Numericals on semiconductors

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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
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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)
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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) ?
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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
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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
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Numericals on semiconductors

• 5

contd
Density of available state n (E)
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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)
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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)
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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)
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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
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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

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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

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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
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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
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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
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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
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Numericals on semiconductors
Since the minority carrier concentration p lt ni
Conductivity is given by
From Ohms law
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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
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Numericals on semiconductors

• From law of mass action

Electrical conductivity
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Numericals on semiconductors
12 Contd

Resistance Of the Ge bar R
Voltage drop across the Ge bar
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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)
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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
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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 ?

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Numericals on semiconductors

• 15 Contd