Submonolayer Quantum Dots for High Speed Surface Emitting Lasers
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We report on progress in growth and applications of submonolayer (SML) quantum dots (QDs) in high-speed vertical-cavity surface-emitting lasers (VCSELs). SML deposition enables controlled formation of high density QD arrays with good size and shape uniformity. Further increase in excitonic absorption and gain is possible with vertical stacking of SML QDs using ultrathin spacer layers. Vertically correlated, tilted or anticorrelated arrangements of the SML islands are realized and allow QD strain and wavefunction engineering. Respectively, both TE and TM polarizations of the luminescence can be achieved in the edge-emission using the same constituting materials. SML QDs provide ultrahigh modal gain, reduced temperature depletion and gain saturation effects when used in active media in laser diodes. Temperature robustness up to 100 °C for 0.98 μm range vertical-cavity surface-emitting lasers (VCSELs) is realized in the continuous wave regime. An open eye 20 Gb/s operation with bit error rates better than 10−12has been achieved in a temperature range 25–85 °Cwithout current adjustment. Relaxation oscillations up to ∼30 GHz have been realized indicating feasibility of 40 Gb/s signal transmission.
KeywordsQuantum dots Nanophotonics Semiconductor lasers Surface-emitting lasers Self-organized growth
Presently, data traffic crossing optical fiber networks increases three orders of magnitude per decade . To cope with this increase, there exists a growing demand in adding more channels per a single link, increasing the bit rate per link and installing new links. The maximum commercial single-channel data transmission rate is increasing 4-fold each 5 years. In telecom-range systems it entered 40 Gb/s transmission range with 100 Gb/s to come in the nearest future. External intensity modulation is used in telecom transmitters to match both speed and spectral and beam quality requirements. In datacom, however, where the bit rate has already entered the 10 Gb/s range, directly modulated devices are used due to cost requirements. Further significant increase in the bit rate in this approach is becoming more and more demanding, because of the extreme power densities in the cavity needed to match the requested time response. Furthermore, high differential capacitance under forward bias, bit error rate (BER) requirements requesting a proportional power increase with the speed increase and the related high power consumption are limiting factors for the performance and competitiveness. At the same time the bit rate increase is also characteristic for copper electrical interconnects, where the market approached ∼US$40B in 2006 with an annual growth rate of ∼16%. As the attenuation of signal at 10 Gb/s makes cost-effective transmission through copper prohibitively expensive and complex at distances ∼3–10 m, this segment is to be covered by optical interconnects at speeds higher 10 Gb/s. Fiber optic links based on vertical-cavity surface-emitting lasers (VCSELs) are broadly believed to be the best candidates [2, 3, 4] for these applications in the foreseeable future, however, the device performance must match the performance demand and respond the above listed challenges.
Moreover, lack of components, operating in a robust way even at 20 Gb/s in the requested temperature and BER ranges, raises questions concerning the further perspectives of the VCSEL technology. To respond the demands, directly modulated devices need to overcome the following challenges:
a 4-fold increase in the modulation speed requires a 16-fold increase in the current density, assuming the similar device geometry (the relaxation oscillation frequency, characterizing the time-response of the active medium, scales with the square root of the power density in the laser cavity);
a 4-fold increase in the modulation speed requests a proportional increase in the output power to provide the same power per pulse to keep the same BER. This translates to ∼3 mW of “in-fiber” power for 40 Gb/s VCSELs;
with transmission speed increase and the related ultrahigh power densities, the wavelength chirp, dynamic beam degradation, and spatial hole-burning are becoming pronounced, deteriorating the optical transmission, even in case where single mode devices are used;
increased current density results in a significant overheating and accelerated degradation rate, even when all the other parameters of the device are met.
A significant increase of the modulation speed of VCSELs combined with the demands for power, degradation robustness and speed of next generation ultrahigh speed systems require new material and device concepts.
This paper addresses VCSEL prospects in parts of using of novel types of submonolayer quantum dot (SML QD) active media [5, 6] capable to ultrahigh modal gain, keeping all the other key QD advantages in place, such as excitonic gain mechanism, suppressed carrier diffusion and low degradation rate. We underline also the role of the novel VCSEL design, which avoids dangerous parasitic cavity modes causing gain depletion, self-pulsation and radiative leakage.
We believe that further VCSEL development, being based on nanophotonic approaches, will ensure the necessary pace of the device performance to cope with the tasks of the decades to come.
Stranski-Krastanow Quantum Dot Gain Media
Lasing in self-organized Stranski-Krastanow QDs (SK-QDs) at room and low temperatures was reported in 1993 applying edge-emitting geometry and photopumped excitation . Soon after (1994) current injection lasing in QDs  up to 300 K was reported. In 1995 injection lasing in QDs at 80 K with the threshold current density of 815 A/cm2[9, 10, 11] was observed. SK-QDs have been also used in the active region of VCSELs . In 1996 high-performance VCSELs based on vertically coupled QDs have been realized  by MBE and, later, MOCVD . Later, however, the main interest has shifted towards long-wavelength 1.3 μm devices. Indeed, the first-ever GaAs-based VCSEL emitting beyond 1.3 μm was realized using SK InAs QDs . There has been a lot of activities to improve the device. However, in spite of the fact that the basic performance at room temperature in the CW mode was significantly improved , high-temperature operation and high-speed modulation remained a big issue, opposite to 1300 nm-range edge-emitters based on the same epitaxial QD material [16, 17]. Low modulation bandwidth [16, 18] and insufficient temperature robustness  appeared to be a problem for 1.3 μm GaAs SK-QD VCSELs. More recently, a new explosion of interest, also for 850–1,100 nm spectral range occurred, being sparked by the need to extend dramatically the speed of directly modulated devices for optical interconnects, but avoid the risk of device degradation. The extreme robustness of edge-emitting QD lasers to degradation [19, 20] and the temperature stability of their characteristics [21, 22] motivated the research.
Growth of QDs Using Submonolayer Deposition
The spontaneous formation of ordered arrays of islands has been studied theoretically and experimentally for a long time (see, e. g., a review in ). The formation of ordered (“parquet”) structures on crystal surfaces has been shown to occur if two phases with different values of intrinsic surface stress (τij) coexist on the surface . The surface of the crystal is intrinsically stressed due to the necessity to follow the lattice parameter of the bulk where the atom arrangement is different. If the values of this surface stress are different for the two phases co-existing on the crystal surface (heteroepitaxial deposits, domains of surface reconstruction, adsorbate phases, etc.), formation of boundaries will always result in some elastic energy relaxation (Fig 1) of the more stressed phase along the boundaries between the domains, making ripening of the domains energetically unfavorable. For strained 2D islands there always exists a total energy minimum for a particular island size [23, 30].
At finite temperature the island size distribution somewhat broadens , and another peak in the island size distribution appears near the zero island size, corresponding to the finite concentration of free adatoms and their associates on the surface. The mean size and density of the equilibrium islands decrease with increasing substrate temperature . At very high temperatures only the peak in the size distribution curve at zero island size survives and the island size dispersion becomes very pronounced.
As the localization energy of SML QDs is relatively small, their stacking appears to be particularly important.
Electronic Properties of Submonolayer QDs
Small lateral size of the islands formed by ultrathin insertions raises a question on the applicability of QD model to explain the properties of SML insertions. A clear signature of QD states is observation of discrete luminescence lines due to single QDs , which survive up to high temperatures.
Another unique possibility, which was first discovered in SML QDs , and was later translated to SK QDs [32, 33] is a possibility to control polarization of the luminescence of QD structures in edge geometry. Indeed, vertically coupled growth results in strain and wavefunction modifications which favor unpolarized or even TM-polarized emission in edge geometry, opposite to the case of uncoupled QDs, always demonstrating TE-polarized emission, similar to the case of compressively strained or lattice-matched quantum wells.
It is also very important to note that the electron and hole confinement in vertically coupled QDs is significantly increased as compared to the wetting layer and matrix continuum, further improving temperature stability of the QD luminescence.
In the case of vertically correlated growth at very thin spacer layers, the surface morphology of the (In,Ga)As insertions becomes significantly affected, the dot size increases, and a periodic interface corrugation occurs.
For ultrahigh-speed directly modulated VCSEL applications it is extremely important to create an active media, which is capable to ultrahigh modal gain at extremely high temperatures and current densities. The problem of conventional QW active media is the step-like density of states for intersuband transitions, which results in hole-burning effects at high current densities and gain depletion due to overheating. In spite of the fact that ultrahigh exciton oscillator strength can be realized in absorption spectra of QWs, the excitons do not play any positive role under the lasing conditions. At first, the excitons can be partially dissolved at room temperature. However, even in structures made of II–VI materials, where the exciton oscillator strength is high and the excitons dominate up to high excitation densities and observation temperatures, the predominant lasing mechanism is related to LO-phonon-assisted excitonic gain, which is relatively weak, as it comes from many-particle interactions (predominantly including an exciton and two LO-phonons). At high temperatures and excitation densities the excitons are heated and have a significant in-plane k-vector, making the probability of their zero-phonon radiative annihilation negligibly low [5, 27, 28]. Already in narrow II–VI quantum wells, however, the interface roughness can make a zero-phonon scattering-assisted lasing mechanism dominant. A truly excitonic gain can be realized, however, only in QDs, where the excitons are fully confined. In practical QD structures, at least an order of magnitude higher material gain as compared to QWs at room temperature was manifested, even in case of significantly inhomogeneously broadened ensembles (>kT). The problem of using conventional S-K QDs in VCSELs originates, however, from the fact that the sheet density of QDs is relatively low ∼1–8 × 1010 cm−2 and the carriers can escape from QDs at elevated temperatures populating the matrix and wetting layer states. Increasing the density of QDs by stacking is difficult due to the increased average strain in the structure and the related formation of misfit dislocations. As opposite, very small QDs formed by SML insertions can form efficient confinement centers of ultrahigh density, which can lift effectively the k-selection rule, but do not degrade the structural quality of the system. Pure exctionic lasing mechanism up to high temperatures and excitation densities can be realized on one side, while an ultrahigh density of QDs can be achieved on the other. Thus, gain coefficients comparable to the absorption coefficients in narrow QWs can be potentially, realized. To achieve this goal, however, one needs to keep the lateral size of the localizing insertions to be comparable or less than the effective exciton radius in the narrow QWs (about 5–8 nm). The confinement potential should be made as large as possible to provide the strongest confinement of the localized exciton with respect to the continuum states. The lateral separation between the localizing centers should be sufficient to prevent coupling of QD excitons to broad minizones staying above 3–5 nm, depending on the confinement potential (the size inhomogeneity may reduce the coupling even at very small average lateral separations). As a result of the above consideration, the material arrangement presented in Fig. 13 seems to be particularly interesting for applications in VCSELs.
Thus, in the case of the particular SML QDs used for the VCSEL structures processed and studied in this work, the SML growth proceeded in a mode with ten 0.5 ML InAs deposition cycles separated by 2.2 ML GaAs spacers at a substrate temperature of 490 °C. 10 s growth interruptions were introduced at the GaAs interfaces to ensure reproducible surface morphology for the InAs nucleation. Three sheets of stacked SML QD insertions separated by 13-nm-thick GaAs spacer layers were used as an active region .
Similarly, for the double-peak feature in the PLE spectra at 1.43 and 1.49 eV light-hole-like ground and excited exciton states might be responsible.
VCSEL Cavity Design
The radiative recombination probability of the dipole can be changed by changing the effective refractive index of the media to which the photon is emitted. Multilayer media open dramatic possibilities in redistribution of the oscillator strength, increase in the differential gain and suppression of the parasitic modes. The easiest approach to improve VCSEL device performance is to apply an antiwaveguiding design  with the cavity region having a smaller refractive index as compared to the average refractive index of the distributed Bragg reflectors (DBRs).
In conventional VCSELs, the cavity region is typically composed of the material having a higher refractive index. In this situation in-plane waveguide modes are possible. It is well known that VCSEL structures behave as low-threshold high-performance in-plane lasers, if processed in stripe-laser geometry. Assuming a standard high-speed oxide-confined VCSEL design with relatively small deep-etched VCSEL mesa, two types of in-plane confined modes, which do not penetrate into the DBRs, are possible. High quality factor (Q) modes are associated with the etched mesa, which is typically small enough to reduce the parasitic capacitance. Low-Q modes are associated with the oxide aperture . As the VCSEL is operating under high current densities, the absorbing regions of the mesa, which are not electrically pumped by current injection become transparent by photoexitation due to in-plane spontaneous and stimulated emission.
These high Q modes behave as whispering gallery modes in microdisc structures, or, in some sense, similar to the modes existing in four-side facet-cleaved laser diodes. High power density accumulated in these modes can dramatically reduce the radiative lifetime and prevents low-threshold lasing for the VCSEL mode. Higher order high Q whispering gallery modes penetrate deep into the VCSEL mesa up to the distance ∼R/n, where R is the radius of the VCSEL mesa and n is the effective refractive index of the waveguide medium .
The whispering gallery modes associated with the oxide aperture is characterized by lower Q values due to the lower effective refractive index step in the outer region .
Further suppression of the parasitic tilted modes is possible in a multi-periodicity DBR VCSEL design, when the tilted modes can be suppressed by a second DBR periodicity.
Experimental Studies of 980 nm Sml QD Avcsels
Static Device Characteristics
The 980 nm VCSEL structures using InGaAs SML QDs,  were realized in an antiwaveguiding design [38, 39] with a high Al-content cavity and doped bottom and top distributed Bragg reflectors with 32 and 19 pairs respectively (see Fig. 16). A single AlAs-rich aperture layer, being partially oxidized, was placed in a field intensity node on top of the 3λ/2 cavity. High speed and high-efficiency devices with a co-planar layout were processed using standard lithographic, metal deposition and dry etching techniques. The selective oxidation procedure to create the oxide apertures was performed under carefully optimized conditions  to avoid formation of parasitic precipitates causing strain, degradation and increasing scattering loss in the devices.
Small Signal Modulation
Large Signal Modulation
Development of novel types of QD media capable to ultrahigh current densities without suffering from gain saturation and lifetime degradation effects is a must to realize ultrahigh-speed directly modulated high-temperature VCSELs. SML QDs provide such an opportunity. The performance of SML QDs can be additionally enhanced by properly engineered VCSEL design. A significant further improvement in the performance of directly modulated VCSEL can be expected with proper optimization of SML QDs. Future work will also include wavelength adjustment of SML QDs to 850 nm and 1300 nm spectral ranges.
V. Savel’ev—on leave from the Abraham Ioffe Physical Technical Institute, Politekhnicheskaya 26, 194021, St. Petersburg, Russia.
The authors appreciate support from the German Ministry for Education and Research bmb+f (NanOp), the State of Berlin (TOB), the SANDiE Network of Excellence of the European Commission (NMP4-CT-2004–500101), NL-Nanosemiconductor (Innolume) GmbH and Discovery Semiconductors Inc. NJ.