semiconductor electronic structure & optical processes
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
More Details: Occupancy, Gain, Nonradiative
Processes
More Exotic Lasers:VCSELs, QCLs
In This Lecture:
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Take into Account State Occupancy:
f(E): occupation probability at the energy E
transition must be from an occd to unoccd state
i,f
under parabolic approximation, the upper subband is
only shifted verrtically upward by E2-E
1
Assume the 2nd subband to be empty; the sum over final states is
zero except at the resonance
e concentration in the 1st subband
Delta fn absorption at resonance
Wabs
E2-E1
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Take into Account Broadening:In reality, the nonparabolicity and scattering mechanisms introduce
broadening to the absorption spectrum
Assume a Gaussian broadening:
Absorption coefficient for
z-polarized light:
NB: There is no absorption for vertically-incident (x-y pold) light; extra mirrors
need to be introduced for polarization conversion; this is the main drawback in
quantum well intersubband photodetectors (QWIPs)
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Gain in Se/cGain= emission coefficient absorption coefficient
proportional to fe
fh
proportional to (1-fe)( 1-fh)
Energies in the expression:
Ref: Singh
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
In equilibrium: EF(Fermi level)
Under carrier injection: Efn, Efp (quasi-Fermi level)
( ) ( )
Then ( ) 0 and ( ) 0
So that
e e h h f E f E
g =
A positive value of gain occurs for a particular energy when:
population inversion condition
In this case a light wave passing through the material grows instead ofattenuating.
Mind that this is at the expense of constant DC carrier injection (i.e., DC power).
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Gain vs. Injection Density: GaAs
Ref: Singh
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
LEDs vs. Laser DiodesLEDs:
Spontaneous emission (triggered by the vacuum fluctuations)
Emitted photons have a random phase -- incoherent
Spectral width is broadIntensity is low
LDs:
Stimulated emission (triggered by the existing photons)
Emitted photons have phase coherence
Spectral width is narrowIntensity is high
Ref: Singh
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
p-ndiode: Backbone for both LED & LD
Non-radiative
recombination
(defects/Auger)
should be
minimized!
Ref: Singh
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Nonradiative RecombinationNonradiative processes produce (eventually) phonons (i.e., heat) instead of
light and can occur through defect levels or through the Auger processes
Defect Capture:
Nonradiative trapping rate to a
defect state is given by:
where
where we are assuming:
Capture x-section
defect density
Shockley-Read-Hall:
carrier velocity
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Ref: Singh
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Auger Processes in BulkAuger rate: undern=p
Auger coef.
Ref: Singh
This process becomes very
effective forEg
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
LED
LDHow to achieve lasing out of ap-njunction?
Enclose the structure in an optical cavity (Fabry-Perot)
Increase the pumping/injection beyond transparency
Cavity: Just a polished
surface and index
difference between air
and say GaAs is enough
Ref: Singh
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Modal gain: fraction of optical intensity
overlapping with the gain medium
Transparency
condition
Ref: Singh
material gain
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
VCSEL: Vertical Cavity Surface Emitting Laser
Ordinary LEDs and LDs are edge emitters:
A much more convenient structure is the VCSEL (pronounced as vixel)
Cavity: Distributed
Bragg Reflectors
Light out
Light out
p-type
n-type
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Advantages of VCSELs The structure can be integrated in two-dimensional array configuration. Low threshold currents enable high-density arrays.
Surface-normal emission and nearly identical to the photo detector geometry
give easy alignment and packaging.
Circular and low divergence output beams eliminate the need for corrective optics.
Passive versus active fiber alignment, combined with high fiber-coupling efficiency.
Low-cost potential because the devices are completed and tested at the wafer level.
Lower temperature-sensitivity compared to edge-emitting laser diodes.
High transmission speed with low power consumption.
VCSELs have been constructed that emit energy at 850 nm and 1300 nm.
Common se/c VCSELs: GaAs, AlGaAs, GaInNAs
The main challenge facing engineers today is the development of a high-power
VCSEL device with an emission wavelength of 1550 nm.
Current Status of VCSELs
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8/6/2019 Semiconductor Electronic Structure & Optical Processes
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Quantum-Cascade Lasers A quantum-cascade (QC) laser is based on intraband (better called
intersubband)-transitions of electrons inside a QW.
Unlike other semiconductor light sources, the emitted wavelength is not
determined by the band gap of the used material but on the thickness of
the constituent layers.
Idea at least goes back to 1971, Kazarinov & Suris (Ioffe) who proposed
population inversion by tunelling injection.
Faist & Capasso (Bell) in 1994 demonstrated the first QC laser.
Ref: Lucent-web
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
QC Lasers: Operation
Ref: C. Gmachl et al. Rep. Prog. Phys. 64, 1533 (2001)
Applied DC field causing the
slope and resonant tunelling
Carrier scatterings
and intersubband
dynamics becomevery important
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C. Bulutay Lecture 18Semiconductor Electronic Structure & Optical Processes
Conventional vs. QC Lasers An e-h pair is exhausted at each emission
Both es and hs take part: bipolar device
Wavelength controlled by material band gap
Different wavelength requires different material
One e can emit multiple photons (~10) It is a unipolar device
Wavelength controlled by QW width (design)
Output energy depends on the # cascade stages
THz frequencies can be reached (no conventional laser)
Ideal for trace chemical pollutant detection etc.
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