Semiconductor Optics Absorption Gain in Semiconductors Some Applications

Semiconductor Optics Absorption & Gain in Semiconductors: Some Applications Semiconductor Lasers (diode lasers) Low Dimensional Materials: Quantum wells, wires & dots Quantum cascade lasers Semiconductor detectors

More Applications Light Emitters, (including lasers & LEDs) Detectors, Sensors, Amplifiers, Waveguides & Switches, Absorbers & Filters Nonlinear Optics

Energy Bands One atom 2 interacting atoms N interacting atoms Eg

Insulator Conductor (metals) Semiconductors

Doped Semiconductors n-type p-type

Interband Transitions nanoseconds in Ga. As

Intraband Transitions < ps in Ga. As n-type

UV “Bandgap Engineering”

Ga. As Zn. Se In. P

Bandgap “Rules” 1. The Bandgap Increases with decreasing Lattice Constant. 2. 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

Interband transitions E Conduction band k Valence band

E Conduction band Eg k Valence band Examples: mc=0. 08 me for conduction band in Ga. As mc=0. 46 me for valence band in Ga. As

Direct vs. Indirect Band Gap k Ga. As Alx. Ga 1 -x. As x<0. 3 Zn. Se k Si Al. As 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 E EF 0. 5 1 f(E)

Fermi-Dirac Distribution Function For electrons k. T = 25 me. V at 300 K k. T For holes E EF 0. 5 1 f(E)

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

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

Interband carrier recombination time (lifetime) ~ nanoseconds in III-V compound (Ga. As, In. Ga. As. P) ~ microseconds in silicon

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

E fe # of carriers EF e x EF h =

E Condition for net gain >0 EF c Eg EF v

P-n junction unbiased EF

P-n junction Under forward bias EF

Heterojunction Under forward bias

Homojunction hv N p

Heterojunction waveguide n x

Heterojunction 10 – 100 nm EF

Heterojunction A four-level system 10 – 100 nm Phonons

Absorption and gain in semiconductor g Eg E

Absorption (loss) g Eg Eg

Gain g Eg Eg

Gain at 0 K g EFc-EFv Eg Density of states

Gain and loss at 0 K g Eg EF=(EFc-EFv) E=hv

Gain and loss at T=0 K at different pumping rates g EF=(EFc-EFv) Eg E N 1 N 2 >N 1

Gain and loss at T>0 K laser g Eg N 1 N 2 >N 1 E

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

A diode laser Larger bandgap (and lower index ) materials <0. 2 m p <0. 1 mm n Substrate Smaller bandgap (and higher index ) materials <1 mm Cleaved facets w/wo coating

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

Wavelength selection by grating tuning

A distributed-feedback diode laser with imbedded grating <0. 2 m p n Grating

Typical numbers for optical gain: Gain coefficient at threshold: 20 cm-1 Carrier density: 10 18 cm-3 Electrical to optical conversion efficiency: >30% Internal quantum efficiency >90% Power of optical damage 106 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

Density of states 3 -D (bulk) E

Low dimensional semiconductors When the dimension of potential well is comparable to the de. Broglie wavelength of electrons and holes. Lz<10 nm

2 - dimensional semiconductors: quantum well Example: Ga. As/Al. Ga. As, Zn. Se/Zn. Mg. Se Al 0. 3 Ga 0. 7 As Ga. As Al 0. 3 Ga 0. 7 As E constant For wells of infinite depth E 2 E 1

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

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

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

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

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

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

Multiple quantum well: coupled or uncoupled

1 -D (Quantum wire) E Quantized bandgap Eg

0 -D (Quantum dot) An artificial atom E Ei

Quantum cascade lasers