Impact of the Quantum Well Gain-to-Cavity Etalon Wavelength Offset on the High Temperature Performance of High Bit Rate 980-nm VCSELs

IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 50, NO. 8, AUGUST 2014 613

Impact of the Quantum Well Gain-to-Cavity EtalonWavelength Offset on the High Temperature

Performance of High Bit Rate980-nm VCSELs

Hui Li, Philip Wolf, Philip Moser, Student Member, IEEE, Gunter Larisch, Alex Mutig,James A. Lott, Senior Member, IEEE, and Dieter H. Bimberg, Fellow, IEEE

Abstract— Highly temperature stable, high bit rate oxide-confined vertical-cavity surface-emitting lasers (VCSELs) emit-ting at 980 nm are presented. Error-free data transmission at38 Gb/s at 25 °C, 45 °C, 65 °C, and 85 °C is achieved withoutany change of working point and modulation condition. Staticand high-speed properties are analyzed experimentally and theo-retically. We numerically investigate the temperature dependenceof the differential gain of our quantum well (QW) active regiondesign to explain why a −15-nm QW gain-to-etalon wavelengthoffset facilitates our 980-nm VCSELs to show simultaneouslyhigh bit rate, temperature stability, and energy efficiency.Our VCSELs operate error-free at 42 and 38 Gb/s at 25 °Cand 85 °C, respectively, with very low power consumption.Record low 175 fJ of dissipated heat per bit is achievedfor 35-Gb/s error-free transmission at room temperature and177 fJ/bit for 38-Gb/s error-free transmission at 85 °C. SuchVCSELs are especially well suited for very-short-reach (<1 m)optical interconnects in high-performance computers and board-to-board and chip-to-chip integrated photonics.

Index Terms— Temperature-stable, high-speed modulation,vertical-cavity surface-emitting lasers, energy-efficiency, opticalinterconnects, short-reach fiber optic links, quantum well lasers.

I. INTRODUCTION

VERTICAL-CAVITY surface-emitting lasers (VCSELs)are the decisive light emitting devices for short-reach

(up to ∼300 m) optical data transmission [1] using multi-mode fiber. Considering cost, energy consumption, long-term

Manuscript received April 13, 2014; revised May 26, 2014; acceptedJune 4, 2014. Date of publication June 12, 2014; date of current versionJune 24, 2014. This work was supported by the Cooperative Research Center,Deutsche Forschungsgemeinschaft under Grant 787.

H. Li, P. Wolf, P. Moser, G. Larisch, and J. A. Lott are with theInstitut für Festkörperphysik und Zentrum für Nanophotonik, Technis-che Universität Berlin, Berlin D-10632, Germany (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]).

A. Mutig was with the Institut für Festkörperphysik und Zentrum fürNanophotonik, Technische Universität Berlin, Berlin D-10632, Germany. He isnow with Infineon Technologies AG, Regensburg D-93049, Germany (e-mail:[email protected]).

D. H. Bimberg is with the Institut für Festkörperphysik und Zentrum fürNanophotonik, Technische Universität Berlin, Berlin D-10632, Germany, andalso with the King Abdulaziz University, Jeddah 22254, Saudi Arabia (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JQE.2014.2330255

system sustainability and reliability, these optical interconnectsshould show stable operation without extra cooling at leastup to 85 °C or even higher. In order to realize both highspeed and temperature independence, we must carefully designthe active region and additionally the difference (or offset)between the peak quantum well gain wavelength and theVCSEL’s Fabry-Pérot (fundamental cavity mode) etalon res-onance wavelength (the gain-to-etalon wavelength offset) at agiven temperature [2]. The modulation bandwidth of VCSELsis intrinsically limited by the differential gain of the QWs[3]. By introducing a proper QW gain-to-cavity etalon wave-length offset we can simultaneously improve the temperature-stability, the maximum bit rate at high temperature (∼85 °C),and the energy efficiency. In this paper we show that VCSELswith a −15 nm gain-to-etalon wavelength offset are well suitedfor temperature stable operation. Detailed theoretical studies,and systematic experimental characterization including staticmeasurements, small signal analysis and data transmissionexperiments are presented.

II. DEVICE STRUCTURE

The structure we studied in this work is similar to the epi-taxial structure previously reported in [4] and [5], designed forhigh-speed, temperature-stable, and energy-efficient operationat 980 nm. The active region contains five ∼4.2 nm-thickIn0.21Ga0.79As QWs with ∼6 nm-thick GaAs0.88P0.12 barrierlayers and a −15 nm gain-to-etalon wavelength offset. TheQWs together with the strain compensating layers are sur-rounded by two 20 nm-thick Al0.35Ga0.65As barrier layersto improve carrier localization in the active region. Theoptical thickness of the cavity is 1.5λ. We also implementa 70 nm-thick linear grading from the barrier layers to theAl0.90Ga0.10As layers. We employ 24-period p-doped top and37.5-period n-doped bottom AlxGa1−xAs distributed Braggreflectors (DBRs) with x = 0.12 and 0.90 high and lowrefractive index layers, respectively, including 20 nm-thicklinearly graded interfaces with modulation doping to min-imize series resistance. In order to reduce electrical para-sitic, two 30 nm-thick (as grown before selective oxidation)oxide aperture layers are formed in two adjacent low-index

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614 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 50, NO. 8, AUGUST 2014

(p)DBR layers just above the cavity by selective wet oxidationof aluminum-rich (p)Al0.98Ga0.02As layers using a proprietaryoxidation set-up.

A. Strained In0.21Ga0.79As QWs for High-Speed Operation

Compressively strained InGaAs QWs with GaAs barrier lay-ers were historically used for the active region of GaAs-based980 nm VCSELs [2], [6]–[8]. The indium concentration can bevaried, to vary the lattice-mismatch strain from 0 up to about−6.69 % for InAs on GaAs at 300 K. The strain increaseswith increasing indium content until the epitaxial layer plas-tically relaxes via dislocations. For a single pseudomorphicIn0.21Ga0.79As QW surrounded on both sides by infinitely-thick GaAs barrier layers the in-plane lattice mismatch strainis −1.48 % at 300 K and the critical layer thickness(i.e., for a double kink relaxation mechanism) using theMatthews-Blakeslee strain balance model [9] is about 10.8 nm.The differential gain is increased by employing largerstrain [10], thus improving the maximum bit rate of suchGaAs-based VCSELs. The emission wavelength initiallyincreases with increasing indium content because addingindium (forming strained InGaAs) initially decreases theenergy gap. However, as is well known for pseudomorphicInGaAs on GaAs, adding indium simultaneously splits thedegeneracy of the heavy-hole and light-hole bands at the�-point and the associated in-plane (001)-oriented surfacebiaxial compression results in an increase in the InGaAsenergy gap. The net resulting QW peak emission wavelengthdepends on the indium content in the QWs and the thicknessesof the InyGa1−yAs layer. Considering both, the influencesof the strain and the QW thickness, we employ ∼4.2 nm-thick In0.21Ga0.79As QWs (neglecting for now the increase ofthe lattice-constant in the growth direction) and ∼6 nm-thickbarriers for our 980 nm VCSEL active region as describednext.

B. Strain-Compensated InGaAs/GaAsP QWs for High-SpeedTemperature Stable 980 nm VCSELs

Tensile strained GaAsP is another candidate for the barriermaterial [4], [5], [11]–[13] of InGaAs QWs, where the GaAsPlayers serve to balance the compressive QW strain and toincrease the depth of the QWs compared to GaAs barrierlayers for both electrons and holes. For our VCSEL activeregion, with compressively-strained In0.21Ga0.79As QWs, thein-plane strain for the GaAs0.88P0.12 barrier layers is +0.43 %relative to GaAs. Since we use multiple compressively-strainedInGaAs layers surrounded by tensile-strained GaAsP layers,latticed-matched to thick multiple AlGaAs/GaAs claddinglayers, the resultant critical thickness of the composite gainand barrier layers in the active region is more complicated,than for a single strained epitaxial layer on an infinitesubstrate. From the equations in [14] neglecting differencesin the epitaxial layer elastic constants [15] the average in-plane strain for our composite QW/barrier layers using asimple thickness-weighted-method is about −0.29 %, thus ourcomposite active region is compressively-strained. Althoughwe could increase the barrier layer thickness, the amount

Fig. 1. Real-space energy-band diagram showing the conduction and valencebands of an In0.21Ga0.79As QW with GaAs0.88P0.12 barrier layers (a) andIn0.21Ga0.79As QW with GaAs barrier layers (b). K-space dispersion ofthe valence heavy-hole and light-hole subbands for In0.21Ga0.79As QWssurrounded by GaAs0.88P0.12 barriers (c) and for In0.21Ga0.79As QWssurrounded by GaAs barriers (d) with the hole subband energies versus thein-plane (transverse) wave vector kt normalized by 2π /a.

of phosphorous in the barrier layers, or both, such thatthe net mismatch strain is ∼0 %, we experience greaterepitaxial growth accuracy by limiting these parameters toconservative values. The band alignment of the In0.21Ga0.79As/GaAs0.88P0.12 QW/barrier epitaxial layers is calculated usingthe model-solid theory [16]. The results are shown in Fig. 1(a).For comparison the band alignment for In0.21Ga0.79As/GaAs QW/barrier layers is shown in Fig. 1(b). The use ofGaAsP barrier layers results in larger conduction and valenceband offsets compared to standard In0.21Ga0.79As/GaAsQW/barrier layers. For In0.21Ga0.79As/GaAs the conductionband offset is 0.15 eV. The conduction band offset ofIn0.21Ga0.79As/GaAs0.88P0.12 QWs is 0.18 eV, 20 % largerthan for In0.21Ga0.79As/GaAs QWs. An increased conductionband offset and valence band offset is beneficial for theelectron and hole confinement [17] and reduces the thermalescape of carriers [18]. Thus VCSELs with strain compen-sated In0.21Ga0.79As/GaAs0.88P0.12 QWs will have a smallertemperature sensitivity, enabling the VCSELs to have a betterhigh temperature performance, as has been experimentallydemonstrated [19]. The larger conduction band offset willalso improve the material gain due to the lighter electronmasses [20], [21]. The valence subbands are calculated using8-band k·p theory [22], [23]. The results are shown inFig. 1(b). In order to compare the two barrier materials,we also show their valence subband structures in Fig. 1(c).One can see that In0.21Ga0.79As with GaAs0.88P0.12 barrierlayers has a larger hole energy-level separation at the �-pointbetween the first heavy-hole (HH1) and the first light-hole(LH1) subband compared to standard In0.21Ga0.79As/GaAsstructures. In addition, the degree of band warping is lowerbecause of the reduced band mixing that reduces spectral holeburning effects [24]. We also note that the effective mass ofthe heavy-holes become lighter [25], and thus the density ofstates in the valence and conduction bands are more closelymatched, resulting in a much higher differential gain and lowertransparency carrier density [26], [27].

LI et al.: IMPACT OF THE QW GAIN-TO-CAVITY ETALON WAVELENGTH OFFSET 615

Fig. 2. Calculated material gain spectra (a) at different temperatures for afixed injected carrier density of 3 × 1018 cm−3, and peak gain wavelength(b) versus temperature for a single In0.21Ga0.79As QW surrounded byGaAs0.88P0.12 barrier layers.

III. THEORETICAL STUDY OF TEMPERATURE

STABLE 980 nm VCSELS

In this section, we briefly explain why a −15 nm QWgain-to-etalon wavelength offset is particularly suitable fortemperature-stable VCSELs. We discuss the effects of thegain-to-etalon wavelength offset on both static and high-speed modulation properties of VCSELs. We seek simultane-ously high bit rate operation from 25 to 85 °C and highlytemperature stable operation across the same temperaturerange.

A. The Effect of QW Gain-to-Etalon Wavelength Offseton the Static Properties of 980 nm VCSELs

The three-dimensional cavity resonant modes determine theemission wavelengths of VCSELs. Due to the typically shorthorizontal planar cavity with perpendicular, z-direction opticalthickness of an integer multiple of λ/2 the VCSEL’s free-spectral range is typically larger than the spectral width of theQW gain, thus only one longitudinal resonant cavity etalonmode overlaps with the gain. As is well known a roomtemperature offset between the QW’s gain peak wavelengthand the cavity etalon wavelength can be introduced in VCSELssuch that these wavelengths align at elevated operating temper-atures [2]. The result may be a relatively flat threshold currentversus temperature behavior across a broad range of tempera-tures and a highly temperature insensitive output power againstcurrent (L-I) characteristic from threshold up to several mAof forward bias. The QW gain shift due to a temperaturechange can be calculated based on the standard 8-band k·ptheory [22]. In our calculations we use linear interpolation toobtain the values of the ternary materials and for the binarysemiconductors we use the data described in [28]. Fig. 2(a)shows the calculated material gain for our In0.21Ga0.79AsQWs with GaAs0.88P0.12 barrier layers at a fixed car-rier density of 3 × 1018 cm−3 for transverse-electric (TE)polarization at different temperatures from 300 to 380 K.The QW gain peak wavelengths change with active regiontemperature as shown in Fig. 2(b), with a calculated gain shiftrate of 0.396 nm/K.

Fig. 3. Calculated power reflectance at normal incidence for the full 980 nmVCSEL epitaxial structure at different temperatures (a) and the resultant cavitylongitudinal resonance (etalon dip) wavelength (b) versus the active regiontemperature.

Fig. 4. Peak gain wavelength of a single In0.21Ga0.79As/GaAs0.88P0.12QW/barrier active region and the etalon resonance wavelength of our 980 nmVCSEL versus temperature for gain-to-etalon wavelength offsets fixed at300 K at 0, −15, and −25 nm relative to the peak QW gain.

We calculated the power reflectance of our 980 nm VCSELsas a function of increasing temperature and the results areshown in Fig. 3(a), where we fixed the cavity etalon wave-length at precisely 980 nm at 300 K. The correspondingextracted cavity resonance wavelength shift with temperatureis depicted in Fig. 3(b). We note that the cavity resonancewavelength shifts to longer wavelengths as the temperatureincreases, as does the QW peak gain, but at a smaller rateof 0.061 nm/K compared to 0.396 nm/K for the QW gainpeak. Given these rates of wavelength-shift versus temper-ature we can choose a gain-to-etalon wavelength offset atroom temperature so the offset is equal to zero at a certainelevated temperature to facilitate highly temperature stableor possibly temperature insensitive operation within a limitedoperating range. The peak QW gain wavelength change ofour In0.21Ga0.79As/GaAs0.88P0.12 QW system and the 1Dfundamental longitudinal etalon resonance wavelength changefor three different VCSEL cavities with a gain-to-etalon wave-length offset at 300 K of 0, −15, and −25 nm is shownin Fig. 4. The intersection between the QW gain peak andthe cavity resonance occurs at a specific temperature, whichis 300, 347, and 376 K for 0, −15 and −25 nm offset,respectively. This temperature corresponds to the threshold,i.e., the best static working point for efficient operation.


Fig. 5. Calculated differential gain spectra for our QW active region designedfor a room temperature gain peak of 965 nm. The curves are shown for activeregion temperatures ranging from 300 to 420 K.

B. The Effect of QW Gain-to-Etalon Wavelength Offseton the High Speed Modulation Properties of VCSELs

The QW gain-to-etalon wavelength offset not only has animportant influence on the static performance, but also a largeimpact on the high-speed modulation properties [29], as thechange of the differential QW gain for a temperature increaseis noticeably reduced. This effect can be predicted based ontemperature dependent calculations of the differential gain.The differential gain versus wavelength at the threshold-gain-point for different temperatures is calculated by: 1) determin-ing the threshold gain of our VCSEL at a given temperatureaccounting for mirror losses and absorption; 2) using thesame approach as in Fig. 2(a) to determine the parametersfor the specific required QW gain; and 3) calculating thedifferential gain at this threshold-gain-point. The thresholdgain is calculated to be 472 cm−1 at 300 K for the cavitydesign we use for an emission wavelength of 980 nm. We usethis specific threshold gain for the following calculations.As expected, the calculations show that the differential gainpeak moves to longer wavelengths with elevated temperaturesand at the same time the maximum gain decreases slowly, asshown in Fig. 5.

We desire an active region with high differential gain forour VCSELs. A higher differential gain leads to a largerD-factor and thus a faster increase of relaxation resonancefrequency with current. This enables the VCSEL to reach alarger modulation bandwidth before it is limited by dampingor thermal effects [3]. In order to illustrate the importanceof the change in differential gain with temperature to thetemperature stability of our devices, we present here resultsfor gain-to-etalon wavelength offsets of 0, −15, and −25 nm.The results are depicted in Fig. 6. For this calculation the1D cavity etalon resonance wavelength values from Fig. 4were used. The highest differential gain is obtained whenthe gain-to-etalon wavelength offsets is 0 nm and the activeregion temperature is 300 K, and the differential gain decreasesrapidly with increasing temperature. The active region tem-perature Tactive increases fast with increasing operating biascurrent, and can be estimated for the linear L-I region usingTactive = Tambient + Rth × (I × V − Pout) [30], where Rth isthe thermal resistance, I and V are bias current and voltage,and Pout is the optical output power. By taking our ∼4.0 μm

Fig. 6. Differential gain versus temperature for 300 K gain-to-etalonwavelength offsets of 0, −15, and −25 nm. The lines are calculated resultsbased on 8-band k·p theory and the diamonds are experimental resultsextracted from small signal measurements on our 980 nm VCSELs.

aperture 980 nm VCSEL as an example, using an ambienttemperature of 25 °C, a bias current and voltage of 5.4 mAand 2.59 V, respectively, an optical output power of 1.78 mW,and a measured thermal resistance of 4.68 K/mW, we esti-mate an active region temperature of 82.1 °C (355.25 K),which is 57.1 °C higher than the ambient temperature. Thetemperature of the active region is always larger than theambient temperature, thus a large differential gain value atelevated temperatures is clearly important for a temperaturerobust VCSEL. The −15 nm gain-to-etalon wavelength offsetdesign has a smoother change of the differential gain across thetemperature range of 25-85 °C compared to offsets of 0 nm and−25 nm. The −15 nm offset also results in higher differentialgain at temperatures above 350 K as compared to a VCSELwith a 0 nm gain-to-etalon wavelength offset. This is clearlybeneficial for operation at high bit rates at high temperaturesfor temperature stability. Also, this larger differential gainresults in a large D-factor, which is an important factor forVCSELs reach a certain bandwidth at a low bias current, toenable a low operating power consumption. A larger offset,for example −25 nm, results in a lower differential gain at300-340 K. In addition, we note that from ∼360–385 K thedifferential gain is less than what is possible with a −15 nmoffset.

IV. EXPERIMENTAL STUDY OF TEMPERATURE

STABLE 980 nm VCSELS

The epitaxial wafers are grown by metal-organic chemical-vapor deposition (MOCVD) on n-doped GaAs-substrates byIQE plc (Cardiff, UK). We employ double mesa VCSELgeometries to facilitate improved heat dissipation. Thick pho-tosensitive bisbenzo-cyclobutene (BCB) is used, for producinga relatively flat and thick (>8 μm) dielectric planarizing layerthat serves to reduce the parasitic pad capacitance and providesa clean surface for high frequency (HF) coplanar contact pads.The coplanar ohmic contact pads for on-wafer HF probing areevaporated onto patterned photoresist by e-beam metal deposi-tion in the shape of a high-speed ground-signal-ground (GSG)configuration. The photon lifetime is modified during thefabrication process by etching the topmost (p)-GaAs DBRlayer to change the reflectivity magnitude and reflectivityphase of the top DBR to improve the dynamic modulation


Fig. 7. Static characteristics of a 980 nm VCSEL with an oxide-aperturediameter of ∼4.0 μm. (a) L-I-V-characteristics at 25 to 95 °C and the changewith temperature of (b) the threshold current (Ith) together with our calculatedminimum at 347 K, and (c) the threshold electrical power (Pth).

properties, increase the differential L-I slope, and increase theoutput power [31]. We remove ∼50 nm of the topmost layerby using a low etch-rate RIE plasma. This leads to a increaseof optical output power.

A. Static Characteristics

The static light output power-current-voltage (L-I-V) char-acteristics are measured and evaluated using our home-builtautomated wafer mapping system. Fig. 7(a) shows the L-I-Vresults for a ∼4.0 μm oxide-aperture diameter 980 nm VCSELbetween 25 and 95 °C. We determine the approximate oxideaperture diameters by measuring the emission spectra of ourVCSELs and calculate the related mode spacing as describedin [32]. As expected the threshold current (Ith) and thresholdelectrical power (Pth = Ith × Vth) decrease with increasingtemperature reaching a minimum and then increasing in aparabolic shape as shown in Fig. 7(b) and Fig. 7(c). Themeasured threshold current reaches a minimum value at around75 °C (348.15 K), very close to the calculated value of 347 Kwith a gain-to-etalon wavelength offset of −15 nm. At 25 °Cthe threshold current is 0.33 mA, and decreases to a minimumvalue of 0.25 mA at 75 °C, then increases slightly to 0.26 mAat 85 °C, with a relatively small change of only −24 % whenthe temperature increases from 25 to 85 °C.

Emission spectra are measured to compare to our one-dimensional (1D) simulation of the fundamental longitudinaletalon mode. We also use the emission spectra to determinethe thermal resistance of our 980 nm VCSELs. In Fig. 8 theemission spectrum of a ∼4 μm VCSEL is depicted at differentbias currents and temperatures. From the fundamental LP01mode peak emission we determine the cavity etalon resonancewavelength shift rate versus dissipated power �λ/�Pdiss,where Pdiss = I × V − Pout, and versus heat-sink temperature(�λ/�T ). According to [33], thermal resistance Rth canthen be determined by Rth = (�λ/�Pdiss)/(�λ/�T ). Forsmall oxide aperture diameter VCSELs (∼5 μm or smallerfor 980 nm VCSELs) the full (actual) 3D cavity resonancewavelength is shorter than for the 1D simulated wavelengthfor a given planar vertical layer structure. At larger oxideaperture diameters (>10 μm) the 3-D resonant wavelengths

Fig. 8. Measured emission spectra of our ∼4 μm VCSEL (a) at 0.4 mA atdifferent heat-sink temperatures; and (b) at 25 °C at different bias currents.

Fig. 9. Measured peak wavelength of the LP01, LP11 and LP21 modesas a function of the oxide aperture diameter (a) and change of the peakwavelength (b) of the fundamental mode versus dissipated heat and versusheat-sink temperature, and the thermal resistance Rth (c), all as a function ofthe oxide aperture diameter.

merge toward the large (infinite) area 1D values [34]–[36],as is implied by Fig. 9(a). The measured shift-rate of thecavity resonance wavelength is quite constant 0.062 nm/K asshown in Fig. 9(b), and increases slightly for oxide aperturediameters greater than ∼3.5 μm. This rate is in excellentagreement with the calculated value of 0.061 nm/K. We alsoshow the cavity resonance wavelengths shift rate with appliedelectrical power for different aperture diameters, which isaperture dependent, demonstrating the thermal resistance tobe aperture dependent. For very small aperture diameters, theVCSELs suffer from large active region temperatures due tothe large thermal resistance. In Fig. 9(c), we show a plot ofthermal resistance as a function of oxide aperture diameterusing the data in Fig. 9(b).

B. Dynamic Small Signal Modulation Analysis

We perform small-signal modulation response and reflectionmeasurements at different currents and heat-sink temperatures.We previously reported temperature dependent small signalanalysis results [37]. With our newly processed VCSEL wafersreported here, using a new mask set, we perform a morein-depth study of temperature stability. Also, we adjusted thephoton lifetime of these devices to improve the bandwidthas well as the optical output power [31]. The small signalresponse (i.e., the measured S21 scattering parameters) of aVCSEL with a ∼4.0 μm oxide-aperture diameter is shown


Fig. 10. Measured small signal modulation response together with fits ofthe small signal transfer function at increasing bias currents for a ∼4.0 μmoxide aperture diameter 980 nm VCSEL (a) and −3dB bandwidth versus biascurrent (b) at 25, 45, 65 and 85 °C.

Fig. 11. Real (a) and imaginary parts (b) of s-parameters reflectionmeasurements (S11) on a 980 nm VCSEL. The circles are the measured data,and the solid lines represent the curve fits using an equivalent circuit model.

Fig. 10(a) at the bias current (5.4 mA) of a 38 Gb/s datatransmission experiments at 25, 45, 65 and 85 °C (shownlater in Fig. 14), together with fits to the data using a transferfunction [3] to extract the relaxation resonance frequency ( fr)and the damping factor (γ ). The response of the detector(New Focus 1434) is subtracted to eliminate its influenceon the measured response. To obtain the parasitic cut-offfrequencies we perform S11 reflection measurements and fitthe data to a small-signal electrical equivalent circuit model[38], [39]. Fig. 11 shows the S11 measurement results and thefit for the ∼4.0 μm VCSEL operated at different currents at25 °C. The fits and measurement data match very well thuswe believe the equivalent circuit model suits our VCSELs.The −3dB bandwidth f−3dB is an important parameter todetermine the high-speed capability of VCSELs, since itis directly related to the maximum achievable bit rate. Byplotting the −3dB bandwidth versus the bias current fortemperatures of 25, 45, 65, and 85 °C as depicted in Fig. 10(b),we find for currents smaller than 3 mA our VCSELs havelarger −3 dB bandwidths at the higher temperatures, thus at85 °C our VCSELs achieve a higher bandwidth compared to25 °C. For currents above ∼4 mA our VCSELs operate fasterat 25 °C compared to higher temperatures, where thermaleffects introduced by Joule heating lead to a reduced f−3dBat a given current. With our VCSELs a very temperaturestable modulation bandwidth is demonstrated with a smallchange of only 1.4 GHz across the temperature range from

Fig. 12. (a) Relaxation resonance frequency versus square root of bias currentminus threshold current for a ∼4.0 μm oxide aperture diameter VCSEL at25, 45, 65 and 85 °C. (b) The extracted (dots) and calculated (line) D-factors;(c) extracted (dots) and calculated (line) relaxation resonance frequencies, and(d) −3dB bandwidth at different temperatures at the bias condition (5.4 mA)of the temperature-stable 38 Gb/s data transmission experiments.

25 to 85 °C, as shown in Fig. 10(a). For 5.4 mA bias current,the −3dB bandwidth is 20.5, 20.7, 19.6, and 18.3 GHz for25, 45, 65, and 85 °C, respectively. For a lower current of3.6 mA, our VCSELs also show 38 Gb/s error free transmis-sion at 45, 65, and 85 °C with a low energy consumptionas we recently reported [40]. For these same VCSELs at25 °C a minor adjustment of the bias of plus 0.1 mA toslightly increase the −3dB bandwidth was necessary to obtainerror free operation. We can see from Fig. 10(b), for currentslarger than 3.7 mA the −3dB bandwidth is nearly constantat ∼18 GHz for 85 °C, and larger than 18 GHz at lowertemperatures. Thus our VCSELs can operate across a largecurrent range at high bit rates and at temperatures from 25to 85 °C. A nearly temperature independent high bit rate ispossible. For example, 38 Gb/s error free transmission can beachieved at currents above 3.7 mA with no need to change thebias or the modulation conditions from 25 to 85 °C.

The dependence of the relaxation resonance frequency fron the bias current and the D-factor (D) can be derivedfrom standard laser diode rate-equation theory [3] and canbe expressed as:

fr = D√

(I − Ith) (1)

with D = 1

2π

√ηi�vg

qva· ∂g/∂n

χ(2)

where ηi is the internal quantum efficiency, � is the opticalconfinement factor, νg is the group velocity, Va the activeregion volume, ∂g/∂n is the differential gain, and χ is thetransport factor. The D-factor is an important parameter forVCSEL dynamics it describes how fast the relaxation reso-nance frequency fr increases with increasing bias current (I )above the threshold current (Ith). A large D-factor implies theVCSEL can reach large relaxation resonance frequencies frat low bias currents. The D-factor is obtained from the lineardependence of the relaxation resonance frequency on thesquare root of current above threshold at low currents, wherethe increase of the active region temperature due to self-heating is small.


Fig. 13. Bit error ratio versus received optical power for 980-nm VCSELswith oxide-aperture diameters of ∼4.0 μm operating at 35, 38 and 42 Gb/s at25 °C, respectively, across 5 m of MMF with a PRBS word length of 27−1 bitand an NRZ modulation scheme. Optical eye diagrams at the correspondingbit rates and modulation conditions are also shown.

The extracted frequencies fr and the corresponding linearfits for our 980 nm VCSELs are shown in Fig. 12(a). Thesecurves are different from what is typically observed, since ourD-factor is larger at 85 °C compared to the value at 25 °C.For our specific design with a −15 nm gain-to-etalon wave-length offset, a reverse point, where the relaxation resonancefrequency at low temperature starts to exceed the value athigher temperatures, can easily be seen. Although the D-factoris larger for higher operating temperatures, the relaxation res-onance frequency reaches a maximum at room temperature, asshown in Fig. 12(b). This can be explained by the differentialgain change with temperature. As the current increases, theactive region temperature increases and the differential gainachieves a maximum value at around 360 K (∼87 °C). Startingat ∼25 °C the differential gain increases with increasing biascurrent, such that higher relaxation resonance frequencies canbe reached before a thermal limitation is induced by resistiveheating. Also the differential gain for different temperatures isextracted from the corresponding D-factors by using equation(2) [10], [41]. By comparing these values with the calculatedones we observe excellent agreement between theory andexperiment, as shown by the diamonds in Fig. 6. As we knowfrom theoretical analysis, these stable D-factors are a result ofthe proper −15 nm etalon-to-gain wavelength offset design,resulting in a relatively small change in differential gainwith temperature. With similar high values of the D-factor atroom temperature and at high temperatures, we achieve high-speed operation and energy efficiency from room temperatureto 85 °C.

C. Data Transmission Experiments

We perform data transmission measurements at variousbit rates and heat-sink temperatures. The pseudorandom bitpatterns were generated by a 12100B bit pattern generatorfrom SHF Communication Technologies AG (Berlin, Ger-many) followed by an +8 dB amplifier and a −3 dB elec-trical attenuator to compensate for the losses of the electricalwires. After amplification, the signal was superimposed tothe DC biased VCSEL using a 65-GHz SHF bias-tee and a

Fig. 14. Bit error ratio versus received optical power for 980-nm VCSELswith oxide-aperture diameters of ∼4.0 μm operating at 38 Gb/s at 25, 45,65 and 85 °C, respectively, across 5 m of MMF with a PRBS word lengthof 27 − 1 bit and an NRZ modulation scheme. Optical eye diagrams at thecorresponding temperatures and modulation conditions are also shown.

67 GHz-rated coplanar GSG probe. We use simple fiber-to-VCSEL butt-coupling into 5 m long OM2 multi-modefiber. We use a variable optical attenuator in front of thephotoreceiver for both the determination of the bit error ratio(BER) and for measurements of the optical eye diagrams.Optical eye diagrams and bit error ratio measurements werestudied using a 70 GHz Agilent sampling oscilloscope 86100Cand a SHF 11100B error analyzer. We use an u2t PhotonicsAG photoreceiver with an integrated limiting transimpedanceamplifier having a bandwidth of ∼28 GHz for recordingthe optical eye diagrams and for measuring the BERs. Theresults of these BER data transmission measurements forerror-free operation (defined as a BER <1 × 10−12) at42, 38, and 35 Gb/s are shown in Fig. 13 along withthe corresponding optical eye diagrams. For all transmis-sion measurements we use a standard non-return to zero(NRZ) modulation scheme with a 27 − 1 bit word-lengthin a pseudorandom binary sequence (PRBS). The values ofthe electrical energy-to-data ratio (EDR) and the dissipatedheat-to-bit rate ratio (HBR) defined as EDR = Pel/BR andHBR = (Pel − Popt)/BR, where Pel is the input CW power,Popt is the output power and BR is the bit rate [42], areshown in Fig. 13. The devices are measured at operatingcurrents that require the minimum energy per bit. Thus, atthe given bit rate, the VCSELs are operated at the lowestcurrents where still error-free transmission can be observed.We achieve 35 Gb/s error free transmission with only 175 fJof dissipated heat energy per bit at room temperature. Thisis a record low value for 980 nm VCSELs. At 38 Gb/sfor error-free transmission at 85 °C we achieve an energyefficiency of 177 fJ/bit [40]. The maximum bit rate of 4.0 μmoxide aperture diameter VCSEL decreases from 42 Gb/s to38 Gb/s, a 9.5 % decrease, when the temperature increasesfrom 25 to 85 °C. The HBR at 38 Gb/s decreases from 197 to177 fJ/bit, a 10 % decrease, when the temperature increasesfrom 25 to 85 °C. We also achieve error-free operation at38 Gb/s at 25, 45, 65, and 85 °C at the same biasing andmodulation conditions. In Fig. 14 we find that up to tempera-tures of 65 °C no penalty of the received optical power occurs.We attribute this simultaneous high temperature stability, highbit rate, and low energy dissipation per bit performance


primarily to the −15 nm etalon-to-gain wavelength offsetdesign.

V. CONCLUSION

In our GaAs-based 980 nm VCSELs composed ofInGaAs/GaAsP QW/barrier layers and AlGaAs DBRs wefind that a −15 nm QW gain-to-cavity etalon wavelengthoffset facilitates simultaneously temperature stable, energyefficient, and high bit rate operation. We experimentallydemonstrate high-bit-rate, temperature-stable, energy-efficient980 nm VCSELs, operating at 42 and 38 Gb/s at 25 and 85 °Cwith low power consumption, respectively. Record low 175 fJof dissipated heat energy per bit is demonstrated for 35 Gb/serror-free transmission at room temperature. Most important,our VCSELs can operate error-free at a bit rate of 38 Gb/s at25, 45, 65, and 85 °C, without any change of the operatingpoint or the modulation conditions. Our VCSELs demonstratevery temperature insensitive static and dynamic characteristics.We attribute these results to our use of an InGaAs QW andGaAsP barrier layer active region design, and our gain-to-etalon wavelength offset.

ACKNOWLEDGMENT

We very gratefully thank u2t Photonics AG (Berlin,Germany) for providing the photoreceiver.

REFERENCES

[1] M. A. Taubenblatt, “Optical interconnects for high-performance com-puting,” J. Lightw. Technol., vol. 30, no. 4, pp. 448–457, Feb. 15, 2012.

[2] D. B. Young et al., “Enhanced performance of offset-gain high-barriervertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.,vol. 29, no. 6, pp. 2013–2022, Jun. 1993.

[3] L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic IntegratedCircuits. New York, NY, USA: Wiley, 1995, pp. 195–245.

[4] A. Mutig et al., “Modulation characteristics of high-speed and high-temperature stable 980 nm range VCSELs operating error free at25 Gbit/s up to 85 °C,” IEEE J. Sel. Topics Quantum Electron., vol. 17,no. 6, pp. 1568–1575, Nov./Dec. 2011.

[5] A. Mutig and D. Bimberg, “Progress on high-speed 980 nm VCSELsfor short-reach optical interconnects,” Adv. Opt. Technol., vol. 2011,pp. 1–15, Jun. 2011.

[6] Y.-C. Chang and L. A. Coldren, “Efficient, high-data-rate, tapered oxide-aperture vertical-cavity surface-emitting lasers,” IEEE J. Sel. TopicsQuantum Electron., vol. 15, no. 3, pp. 704–715, May/Jun. 2009.

[7] R. Safaisani, J. R. Joseph, and K. L. Lear, “Scalable high-CW-powerhigh-speed 980-nm VCSEL arrays,” IEEE J. Quantum Electron., vol. 46,no. 11, pp. 1590–1596, Nov. 2010.

[8] P. Moser et al., “85 °C error-free operation at 38 Gb/s of oxide-confined 980-nm vertical-cavity surface-emitting lasers,” Appl. Phys.Lett., vol. 100, no. 8, pp. 081103-1–081103-3, Feb. 2012.

[9] J. W. Matthews and A. E. Blakeslee, “Defects in epitaxial multilayers: I.Misfit dislocations,” J. Cryst. Growth, vol. 27, pp. 118–125, Dec. 1974.

[10] S. B. Healy et al., “Active region design for high-speed 850-nmVCSELs,” IEEE J. Quantum Electron., vol. 46, no. 4, pp. 506–512,Apr. 2010.

[11] H. Q. Hou, K. D. Choquette, K. M. Geib, and B. E. Hammons,“High-performance 1.06-μm selectively oxidized vertical-cavity surface-emitting lasers with InGaAs-GaAsP strain-compensated quantum wells,”IEEE Photon. Technol. Lett., vol. 9, no. 8, pp. 1057–1059, Aug. 1997.

[12] A. N. Al-Omari, G. P. Carey, S. Hallstein, J. P. Watson, G. Dang, andK. L. Lear, “Low thermal resistance high-speed top-emitting 980-nmVCSELs,” IEEE Photon. Technol. Lett., vol. 18, no. 11, pp. 1225–1227,May/Jun. 15, 2006.

[13] H. Hatakeyama et al., “Highly reliable high-speed 1.1-μm-rangeVCSELs with InGaAs/GaAsP-MQWs,” IEEE J. Quantum Electron.,vol. 46, no. 6, pp. 890–897, Jul. 2010.

[14] N. J. Ekins-Daukes et al., “Strain-balanced GaAsP/InGaAs quantumwell solar cells,” Appl. Phys. Lett., vol. 75, no. 26, pp. 4195–4197,Dec. 1999.

[15] N. J. Ekins-Daukes, K. Kawaguchi, and J. Zhang, “Strain-balancedcriteria for multiple quantum well structures and its signature inX-ray rocking curves,” Cryst. Growth Design, vol. 2, no. 4, pp. 287–292,Apr. 2002.

[16] C. G. Van de Walle, “Band lineups and deformation potentials inthe model-solid theory,” Phys. Rev. B, vol. 39, no. 3, pp. 1871–1883,Jan. 1989.

[17] J.-W. Pan and J.-I. Chyi, “Theoretical study of the temperature depen-dence of 1.3-μm AlGaInAs–InP multiple-quantum-well lasers,” IEEE J.Quantum Electron., vol. 32, no. 12, pp. 2133–2138, Dec. 1996.

[18] J. Tignon et al., “Carrier dynamics in shallow GaAs/AlGaAs quantumwells,” Phys. E, vol. 2, no. 1, pp. 126–130, Jul. 1998.

[19] C. Chen, P. O. Leisher, A. A. Allerman, K. M. Geib, andK. D. Choquette, “Temperature analysis of threshold current in infraredvertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron.,vol. 42, no. 10, pp. 1078–1083, Oct. 2006.

[20] K. M. Lau, “Ultralow threshold quantum well lasers,” in QuantumWell Laser, P. S. Zory, Ed. San Diego, CA, USA: Academic, 1993,pp. 198–203.

[21] A. R. Adams, “Strained-layer quantum-well lasers,” IEEE J. Sel. TopicsQuantum Electron., vol. 17, no. 5, pp. 1364–1373, Sep/Oct. 2011.

[22] T. Fujisawa et al., “Successful application of the 8-band theory to opticalproperties of highly strained In(Ga)As/InGaAs quantum wells withstrong conduction-valence band coupling,” IEEE J. Quantum Electron.,vol. 45, no. 9, pp. 1183–1191, Sep. 2009.

[23] S. L. Chuang, “Efficient band-structure calculations of strained quantumwells,” Phys. Rev. B, vol. 43, no. 12, pp. 9649–9661, Apr. 1991.

[24] D. Ahn, “Theoretical studies of strained-layer quantum-welllasers,” in Strained-layer Quantum Wells and their Applications,M. O. Manasreh, Ed. Amsterdam, The Netherlands: CRC Press, 1997,pp. 18–20.

[25] D. Lancefield et al., “The light-hole mass in a strained InGaAs/GaAssingle quantum well and its pressure dependence,” J. Phys. Chem. Solids,vol. 56, nos. 3–4, pp. 469–473, Jan. 1995.

[26] Y.-A. Chang, J.-R. Chen, H.-C. Kuo, Y.-K. Kuo, and S.-C. Wang,“Theoretical and experimental analysis on InAlGaAs/AlGaAs activeregion of 850-nm vertical-cavity surface-emitting lasers,” J. Lightw.Technol., vol. 24, no. 1, pp. 536–543, Jan. 2006.

[27] N. K. Dutta et al., “Strain compensated InGaAs-GaAsP-InGaP laser,”IEEE Photon. Technol. Lett., vol. 8, no. 7, pp. 852–854, Jul. 1996.

[28] I. Vurgaftman, J. R. Meyer, and L. R. Ram-Mohan, “Band parametersfor III–V compound semiconductors and their alloys,” J. Appl. Phys.,vol. 89, no. 11, pp. 5815–5875, Feb. 2001.

[29] E. S. Björlin, J. Geske, M. Mehta, J. Piprek, and J. E. Bowers,“Temperature dependence of the relaxation resonance frequency of long-wavelength vertical-cavity lasers,” IEEE Photon. Technol. Lett., vol. 17,no. 5, pp. 944–946, May 2005.

[30] T. Flick, K. H. Becks, J. Dopke, P. Mattig, and P. Tepel, “Measurementof the thermal resistance of VCSEL devices,” J. Instrum., vol. 6, no. 1,pp. 1–5, Jan. 2001.

[31] P. Westbergh, J. S. Gustavsson, B. Kögel, Å. Haglund, and A. Larsson,“Impact of photon lifetime on high-speed VCSEL performance,” IEEEJ. Sel. Topics Quantum Electron., vol. 17, no. 6, pp. 1603–1613,Nov./Dec. 2011.

[32] C. H. Wu, F. Tan, M. K. Wu, M. Feng, and N. Holonyak, “The effectof microcavity laser recombination lifetime on microwave bandwidthand eye-diagram signal integrity,” J. Appl. Phys., vol. 109, no. 5,pp. 053112-1–053112-9, Jan. 2011.

[33] R. Michalzik, “VCSEL Fundamentals,” in VCSELs: Fundamentals,Technology and Applications of Vertical-Cavity Surface-Emitting Lasers,vol. 166, R. Michalzik, Ed. Berlin, Germany: Springer-Verlag, 2013,pp. 19–75.

[34] M. J. Noble, J.-H. Shin, K. D. Choquette, J. P. Loehr, J. A. Lott, andY.-H. Lee, “Calculation and measurement of resonant-mode blueshifts inoxide-apertured VCSELs,” IEEE Photon. Technol. Lett., vol. 10, no. 4,pp. 475–477, Apr. 1998.

[35] M. J. Noble, J. P. Loehr, and J. A. Lott, “Analysis of microcavityVCSEL lasing modes using a full-vector weighted index method,” IEEEJ. Quantum Electron., vol. 34, no. 10, pp. 1890–1903, Oct. 1998.

[36] P. Bienstman et al., “Comparison of optical VCSEL models on thesimulation of oxide-confined devices,” IEEE J. Quantum Electron.,vol. 37, no. 12, pp. 1618–1631, Dec. 2001.


[37] A. Mutig et al., “Highly temperature-stable modulation characteristics ofmultioxide-aperture high-speed 980 nm vertical cavity surface emittinglasers,” Appl. Phys. Lett., vol. 97, no. 15, pp. 151101-1–151101-3,Oct. 2010.

[38] A. Bacou et al., “VCSEL intrinsic response extraction using T -matrixformalism,” IEEE Photon. Technol. Lett., vol. 21, no. 14, pp. 957–959,Jul. 15, 2009.

[39] Y.-C. Chang and L. A. Coldren, “High-efficiency, high-speed VCSELsfor optical interconnects,” Appl. Phys. A, vol. 95, no. 4, pp. 1033–1037,Feb. 2009.

[40] H. Li et al., “Energy-efficient and temperature-stable oxide-confined980 nm VCSELs operating error-free at 38 Gbit/s at 85 °C,” Electron.Lett., vol. 50, no. 2, pp. 103–105, Jan. 2014.

[41] Y. Wei, J. S. Gustavsson, M. Sadeghi, S. M. Wang, and A. Larsson,“Dynamics and temperature-dependence of 1.3-μm GaInNAs doublequantum-well lasers,” IEEE J. Quantum Electron., vol. 42, no. 12,pp. 1274–1280, Dec. 2006.

[42] P. Moser et al., “81 fJ/bit energy-to-data ratio of 850 nm vertical-cavity surface-emitting lasers for optical interconnects,” Appl. Phys.Lett., vol. 98, no. 23, pp. 231106-1–231106-3, Jun. 2011.

Hui Li received the B.S. and M.S. degrees in physicsfrom Shandong Normal University, Jinan, China,and Zhengzhou University, Zhengzhou, China, in2008 and 2011, respectively. She is currently pur-suing the Ph.D. degree in physics with the Centerof Nanophotonics, Technische Universität Berlin,Berlin, Germany.

Her research interests include the fabrication, mod-eling, and characterization of VCSELs for opticalinterconnects.

Philip Wolf received the Diploma (M.S. equivalent)degree in applied physics from Technische Univer-sität Berlin, Berlin, Germany, in 2011, where he iscurrently pursuing the Ph.D. degree in physics withthe Center of Nanophotonics.

His main research interests include the fabrica-tion and characterization of ultrahigh-speed, energy-efficient and temperature-stable surface emitters foroptical interconnects.

Mr. Wolf was a recipient of the SPIE GreenPhotonics Award for Communications in 2012 and

2014.

Philip Moser (S’12) was born in Berlin, Germany,in 1983. He received the Diploma (M.S. equivalent)degree in applied physics from the Technical Univer-sity of Berlin, Berlin, in 2008, where he is currentlypursuing the Ph.D. degree in physics with the Centerof NanoPhotonics.

His research interests include the fabrication andcharacterization of directly and indirectly modulatedhigh-speed vertical-cavity surface-emitting lasersand related nano and micrometer-scale quantumdevice structures.

Mr. Moser was a recipient of the SPIE Green Photonics Award in Commu-nications in 2012 and 2014, the European Commission’s Photonics21 StudentInnovation Award for his work on energy-efficient vertical-cavity surface-emitting lasers in 2014, and the Dimitri N. Chorafas Foundation Award forhis doctoral research to date in 2012.

Gunter Larisch received the Diploma (M.S. equiv-alent) degree in applied physics from TechnischeUniversität Berlin, Berlin, Germany, in 2011, wherehe is currently pursuing the Ph.D. degree in appliedphysics. His current work includes the fabrica-tion, characterization, and application of high-speedVCSELs.

Alex Mutig received the M.S. degree in physicsand the Ph.D. degree from the Research Group ofProf. D. Bimberg, Technical University of Berlin(TUB), Berlin, Germany, in 2004 and 2010, respec-tively. During the Ph.D. research, he developed high-speed and high-temperature stable VCSELs for shortreach optical interconnects. For the Ph.D. research,he received the Springer Theses Prize in 2011 andthe SANDiE Ph.D. Prize from 2008 to 2010. From2010 to 2012, he was a Post-Doctoral Scholar withthe Research Group of Prof. Yablonovitch, Univer-

sity of California at Berkeley, Berkeley, CA, USA, where he investigated novelenergy-efficient electronic devices based both on Si and III–V semiconductorsfor future computing applications. Since 2012, he has been with InfineonTechnologies AG, Munich, Germany, as a Project Manager in TechnologyDevelopment, where he is managing projects for new generations of Infineon’sproducts.

James A. Lott (SM’99) was born in Sunnyvale, CA,USA. He received the B.S. degree in electrical engi-neering and computer science from the Universityof California at Berkeley, Berkeley, CA, USA, in1983, and the Ph.D. degree in electrical engineeringfrom the University of New Mexico, Albuquerque,NM, USA, in 1993. He performed research at SandiaNational Laboratories, Albuquerque, from 1988 to1993. From 1993 to 2006, he was a Professorwith the Air Force Institute of Technology, Wright-Patterson AFB, OH, USA, including sabbatical peri-

ods at the NEC Optoelectronics Research Laboratories, Tsukuba, Japan, in1995, and at Samsung Electronics Company, Suwon, Korea, in 1996. He iscurrently a Visiting Professor with the Technische Universität Berlin, Berlin,Germany.

Dieter H. Bimberg (F’13) received the Ph.D.degree. He was a Principal Scientist with the MaxPlanck Institute for Solid-State Research, Grenoble,France, after the Ph.D. study. After serving as aProfessor of Electrical Engineering with the Tech-nical University of Aachen, Aachen, Germany, he iscurrently the Chair of Applied Solid-State Physicswith the Technical University of Berlin, Berlin,Germany, where he is also the Director of the Centerof NanoPhotonics. He was a Guest Professor withTechnion, Haifa, Israel, the University of California

at Santa Barbara, Santa Barbara, CA, USA, Hewlett-Packard, Palo Alto, CA,USA, and King Abdulaziz University, Jeddah, Saudi Arabia. He is a memberof the Russian Academy of Sciences and the German Academy of SciencesLeopoldina, an Associate of the National Institute of Engineering, and a fellowof the American Physical Society. He has authored more than 1400 papersand six books, and holds 24 patents. His work has been cited more than44 000 times and his h-index (Hirsch index) is 91. His research interestsinclude the physics and technology of nanostructures and nanostructuredphotonic devices.

Documents

Impact of the Quantum Well Gain-to-Cavity Etalon Wavelength Offset on the High Temperature Performance of High Bit Rate 980-nm VCSELs