9. Semiconductors Optics Absorption and gain in semiconductors Principle of semiconductor lasers (diode lasers) Low dimensional materials: Quantum wells, wires and dots Quantum cascade lasers Semiconductor detectors

Semiconductors Optics Semiconductors in optics: Light emitters, including lasers and LEDs Detectors Amplifiers Waveguides and switches Absorbers and filters Nonlinear crystals

One atomTwo interacting atomsN interacting atoms The energy bands EgEg

Insulator Conductor (metals) Semiconductors

Doped semiconductor n-type p-type

Interband transistion   nanoseconds in GaAs

n-type Intraband transitions   < ps in GaAs

UV Optical fiber communication

GaAs InP ZnSe

Bandgap rules The bandgap increases with decreasing lattice constant. The bandgap decreases with increasing temperature.

Interband vs Intraband Interband: Most semiconductor devices operated based on the interband transitions, namely between the conduction and valence bands. The devices are usually bipolar involving a p- n junction. Intraband: A new class of devices, such as the quantum cascade lasers, are based on the transitions between the sub-bands in the conduction or valence bands. The intraband devices are unipolar. Faster than the intraband devices C V C

E k Conduction band Valence band Interband transitions

E k Conduction band Valence band Examples: m c =0.08 m e for conduction band in GaAs m c =0.46 m e for valence band in GaAs EgEg

Direct vs. indirect band gap k k GaAs Al x Ga 1-x As x<0.3 ZnSe Si AlAs Diamond

Direct vs. indirect band gap Direct bandgap materials: Strong luminescence Light emitters Detectors Direct bandgap materials: Weak or no luminescence Detectors

Fermi-Dirac distribution function f(E) E 10.5 EFEF

Fermi-Dirac distribution function f(E) E 10.5 EFEF For electrons For holes kT kT=25 meV at 300 K

Fermi-Dirac distribution function f(E) E 10.5 EFEF For electrons For holes kT kT=25 meV at 300 K

E Conduction band Valence band

E Conduction band Valence band For filling purpose, the smaller the effective mass the better.

E Conduction band Valence band Where is the Fermi Level ? Intrinsic P-doped n-doped

Interband carrier recombination time (lifetime) ~ nanoseconds in III-V compound (GaAs, InGaAsP) ~ microseconds in silicon Speed, energy storage,

E Quasi-Fermi levels EE Immediately after Absorbing photons Returning to thermal equilibrium E f e E f h

E EFeEFe EFhEFh x= fefe # of carriers

E E F c E F v EgEg Condition for net gain >0

P-n junction unbiased EFEF

P-n junction Under forward bias EFEF

Heterojunction Under forward bias

Homojunction hv Np

Heterojunction waveguide n x

Heterojunction 10 – 100 nm EFEF

Heterojunction A four-level system 10 – 100 nm Phonons

E EgEg  g Absorption and gain in semiconductor

 EgEg EgEg Absorption (loss) g

g EgEg Gain  EgEg

g EgEg Gain at 0 K  EgEg E Fc -E Fv Density of states E Fc -E Fv

E=hv  g EgEg Gain and loss at 0 K E F =(E Fc -E Fv )

E  g EgEg N 2 >N 1 N1N1 Gain and loss at T=0 K at different pumping rates E F =(E Fc -E Fv )

E  g EgEg N 2 >N 1 N1N1 Gain and loss at T>0 K laser

E  g EgEg N 2 >N 1 N1N1 Gain and loss at T>0 K Effect of increasing temperature laser At a higher temperature

Larger bandgap (and lower index ) materials Substrate Smaller bandgap (and higher index ) materials Cleaved facets w/wo coating <0.2  m p n A diode laser <1 mm <0.1 mm

Wavelength of diode lasers Broad band width (>200 nm) Wavelength selection by grating Temperature tuning in a small range

Wavelength selection by grating tuning

<0.2  m p n A distributed-feedback diode laser with imbedded grating Grating

Typical numbers for optical gain: Gain coefficient at threshold: 20 cm -1 Carrier density: cm -3 Electrical to optical conversion efficiency: >30% Internal quantum efficiency >90% Power of optical damage 10 6 W/cm 2 Modulation bandwidth >10 GHz

Semiconductor vs solid-state Semiconductors: Fast: due to short excited state lifetime ( ns) Direct electrical pumping Broad bandwidth Lack of energy storage Low damage threshold Solid-state lasers, such as rare-earth ion based: Need optical pumping Long storage time for high peak power High damage threshold

Strained layer and bandgap engineering Substrate

3-D (bulk) E  Density of states

Low dimensional semiconductors When the dimension of potential well is comparable to the deBroglie wavelength of electrons and holes. L z <10nm

2- dimensional semiconductors: quantum well E  constant Example: GaAs/AlGaAs, ZnSe/ZnMgSe Al 0.3 Ga 0.7 As GaAs E1E1 E2E2 For wells of infinite depth

2- dimensional semiconductors: quantum well E 1v E 2c E 1c E 2v

2- dimensional semiconductors: quantum well E 1v E 2c E 1c E  (E) E 2v

2- dimensional semiconductors: quantum well E 1v E 2c E 1c E 2v g  N 0 =0 N 1 >N 0 N2>N1N2>N1 T=0 K

2- dimensional semiconductors: quantum well E 1v E 2c E 1c E 2v g  N 0 =0 N 1 >N 0 N2>N1N2>N1 T=300K E=hv

2- dimensional semiconductors: quantum well E 1v E 2c E 1c E 2v g  N 0 =0 N 1 >N 0 N2>N1N2>N1 E=hv Wavelength : Determined by the composition and thickness of the well and the barrier heights

3-D vs. 2-D E 2v g  T=300K E=hv 3-D 2-D

Multiple quantum well: coupled or uncoupled

1-D (Quantum wire) E  EgEg Quantized bandgap

0-D (Quantum dot) An artificial atom E  EiEi

Quantum cascade lasers