Semiconductor Electronic Structure & Optical Processes

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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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


3/18


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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Gain in Se/cGain= emission coefficient absorption coefficient

proportional to fe

fh

proportional to (1-fe)( 1-fh)

Energies in the expression:

Ref: Singh


5/18


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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Gain vs. Injection Density: GaAs

Ref: Singh


7/18


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


8/18


p-ndiode: Backbone for both LED & LD

Non-radiative

recombination

(defects/Auger)

should be

minimized!

Ref: Singh


9/18


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


10/18


Ref: Singh


11/18


Auger Processes in BulkAuger rate: undern=p

Auger coef.

Ref: Singh

This process becomes very

effective forEg


12/18


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


13/18


Modal gain: fraction of optical intensity

overlapping with the gain medium

Transparency

condition

Ref: Singh

material gain


14/18


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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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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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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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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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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Semiconductor Electronic Structure & Optical Processes