Silicon-Compatible Lasers (Hybrid III-V, Epitaxial Quantum-Dot and Ge-GeSn)

1. Theory

• Definition: A silicon-compatible laser is a laser that sits on or is made on a silicon wafer so that its light can be guided in silicon photonic circuits; it is needed because silicon is an indirect-gap semiconductor, with its conduction-band minimum near the X point and the $\Gamma$ valley much higher, so it is a poor light emitter.
• Hybrid III-V on silicon: Layers of III-V gain material (InGaAlAs or InGaAsP quantum wells on InP) are bonded to a silicon-on-insulator waveguide, which defines the cavity, and the light passes between them by evanescent coupling or by an adiabatic taper; an early device was optically pumped (30 mW pulsed threshold, 1.4 mW at 1538 nm), and electrically pumped devices followed in 2006.
• Bonded structure: The mode lies mostly in the silicon (about 59 to 75%), with 3 to 5.2% in the 5 to 9 quantum wells, or about 13% in the wells of a device with a planarized bonding layer; Fabry-Perot, DFB, DBR and racetrack-ring cavities have been made.
• Bonding: Oxygen-plasma direct bonding through a thin oxide (about 10 nm of $\mathrm{Si}{\mathrm{O}}_2$ in one process, with a yield of 95% wafer to wafer and above 85% die to wafer) or adhesive bonding with BCB (index 1.54, yield about 80%).
• Epitaxial III-V on silicon: InAs quantum-dot lasers are grown directly on silicon through a GaP layer and a GaAs buffer with dislocation filters (threading dislocation density $7.3\times 10^6\mathrm{c}{\mathrm{m}}^{-2}$) and emit at 1.3 $\mu$m; ridge Fabry-Perot lasers reached 6.2 mA threshold and a wall-plug efficiency of up to 31% in continuous wave.
• Germanium on silicon: Ge is nearly direct, with the L valley only about 140 meV below $\Gamma$, and an electrically pumped laser of 2012 used 0.2 to 0.25% tensile strain and n-type doping above $4\times 10^{19}\mathrm{c}{\mathrm{m}}^{-3}$ to lase between 1520 and 1700 nm in pulses.
• GeSn: Alloying Ge with Sn makes the gap direct above about 8% Sn; optically pumped GeSn lasers (whispering-gallery microdisks of 4 to 9 $\mu$m) emit at 2 to 3.6 $\mu$m, up to 300 K for a strained disk, while electrical pumping has been shown only up to 100 K.

2. Working Principle

• Gain and loss: The modal gain of the wells, ${\Gamma }_{QW}g$, must equal the sum of the internal and mirror losses; because ${\Gamma }_{QW}$ is only a few percent, the material gain at threshold is large.
• Light transfer: Two coupled waveguides exchange power as ${\sin }^2(sL)$ with a full transfer after a coupling length $\pi /2\kappa$ when their propagation constants match; a taper that changes the width slowly carries the mode from the III-V to the silicon with no beating.
• Cavity in the silicon: The wavelength is set by the silicon waveguide and its gratings, which are made with CMOS-compatible processing, and not by the III-V material.
• Temperature: The threshold rises as $\exp (T/T_0)$, with $T_0$ of about 80 K in the bonded laser and about 30 K in the quantum-dot laser on silicon, which is raised to about 100 K by p-type modulation doping.
• Dislocations: Carriers localized in quantum dots diffuse about 1 $\mu$m, against 3 to 5 $\mu$m in a quantum well, so the dots are less sensitive to threading dislocations and the lifetimes extrapolate to more than $10^7$ hours.
• Germanium: Tensile strain and heavy n-type doping make Ge a gain medium, but the device had a threshold of 280 $kA/c{\mathrm{m}}^2$, 1.9% differential efficiency and about 1 mW output.
• GeSn: The gap is direct when the L valley lies above the $\Gamma$ valley, and a lower threshold follows from more Sn up to about 8%, from relaxing the compressive strain by undercutting the disk, and from removing the misfit dislocations at the interface by the etch.

3. Applications

• Light sources for silicon photonic circuits (research and development in the sources read): Low-cost, highly integrated sources for optical communications; a bonded DFB laser with SMSR of 50 dB and a racetrack laser with an integrated photodetector were demonstrated.
• Direct modulation: A bonded laser gave a small-signal bandwidth of about 6 GHz and a 5 Gbit/s eye, and a quantum-dot laser on silicon 5.8 GHz.
• Mid-infrared sources on silicon (research): GeSn lasers for the 2 to 5 $\mu$m range.

Name	Formula	Related Formulae	Variables/Constants
Threshold of a hybrid III-V on silicon laser	${\Gamma }_{QW}{g}_{th}={\alpha }_i+{\alpha }_m$	${\alpha }_m=\frac{1}{L}\ln \frac{1}{R}$ $g_{th}=\frac{{\alpha }_i+{\alpha }_m}{{\Gamma }_{QW}}$	$\begin{array}{r}{\Gamma }_{QW}:confinementfactoroftheIII-V\\ quantumwells,only3to5.2\%inbonded\\ deviceswithasiliconwaveguide(3\%\\ with75\%inthesiliconfora\\ Fabry-Perotdevice,5.2\%with59.2\%\\ foraDFBdevice,4.4\%with66\%fora\\ DBRdevice)andabout13\%inadevice\\ withfivewellsandaplanarizedbonding\\ layer\end{array}$ $g_{th}:materialgainofthewellsatthreshold$ $\begin{array}{r}{\alpha }_i,{\alpha }_m:internallossandmirrorloss,as\\ intheFabry-Perotlaserpage\end{array}$ $\begin{array}{r}L,R:cavitylengthandpowerreflectance\\ ofthefacets(860\mu \mathrm{m}andabout30\%in\\ onedevice,whichgives{\alpha }_{m}ofabout14\\ c{m}^{-1})\end{array}$
Coupling between the III-V and silicon waveguides	$\frac{P_2\left(L\right)}{P_1\left(0\right)}=\frac{{\kappa }^2}{s^2}{\sin }^2\left(sL\right)$	$s^2={\kappa }^2+{\delta }^2,\delta =\frac{{\beta }_2-{\beta }_1}{2}$ $L_c=\frac{\pi }{2\kappa }$ $\frac{P_2}{P_1}{|}_{max}=\frac{{\kappa }^2}{{\kappa }^2+{\delta }^2}$	$\begin{array}{r}{P}_1,P_2:powersinthefirstandsecond\\ waveguide,lightbeinglaunchedintothe\\ firstonly\end{array}$ $\begin{array}{r}\kappa :couplingcoefficientofthetwo\\ waveguides,whichfallsexponentiallywith\\ theirspacingbecausethefieldofone\\ waveguidereachestheotherasan\\ evanescenttail\end{array}$ $\begin{array}{r}{\beta }_1,{\beta }_2:propagationconstantsofthetwo\\ uncoupledmodesand\delta :theirdetuning\end{array}$ $\begin{array}{r}{L}_c:couplinglength,thelengthoffull\\ transferfor\delta =0\end{array}$ $\begin{array}{r}(ataperedwaveguidechanges{\beta }_2-{\beta }_{1}slowly\\ alongzandpassesthrough\delta =0,which\\ transfersthepowerwithnobeatingwhen\\ thetaperislongenough,about100\mu \mathrm{m}in\\ onedesign)\end{array}$
Temperature dependence of the threshold and of the wavelength	$I_{th}\left(T\right)=I_0\exp \left(\frac{T}{T_0}\right)$	$\frac{d\lambda }{dT}\approx 0.045nm/K$	$I_{th}:thresholdcurrentatthetemperatureT$ $\begin{array}{r}{I}_0,T_0:fittingconstants,T_{0}beingthe\\ characteristictemperature,of80K(given\\ inthesourceas80{}^{\circ }C)forabonded\\ devicewith{I}_0=9.92mA,of29.8Kfora\\ quantum-dotlasergrownonsiliconand\\ betweenabout30K(undopeddots)and\\ about100K(p-modulation-dopeddots)in\\ another\end{array}$ $\begin{array}{r}d\lambda /dT:wavelengthdriftofabondeddevice\\ (fromonesource)\end{array}$
Biaxial strain and the conduction-band edges of Ge and GeSn	${\epsilon }_{xx}={\epsilon }_{yy}=\frac{a_s-a_l}{a_l},{\epsilon }_{zz}=-\frac{2C_{12}}{C_{11}}{\epsilon }_{xx}$	$\Delta E_{\Gamma }=a_c\left(2{\epsilon }_{xx}+{\epsilon }_{zz}\right)$ $\Delta E_L=a_L\left(2{\epsilon }_{xx}+{\epsilon }_{zz}\right)$	$\begin{array}{r}{a}_s,a_l:latticeconstantsofthesubstrate\\ andoftherelaxedlayer,sothat{\epsilon }_{xx}>0is\\ tensile\end{array}$ $C_{11},C_{12}:elasticconstants$ $\begin{array}{r}\Delta E_{\Gamma },\Delta E_L:shiftsoftheGammaandL\\ conduction-bandedgesduetothevolume\\ strain,withthedeformationpotentials{a}_c\\ and{a}_L(theshiftofthevalencebandmust\\ beaddedtoobtainthegaps)\end{array}$ $\begin{array}{r}abiaxialtensilestrainlowersthedirect\\ gapfasterthantheindirectgap,whichis\\ theoriginofthedirect-gaptransitionof\\ Ge(about2.1\%biaxialat20Kinone\\ modeland1.8\%inanother)\end{array}$
Directness and composition of GeSn	$\Delta E_{L\Gamma }=E_L-E_{\Gamma }$	$E^{\Gamma ,L}=x_{Ge}{E}_{Ge}+x_{Sn}{E}_{Sn}+b_{GeSn}{x}_{Ge}{x}_{Sn}$	$\begin{array}{r}\Delta E_{L\Gamma }:energyoftheLvalleyabovethe\\ Gammavalley,positiveforadirectgap\\ (about-140meVinGe,92meVinG{e}_{0.86}S{n}_{0.14}\\ whenitisrelaxedorcompressedand165\\ meVunder0.44\%tensilestrain)\end{array}$ $\begin{array}{r}{x}_{Ge},x_{Sn}:atomicfractions,withadirect\\ gapaboveabout8\%SninunstrainedGeSn\end{array}$ $\begin{array}{r}{E}_{Ge},E_{Sn}:valleyenergiesofthetwo\\ elementsand{b}_{GeSn}:bowingparameterofthe\\ alloy(anegativevaluelowersthegap)\end{array}$
Absorbed pump power of an optically pumped GeSn laser	$P_{abs}=\left(1-R_s\right)P_{inc}$	$P_{abs}\approx 0.65P_{inc}$	$\begin{array}{r}{P}_{inc}:incidentpumppower(orpower\\ density),quotedasthethresholdofmost\\ opticallypumpedGeSnlasers\end{array}$ $\begin{array}{r}{R}_s:reflectivityofthesurfaceofthe\\ GeSnatthepumpwavelength,about35to\\ 37\%inonedevice,whichleaves65\%\\ absorbed\end{array}$
Wall-plug and differential efficiency	${\eta }_{wp}=\frac{P}{IV}$	${\eta }_d=\frac{q}{h\nu }\frac{dP}{dI}$	$\begin{array}{r}{\eta }_{wp}:wall-plugefficiency,upto31\%at\\ 185mWand20{}^{\circ }Cforaquantum-dotlaser\\ grownonsilicon\end{array}$ $P,I,V:opticalpower,currentandvoltage$ $\begin{array}{r}{\eta }_d:differentialquantumefficiency,1.9\\ \%intheelectricallypumpedGe-on-Si\\ laserof2012\end{array}$ $q,h\nu :electronchargeandphotonenergy$

Important Questions

Ques: Why can silicon not be made into an efficient laser, and what does bonding a III-V layer to it change?

Silicon has its conduction-band minimum near the X point, far from the Γ point where the valence-band maximum is, and its direct Γ valley is much higher, so an electron must change momentum before it recombines, and alloying with Ge does not make the gap direct. A III-V material such as InP with InGaAlAs wells is direct and gives gain, while silicon gives a low-loss waveguide with CMOS-compatible gratings and a well-controlled wavelength. In a bonded device the two roles are shared: the wells hold only 3% to 5.2% of the mode, while 59% to 75% of it is in the silicon. The price is a threshold gain larger by the ratio of the confinement factors, and an alignment of the two waveguides, which the taper and the bonding layer provide. Reference: Lasing in Group-IV materials, arXiv:2012.10220; Hybrid lasers, CEA-Leti slides (Ben Bakir et al., 2011); Coldren, Corzine and Mašanović, Diode Lasers and Photonic Integrated Circuits, 2nd ed. (Wiley, 2012), Section 2.5 (Eqs. 2.21 to 2.28).

Ques: Why is the confinement factor of the wells only a few percent, and what does it cost?

The mode is held by the high-index silicon waveguide, and the wells, which sit above it on the other side of the bonding layer, are reached by only the evanescent tail, so most of the power is in the silicon (59% to 75%). The threshold gain is $g_{th}=({\alpha }_i+{\alpha }_m)/{\Gamma }_{QW}$, so a change of ${\Gamma }_{QW}$ from 3% in a Fabry-Perot device to 13% in the device with a planarized bonding layer and five wells lowers the required material gain by a factor of 4.3 (computed). The cost of a larger ${\Gamma }_{QW}$ is that the mode is pulled out of the silicon, where a taper with more than 94% transfer is needed, so the design is a compromise between gain and the share of power that can be sent to the silicon. Reference: CEA-Leti slides (Ben Bakir et al., 2011), with the measured ${\Gamma }_{QW}$ and ${\Gamma }_{Si}$ of the Fabry-Perot, DFB and DBR devices; Coldren et al., 2nd ed., Section 2.5 (Eqs. 2.21 to 2.28).

Ques: How does the light get from the III-V gain region into the silicon waveguide, and why is a taper used?

The mode of one waveguide has an evanescent tail in the other, which couples them. In the coupled-mode theory of the book, power is transferred as $({\kappa }^2/s^2){\sin }^2(sL)$ with $s^2={\kappa }^2+{\delta }^2$, so a full transfer needs $\delta =0$, that is equal propagation constants, and the maximum transfer is ${\kappa }^2/({\kappa }^2+{\delta }^2)$ otherwise. The III-V and silicon waveguides are not equal, and the power would beat back and forth with the length. A taper that changes the silicon width slowly passes through $\delta =0$ and moves the mode adiabatically into the silicon supermode; in one design, a taper whose width goes from 430 nm to 1930 nm over at least about 100 $\mu$m scattered 2% into the unwanted mode and gave more than 94% transfer, and a variation of the silicon width of 50 nm kept it above 90%. Reference: Coldren et al., 2nd ed., Section 6.4 (Eqs. 6.68, 6.75, 6.78 and 6.83); CEA-Leti slides (Ben Bakir et al., 2011).

Ques: Which bonding layer is used, and how thick is it?

Two families are used. In direct molecular bonding a thin oxide of about 10 nm of PECVD SiO${}_2$ is deposited on a surface with roughness below 0.5 nm, giving a yield of 95% wafer to wafer and above 85% die to wafer. In the Intel and UCSB process, an oxide described as about 25 atoms thick, formed by oxygen plasma, fuses the InP-based material and the silicon under heat and pressure, and it is of the same order, perhaps 5 nm to 10 nm (estimated, assuming 0.2 nm to 0.4 nm per atomic layer). Adhesive bonding with BCB, whose index of 1.54 at 1.55 $\mu$m is close to that of SiO${}_2$, tolerates roughness and particles better, had a yield of about 80%, and allows the silicon waveguide to be planarized, which gave the 13% confinement in the wells quoted above. A direct-bonding oxide has to be thin so that the mode can reach the wells. Reference: CEA-Leti slides (Ben Bakir et al., 2011); Semiconductor Today, Intel and UCSB hybrid silicon laser (September 2006); A.W. Fang, H. Park, O. Cohen, R. Jones, M.J. Paniccia and J.E. Bowers, Electrically pumped hybrid AlGaInAs-silicon evanescent laser, Opt. Express 14, 9203 (2006); Laser Focus World, Hybrid laser combines III-V gain with silicon waveguide.

Ques: Why do quantum-dot lasers survive the dislocations of growth on silicon better than quantum-well lasers?

A mismatch between III-V and silicon leaves threading dislocations, which are nonradiative centres; carriers in a quantum well diffuse about 3 $\mu$m to 5 $\mu$m and many reach one, whereas carriers localized in dots diffuse about 1 $\mu$m, which makes the active region less sensitive to the defects and also to the sidewalls. Under injection, misfit dislocations also grow by recombination-enhanced glide, and the localization suppresses the growth of the dark-line defects. The reported effect is large: the best quantum-well lasers on GaAs/Si lasted about 200 h, while a lowering of the dislocation density from $2.8\times 10^8$ to $7.3\times 10^6$ cm${}^{-2}$ in dot lasers raised the lifetime from 355 h and about 1097 h (first-generation lasers in the original paper; the other paper quotes a few thousand hours) to an extrapolated more than $10^7$ h. Reference: C. Shang et al., IEEE J. Sel. Top. Quantum Electron. (2019); D. Jung et al., Appl. Phys. Lett. 112, 153507 (2018); dislocations in InAs quantum-dot emitters on silicon, arXiv:2301.03671.

Ques: How credible are lifetimes of ten million hours for lasers on silicon?

They are extrapolations. The time to double the threshold current was 6.4 million and 26.8 million hours from a 1500 h test at 35 ${}^{\circ }$C in one paper, and more than $10^7$ h from the slow increase of the bias current in a 4000 h test in another, so the two papers agree on the order but not on the number. The accelerated tests are shorter and give less: about 2500 h at 60 ${}^{\circ }$C for undoped dots, and about 65,000 h by extrapolation for p-modulation-doped dots. The first generation, with a dislocation density of $2.8\times 10^8$ cm${}^{-2}$, lasted 355 h and about 1097 h. The lower, accelerated values are the more likely to be reached in use, because the extrapolation assumes that the degradation continues at the same slow rate. Reference: D. Jung et al., Appl. Phys. Lett. 112, 153507 (2018); D. Jung et al., ACS Photonics (2017), silicon-based quantum-dot laser.

Ques: Why is germanium strained and doped n-type to lase, and is the electrically pumped Ge-on-Si laser practical?

The L valley of Ge is only about 140 meV below Γ, so tensile strain of 0.2% to 0.25% narrows the direct gap, and phosphorus doping above $4\times 10^{19}$ cm${}^{-3}$ is reported to raise the gain to more than 400 cm${}^{-1}$. The usual explanation is that donor electrons fill the L valley, so that fewer injected carriers are needed in the Γ valley. The laser worked in pulses of 20 $\mu$s to 100 ms at 15 ${}^{\circ }$C, from 1520 nm to 1700 nm, but with a threshold of 280 kA/cm${}^2$, about 1 mW output and 1.9% differential efficiency. A later design study, which fitted the model to these data, concludes that the device cannot be practical without a large reduction of the threshold and a better efficiency, and predicts 3.3 mA only for a model design. Reference: R. Camacho-Aguilera et al., An electrically pumped germanium laser, Opt. Express 20, 11316 (2012); X. Li et al., Design Considerations of Biaxially Tensile-Strained Germanium-on-Silicon Lasers, arXiv:1511.05972.

Ques: What Sn content makes GeSn direct, and why do the reported thresholds range from 1 kW/cm² to 550 kW/cm²?

The chapter on group-IV lasers gives about 8% Sn for unstrained GeSn. The suspended microdisks lased at 7% Sn, so the value is approximate, and the strain relaxation in the disk matters. The thresholds depend on the temperature, the strain, the surface and the method: 8 kW/cm${}^2$ to 19 kW/cm${}^2$ at 25 K for 7% to 10.5% Sn, 12 kW/cm${}^2$ at 75 K and about 550 kW/cm${}^2$ at 300 K for a strained 14% Sn disk, and about 1 kW/cm${}^2$ for an all-around stressed structure. The same 10.5% layer gave about 145 kW/cm${}^2$ (10 $\mu$m disk) after a CF${}_4$ etch and 11.6 kW/cm${}^2$ (8 $\mu$m disk) after an SF${}_6$ etch that removes the interface dislocations, so process matters as much as composition. The 1 kW/cm${}^2$ is the least comparable, as no temperature is given for it. Reference: S. Wirths et al., Lasing in direct-bandgap GeSn alloy grown on Si, Nat. Photonics 9, 88 (2015), the first GeSn laser; Lasing in Group-IV materials, arXiv:2012.10220; Reduced laser thresholds in GeSn microdisks, ACS Photonics (Université Paris-Saclay); GeSn microdisk lasers at room temperature, Adv. Opt. Mater. (Université Paris-Saclay).

Ques: Why is GeSn pumped optically, with electrical operation only at 100 K?

The obstacles listed for electrical injection are Fermi-level pinning at metal and Ge(Sn) interfaces, the difficulty of high active doping, and the thermal stability of Ni-based stanogermanide contacts. The most recent electrically pumped GeSn laser works up to 100 K. Optical pumping avoids the contacts altogether, and an optically pumped strained disk lased at 300 K with a pump of about 550 kW/cm${}^2$, of which 65% is absorbed (0.65 of the incident power). Reference: Lasing in Group-IV materials, arXiv:2012.10220; GeSn microdisk lasers at room temperature, Adv. Opt. Mater. (Université Paris-Saclay).

Related pages in this vault: Distributed Bragg Reflector Laser (DBR), Distributed Feedback Laser (DFB), Nanolaser (Microdisk, Microring and Photonic Crystal), Vertical-External-Cavity Surface-Emitting Laser (VECSEL), Quantum-Dot Laser, Germanium and Silicon-Germanium Electroabsorption Modulator, Waveguide Photodiode, Indium Phosphide Quantum-Well Electroabsorption Modulator, Semiconductor Lasers (Edge-Emitting and VCSEL).