GRADED SEMICONDUCTORS

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GRADED SEMICONDUCTORS

• Assume thermal equilibrium and that no carriers
  are injected into the sample from any external
  source (zero excitation)
• Setting JP 0 and using the Einstein
  relationship we obtain

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• If the doping concentration p(x) is known and
• Hence
• Integration (from x1 to x2)

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• The previous equation may be expressed in the
  form
• (Boltzman relationship of kinetic gas theory)
• Also

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• Multiplying both equations

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An Open-Circuited Step-Graded Junction

• a builtin potential between these two sections
  called the contact difference of potential Vo

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• because p1 ppo thermal equilibrium hole
  concentration in the p side and
• p2 pno thermal equilibrium hole
  concentration in the n side.
• But ppo NA, and pno ni2 /ND, so that

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CHAPTER 2
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PN junction

• If you take a block of silicon and dope half of
  it with acceptors and the other half with donors,
  a boundary called-the pn junction is formed
  between the resulting p-type and n-type portions.
  
• The pn junction is the feature that allows
  diodes, transistors, and other devices to work.

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• The p region has many holes (majority carriers)
  from the impurity atoms and only a few electrons
  (minority carriers). The n region has many free
  electrons (majority carriers) from the impurity
  atoms and only a few holes (minority carriers).

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Formation of the Depletion Region

• the free electrons in the n region are randomly
  drifting in all direction At the instant of the
  pn junction formation, the free electrons near
  the junction in the n region begin to diffuse
  across the junction into the p region where they
  combine with holes near the junction

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• The term depletion refers to the fact that the
  region near the pn junction is depleted of charge
  carriers (electrons and holes) due to diffusion
  across the junction.
• After the initial surge of free electrons across
  the pn junction, the depletion region has
  expanded to a point where equilibrium is
  established and there is no further diffusion of
  electrons across the junction.

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Barrier Potential

• Any time there is a positive charge and a
  negative charge near each other, there is a force
  acting on the charges as described by Coulomb's
  law. In the depletion region there are many
  positive charges and many negative charges on
  opposite sides of the pn junction.
• The forces between the opposite charges form an
  electric field.
• This electric field is a barrier to the free
  electrons in the n region.
• External energy must be applied to get the
  electrons to move across the barrier of the
  electric field in the depletion region. .

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