EE 60556: Fundamentals of Semiconductors Lecture Note

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EE 60556 Fundamentals of SemiconductorsLecture
Note 23 (11/18/09)Absorption, recombination,
and quasi-Fermi level

• Outline
• Last class electron motions in electric and
  magnetic fields
• Energy dependence of absorption coefficient
• Quasi-Fermi level
• Recombination
• Schockley-Reed-Hall (defect assisted
  recombination) more reading from Pierret Ch.5
• Auger recombination
• XPS, another example of high energy particle
  exciting electrons inside the material.
• X-ray photoelectron spectroscopy
• Beer-Lamberts law (did not get to cover it in
  class)
• Reading materials Pierret Ch.5
• Note that we discuss only several most
  important phenomena here. For more details,
  refer to textbook Pierret Ch.5 and other
  references including Kittel.

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Example CdSe nanowire - based photodetectors

• Polarization sensitive photodetectors based on
  solution-synthesized semiconductor nanowire based
  quantum-wire solids.
• A. Singh, X. Liu, G. Galantai, V. Protasenko, M.
  Kuno, H. Xing D. Jena. Nano. Lett., (2007).

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Absorption coefficients of some semiconductor
materials. The indirect-gap materials are shown
with a broken line. Based on data from References
1 and 2. Figure 11.4
Difference between indirect and direct bandgap
semiconductors?
Absorption coefficients Its dependence on energy
depends on DOS and what particles are involved in
the absorption processes?
1 µm absorption length.
low absorption therefore very thick Si is
necessary in the solar cells.
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Major absorption mechanisms I allowed direct
transitions
Joint density of states Absorption coefficient
Pankove (optional reading, contact me if you are
interested in knowing more)
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Example direct transition dominated absorption -
GaAs

• Theory and experiments agree reasonably well
• The bandgap can be extracted from the fit,
  1.43 eV _at_ RT
• Deviation in the energy range just below
  bandgap. Ideally, there should be no absorption.
  Why in reality there is always a band tail?

• Culprits
• Impurties move the band edge up and down
  randomly in the crystal
• Deformation potential because impurities have
  difference size from the host atom
• Other defects.

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Major absorption mechanisms II indirect
transition between indirect valleys
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II energy square dependence
A correction from class Square root of
absorption coeff. is proportional to energy, not
absorption coeff.
Note the difference in scale one is linear plot
and the other is semilog plot
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Quasi Fermi Level
In dark
Under superbandgap illumination
EC EFn Ei EFp EV
EC EFEFnEfp Ei EV
EC EFn Ei EFp EV
Weak illumination Majority carrier conc. stays
about the same Minority carrier conc. changes
substantially
Strong illumination Both majority carrier conc.
minority carrier conc. change substantially
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XPS x-ray photoelectron spectroscopy
Photoelectron energy
An example XPS spectrum
Sketch of an example energy Band distribution in
a semiconductor

• X-ray beam bounces off from the material
• Photoelectrons are generated (Einstein won his
  Nobel prize for the photoelectron effect)
• Luminescence (some of them may be in the visible
  range so that we can see them)

Images from wikipedia.com
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Terminology

• Photoluminescence radiative emission as a result
  of optical excitation
• Electroluminescence radiative emission as a
  result of electrical excitation
• Cathodoluminescence radiative emission as a
  result of electron excitation
• Chemiluminescence radiative emission as a result
  of chemical reaction
• Triboluminescence radiative emission as a result
  of mechanical excitation
• Fluorescence luminescence that occurs only
  during excitation
• Phosphorescence luminescence that continues for
  some time after the excitation is terminated.

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Generation processes
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Recombination processes
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What is this staircase energy loss process?

• I got an excellent question from the class that I
  want to share with you.
• when I said a hot electron (i.e. not in thermal
  equilibrium) losses its excessive energy
  (measured by how far it is above the band edge),
  it emits lots of phonons, therefore, the
  staircase like steps in the band diagram).
• The question is, why can not the electron emit
  photons?

The answer lies in, we need to scrutinize the
electron transition from one state to anther in
the E-k diagram! As shown on the left, it is
nearly impossible for photon to meet the
requirement in this process both energy and
momentum need to be conserved! Recall, photons
have smaller momentum than electrons for the same
energy That is why in this process, electron
loses its energy within the band by emitting
phonons not photons.
E
k
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Energy band diagram of the semiconductor of
Figure 3.18, under electrical bias and optical
illumination. The combination rate R, thermal
generation rate Gth, and the optical generation
rate Gop are illustrated. Figure 3.19

• Resistance changes with optical illumination
  intensity
• Photodetectors based on photo conductivity
• How to calculate Gop?
• We can measure how many photons (cm-2s-1, Flux)
  impinge on the sample surface. But do we convert
  it into Gop, per volume?
• If we know how photon flux (equivalently optical
  power) varies along the sample depth, assuming
  every photon is absorbed to generate
  Electron-Hole Pair (EHP), we know Gop!
• Therefore, we need this Beer-Lamberts Law
• We will have to measure carrier lifetime t
  separately. Then we can calculate the net
  carriers generated under steady state ?n?p.

Anderson