a Vd8'0104 Vm0'50 m4'0104 V

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Example A proton moves from rest in an electric
field of 8.0?104 V/m along the x axis for 50 cm.
Find a) the change in in the electric potential,
b) the change in the electrical potential
energy, and c) the speed after it has moved 50
cm.

• a) ?V-?d-(8.0?104 V/m)(0.50 m)-4.0?104 V
• b) ?Uq ?V(1.6?10-19 C)(-4.0 ?104 V)-6.4 ?10-15
  J

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• KEiUiKEfUf,
• KEi0
• KEfUi-U?U,
• mpv2/26.4?10-15 J
• mp1.67?10-15 kg

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The Concept of a Potential-Energy Barrier
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The Concept of a Potential-Energy Barrier
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CONDUCTION IN METALS

• In a metal the valence electrons of an atom are
  as much associated with one ion as with another,
  so that the electron attachment to any individual
  atom is almost zero.
• Depending on the metal, at least one (and
  sometimes two or three) electron (or electrons)
  per atom is (are) free to move throughout the
  interior of the metal under the action of applied
  fields

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• A metal is visualized as a region containing a
  periodic three-dimensional array of heavy,
  tightly bound ions permeated with a swarm of
  electrons that may move about quite freely.
  (electron-gas description of a metal.)
• Mean free path
• Total current is zero

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• if a constant electric field ? is applied to the
  metal
• A steady-state condition is reached when an
  average value of drift velocity vd is attained
  its direction is opposite to that of the electric
  field
• The speed between two collisions is
• Where
• Hence
• where µ is called the mobility (m2/voltsec)

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Current Density

• N electrons are distributed uniformly throughout
  a conductor of length L and cross-sectional area
  A. An electron, under the influence of an
  electric field ? travels L meters in T seconds,
• thus
• The current I is

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• The current density is
• LA is the volume containing the N electrons. The
  volume concentration of electrons or simply the
  electron concentration n is then
• Where ? is the charge density in C/m3

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• Where is the
  conductivity of the material

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Example

• A conducting line on an IC chip is 2.8 mm long
  and has a rectangular cross section 1 x 4 µm. A
  current of 5 mA produces a voltage drop of 100 mV
  across the line. Determine the electron
  concentration given that the electron mobility is
  500 10-4

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Solution
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THE INTRINSIC SEMICONDUCTOR

• Silicon, germanium, and gallium arsenide are the
  three most widely used semiconductors.
• The crystal structure of silicon consists of a
  regular repetition in 3D of a unit cell having
  the form of a tetrahedron with an atom at each
  vertex.

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• Silicon has a total of 14 electrons in its atomic
  structure,
• 4 valence electrons,
• The binding forces between neighboring atoms
  result from the fact that each valence electron
  of a silicon atom is shared by one of its four
  nearest neighbors.

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2D representation
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The Hole

• At a very low temperature (say, 0 K) the crystal
  behaves as an insulator
• At room temperature, some of the covalent bonds
  will be broken because of the thermal energy
  supplied to the crystal, and conduction is made
  possible.
• The absence of the electron in the covalent bond
  is represented by the small circle and is called
  a hole. The hole serves as a carrier of
  electricity comparable in effectiveness with the
  free electron.

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The mechanism by which a hole contributes to the
conductivity

• Holes move one more step in the direction
  opposite to the motion of the electron.
• A mechanism for the conduction of electricity
  which does not involve free electrons.
• The motion of the hole in one direction actually
  means the transport of a negative charge an equal
  distance in the opposite direction.

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Conduction in Intrinsic Semiconductors

• The crystal structure displayed assumed a pure
  sample of silicon that is, the sample contains
  no foreign atoms. Such pure crystals are called
  intrinsic semiconductors
• breaking a covalent bond results in both a free
  electron and a hole
• Hole concentration p and electron concentration n
  must be equal and
• p n ni
• Where ni is the intrinsic concentration
  (temperature dependent)

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• The current density J that results from an
  electric field ? is
• And the conductivity is
• For intrinsic semiconductors

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Properties of intrinsic Silicon
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Example

• An intrinsic silicon bar
• L3 mm , A (rectangular) 50100 µm
• AT 300 K, determine ? in the bar and V across the
  bar when I1 µA is applied

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Solution