UNIT 3 : SOLID STATE PHYSICS

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Electrical conduction, conductivity, drift velocity, the band theory of solids, energy bands, energy gap, classification of solids in conductors, insulators and semiconductors, energy band diagram for silicon and germanium semiconductors, electron distribution function, Fermi - Dirac distribution function, fermi energy, intrinsic semiconductor, holes, intrinsic carriers, electron and hole concentration, fermi level in an intrinsic semiconductor, intrinsic density, ni, intrinsic conductivity, doping of impurities, n - type semiconductor, p - type semiconductor, temperature variation of carrier concentration in extrinsic semiconductors, extrinsic conductivity, law of mass action, charge neutrality condition, fermi level in extrinsic semiconductors, effect of variation of impurity concentration on position of fermi level, electrical conduction in extrinsic semiconductors, drift current and diffusion current, Hall effect, pn junction at equilibrium, diffusion of majority carriers, depletion region and the potential barrier, drift of minority carrier equilibrium condition, energy band diagram of pn junction at equilibrium, calculation of the built in potential barrier Vo, pn junction under forward bias, energy band diagram of pn junction under forward bias, the law of the junction, injection of minority carriers, diffusion of minority carriers, carrier movement in forward biased circuit, the rectifier equation, pn junction under reverse bias, energy band diagram of reverse biased pn junction, reverse saturation current, volt - ampere characteristics, application of pn junction as half wave rectifier, transistor structure, biasing the transistor, circuit configurations, energy band diagram of an unbiased transistor, action of the bias, transistor action, energy band diagram of a biased transistor, relation between the currents in common base configuration, common emittor configuration, energy band diagram of a transistor connected in common emittor configuration, current relation in common emittor configuration, transistor as an amplifier in common base and common emitter modes.


Edited by:- Dr. A. W. Pangantiwar

Show that at 0 degrees K the fermi level lies midway between donor level and the bottom of conduction band for n-type semiconductor with high doping concentration.

Intrinsic Silicon has a resistivity of 2000 ohm-m at room temperature and the intrinsic concentration is 14000000000000000 per square metre. Calculate the resistivity of the sample containing acceptor concentration of 1000000000000000000000 per square metre. Assume that mobility of holes remains as for intrinsic silicon and that mobility for holes is equal to 0.25 times mobility of electrons.

What is fermi function?

Draw the energy band diagram for the p-n junction diode in equilibrium, and hence obtain an expression for the contact potential.

The bulk n-type region of a germanium junction has a conductivity of 10000 s/m at 300 degrees K and that for the p-region is 100 s/m. Find the voltage drop across the junction in equilibrium at 300 degrees K, assuming intrinsic conductivity Ni = 250000000000 /cubic metre, mobility for electrons = 0.36 and mobility for holes = 0.17 square metre/V-s.

A rectangular block of a solid is connected to a dc voltage source. Obtain the expressions:
(i) for the current density flowing through the block and
(ii) for the conductivity of the material in terms of the concentration of carriers in it.

Explain the terms:
(i) Drift velocity and
(ii) Carrier mobitlty.

Describe an experiment to determine the concentration of current carriers in a solid. Draw a neat sketch of the experimental arrangement. Derive the formula required for the computation of current carriers in a p-type semiconductor.

draw a neat energy band diagram of intrinsic semiconductor. Label the various energy levels. Prove that the Fermi levels lies lies at the middle of the bandgap.

Draw a neat energy band diagram of a p-n junction at equilibrium.
Explain the origin of the internal potential barrier eVo.

Draw a neat energy band diagram of a npn transistor biased for normal operation in common base configuration.
using the diagram explain how a large current can flow through the reverse-biased collector base junction.

State Fermi-Dirac function for the probability that a particle in an assembly has an energy E. Show that the probability of its occupancy by an electron is zerof E is greater than Ef and unity if E is less than Ef at temperature 0 degrees K. How does this change with temperature?

Why are holes not generated in a metal? can the electrical conductivity of a metal be altered to the extent possible in a semiconductor? Discuss.

The forbidden band gap in pure Silicon is 1.1 eV. compare the number of conduction electrons at temperature 27 degrees centigrade and 37 degrees centigrade.

Draw the energy band diagram for p-n junction in an unbiased condition and prove that the equilibrium contact potential Vo across the idealized junction is
KT/e log (Nn/Np)
where Nn and Np are conduction band electron densities in n-type and p-type segements of the p-n junction and all other symbols have the usual meanings.

Draw energy band diagram for p-n-p transistor under conditions of:
(i) No bias, (ii) Proper bias.

The saturation current in a reverse biased p-n junction is 5 microamperes. calculate the current across the junction when it is forward biased at 300 millivolts (Temperature of the junction is 27 degrres Centigrade).

How does the Fermi level changes with the increasing temperature in the extrinsic semiconductor? Sketch the diagram.

A sample of "Ge" is doped to the extent of 100000000000000000000 donor atoms/cubic metre and 70000000000000000000 acceptor atoms/cubic metre. At the temperature of the sample the resistivity of intrinsic Germanium is 0.6 ohm-m. If the applied electric field is 200 V/m, find the total conduction current density. Assume mobitily of electron = 0.38 and mobility of hole = 0.18 square metre/V.s.

What is Hall effect? Mention its importance in the field of semiconductors.

Obtain an expression for the Hall Coefficient for an extrinsic semiconductor. show that the result of the Hall effect may be used to deduce carrier concentration.

A copper strip 2.0 cm wide and 1.0 mm thick is placed in a magnetic field with B= 1.5 wb/square meter. if a current of 200 A is set up in the strip, calculate Hall voltage that appears across the strip.

Draw energy band diagram of p-type and n-type semiconductor at 0 degrees K and at room temperature.

Show that the probability that a state deltaE above the fermi level Ef is filled, equals the probability that a state deltaE below Ef is empty.

Find the fraction of electrons in the valence band of intrinsic germanium which can be thermally excited across the forbillen energy gap at 0.7 eV into the conduction band at:
(i) 50 Degrees K, (ii) 300 Degrees K, (iii) 1000 degrees K.

Draw energy band diagram of an unbiased pn junction in equilibrium and when forward bias is applied.

Derive the diode rectifier equation.

What is transistor? Why base is thin and lightly doped in a transistor? Explain the working of transistor as an amplifier.