Extrinsic Semiconductors

1
Extrinsic Semiconductors
2
n-type Semiconductor

• Antimony, phosphorus, and arsenic donate excess
  electron carriers and are referred to as donor,
  or n-type, impurities
• The number of electrons increases and the number
  of holes decreases below that which would be
  available in the intrinsic semiconductor.
• The number of holes decreases because the larger
  number of electrons present causes the rate of
  recombination of electrons with holes to increase
• The dominant carriers are the negative electrons

3
(No Transcript)
4
(No Transcript)
5
p-type Semiconductor

• Boron, gallium, and indium are trivalent atoms
  that provide electrons to fill only three
  covalent bonds. The vacancy that exists in the
  fourth bond constitutes a hole
• This type of impurity makes positive carriers
  available because it creates holes which can
  accept electrons.
• Called acceptors and form p-type semiconductors
  in which holes are the predominant carriers

6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
Mass-Action law

• Under thermal equilibrium, the product of the
  free negative and positive concentrations is a
  constant independent of the amount of donor and
  acceptor impurity doping. This relationship is
  called the mass-action law and is given by
• Majority and minority carriers

10
Carrier concentration

• Let ND be the concentration of donor atoms and NA
  the concentration of acceptor atoms.
• Since these impurities are practically all
  ionized, they produce positive-ion and
  negative-ion densities of ND and NA,
  respectively.
• To maintain the electric neutrality of the
  crystal,
• ND p NA n
• Let us now consider an n-type material having NA
  0.
• Since (n gt p)
• n ND
• In an n-type material the free-electron
  concentration is approximately equal to the
  density of donor atoms.

11

• The concentration p of holes in the n-type
  semiconductor is obtained as
• Similarly, in a p-type semiconductor, with ND
  0, we have p NA

12
Example

• An n-type silicon bar
• L3 mm , A (rectangular) 50100 µm
• AT 300 K, donor concentration is 51014 cm-3
• determine the electron and hole concentrations,
  the conductivity and V across the bar when I1 µA
  exists in the bar

13
Solution
14

• It is possible to add donors to a p-type crystal
  or, conversely, to add acceptors to n-type
  material. If equal concentrations of donors and
  acceptors permeate the semiconductor, the
  semiconductor remains intrinsic.
• If the concentration of donor atoms add to a
  p-type semiconductor exceeds the acceptor
  concentration (ND gt NA), the specimen is changed
  from a p-type to an n-type semiconductor.
  Conversely, the addition of a sufficient number
  of acceptors to an n-type sample results in a
  p-type semiconductor.

15
Generation and Recombination of Charges

• In an intrinsic semiconductor the number of holes
  is equal to the number of free electrons. Thermal
  agitation, however, continues to generate g new
  hole-electron pairs per unit volume per second,
  while other hole-electron pairs disappear as a
  result of recombination.
• On an average, a hole (an electron) will exist
  for ?p (? n) seconds before recombination. This
  time is called the mean lifetime of the hole
  (electron).

16
VARIATIONS IN THE PROPERTIES OF SILICON

• The conductivity of a semiconductor depends on
  both p and n and µp andµn. Because semiconductor
  devices are subject to a wide range of operating
  temperatures, the variations of these parameters
  with temperature are important.

17
Intrinsic Concentration

• With increasing temperature, the density of
  hole-electron pairs increases in an intrinsic
  semiconductor.
• where
• EG0 is the energy gap (the energy required to
  break a covalent bond) at 0 K in electron volts,
• k is the Boltzmann constant in electron volts per
  degree kelvin (eV/K)
• Ao is a constant independent of T.

18
Mobility

• Mobility µ decreases with temperature
• Mobilities are also functions of the electric
  field intensity and doping levels.
• In n-type silicon, µ is constant at a given
  temperature only if ? lt 103 V/cm.
• For ? gt 104 V/cm, µn is inversely proportional to
  ? and drift velocities approach 107 cm/s
• Between 103 and 104 V/cm, µn varies
  approximately as ?-1/2 .

19
Conductivity

• The conductivity of an intrinsic semiconductor
  increases with increasing temperature because the
  increase in hole-electron pairs is greater than
  the decrease in their mobilities.
• For extrinsic semiconductors, in the temperature
  range 100 to 600 K, the number of majority
  carriers is nearly constant but diminished
  mobility causes the conductivity to decrease with
  temperature.

20
DIFFUSION

• It is possible to have a nonuniform concentration
  of particles in a semiconductor. .
• concentration gradient dn/dx in the density of
  carriers
• In a given time interval, more electrons will
  cross the surface from the side of greater
  concentration to the side of smaller
  concentration than in the reverse direction. This
  constitutes a current in the positive x
  direction.

21

• where Dn (m2 /sec) is called the diffusion
  constant for electrons.
• Repeating the same derivation for holes yields

22
Total Current

• It is possible for both a potential gradient and
  a concentration gradient to exist simultaneously
  within a semiconductor. In such a situation the
  total electron current density is
• And
• The total current

23
The Einstein Relationship

• Since both diffusion and mobility are statistical
  thermodynamic phenomena, D and µ are not
  independent. The relationship between them is
  given by the Einstein equation
• where VT is the "volt equivalent of temperature
  defined by
• where k is the Boltzmann constant in joules per
  Kelvin.