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Numericals on semiconductors

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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 ... – PowerPoint PPT presentation

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Title: Numericals on semiconductors


1
Numericals on semiconductors
  1. 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
2
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)
3
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) ?
4
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
5
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
6
Numericals on semiconductors
  • 5

contd
Density of available state n (E)
7
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)
8
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)
9
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)
10
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
11
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

12
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

13
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
14
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
15
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
16
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
17
Numericals on semiconductors
Since the minority carrier concentration p lt ni
Conductivity is given by
From Ohms law
18
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
19
Numericals on semiconductors
  • From law of mass action

Electrical conductivity
20
Numericals on semiconductors
12 Contd

Resistance Of the Ge bar R
Voltage drop across the Ge bar
21
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)
22
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
23
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 ?

24
Numericals on semiconductors
  • 15 Contd
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