IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 51, NO. 1, JANUARY 2015 2000109

Effect of Undercut Etch on Performance andFabrication Robustness of Metal-Clad

Semiconductor NanolasersJanelle Shane, Qing Gu, Alan Potterton, and Yeshaiahu Fainman, Fellow, IEEE

Abstract— We use optical, thermal, and electrical simulationto evaluate the effects of using varying amounts of undercut etchon wavelength-scale and subwavelength metal-clad semiconduc-tor nanolasers (MCSELs). We find that as MCSEL diameterdecreases, the optical performance becomes more sensitive toslight amounts of sidewall tilt. A modest amount of undercut(25%) dramatically improves the optical performance, reducingmodal threshold gain to 100 cm−1 or less for lasers withcore radius of 225, 550, or 775 nm, even in the presenceof significant sidewall tilt (20° gain sidewall or ±8° pedestalsidewall tilt). Finally, we examine the effects of the increasedundercut on nanolaser thermal performance and find that theincreased resistive heating is insignificant near threshold, evenfor subwavelength nanolasers.

Index Terms— Semiconductor lasers, nanoscale devices, ther-mal management, design optimization, nanofabrication.

I. INTRODUCTION

METAL-CLAD semiconductor nanolasers (MCSELs)have been improving in robustness and reliability

since their first demonstration by Hill and colleagues in2007 [1]. This class of laser has a cavity enclosed by metal,providing mode confinement [2], [3] and thus decreasinglaser and mode footprint to subwavelength scale in all threedimensions [1]. Attractive as wavelength-scale or subwave-length light sources for sensing or dense chip-scale photonicintegration, MCSELs have advanced beyond their originaloptically-pumped [4] and/or cryogenic [1], [5] demonstrationsto CW electrically-pumped subwavelength sources operatingat room temperature [6]. As MCSELs move beyond these firstproof-of-principle demonstrations, efficiency and robustnessare both issues that future laser designs will need to address.

A major measure of the efficiency of a nanolaser is thethreshold gain of the lasing mode. A low threshold gain

Manuscript received August 15, 2014; revised November 12, 2014; acceptedNovember 14, 2014. Date of publication November 20, 2014; date of currentversion December 15, 2014. This work was supported in part by the CymerCorporation, in part by the National Science Foundation under Grant ECCS-1229677, Grant ECE-3972, Grant EEC-0812072, and Grant Y502629, in partby the Defense Advanced Research Projects Agency, Arlington, VA, USA,under Grant N66001-12-1-4205, in part by the Office of Naval Research,Arlington, VA, USA, under Grant N00014-13-1-0678.

J. Shane, Q. Gu, and Y. Fainman are with the Department of Elec-trical and Computer Engineering, University of California at San Diego,La Jolla, CA 92093 USA (e-mail: janelle.shane@gmail.com; qigu@uscd.edu;fainman@ucsd.edu).

A. Potterton is with the Department of Physics, San Diego City College,San Diego, CA 92101 USA (e-mail: alan.potterton@yahoo.com).

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.2014.2371851

not only makes the most efficient use of the pump, butalso minimizes the effects of self-heating, which includesterms with square and cubic dependencies on pump current.At higher pump currents, the phenomenon of self-heatingcan raise the temperature in the gain region, here referred toas the laser’s operating temperature, well above that of theambient temperature. At higher temperatures, the cavity metalbecomes more lossy [7], a particularly detrimental effect fornanolasers with high modal overlap with metal [8]. Additionalself-heating will reduce the available material gain, and atextreme temperatures may destroy the laser. Even if heat canbe effectively dissipated, the gain spectrum broadens and blue-shifts at higher currents, which can shift the gain maximumaway from the designed cavity mode [7]. To increase laseroutput power and efficiency while avoiding the detrimentaleffects of self-heating, it is critical to reduce threshold gain.

Many strategies have been employed to reduce thresholdgain in nanolasers. The threshold gain gth of a lasing mode isdefined as

gth = nω0

c�Q

where ω0 is the modal frequency, n is the refractive index ofthe gain medium, c is the speed of light in vacuum. � is themode-gain overlap, related to how well the cavity confines themode to the gain region, while Q is the mode’s quality factor,related to the amount of scattering and material absorptionloss the mode experiences. Efforts to reduce threshold gainin MCSELs need to target �, Q, or both. For example,adding a thick dielectric shield between the gain and themetal cladding reduced the amount of modal overlap withthe metal, increasing Q enough to allow room temperatureoperation [4], [8]. For electrically pumped MCSELs, an addedchallenge is the necessity of providing a pathway for electricalinjection of carriers into the gain region; this necessitatesthe use of doped semiconductor pedestal layers above andbelow the gain region, impacting gain confinement due tothe low refractive index contrast between pedestal and gain.A strategy used to reduce threshold gain in electrically pumpednanolasers is to undercut the pedestal layers, decreasing modepenetration into the surrounding semiconductor layers [5].An example electrically pumped MCSEL with dielectric shieldand undercut pedestals is shown in Fig. 1.

Any nanolaser design needs to not only have low gth , butshould also be robust with respect to fabrication variation.

0018-9197 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

2000109 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 51, NO. 1, JANUARY 2015

Fig. 1. Diagram of an example simulated nanolaser, with gain sidewallangle θg and pedestal sidewall angle θp both positive. In the optical simula-tions, the area surrounding the silver cladding layer is also silver, since theskin depth of the emission wavelength is only a few nanometers. In the thermalsimulations, the area surrounding the cladding is air. The laser is allowed todissipate heat through the bottom of the 350 μm thick InP substrate, throughradiation to air, and through a thermally conductive contact wire attached tothe cladding 20 μm away.

One of the major issues encountered during MCSEL fab-rication is non-vertical gain and pedestal sidewalls. Even aslight sidewall tilt of a degree or less can be enough toprofoundly affect the gth of a fabricated nanolaser [9], [10].Gu and coworkers analyzed the performance of a fabricatedelectrically-pumped device and found that the non-zero side-wall tilt achieved during fabrication raised gth to the degree towhich lasing was unlikely even at cryogenic temperatures [11].One method of dealing with the detrimental effects of sidewalltilt is careful calibration of the etching process to compen-sate for regular fluctuation in etching chamber conditions; toconsistently achieve sidewalls with less than a degree of tiltseveral calibration test samples must be etched and imagedbefore each nanolaser sample is etched [10].

In this paper, we show that undercut etching, already usefulfor reducing MCSEL gth , also makes the nanolaser resistant tothe effects of sidewall tilt. In Section II-A we first expand onthe work of Ding and coworkers [10] by examining the effectsof sidewall tilt on nanolasers without undercut, having coreradii of 225nm, 550nm, and 775nm. We find that the effectsof sidewall tilt become more dramatic as core radius decreases.In Section II-B we show that a moderate undercut (25%)eliminates the detrimental effects of sidewall tilt, producingthreshold gains that would allow room-temperature operationeven for nanolasers with gain sidewall tilts of 20°. We find thata 25% undercut will produce similarly good results regardlessof nanolaser diameter, gain sidewall angle, or pedestal sidewallangle. In Section III we then analyze the effects of theseundercuts on the heat generated by the nanolaser, and findthat the additional undercut has no significant effect on thenanolaser self-heating, or on final operating temperature fora laser operating within an order of magnitude of threshold.We conclude that undercutting is a robust strategy for reducingthreshold gain and sensitivity to sidewall angle, while carryingno significant heat penalty.

Fig. 2. (a) Threshold gain of the lowest-threshold modes for modeled laserswith average gain radius of 225nm (blue solid line), 550nm (red dashed line),and 775nm (green dotted line), as a function of laser sidewall angle. Theselasers have no undercut etch. (b–d) Electric field of the lowest thresholdmode for lasers with enough sidewall tilt to give them thresholds of about1000 cm−1. (b) Laser with rcore = 225nm and sidewall angle of 0.5°.(c) Laser with rcore = 550nm and sidewall angle of 2°. (d) Laser withrcore = 775nm and sidewall angle of 3°.

II. OPTICAL SIMULATION

A. Effect of Sidewall Tilt on Threshold Gain forLasers Without Undercut

The typical pedestal MCSEL fabrication process begins withthe use of electron beam lithography to create a mask thatdefines the pillar’s footprint, followed by reactive ion etching(RIE) to create the pillar. Depending on small fluctuations inetching chamber conditions, an etching recipe calibrated tocreate vertical sidewalls may often produce angled sidewalls.Ding and Ning examined the effects of angled sidewalls on theTE01 mode of a nanolaser with 230nm radius and found thateven a slight 1–2° sidewall tilt causes a factor of 5 decreasein cavity Q [10].

We use 3D finite element simulation (COMSOL) to sim-ulate the effects of different amounts of sidewall tilt onnanolasers of different core radius. Each nanolaser is cre-ated from the InP/InGaAs/InP double heterostructure usedin [1], [5], and [11], whose gain medium is a 300nm thicklayer of intrinsic bulk In0.53Ga0.47As. The lasers each have170nm thick shields of α-Al2O3 (amorphous aluminum oxide),surrounded by silver cladding. We model the materials usingtheir optical parameters at a temperature of 300K and awavelegth of 1550nm; the permittivity used for silver is−130.6–3.33j, as calculated using a temperature-dependentDrude model and data from Johnson and Christy [12] bySmalley et al [7]. Each laser is fully etched to the bottomcontact layer, giving the laser a height of 1745nm measuredfrom the top of the top contact to the bottom of the pillar.We vary the angle of each laser’s sidewalls while keeping theaverage gain radius constant; results are shown in Fig. 2.

From the simulation results, we find that nanolasers of225nm, 550nm, and 775nm core radius are all sensitive to theeffects of sidewall tilt, with the lasers suffering from increasedradiative loss through the laser pedestal and decreased modeconfinement as tilt increases. The effects of sidewall tiltbecome more extreme as gain radius decreases. In agreement

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with Ding and Ning [10], we find that a subwavelengthnanolaser designed for the TE01 mode is extremely sensitiveto sidewall angle. For the laser with core radius of 225nm(Fig. 2b), a sidewall tilt of just 0.5° yields a threshold gainexceeding 1000 cm−1, making room-temperature operationunlikely for our gain material at this wavelength, and inef-ficient for other gain materials. For larger nanolasers, theeffects of sidewall tilt are still severe, with threshold exceeding1000 cm−1 at 2° tilt for the 550nm core laser (Fig. 2 c), andat 3° tilt for the 775nm core laser (Fig. 2 d).

Some method of dealing with sidewall tilt is clearly neededif nanolasers are to be reliably produced for room-temperatureoperation. One strategy that has been successfully employed isto recalibrate the etching recipe each time a nanolaser sampleis to be etched [10]. An alternative strategy that would avoidthe time and expense of frequent recalibration is to develop ananolaser design that is insensitive to the effects of sidewalltilt.

B. Effect of Undercut Etching on Threshold Gainfor Lasers With Sidewall Tilt

Here, we investigate the strategy of undercut etching forconsistently producing MCSELs with low threshold gain, evenin the presence of significant sidewall tilt. In this paper,“undercut” refers to the lower undercut, defined as the dif-ference between the average radius rcore of the gain coreand the average radius of the lower pedestal, as a percentageof rcore (see diagram in Fig. 1).

Undercut etching was used by Lee and colleagues toincrease the vertical confinement in pedestal nanolasers byreducing the diameter of the pedestals relative to the gainregion [5]. Another investigation looked at the effect of under-cut etching on the optical properties and operating temperatureof an optically pumped laser, where the self-heating is assumedto be independent of the amount of undercut etch [13]. Both ofthese investigations only considered vertical gain and pedestalsidewalls, and a single laser diameter. In our case, we considerthree laser diameters and a variety of gain and pedestalsidewall angles, based on those achieved during our nanolaserfabrication.

An example nanolaser with undercut etching and sidewalltilt is drawn in Fig. 1. Since the wet etching chemistryselectively etches the pedestal semiconductor layers and leavesthe gain region intact, the amount of undercut can be controlledby adjusting the length of the wet etch step, usually onthe order of a couple of seconds. The use of a two-stepundercut etching process, with each step producing positivelyor negatively sloped pedestal sidewalls, allows the angle of thepedestal sidewall to be controlled [11].

The resulting etched nanolasers can have pedestal sidewallangles θp that are positive, negative, or zero, independent ofthe gain sidewall angle θg . Because the gain sidewalls anglesare determined by the RIE step, these sidewalls always haveθg ≥ 0. For this semiconductor material stack [1], [5], [11],because of the difference in doping type between the n-dopedupper pedestal and the p-doped lower pedestal, the selectiveetching acts more quickly on the upper pedestal than on the

Fig. 3. SEM images of three example nanolasers fabricated using the two-stepundercut etching process [11]. (a) has a core radius of 803 nm, θp = −16°,θg = +1.5°, an undercut ratio of 0.93, and an undercut of 12%. (b) has a coreradius of 417 nm, θp = +7°, θg = +11°, an undercut ratio of 0.53, and anundercut of 15%. (c) has a core radius of 201 nm, θp = −6° (for the lowerpedestal), θg = +6°, an undercut ratio of 0.61, and an undercut of 43%. Thenanolaser in (c) has a slightly different layer composition than the others inthis paper.

lower pedestal. The result is a laser with a ratio of upper tolower undercut of <1. Our simulations use an experimentally-measured upper to lower undercut ratio of 0.81; this ratio canvary in practice.

Three example lasers fabricated using the two-step etchingprocess are shown in Fig. 3. The laser in Fig. 3(a) has a coreradius of 803 nm, θp = −16°, θg = +1.5°, an undercut ratioof 0.93, and an undercut of 12%, while the laser in Fig. 3(b)has a core radius of 417 nm, θp = +7°, θg = +11°, anundercut ratio of 0.53, and an undercut of 15%. The laserin Fig. 3(c) has a core radius of 201 nm, θp = −6° (for thelower pedestal), θg = +6°, an undercut ratio of 0.61, and anundercut of 43%. These examples illustrate the variation insidewall angle, as well as the range of undercuts that can beachieved.

To determine the effect of gain sidewall angle, pedestalsidewall angle, and undercut amount, we modeled a variety ofnanolasers using COMSOL. The materials and shield thick-ness are the same as in Section II-A. For each nanolaser,we searched for modes in the wavelength range near themaximum of the available room-temperature gain. For thercore = 550 nm and rcore = 775 nm lasers, we search inthe free-space wavelength range λ0 = 1500 to 1700 nm,which matches the available room-temperature material gainat a moderate carrier density of N = 3 × 1018cm−3 for ourgain material. For the rcore = 225 nm laser, we expandthis wavelength range to 1400–1820 nm so that as increasingamounts of undercut change the wavelength of the TE01 mode,we can still track its behavior. We tested undercut amountsfrom 0%–30% for nanolasers of each diameter, and inde-pendently varied the gain sidewall angle from θg = 0° to+20°, and the pedestal sidewall angle from θp = −8° to +8°.Each laser simulated had a dielectric shield of α-Al2O3 ofthickness tshield = 170nm, near the optimum shield thicknessfor minimum gth . The threshold gain of the lowest-thresholdmode for each nanolaser is shown in Fig. 4. In Fig. 5 we plotother characteristics (λ0, Q, �, and substrate confinement) ofthe lowest-threshold mode for the rcore = 225nm laser at gainsidewall angles of θg = 0° and +20°; these characteristicsdisplay similar behavior for the individual modes of othernanolaser sizes and sidewall angles.

From Fig. 4 it is evident that threshold gain decreaseswith increasing undercut for nanolasers of all three diameters.

2000109 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 51, NO. 1, JANUARY 2015

Fig. 4. Threshold gain of the lowest-threshold mode for nanolasers ofrcore = 225nm (a-b), 550nm (c-d), and 775nm (e-f). In the left column,the gain sidewall angle θg is set to 0° (black solid line) or +20° (red dashedline), while the pedestal sidewall θp is kept vertical at 0°. In the right column,the gain sidewall angle θg is kept vertical at 0° while the pedestal sidewallθp is varied from −8° to +8°.

Fig. 5. Effect of increasing undercut amount on the characteristics of thelowest-threshold mode (TE01) for the rcore = 225nm laser. Gain sidewallangle θg is set to 0° (black solid line) or +20° (red dashed line), while thepedestal sidewall θp is kept vertical at 0°. (a) free-space modal wavelength, λ0.(b) cavity quality factor, Q. (c) percentage of mode confined to the gain, �.(d) percentage of mode confined to the substrate.

Threshold gain is very sensitive to sidewall angles for laserswith little to no undercut, but by about 25% undercut,threshold gain is at or below 100 cm−1 for lasers of anydiameter, regardless of the gain or pedestal sidewall angle.

Increasing undercut past 25% yields little to no improvement.Fig. 5 shows that by 25% undercut, Q no longer increasessignificantly (b), and radiation to the substrate becomes aninsignificant source of loss (d); the limitation on Q becomesmetal absorption, which is relatively unaffected by undercut.

For the rcore = 225nm laser, the decrease in threshold gainis monotonic as undercut increases; this is because the modewavelength window is chosen such that the TE01 mode isalways within range, even as the increasing undercut shifts themode wavelength (Fig. 5 (a)). For the larger-radius lasers, thethreshold gain of each individual mode still decreases monot-ically. However, the decrease in mode wavelength causedby undercutting is more dramatic for these larger lasers, sothat modes that are within the 1500nm–1700nm wavelengthwindow at 0% undercut quickly are shifted out of the win-dow as undercut increases. For these larger lasers, multiplemodes are in the gain window simultaneously, so once thelowest-threshold mode exits the gain window, the new lowest-threshold mode may have a higher or lower threshold thanthe previous lowest-threshold mode. By the time undercutincreases to around 15%, the mode is highly confined tothe gain region, and therefore becomes less sensitive to thepedestal radius. Both the mode wavelength and the thresholdgain change less as undercut increases further.

Fig. 4 (a) shows that for the rcore = 225nm laser, whenthe gain sidewall alone is tilted and the pedestal sidewallsare vertical, at slight undercut amounts a severely tilted gainsidewall actually produces lower threshold than a laser withthe same undercut and straight sidewalls. This is because thebottom of a gain region with angled sidewalls overhangs thelower pedestal more than that of a straight-sided gain region,reducing leakage into the substrate for modes such as TE01and whispering gallery modes, which are concentrated aroundthe laser perimeter. Fig. 5 (c) shows the slightly higher gainconfinement of the angled design, while Fig. 5 (d) showsthe significantly reduced radiation into the substrate of theangled design. As the amount of undercut increases, this extraoverhang becomes less significant, and the performance of theangled and non-angled sidewalls becomes comparable. For thercore = 550nm and 775nm lasers, the lowest-threshold modesat 0 undercut have a higher radial mode order than the TE01and whispering gallery modes, and these modes are penalizedby a gain sidewall angle, as seen in Fig. 4 (c) and (d).

Due to the crystal structure of the pedestal layers, the wetetching steps that produce undercut etching are anisotropic,sometimes resulting in pedestals with square or partly squarecross sections. This effect can be seen, for example, in thefabricated nanolaser in Fig. 3 (a). At 25% undercut, however,the effect of this square pedestal on threshold gain is minimal;an rcore = 225nm laser with an ideal round pedestal andstraight sidewalls has a threshold gain of gth = 86 cm−1,while a laser with square pedestals of the same cross-sectionalarea has gth = 101 cm−1. Other modes are affected moreby pedestal cross-section; for the rcore = 775nm laser, squarepedestals cause the lowest-threshold mode of the 25% undercutround-pedestal laser to be replaced by another with lesssensitivity to square pedestal shape. The resulting change inlaser threshold gain, an increase from 28 cm−1 to 197 cm−1,

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is larger than that experienced by the rcore = 225nm laser, butstill allows for room-temperature operation.

The simulation results in Fig. 4 show the potential ofundercut etching as a strategy for producing low-thresholdnanolasers that are resistant to the effects of sidewall tilt.An undercut of 25% (measured by comparing the averagediameter of the gain region and the lower pedestal region)produces a threshold gain at or below 100 cm−1 at roomtemperature, low enough for room-temperature lasing. At thisamount of undercut, the nanolaser performance is affectedlittle by gain sidewall angles of 20° and plug sidewall anglesof ±8°, or by error in the amount of undercut.

However, the decrease in pedestal diameter is expectedto increase the Ohmic resistance of these nanolasers, poten-tially leading to increased laser self-heating. In Section III,we perform electrical and thermal simulations of the undercutnanolasers to determine whether a 25% undercut will havedetrimental effects on a nanolaser’s operating temperature.

III. ELECTRICAL AND THERMAL SIMULATION

Due to their extremely small radius, Joule heating innanolasers can be a significant contributor to nanolaser self-heating and can ultimately limit nanolaser performance, partic-ularly for lasers with high threshold currents. The strategy ofundercut etching in MCSELs has benefits in terms of opticalperformance and insensitivity to sidewall tilt (Section II-B),but the reduction in pedestal diameter results in increasedOhmic resistance. Here, we simulate the effects of undercutetching on nanolaser resistance, total heat production, andthe resulting nanolaser operating temperature at and abovethreshold.

A. Ohmic Resistance

We calculate the Ohmic resistance of each nanolaser layerseparately based on its radius, thickness, and conductivityusing the standard formula for stack resistance [14]. Detailsof this calculation, as well as the layer doping levels andmobilities used to calculate conductivity, are given in [15].In the total nanolaser resistance, we also include the resistanceof the bottom contact layer, which behaves like a cylin-drical thin film contact [16]. Although in these simulationsthere is no unetched InP layer above the bottom contact,in the case where the laser is not completely etched to thebottom contact, we would use the geometry in the workby Zhang and colleagues [17]. We do not consider the wirecontact resistance in these simulations; they are indepen-dent of undercut etching and the resistive heat generated iseasily removed via conduction through the wires. We usestraight gain and pedestal sidewalls in this calculation; extremeamounts of sidewall tilt will reduce the pedestal diameter atthe top or bottom of the pedestal (depending on the directionof the tilt) and will increase the Ohmic resistance at thatpoint, while decreasing it elsewhere. We also assume, as inthe optical simulations, that the laser has an undercut ratioof 0.81; an extreme undercut ratio will increase the amount ofJoule heating contributed by the upper pedestal. The resultingtotal Ohmic resistance, calculated for lasers of rcore = 225nm,

Fig. 6. (a) Total nanolaser resistance, calculated as a function of undercutfor nanolasers with core radius of 225nm (blue solid line), 550nm (red dashedline), and 775nm (green dotted line). Undercut is defined as the differencebetween the average radius of the gain region and the lower pedestal, as apercentage of the gain radius. Here, the lasers have an undercut ratio of 0.81,meaning that the upper pedestal’s radius is 81% that of the lower pedestal.Resistance is the total Ohmic resistance for the entire nanolaser, including thebottom contact layer but excluding contact wire resistance. (b-d) Electric fieldof lowest-threshold mode for lasers with vertical sidewalls, 25% undercut, and(b) rcore = 225nm, (c) rcore = 550nm, and (d) rcore = 775nm.

550nm, and 775nm at increasing amounts of undercut etching,is shown in Fig. 6.

As expected from the fact that Ohmic resistance is propor-tional to 1/rcore

2, the total resistance of the rcore = 225nmlaser is significantly higher than that of the larger-diameterlasers, and is more sensitive to the effects of undercut. Between0% and 30% undercut, the resistance of the rcore = 225nmlaser approximately doubles. Due to the different doping andmobilities of the different semiconductor layers, the layerthat contributes the most resistive heating is the highly-doped region of the bottom pedestal, followed by the bottomcontact layer. Because the bottom contact serves as a highthermal conductivity connection to the heat-conducting contactwire, the Joule heating contributed by these sources can bedissipated more effectively than heat sources located nearer tothe gain region.

B. Self-Heating

To calculate the final operating temperature of thenanolasers, we need to calculate not only Joule heating, butalso Auger, surface recombination, junction, and heterojunc-tion heating. Following the methods in [15], we calculate theamount of each self-heating source as a function of pumpcurrent for nanolasers of rcore = 225nm, 550nm, and 775nm.As in Section III-A, we assume an undercut ratio of 0.81; inpractice, this undercut ratio will vary.

With the exception of Joule heating, for every heatingsource calculation we simulate the laser’s electrical behaviorin SILVACO’s ATLAS, a 2D electronic device simulator thatself-consistently solves the Poisson equation, the Schrödingerequation, and the carrier transport equation, yielding thevoltage drop at each point in the laser, the carrier density,and the quasi-Fermi level separation.

Auger heating is calculated as PA = UA · QF L, whereQF L is the quasi-Fermi level from SILVACO simulation and

2000109 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 51, NO. 1, JANUARY 2015

UA is the Auger recombination rate. This Auger recombinationrate UA is given by UA = An3Vactive where A is theAuger recombination coefficient, n is the carrier density fromSILVACO simulation, and Vactive is the volume of the gainregion. For A, we use 9.8 × 10−29cm6/s, the value given forInGaAs at 300K by [18].

We calculate surface recombination heating using Ps = Us ·Vactive · QF L, where Us is the rate of surface recombinationin the gain region, Vactive is the volume of the active region,and QF L is the quasi-Fermi level from SILVACO simulation.Us is given by Us = n

τs, where n is the carrier density from

SILVACO simulation, and τs is the carrier lifetime, given by1τs

= AactiveVactive

υs . Here, Aactive is the surface area of the activeregion, and υs is the surface recombination velocity of InGaAsat 300K, calculated to be υs = 1.3 × 104 cm/s in [15] fromvalues reported by Hill and colleagues [1].

The amount of self-heating at each junction is given byPjn = I Vjn , where I is the pump current and Vjn isthe voltage change at the nth junction. For operation abovethreshold, the heat produced at the heterojunctions (the twojunctions adjacent to the gain region) is limited to the amountproduced at threshold. In our calculation of device self-heating we make no assumptions about threshold current, sinceother experimental factors may increase threshold beyond thatpredicted by electrical and optical simulation. Therefore, wedo not limit the heterojunction heating, which gives us aworst-case thermal performance. As the results will show,above the threshold currents for the undercut laser designs,heterojunction heating is a relatively minor contributor to totallaser heating, so the heating is only slightly overestimated.

Fig. 7 shows the calculated self-heating generated innanolasers of different core radii and undercuts, as a functionof pump power. To compare self-heating behavior near andabove lasing threshold, we first calculate the threshold currentsenabled by each nanolaser design. For our threshold currentcalculations, we use the modal gain threshold from II-B,compared with calculations of the material gain availableat 300K [7] for the SILVACO-simulated carrier densitiesgenerated by each pump current. We compare modal thresholdwith the maximum material gain available at any wavelength,since each laser can be scaled in radius to match modalwavelength to gain maximum with minimal impact on modalthreshold gain. This yields a threshold current of 0.6–8μA forthe nanolasers with 25% and higher undercut, with the smaller-radius nanolasers having lower threshold currents thanks tothe concentration of current in a smaller radius. Fig. 7 a, c, e)shows the range of pump currents near threshold (0–15μA),while b, d, f) shows a range of pump currents up to 500μA, farabove threshold. For each type of nanolaser self-heating, wecalculate heating for lasers with 0%, 25%, and 60% undercut(solid, dashed, and dotted lines).

As expected from the different dependencies of each self-heating source on pump current, the dominant self-heatingsources in the near-threshold and high-current regimes willvary.

Near threshold (Fig. 7 a, c, e), surface recombination heatingdominates, with Auger and junction/heterojunction heating

Fig. 7. Amount of Auger (red), surface recombination (magenta), Joule(blue), and junction + heterojunction (green) self-heating as a function ofpump current. Results are shown for lasers with undercut etch of 0% (solid),25% (dashed), and 60% (dotted). a-b) Laser with rcore = 225nm, c-d) laserwith rcore = 550nm, e-f) laser with rcore = 775nm. Total self-heating ofeach type is shown for a current range near threshold (a, c, e) and well abovethreshold (b, d, f). The upper/lower pedestal undercut ratio used in thesesimulations is 0.81.

gradually becoming more important as current increases.In this regime, the amount of heat generated has little depen-dence on the amount of undercut.

At current levels far above threshold (Fig. 7 b, d, f), due tothe square dependence of resistive power dissipated on current,Joule heating can become more important. For the rcore =225nm lasers, Joule heating is significant in this regime forany amount of undercut, and a 25% undercut increases theamount of Joule heating by roughly half, compared to 0%undercut. At 60% undercut, far above that required for a low-threshold, sidewall tilt-resistant design, the generated heat ismore extreme. For the larger lasers with 550nm and 775nmcore radii, the increase in Joule heating with 25% undercut isslight, and the amount of Joule heat produced by even 60%undercut is less than a quarter of total nanolaser self-heatingat 500μA pump current.

Because these heat sources are located in different regionsof the nanolaser, their heat may be dissipated at different rates.Therefore, the operating temperature of the laser may not havea simple dependence on total heat generated, and detailedthermal simulation is required to determine the thermalperformance.

C. Operating Temperature

To determine the operating laser operating tempera-ture, we performed thermal simulations using COMSOL’s

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Fig. 8. Laser steady-state operating temperature Tss for a pump currentrange near threshold (a, c, e) and well above threshold (b, d, f), with anambient temperature of 300K. Operating temperature is calculated for laserswith undercut etch of 0% (solid), 25% (dashed), and 60% (dotted), and anundercut raio of 0.81. Laser core radii are 225nm (a, d), 550nm (b, e), and775nm (c, f).

thermal package. The thermal material parameters and phys-ical configuration are as described in [15], with the laserallowed to dissipate heat through its pedestal into the substrate,or through its shield into the metal cladding and electricalcontact wires.

The choice and thickness of the dielectric shield materialaffects a MCSEL’s ability to dissipate heat through the shieldinto the metal cladding, [15]. As in the optical simulationabove, the shield consists of α-Al2O3 of 170nm thickness. Thethermal conductivity of α-Al2O3 deposited via atomic layerdeposition (ALD) depends on deposition conditions; the rangereported in the literature is 1.7–20 W · m−1 · K −1 [19]–[21].For our simulations of laser operating temperature, we use themost conservative value, 1.7 W · m−1 · K −1. At this thermalconductivity we find that the shield is still a minor avenue ofheat dissipation, although most heat is dissipated through thepedestal.

The calculated laser operating temperature at pump levelsnear threshold (a, c, e) and far above threshold (b, d, f) areshown in Fig. 8. As in the calculation of heat generated, forthese thermal simulations we assume straight pedestal andgain sidewalls. Highly-angled pedestal sidewalls can createrestrictions in the flow of heat dissipation through the pedestal;for lasers with low-thermal-conductivity shields, the pedestalis the main method of heat dissipation, so this constrictioncould have an effect on the laser operating temperature.

Fig. 8 compares the steady-state operating temperatures oflasers with undercut etch of 0% (solid line), 25% (dashed line),

and 60% (dotted line). In the 0–15μA regime, the temperaturerise is slight, even for the smallest laser with extreme 60%undercut. In this regime, operating temperature has moredependence on undercut than heat generated (Fig. 7), sincethe smaller pedestal size of the higher-undercut lasers meansa smaller conduit for heat dissipation.

At currents far above threshold, undercut has a significanteffect on the rcore = 225nm laser operating temperature,thanks to the 1/Aactive dependence of Ohmic resistance, andthe I 2 dependence of Joule heating. Larger lasers are virtuallyunaffected by undercut, since Joule heating is only a minorsource of self-heating for these lasers. The major source ofself-heating for larger lasers, Auger recombination, actuallydecreases as undercut increases thanks to a change in QFL;however, this benefit is offset by the effects of increased Jouleheating and decreased heat conduction through a narrowerpedestal. Although more heat is generated in the high-currentregime by the larger lasers compared to the rcore = 225nmlasers, the large lasers have a lower operating temperaturethanks to their increased ability to dissipate heat through largerpedestals.

At higher shield thermal conductivities, possible withα-Al2O3 or with other high thermal-conductivity dielectrics,we expect the smallest lasers to see the greatest benefit fromthe ability to dissipate heat through their shields, making theselasers less sensitive to the effects of undercut.

IV. CONCLUSION

We examined undercut etching as a method for simultane-ously decreasing nanolaser threshold and eliminating sensi-tivity to sidewall angle tilt in MCSELs. We first examinedthe effects of sidewall tilt on the threshold gain of laserswithout undercut, and found that for a laser with core radiusof 225nm, a 0.5° sidewall tilt approximately doubles thresh-old gain to above 1000 cm−1, beyond the range for room-temperature operation for many common gain materials. Forlarger nanolasers, the effects of sidewall tilt are still severe,with threshold exceeding 1000 cm−1 at 2° tilt for the 550nmcore laser, and at 3° tilt for the 775nm core laser.

Next, we simulated the effects of undercut etching on thethreshold gain of nanolasers with various diameters and gainor pedestal sidewall tilts. We found that a 25% undercut etch isenough to reduce modal threshold gain to 100 cm−1 or lowerfor lasers with core radius of 225nm, 550nm, or 775nm, evenin the presence of significant sidewall tilt (20° gain sidewall,or ±8° pedestal sidewall tilt). At 25% undercut, the majorlimitation on cavity Q is metal absorption loss rather thanradiation to the substrate; these lasers may benefit in particularfrom optimization of cavity metal quality [10].

To determine whether undercut etching has a significanteffect on the laser’s operating temperature, we used electricaland thermal simulation to determine the heat generated andoperating temperature for lasers with different core radii andamounts of sidewall etch. A 25% undercut, or even an extreme60% undercut, has no significant effect on operating temper-ature near our calculated threshold current of 0.6–8μA. At acurrent of 500μA, far above threshold, a 25% undercut has

2000109 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 51, NO. 1, JANUARY 2015

little or no effect on operating temperature for a laser with coreradius of 550nm or 775nm. The smallest nanolaser considered,with core radius of 225nm, shows little temperature rise at 25%undercut up to a current of 200μA.

Although the wet etching process used for undercut etchingproduces large variation in undercut depth and sidewall angle,our simulations show that the nanolaser optical and thermalperformance is resistant to all but the most extreme undercutdepths and sidewall angles. Even at 60% undercut depth, farbeyond the undercut needed to produce good optical perfor-mance, thermal simulations show no significant heating nearour calculated threshold current. A 25% undercut produceslow threshold gain over the entire range of sidewall angles wehave experimentally observed.

Improvements in the accuracy and repeatability of InPundercut etching, however, would still be of use. There arelimits on the amount of gain and sidewall tilt that can betolerated, even for undercut nanolasers. Large sidewall anglesmay constrict the pedestal enough that the laser becomesmechanically unstable, prone to toppling during fabrication.In addition, these constrictions may produce high localizedOhmic resistance, carrying a larger self-heating penalty thanthe straight-sidewall lasers we considered in our thermalsimulations. Finally, if the material layers are modified toallow for long pedestals, large sidewall tilts would in theorycause the top of the pedestal to protrude beyond the edgesof the gain region, especially for devices with small radii.Although this situation would not be realizable using ourcurrent material layers and fabrication procedure, we includedthese geometries in our simulation for the sake of complete-ness. Careful calibration of the etching recipe, as performedfor example in [22], would allow for better control of emissionwavelength, and would allow undercut amount to be limitedto the range that produces mechanical stability and optimumthermal performance at high pump currents.

Our simulations show the promise of undercut etching asa strategy for reducing threshold gain in MCSELs and com-pensating for the effects of sidewall tilt, with little or no ther-mal penalty. This strategy produces a nanolaser design withincreased robustness, and with a low threshold gain that allowsefficient use of pump current. In addition, these nanolasers canoperate well above threshold with minimal self-heating. Oursimulations used a conservative estimate for the shield thermalconductivity; a higher-conductivity dielectric shield wouldallow for increased heat dissipation through the shield, furtherincreasing the potential of these nanolasers for high-poweroperation. Fabrication of these nanolaser designs is currentlyin progress.

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Janelle Shane was born in MN, USA. She receivedthe B.S. (Hons.) degree in electrical engineeringfrom Michigan State University, Lansing, MI, USA,in 2007, the M.Phil. degree in physics from theUniversity of St Andrews, St Andrews, U.K., in2009, and the M.S. degree in electrical engineeringfrom the University of California at San Diego,La Jolla, CA, USA, in 2011, where she is currentlypursuing the Ph.D. degree with a photonics focus onelectrical engineering, and investigating the thermaland electromagnetic properties of realistic semicon-

ductor nanolasers.Her other research interests include ultrashort laser pulse shaping, optical

trapping, and imaging.She was a recipient of the National Science Foundation Graduate Research

Fellowship and the Achievement Rewards for College Scientists ScholarAward.

SHANE et al.: EFFECT OF UNDERCUT ETCH ON PERFORMANCE AND FABRICATION ROBUSTNESS 2000109

Qing Gu received the B.A.Sc. degree in elec-trical engineering from the University of BritishColumbia, Vancouver, BC, Canada, in 2008, and theM.S. degree in electrical engineering from the Uni-versity of California at San Diego (UCSD), La Jolla,CA, USA, in 2011, where she is currently pursuingthe Ph.D. degree with a photonics focus on electri-cal engineering. Her research interests include thefabrication and testing of semiconductor nanolasers,solid-state physics and quantum optics, and novelnanoresonator design.

She has held undergraduate researcher positions with the Photonics ResearchGroup, University of British Columbia, and the Canada’s National Laboratoryfor Particle and Nuclear Physics, Vancouver.

She was a recipient of the Undergraduate Student Research Award fromthe Natural Sciences and Engineering Research Council of Canada, and theJacobs Bonus for Excellence Scholarship from UCSD.

Alan Potterton is currently pursuing the bachelor’sdegree with the Department of Physics, San DiegoCity College, San Diego, CA, USA.

He was the recipient of the National ScienceFoundation Research Experience for Undergradu-ates Award from the Center for Integrated AccessNetworks Integrated Optics for Undergraduates Pro-gram. In partnership with the Summer TrainingAcademy for Research in the Sciences of theUniversity of California at San Diego (UCSD),La Jolla, CA, USA, this program funded his research

with the Department of Electrical and Computer Engineering, UCSD, inSummer 2014.

Yeshaiahu Fainman is currently a CymerProfessor of Advanced Optical Technologies and aDistinguished Professor of Electrical and ComputerEngineering with the University of California atSan Diego (UCSD), La Jolla, CA, USA, where herecently served as the Chair of the Department ofElectrical and Computer Engineering.

He is directing the research of the Ultrafastand Nanoscale Optics Group at UCSD, andhas made significant contributions to near-fieldoptical phenomena, inhomogeneous materials and

metamaterials, nanophotonics and plasmonics, and nonconventional imaging.The research applications target information technologies and biomedicalsensing. His current research interests are in near-field optical science andtechnology. He contributed over 220 manuscripts in peer-reviewed journalsand over 350 conference presentations and conference proceedings.

He is a fellow of the Optical Society of America and the Society ofPhoto-Optical Instrumentation Engineers. He was a recipient of the Miriamand Aharon Gutvirt Prize, the Lady Davis Fellowship, the Brown Award,and the Gabor Award.