. Suppose an electron in the conduction band combines with a hole in the valence band and the excess energy is released in the form of electromagnetic radiation. Find the maximum wavelength that can be emitted in this process.
Let ΔE denote the energy gap between the valence band and the conduction band. The population of conduction electrons (and of the holes) is roughly proportional to e–ΔE/2kT. Find the ratio of the concentration of conduction electrons in diamond to that in silicon at room temperature 300 K. ΔE for silicon is 1.1 eV and for diamond is 6.0 eV. How many conduction electrons are likely to be in one cubic meter of diamond?
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 meter. Density of silicon is 5 × 1028 atoms per cubic meter.
The product of the hole concentration and the conduction electron concentration turns out to be independent of the amount of any impurity doped. The concentration of conduction electrons in germanium is 6 × 1019 per cubic meter. When some phosphorus impurity is doped into a germanium sample, the concentration of conduction electrons increases to 2 × 1023 per cubic meter. Find the concentration of the holes in the doped germanium.
The conductivity of an intrinsic semiconductor depends on temperature as σ = σ0 e–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.
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. Assumed 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 0K. The concentration of the holes increase 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.
The current voltage characteristic of an ideal p-n junction diode is given by
i = i0 (eeV/kT – 1)
Where the drift current i0 equals 10 μA. Take the temperature T to be 300 K.
(a) Find the voltage V0 for which eeV/kT = 100. One can neglect the term 1 for voltages greater than this value.
(b) Find an expression for the dynamic resistance of the diode as a function of V for V > V0.
(c) Find the voltage for which the dynamic resistance is 0.2 Ω
A load resistor of 2 kΩ is connected in the collector branch of an amplifier circuit using a transistor in common-emitter mode. The current gain β = 50. The input resistance of the transistor is 0.50 kΩ. If the input current is changed by 50 μA,
(a) by what amount does the output voltage change,
(b) by what amount does the input voltage change and
(c) what is the power gain?