Carrier Transport Phenomena

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Chapter 3

• Carrier Transport Phenomena

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Carrier Transport Phenomena

• Carrier drift
• Carrier diffusion
• Generation and recombination
• Continuity equation
• Thermionic emission process
• Tunneling process
• High-field effects
• Summary

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Carrier drift

• Mobility
• Mean free time
• mean free path
• drift velocity
• lattice scattering
• impurity scattering
• Resisitivity
• Drift current
• Four-point probe
• The Hall effect

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Mobility

• Mean free path
• The average distance between collisions.
• Mean free time
• The average time between collisions.
• The electron mobility ?n in units of cm2/V-s
• For hole, ?p?p?

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Lattice scattering

• Thermal vibrations of lattice atoms
• Disturbing the lattice periodic potential
• Allowing energy to be transferred between the
  carriers and the lattice
• Becoming dominant at high temperature
• ?L?T-3/2

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Impurity scattering

• When a charge carrier travels past an ionized
  dopant impurity
• The charge carrier will be deflected owing to
  Coulomb force interaction
• Dependent on the total concentration of ionized
  impurities
• Becoming less significant at higher temperature
• Higher temperature, move faster, remain near the
  impurity atom for a shorter time
• ?I?T3/2/NT

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Scattering
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Conduction process
Drift current The transport of carriers
under the influence of an
applied electric field
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Drift current resistivity
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Four-point probe method
CF correction factor, 4.54 when d/s gt 20
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Resistivity versus impurity concentration for Si
and GaAs.
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The Hall effect

• The carrier concentration may be different from
  the impurity concentration
• To measure the carrier concentration directly
• To show the existence of holes as charge carrier
• Give directly the carrier type
• RH Hall coefficient

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Carrier diffusion

• Diffusion process
• Diffusion coefficient (diffusivity)
• Einstein relation
• Current density equations

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Diffusion process
If there is a spatial variation of carrier
concentration in the semiconductor material. The
carriers tend to move from a region of high
concentration to a region of low Concentration .
The current component is called diffusion
current.
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Einstein relation
From the equipartition of energy
It relates the two important constant
(diffusivity and mobility) that characterize
Carrier transport by diffusion and by drift in a
semiconductor.
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Current density equations

• When an electric field is present in addition to
  a concentration gradient
• Both drift current and diffusion current will
  flow
• Total current is the sum of Jdrift and Jdiff
• Important under low electric field
• At sufficient high electric field
• ?n? and ?p? should be replaced by the saturation
  velocity ?s

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Generation and recombination process

• Direct recombination
• Generation rate, recombination rate, minority
  carrier life time
• Indirect recombination
• Recombination centers, capture cross section
• Surface recombination
• Surface states, low-injection surface
  recombination velocity
• Auger recombination

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Generation and recombination process

• At thermal equilibrium
• Then pnni2
• Nonequilibrium
• If carrier injection, pngtni2
• By thermal, light, or forward bias
• Restore equilibrium
• Release energy
• Emitted as a photon or dissipated as heat to the
  lattice
• Direct recombination or indirect recombination

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Direct recombination
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Decay of photoexcited carriers
The B.C.
Solution
This illustrates the main idea of measuring -the
carrier life time using photoconductivity
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Indirect recombination
Assume the same electron and hole capture
Under a low-injection condition in an n-type, So
that nngtgtpn
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Surface recombination
Us??th?pNst(ps-pno) Slr? ?th ?pNst
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Auger recombination

• Electron hole pair recombination
• Transfer the energy or momentum to a third
  particle (electron of hole)
• Example
• Direct recombination
• release energy
• a second electron in the conduction band absorbs
  the energy
• become a energetic electron
• lose its energy to the lattice by scattering
  events
• Important at high doping or high injection level
• RAugBn2p or Bnp2
• The Auger process involves three particles

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Continuity equation

• Steady-state injection from one side
• Minority carrier at the surface
• The Haynes-Shockley experiment

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Continuity equation
Poissons equation
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Steady state injection from one side
B. C.
Solution
B. C.
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Minority carrier at the surface
The surface recombination leads to a
lower -concentration at the surface. This
gradient of hole concentration yields
a -diffusion current density that is equal to the
-surface recombination current
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The Haynes-Shockley experiment
Localized light pulses generate excess
carriers After a pulse, by setting GL0 and
??/?x0
If no field is applied along the sample, the
solution is
If an electric field is applied along the
sample -x is replaced by x-?p?t All the excess
carriers move toward the negative -end of the
sample with the drift velocity ?p?
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Carrier transport

• Inside the bulk semiconductor
• Drift, diffusion
• At the semiconductor surface
• Carriers may recombine with the recombination
  center (dangling bonds)
• Thermionic emission process
• Tunneling process

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Thermionic emission process

• If the carriers have sufficient energy, they may
  be thermionically emitted into the vacuum.
• If an electron its energy is larger than q?, can
  be thermionically emitted into the vacuum.
• The electron density

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Tunneling Process
The behavior of a particle in the region qV(x)0
The solution are
Inside the potential barrier, the wave equation
is
The solution for EltqVo is
The transmission coefficient
The transmission coefficient decreases
monotonically as E decreases
When ?dgtgt1, then
Small d, low potential, and small effective mass
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High-field effects

• At low electric field
• ???
• ?c is independent of electric field
• As the drift velocity approaches the thermal
  velocity

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Drift velocity versus electric field

• For n-GaAs
• There is a region of negative differential
  mobility
• Due to the energy band structure of GaAs
• Allowing the transfer of conduction electrons
  from a high-mobility energy minimum to
  low-mobility, higher-energy satellite valleys.
• Electron transfer from the center valley to the
  satellite valleys along the 111 direction

Figure 3.22. Drift velocity versus electric
field in Si and GaAs. Note that for n-type GaAs,
there is a region of negative differential
mobility.8,9
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Two valley model
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One possible ?-? characteristic of a two-valley
semiconductor

• If ?1?a is larger than?2?b
• There is a region in which the drift velocity
  decreases with an increasing field
• This material is used in microwave
  transfer-electron devices.

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The avalanche process

• If the electric is field high enough
• The electron gain kinetic energy
• Impact with the lattice
• Break a bind (to ionize a valence electron from
  the valence band to the conduction band, generate
  an e-h pair)
• Also referred to as the impact ionization process

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Ionization energy
After collision, there three carriers the
original electron plus and -electron-hole
pair If the three carriers the same effective
mass, kinetic energy, momentum. To conserve both
energy and momentum before and after the
collision.
Eo must be larger than the bandgap .for the
ionization process to occur. For silicon, Eo3.6
eV for electrons 5.0eV
for holes
Then
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Ionization rate

• The number of electron-hole pairs generated by an
  electron per unit distance traveled
• Ionization rate ?n, ?p
• This expression can be used in the continuity
  equation for device operation under an avalanche
  condition