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Numericals on semiconductors

- Calculate the total number of energy states per

unit volume, in silicon, between the lowest level

in the conduction band and a level kT above this

level, at T 300 K. The effective mass of the

electron in the conduction band is 1.08 times

that of a free-electron.

The number of available states between Ec and (Ec

kT) is given by

Given (E-Ec) kT 1.38?10-23J/K ?300

Numericals on semiconductors

- 2 Calculate the probability that an energy level

(a) kT (b) 3 kT (c) 10 kT above the fermi-level

is occupied by an electron.

Probability that an energy level E is occupied

is given by f(E)

For (E-EF) kT , f(E)

For (E-EF) 3kT, f(E)

For (E-EF) 10kT, f(E)

Numericals on semiconductors

- 3 The fermi-level in a semiconductor is 0.35 eV

above the valence band. What is the probability

of non-occupation of an energy state at the top

of the valence band, at (i) 300 K (ii) 400 K ?

The probability that an energy state in the

valence band is not occupied is

(i) T300K

1-f(E)

Alternate method for EF-EV gt kT

1- f(E) ?

(ii) T400K

1-f(E) ?

Numericals on semiconductors

- 4 The fermi-level in a semiconductor is 0.35 eV

above the valence band. What is the probability

of non-occupation of an energy state at a level

kT below the top of the valence band, at (i) 300

K (ii) 400 K?

The probability that an energy state in the

valence band is not occupied is

for EF- E gt kT

(i) T300K

1 - f(E)

(ii) T400K

1- f(E) ?

Note (E -EF) is -ve

Numericals on semiconductors

- 5 For copper at 1000K (a) find the energy at

which the probability P(E) that a conduction

electron state will be occupied is 90. (b) For

this energy, what is the n(E), the distribution

in energy of the available state? (c) for the

same energy what is n0( E) the distribution in

energy of the occupied sates? The Fermi energy is

7.06eV.

The fermi factor f(E)

0.90

Numericals on semiconductors

- 5

contd

Density of available state n (E)

Numericals on semiconductors

- 5contd

The density of occupied states is (The density

of states at an energy E ) ?( probability of

occupation of the state E)

i.e no (E) n (E) f(E)

Numericals on semiconductors

- 6 An intrinsic semiconductor has energy gap of

(a) 0.7 eV (b) 0.4 eV. Calculate the probability

of occupation of the lowest level in the

conduction band at (i) 0?C (ii) 50?C (iii) 100?C.

?

f(E)

a) (i)

(ii)

(iii)

Numericals on semiconductors

- 6 An intrinsic semiconductor has energy gap of

(a) 0.7 eV (b) 0.4 eV. Calculate the probability

of occupation of the lowest level in the

conduction band at (i) 0?C (ii) 50?C (iii) 100?C.

f(E)

?

b) (i)

(ii)

(iii)

Numericals on semiconductors

- 7 The effective mass of hole and electron in

GaAs are respectively 0.48 and 0.067 times the

free electron mass. The band gap energy is 1.43

eV. How much above is its fermi-level from the

top of the valence band at 300 K?

Fermi energy in an Intrinsic semiconductor is

Write

?

? The fermi level is 0.75eV above the top of the

VB

Numericals on semiconductors

- 8 Pure silicon at 300K has electron and hole

density each equal to1.5?1016 m-3. One of every

1.0 ?107 atoms is replaced by a phosphorous atom.

(a) What charge carrier density will the

phosphorous add? Assume that all the donor

electrons are in the conduction band. (b) Find

the ratio of the charge carrier density in the

doped silicon to that for the pure silicon.

Given density of silicon 2330 kg m-3 Molar

mass of silicon 28.1 g/mol Avogadro constant

NA 6.02 ?10 23 mol -3.

No of Si atoms per unit vol

Carriers density added by P

Ratio of carrier density in doped Si to pure Si

Numericals on semiconductors

- 9 The effective mass of the conduction electron

in Si is 0.31 times the free electron mass. Find

the conduction electron density at 300 K,

assuming that the Fermi level lies exactly at the

centre of the energy band gap ( 1.11 eV). - Electron concentration in CB is

Numericals on semiconductors

- 10 In intrinsic GaAs, the electron and hole

mobilities are 0.85 and 0.04 m2 V-1s-1

respectively and the effective masses of

electron and hole respectively are 0.068

and 0.50 times the electron mass. The

energy band gap is 1.43 eV. Determine the

carrier density and conductivity at 300K.

Intrinsic carrier concentration is given by

ni

Numericals on semiconductors

- 10 In intrinsic GaAs, the electron and hole

mobilities are 0.85 and 0.04 m2 V-1s-1

respectively and the effective masses of

electron and hole respectively are 0.068

and 0.50 times the electron mass. The

energy band gap is 1.43 eV. Determine the

carrier density and conductivity at 300K. - Conductivity of a semiconductor is given by

mho / m

Numericals on semiconductors

- 11 A sample of silicon at room temperature has an

intrinsic resistivity of 2.5 x 103 ? m. The

sample is doped with 4 x 1016 donor atoms/m3 and

1016 acceptor atoms/m3. Find the total current

density if an electric field of 400 V/m is

applied across the sample. Electron mobility is

0.125 m2/V s. Hole mobility is 0.0475 m2/V.s.

Effective doped concentration is

Numericals on semiconductors

- From charge neutrality equation

From law of mass action

Solving for p and choosing the right value for p

as minority carrier concentration

Numericals on semiconductors

Since the minority carrier concentration p lt ni

Conductivity is given by

From Ohms law

Numericals on semiconductors

- 12 A sample of pure Ge has an intrinsic charge

carrier density of 2.5 x 1019/m3 at 300 K. It is

doped with donor impurity of 1 in every 106 Ge

atoms. (a) What is the resistivity of the

doped-Ge? Electron mobility and hole mobilities

are 0.38 m2/V.s and 0.18 m2/V.s . Ge-atom

density is 4.2 x 1028/m3. (b) If this Ge-bar is

5.0 mm long and 25 x 1012 m2 in cross-sectional

area, what is its resistance? What is the

voltage drop across the Ge-bar for a current of

1?A? - No of doped carriers

Since all the atoms are ionized, total electron

density in Ge ? Nd 4.2 x 10 2 2 /m3

Numericals on semiconductors

- From law of mass action

Electrical conductivity

Numericals on semiconductors

12 Contd

Resistance Of the Ge bar R

Voltage drop across the Ge bar

Numericals on semicodnuctors

- 13 A rectangular plate of a semiconductor has

dimensions 2.0 cm along y direction, 1.0 mm along

z-direction. Hall probes are attached on its two

surfaces parallel to x z plane and a magnetic

field of 1.0 tesla is applied along z-direction.

A current of 3.0 mA is set up along the x

direction. Calculate the hall voltage measured

by the probes, if the hall coefficient of the

material is 3.66 ? 104m3/C. Also, calculate the

charge carrier concentration. - Hall voltage is given by

Charge carrier density

Z (B)

Numericals on semiconductors

- 14 A flat copper ribbon 0.330mm thick carries a

steady current 50.0A and is located in a uniform

1.30-T magnetic field directed perpendicular to

the plane of the ribbon. If a Hall voltage of

9.60 ?V is measured across the ribbon. What is

the charge density of the free electrons? - Charge carrier density n is given by

n

Numericals on semiconductors

- 15 The conductivity of intrinsic silicon is 4.17

x 105/? m and 4.00 x 104 / ? m, at 0 ?C and

27 ?C respectively. Determine the band gap

energy of silicon. - Intrinsic conductivity ?

Numericals on semiconductors

- 15 Contd