Quantum-Cascade Laser Quantum-Cascade Laser Laser a cascata quantica (QCL)Laser a cascata quantica (QCL)

Docente: Mauro MoscaDocente: Mauro Mosca

(www.dieet.unipa.it/tfl)(www.dieet.unipa.it/tfl)

Ricevimento: alla fine della lezione o per appuntamento

Università di Palermo – Facoltà di Ingegneria (DEIM)

A.A. 2013-14A.A. 2013-14

The inventor of QCLThe inventor of QCL

Federico Capasso

1994

Laser property depends on quantum-well width,NOT on materials!!

MBE

Banda di conduzione in un QCLBanda di conduzione in un QCL

injectorregion

activeregion

population inversion:

ULL

LLLDPL

The lower level lifetime has to be shorter than the upper level lifetimeThe energy cannot be greater than the conduction band offset

For the most favourable material system, AlGaAs/GaAs, energies are limited to a few tenths of 1 eV

The emission wavelength is independent of the band gap of the materials but dependent

on the width of the quantum wells

In mid-IR (5-20 µm)rapid relaxation from the LLLto the DPL is achieved by making theLLL-DPL energy separation the same asthe longitudinal optical phonon energy so that theprobability of relaxation by single phonon emission is high.

If resonant phonon emission can be used to depopulate the LLL then it can also depopulate the ULL!

If the emission energy of the laser is lowered by widening the quantum well so that the ULL-LLL energy separation approaches phonon resonance, the LLL-DPL separation will naturally move off the resonance, leaving a very short upper lifetime and a relatively longer lower lifetime.

If the ULL-LLL transition energy is reduced below the phonon energy then very careful engineering of the LLL-DPL energy level is necessary to ensure the scattering rate will allow population inversion.

Other relaxation mechanisms, such as electron-electron scattering, become important at such low subband separations

Wannier-Stark ladderWannier-Stark ladder

This is the “quantum”. Now… the “cascade”

An electron leaving the DPL enters the miniband states of the next injector region and is transported through the superlattice into the ULL at the other end

DPL

LLLULL

miniband

Under an applied field the miniband is not flat!...

The miniband breaks up into a series of discrete statescalled a Wannier-Stark ladderIt is necessary to design the injector region so that theelectron states of the interacting quantum wells align under the action of an electric field to produce a mini band that is essentially flat

achieved by grading the thicknesses of the layers and the composition

within the layers, so that under zero applied bias the band

offsets resemble more ofa saw-tooth structure

than a square well

The electrons are re-used in the lasing process,unlike the conventional diode laser where the band recombination removes the electron from the process

In electron transport problems of electron-electron and electron-

-phonon scattering haveto be considered

Differenze con i laser tradizionaliDifferenze con i laser tradizionali

The devices are unipolarThe devices are unipolar

Population inversion between sub-bands Population inversion between sub-bands of a quantum well system rather than of a quantum well system rather than between electron and hole statesbetween electron and hole states

no dependence of the lasing wavelength no dependence of the lasing wavelength on band gapon band gap

Emission wavelengths extend from the Emission wavelengths extend from the near IR to the very far IR, close to 100 µmnear IR to the very far IR, close to 100 µm

Guadagno in un QCL (unipolare) eGuadagno in un QCL (unipolare) ein un laser convenzionale (bipolare)in un laser convenzionale (bipolare)

In QCL the in-plane dispersion in each sub-band is of the same sign, unlike bipolar devices, so even if transitions occur between states at in-plane k ≠ 0 the wavelength is very similar to transitions at k = 0 andthe gain spectrum is correspondingly narrow

Bipolar devices have widely separated maximum andminimum transition energies caused by the separationof the Fermi levels

Similitudini con i laser tradizionaliSimilitudini con i laser tradizionali

Light emission occurs perpendicular to the Light emission occurs perpendicular to the direction of current flowdirection of current flow

Optical confinement is achieved through Optical confinement is achieved through the use of wave guiding structuresthe use of wave guiding structures

The cavity reflectors can be formed by The cavity reflectors can be formed by cleaving or through the fabrication of cleaving or through the fabrication of distributed Bragg reflectorsdistributed Bragg reflectors

Anti-crossingAnti-crossing

Panoramica di QCLPanoramica di QCL

Minibande nei super-reticoli:Minibande nei super-reticoli:modello di Kronig-Penneymodello di Kronig-Penney

We assume that the barrier thickness tends to zero in the limit as U0 tends to infinity and also that the effective masses are both unity

Minibande nei super-reticoliMinibande nei super-reticoliFor smaller values of P the bands will merge at lower values of kA a, but there will always be an energy gap at low energies

kA a

Stati super-reticolari Stati super-reticolari in una struttura periodica GaAs/AlGaAsin una struttura periodica GaAs/AlGaAs

fixed barrier width of 5 m

fixed well width of 5 m

- There are no band gaps at zero well-width

- The first band descend into the well immediately but thetop of the band descendsinto the well when thethickness is 1.7 nm- The band energy decreases with well width, as does the width of the band

(the electrons spend more time in the well than in the barriers, so the probability of communication with neighboring wells is much smaller)

- As the well width increases above 5.3 nm, the secondband descends into the well

-As the barrier width increases the band becomes progressively narrower until eventually it becomes adiscrete state at ~ 70 meV.

-At zero barrier width the band should conform to theGaAs band structure, and theband extends over the wholeenergy range of the well.

Laser a minibande o a super-reticolo Laser a minibande o a super-reticolo (continuum-to-continuum)(continuum-to-continuum)

- If the transitions take place between minibands rather than discrete subbands, the wavelength is determined principallyby the energy separation between the minibands

- Population inversion is easier to achieve in a superlattice active region provided the electron temperature is low enough for the bottom miniband to remain largely empty (if the electron temperature is too high then all the states in the miniband will be full and scattering between states will not occur)

- Similarly the doping level must be such that the Fermi levellies well below the top of the lower miniband

Laser a minibande o a super-reticolo Laser a minibande o a super-reticolo (bound-to-continuum)(bound-to-continuum)

- As well as inter-miniband transitions, structures can be designed so that transitions occur between a bound state and a miniband

- A chirped superlattice gives rise to minibands under theinfluence of an electric field

- No separation of the active and the injection regions occurs, as the lower laser level and the injector are in the same miniband

- However, a single narrow well placed at strategic points within the superlattice gives rise to a discrete state which acts as theupper laser level- Fast depopulation rate of the lower laser level

Guide d’onda nei QCLGuide d’onda nei QCL

- In waveguides based on the conventional refractive index difference the optical penetration into the cladding layers isproportional to the wavelength- If the cladding layer is not thick enough to contain the entire optical field some irreversible leakage out of the guide will occur- Therefore, structures several times thicker than the wavelength need to be grown- Heavily doped GaAs (n ≈ 5 × 1018 cm-3) has a plasma frequency around 11 µm, and around this wavelength the real part of the refractive index decreases- GaAs rather than AlGaAs has to be used because the thickness of AlGaAs is limited by residual strain (max thickness ≈ 1.5 µm)

- Waveguides for longer wavelengths utilise a particular property of thin metal films that at long wavelengths have the real part of the dielectric constant large and negative

- When bounded by a dielectric with a real and positive dielectric constant, they support an electromagnetic mode that propagates over large distances

- The condition on the dielectric constants is not so strict and modes will propagate over a wide variety of wavelengths

- Surface charge density on the metal is induced by the electric field and oscillates with it. It corresponds to the collective oscillation known as a plasmon, hence the guide is often called a surface plasmon guide

Guide d’onda nei QCL: plasmoniGuide d’onda nei QCL: plasmoni

Guide d’onda nei QCL: plasmoniGuide d’onda nei QCL: plasmoni

ApplicazioniApplicazioni

The high optical power output, tuning range and room temperatureoperation make QCLs useful for spectroscopic applications:

- remote sensing of environmental gases and pollutantsin the atmosphere

- homeland security

- vehicular cruise control in conditions of poor visibility

- collision avoidance radar

- industrial process control

- medical diagnostics such as breath analyzers

SommarioSommario