A circular dielectric grating for vertical extraction of single quantum dot emission
M. Davanco, M. T. Rakher, D. Schuh, A. Badolato, K. Srinivasan
aa r X i v : . [ phy s i c s . op ti c s ] S e p A circular dielectric grating for vertical extraction of single quantum dot emission
M. Davan¸co,
1, 2, ∗ M. T. Rakher, D. Schuh, A. Badolato, and K. Srinivasan Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Maryland NanoCenter, University of Maryland, College Park, MD Institute for Experimental and Applied Physics,University of Regensburg, D-93053 Regensburg, Germany Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA (Dated: October 25, 2018)We demonstrate a nanostructure composed of partially etched annular trenches in a suspended GaAsmembrane, designed for efficient and moderately broadband ( ≈ >
80 % with a high numerical aperture (NA=0.7) optic, and with ≈ × Purcell radiative rateenhancement. Fabricated devices exhibit a ≈
10 % photon collection efficiency with a NA=0.42objective, a 20 × improvement over quantum dots in unpatterned GaAs. A fourfold exciton lifetimereduction indicates moderate Purcell enhancement. Efficient extraction of single photons emitted by indi-vidual semiconductor epitaxial quantum dots (QDs) is anecessity for many applications in spectroscopy and clas-sical and quantum information processing [1]. As epitax-ially grown QDs are embedded in semiconductor mate-rial, total internal reflection of the emitted light at thesemiconductor-air interface and radiation divergence cantypically lead to < ≈
53 % (80 %) into aNA=0.42 (0.7) optic. In fabricated devices, we report a ≈
10 % single QD photoluminescence (PL) collection effi-ciency into a NA=0.42 objective, a ≈ × improvementcompared to QDs in unpatterned bulk GaAs. A four-fold reduction in QD lifetime is also observed, indicatingmoderate radiative rate enhancement. ∗ Electronic address: [email protected]
FIG. 1: (a) Top, (b) angled, and (c) cross-sectional SEMimages of suspended circular dielectric grating structure.
Our nanostructure (Fig. 1) consists of a circular di-electric grating with radial period Λ that surrounds acentral circular region of radius 2Λ, produced on a sus-pended GaAs slab of thickness t = 190 nm. The GaAsslab supports single TE and TM polarized modes (elec-tric or magnetic field parallel to the slab, respectively).The grating is composed of ten partially etched circu-lar trenches of width w and depth d , with t/ < d < t .Quantum dots are grown at half the GaAs slab thickness( z = 0), and located randomly in the xy plane. This’bullseye’ geometry favors extraction of emission fromQDs in the central circular region. It is based on (linear)high-contrast second-order Bragg gratings recently intro-duced [4] for light extraction from planar waveguides.While similar circular geometries have been employed forenhanced light extraction from light emitting diodes [5],and for demonstrating annular Bragg lasers [6], here weshow an application in QD single photon extraction.The design process consisted of a series of finite dif-ference time domain simulations that maximized verticallight extraction near the expected QD s-shell emission( λ QD ≈
940 nm), by varying Λ, t , and w . The struc- FIG. 2: Electric field intensity in the (a) xy and (b) xz planes(log scale). (c) Far-field polar plot for the cavity mode withΛ = 360 nm. (d) Collected power ( P col ) as a function ofvarying NA, normalized by the upwards ( P z + ) and total ( P tot )emitted powers. (e) Calculated vertically extracted poweras a function of wavelength, normalized to the homogeneousmedium electric dipole power P Hom for d = 0 . t . Continuouslines: upwards (+ z ) extraction; dotted: downwards ( − z ). (f)Experimental PL spectra for high QD density devices. tures were excited with a horizontally oriented electricdipole at the bullseye center ( x = 0 , y = 0), representingan optimally placed QD. Total radiated power, steady-state upwards emission, and electromagnetic fields werethen recorded at several wavelengths. The grating periodΛ was initially chosen to satisfy the second-order Braggcondition, Λ = λ QD /n T E , to allow for efficient verticallight extraction ( n T E is the GaAs slab TE mode effectiveindex). The dipole orientation was assumed to be alignedalong the xy plane, exciting only TE slab waves. Start-ing values for trench width and depth were w = 100 nmand d = 0 . t , deemed to be easily fabricated. Verticallight scattering at the gratings is partial, so that second-order Bragg reflections towards the center lead to verti-cally leaky cavity resonances as shown in Figs. 2(a) and(b). The large index contrast at the trenches leads tostrong reflections and out-of-slab-plane scattering at thesemiconductor-air interfaces, evident in the strong fieldconcentration at the bullseye center in Fig. 2(a) and thefast field decay within the first couple of trenches fromthe center (Fig. 2(b)). Large differences in propagationconstants in the semiconductor and air produce signif-icant resonance spectral shifts with small variations in trench width. Trench depth ( d ) has a strong influenceon the quality factor ( Q ) and vertical light extraction, asincomplete spatial overlap between a trench and an inci-dent slab-bound wave leads to both coupling to radiatingwaves and lower modal reflectivity. Preferential upwardsvertical extraction results from the grating asymmetry,and is optimized through the trench depth [7]. We notethat in addition to the mode shown in Fig. 1, the cav-ity supports resonances which can be excited by dipolesoffset from the bullseye center. Coupling to these reso-nances can lead to modified spontaneous emission ratesand collection efficiencies [7].Figure 2(e) shows simulated, upwards (continuous) anddownwards (dotted) vertically extracted power as a func-tion of wavelength for structures with Λ = 350 nm,360 nm, and 370 nm, w = 110 nm, and d ≈ . t .All curves are normalized to the homogeneous mediumelectric dipole power, P Hom . Trench parameters reflecta trade-off in cavity Q and vertical light extraction, asdiscussed above. It is apparent that for each Λ, an ≈ z ) light extraction. The upwards extracted power is ≈ × P Hom , an indication of Purcell radiation rate en-hancement due to the cavity [8]. Indeed, for the Λ = 360nm structure, on which we now focus, the enhancement F p at the maximum extraction wavelength ( λ c = 948 . F p = P tot /P Hom = 11 .
0, where P tot is the to-tal radiated power in all directions. This resonance has Q = 200, and its effective mode volume, calculated fromthe field distribution, is V eff = 1 . λ c /n ) ( n is the GaAsrefractive index) [7]. The value for F p predicted by Q and V eff is ≈ P col collected by an optic ofvarying NA. Figure 2(d) shows the fractions of the up-wards emitted ( P z + ) and total ( P tot ) powers collected asa function of the collection optic acceptance angle. ForNA=0 .
42 (24 . ◦ acceptance angle), ≈
60 % of the up-wards emitted power (or ≈
53 % of the total emission)can be collected. For NA > .
7, or an acceptance angle > . ◦ , collection superior to 80 % of the total emissioncan be achieved. We note that our suspended gratingapproach limits radiation into the substrate without theneed to oxidize the AlGaAs, bond the grating to a lowindex layer[6], or utilize a deeply etched geometry [2, 3].Gratings were fabricated in a t = 190 nm GaAs layercontaining a single layer of InAs QDs (density gradi-ent from > µ m − to 0 µ m − along the (01¯1) di-rection) on top of a 1 µ m thick Al . Ga . As sacrifi-cial layer [7]. Fabrication steps included electron-beamlithography, plasma dry etching, and wet chemical etch-
FIG. 3: (a) PL spectrum from a low QD density Λ = 360 nmdevice, for various pump powers. (b) Temperature evolutionof spectrum in (a) (25 nW pump). (c) Temperature evolutionof excitonic energies. Continuous lines are fits. ing. The plasma dry etch was optimized so that the GaAswould be partially etched to a desired depth in the grat-ing region (Fig. 1(b)), and fully etched over the curvedrectangles just outside the grating region (Fig. 1(a)),which were used in the wet etching step to undercut andsuspend the device.Testing was done in a liquid He flow cryostat at ≈ d/t > .
7, for pulsed pumping at a 780 nm wavelength(above the GaAs bandgap). The spectra closely resem-ble the theoretical curves of Fig. 2(e), with three, ≈ ≈
20 nm. Deviations are likely dueto differences in geometry and refractive index betweensimulated and fabricated structures. These results vali-dated our simulations, and served to calibrate the fabri-cation process. Figure 3(a) shows PL spectra at variouspump powers for a device with Λ = 360 nm, now pro-duced in a low QD density region of the sample. Threeisolated exciton lines are observed on top of a broad back-ground near 942 nm. The sharp lines red-shift with in-creasing temperature (Fig. 3(b)) with a dependence thatcan be fit to a model that predicts a red-shift of the InAsbandgap (Fig. 3(c)) [2, 3, 7]. In contrast, the broadbackground observed in Fig. 3(a) shifts more slowly withtemperature, and likely originates from out-coupling ofbroad QD multiexcitonic emission via the leaky cavitymode [11]. This is reinforced by the observation, inFig. 3(b), that the sharp QD lines are maximized in thewavelength range 940 nm < λ <
942 nm, when alignedto the broad cavity peak, and decrease when driven awayfrom it. The slower cavity mode shift with temperaturecorresponds to a shift in refractive index [12].Figure 4(a) shows the detected PL as a function of av-erage pump power for the excitonic lines X and X andthe cavity mode emission from Fig. 3(a). While X andX saturate at ≈
20 nW, the cavity emission increasespast this level. This further supports our assignments ofQD transitions and cavity mode in the Fig. 3(a) spec- tra. Saturated photon rates (collected with a NA=0.42objective) from X and X were at least 20 times higherthan from typical QDs embedded in unpatterned GaAs,as shown in Fig. 4(a). Assuming 100 % QD quantum ef-ficiency, we estimate a collection efficiency of ≈
10 %is achieved with the bullseye pattern [7]. A lifetimemeasurement of X after a ≈
300 pm bandpass filter(Fig. 4(b)) exhibits a multi-exponential decay with a fastlifetime of ≈
360 ps, limited by the ≈
600 ps timing jitterof the detectors. For comparison, the lifetime of a singleQD inside of a suspended GaAs waveguide [13] (dottedin Fig. 4(b)), for which no radiative rate modification isexpected, was ≈ . F p >
4. Notethat since the pump in Fig. 4(a) is pulsed with a 20 nsrepetition period, significantly longer than the lifetime,the increase in detected counts relative to unpatternedGaAs is solely due to enhanced photon extraction andcollection into the objective.
FIG. 4: (a) PL as a function of pump power for X , X andcavity emission from Fig. 3(a), and two QDs in unpatternedGaAs. Error bars are 95% fit confidence intervals. (b) Solid:X lifetime trace with fit. Dotted: lifetime trace for QD em-bedded in a suspended GaAs waveguide. Improved photon extraction efficiency can potentiallybe achieved with a higher NA collection optic (50% in-crease for NA=0.7) and fabrication control [7], while de-terministic QD spatial alignment [14, 15] can enhanceboth the efficiency and Purcell factor. Although single-photon emission from the bullseye is accompanied by un-desirable cavity emission, a few devices exhibited consid-erably less cavity mode feeding, albeit with lesser extrac-tion efficiencies. Since enhanced extraction efficiency isdue to the directional far-field pattern, a trade-off may beachieved between Purcell enhancement and cavity feed-ing for reduced Q . It is also likely that quasi-resonant QDpumping will lead to reduced cavity feeding [16]. Thesepossibilities are under investigation.In summary, we developed a nanophotonic circulargrating that provides ≈
10 % free space collection effi-ciencies for single InAs QD photons within a wavelengthrange of ≈ [1] A. J. Shields, Nature Photonics , 215 (2007), 0704.0403.[2] S. Strauf, N. G. Stoltz, M. T. Rakher, L. A. Coldren,P. M. Petroff, and D. Bouwmeester, Nature Photonics ,704 (2007).[3] J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffren-nou, N. Gregersen, C. Sauvan, P. Lalanne, and J. G´erard,Nature Photonics , 174 (2010).[4] D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss,P. V. Daele, I. Moerman, S. Vertuyft, K. D. Mesel, andR. Baets, IEEE J. Quan. Elec. , 949 (2002).[5] M. Y. Su and R. P. Mirin, Applied Physics Letters ,033105 (2006).[6] W. M. J. Green, J. Scheuer, G. DeRose, and A. Yariv,Appl. Phys. Lett. , 3669 (2004).[7] See EPAPS supplemental material for details on simula-tion, nanofabrication, data fitting and quantum dot tem-perature dependence modeling.[8] J. Vuˇckovi´c, O. Painter, Y. Xu, A. Yariv, and A. Scherer,IEEE J. Quan. Elec. , 1168 (1999).[2] G. Ortner, M. Schwab, M. Bayer, R. P¨assler, S. Fafard,Z. Wasilewski, P. Hawrylak, and A. Forchel, Phys. Rev. B , 085328 (2005). [3] M. Kroner, K. M. Weiss, S. Seidl, R. J. Warburton,A. Badolato, P. M. Petroff, and K. Karrai, physica sta-tus solidi (b) , 795 (2009), ISSN 1521-3951.[11] M. Winger, T. Volz, G. Tarel, S. Portolan, A. Badolato,K. J. Hennessy, E. L. Hu, A. Beveratos, J. Finley,V. Savona, and A. Imamo˘glu, Phys. Rev. Lett., ,207403 (2009).[12] A. Badolato, K. Hennessy, M. Atature, J. Dreiser, E. Hu,P. M. Petroff, and A. Imamo˘glu, Science , 1158 (2005).[13] M. I. Davan¸co, M. T. Rakher, D. Schuh, W. Wegsheider,A. Badolato, and K. Srinivasan, Appl. Phys. Lett. ,121101 (2011).[14] K. Hennessy, A. Badolato, M. Winger, D. Gerace,M. Atature, S. Guide, S. Falt, E. Hu, and A. Imamo˘glu,Nature (London) , 896 (2007).[15] S. M. Thon, M. T. Rakher, H. Kim, J. Gudat, W. T. M.Irvine, P. M. Petroff, and D. Bouwmeester, Appl. Phys.Lett. , 111115 (2009).[16] S. Ates, S. M. Ulrich, S. Reitzenstein, A. L¨offler,A. Forchel, and P. Michler, Phys. Rev. Lett. , 167402(2009). SUPPORTING INFORMATION
1. Design simulations
The following simulation results illustrate the effects of varying trench depths on emission properties of the circulardielectric grating. Figure 1(a) shows total emitted power P tot as a function of wavelength for various trench depths,and Fig. 1(b) shows the corresponding upwards ( P z+ ) and downwards ( P z- ) extracted powers.Apparent in Fig. 1(a) are a significant central wavelength shift and a strong radiative rate modification. Indeed,as shown in Fig. 1(c), the central wavelength blue shifts more than 40 nm for depths increasing from 95 nm to 190nm. The resonance full width at half maximum (FWHM), correspondingly, decreases, indicating an increase in fieldconfinement and, consequently, the Purcell Factor ( F p ), Fig. 1(e). The increased field confinement for deeper trenchesis a consequence of better overlap of the guided field inside the slab and the etched region, which leads to increasedguided wave reflectivity and reduces coupling to out-of-plane radiation. Figures 1(b) and (f) show the effect of gratingasymmetry on the ratio between upwards and downwards emitted powers. For a symmetric grating with d = t ,emission in both directions is the same. Upwards emission is maximized for d/t ≈ .
8, for which P z + /P z − = 2 . d/t = 0 .
7, however for a reduced F p . Clearly, a trade-off must be reached betweenPurcell enhancement and asymmetric emission.
2. Effective mode volume calculation
The bullseye cavity’s effective mode volume V eff =1.29( λ c /n ) quoted in the text was obtained with the expression V eff = R ǫ ( r ) | E ( r ) | d r max n ǫ ( r ) | E ( r ) | o , (1)where E is the modal electric field and ǫ ( r ) the medium permittivity. From V eff and the calculated cavity Q ≈ F p [1]: F p = 3 Q ( λ c /n ) π V eff (2)
900 910 920 930 940 950 960 970 980 990−10−50510 P z ± / P h o m wavelength (nm) | P z ± | / P h o m d / t F p F W H M ( n m ) λ c ( n m ) P t o t / P h o m d / t = 1.0 0.60.9 0.7 0.50.8 (a)(b) (c)(d)(e)(f) P z+ P z- P z+ P z- FIG. 1: (a) Total emitted power P tot as function of wavelength for various trench depths. (b) Vertically emitted power ± z direction (continuous: P z + , upwards; dotted: P z − , downwards), as a function of wavelength. (c) Central wavelength, (d) fullwidth at half maximum, (e) Purcell enhancement factor and (f) maximum upwards ( P z + ) and downwards ( P z − ) emitted poweras functions of trench etch depth d . P hom is the homogeneous space electric dipole emitted power and t is the GaAs slabthickness. where n is the refractive index and λ c is the cavity mode wavelength. The value determined through this calculation, F p = 11 .
8, corresponds well with the value F p = 11 . F p assume perfect dipole orientation with respectto the cavity field and optimal dipole location within the field (i.e., in the bullseye center).
3. Fabrication
Based on simulation parameters, gratings were fabricated on a t =190 nm thick GaAs layer containing a single layerof self-assembled InAs quantum dots on top of a 1 µ m thick AlGaAs sacrificial layer. The epiwafer was grown withmolecular beam epitaxy, and displayed a quantum dot density gradient from > µ m − to 0 µ m − along the (01¯1)direction. Electron-beam lithography was used to define the patterns, and a single, timed, inductively-coupled plasmareactive ion etch (ICP-RIE) step with an Ar/Cl chemistry transferred the gratings into the GaAs. This step wasoptimized so that the GaAs would be partially etched to a desired depth in the grating region (see Fig.1(b)), andfully etched over the large, curved rectangles just outside the grating region seen in Fig.1(a). These open areas wereincluded to give access to the AlGaAs sacrificial layer, which was etched with Hydrofluoric acid in a final step. Deviceswith varying quantum dot (QD) densities were produced by fabricating the devices along the QD density gradient ofthe wafer.
4. Photoluminescence spectra and collection efficiency
The spectra shown in Fig. 3 were obtained with a grating spectrometer and a Si charge-coupled device (CCD). Toobtain the PL intensity from the excitonic lines X and X in Fig. 3(a) without contributions from the broad cavitybackground, Lorentzians were fitted to the corresponding peaks. Emitted photon rates plotted in Fig. 4(a) for X and X and for unpatterned GaAs QD lines correspond to the Lorentzian areas. The integrated cavity photon ratesin Fig. 4(b) were obtained by integrating the spectra between 930 nm and 955 nm and subtracting rates from thetwo excitonic lines.To estimate the collection efficiency, we convert detected CCD counts to photon counts into our NA=0.42 objective.The two are related by a conversion factor that is equal to the product of our detection efficiency ξ , the transmissionthrough the PL setup T path , and the transmission through the cryostat windows T windows . ξ includes the in-couplingefficiency into the spectrometer, the spectrometer’s grating efficiency, and the CCD’s quantum efficiency, and isdetermined by sending a reference laser with known power and wavelength into the spectrometer. In particular, weattenuate a 102 nW laser at 960 nm by 50 dB and acquire a spectrum with a 1 s integration time. Integrating the laserspectrum yielded a count rate of 6 . × s − , which, when compared to the photon rate just before the spectrometer(4 . × s − ), gives a factor of ≈
77 photons per count. Because the QD emission wavelength ( λ X = 941 nm)differs from the calibration wavelength of 960 nm, we multiply this conversion factor by 0.78, which is the ratio ofthe manufacturer-specified CCD quantum efficiencies at these two wavelengths. We therefore get an overall detectionefficiency ξ = 0 . ≡
60 photons per count).The transmission through the optical path (including the collection objective) was T path = 0 . T windows ≈ .
87, and includestransmission through the radiation shield and outer cryostat windows.The QD line X in Fig. 4(a) yields a saturated CCD count rate of R X = 1 . × s − ± . × s − , where theuncertainty is a 95 % fit confidence interval, due to spectrometer resolution and detection noise. Assuming 100 % QDquantum efficiency, the rate of single photons emitted by the saturated QD is equal to the pulsed pump excitationrate, like R ex = 50 MHz. The collection efficiency was then calculated as η = R X R ex · ξ · T path · T windows , (3)Substituting all these values yields a collection efficiency η = 10 . ± .
5. Quantum dot temperature dependence
The temperature dependence of the sharp features X , X and X in Figs. 3(a) and (b) was fitted with theBose-Einstein expression E res ( T ) = E res ( T = 0) − S ~ ω (cid:20) coth (cid:18) ~ ω k B T (cid:19)(cid:21) . (4)This expression models the evolution of the semiconductor bandgap energy with temperature due to electron-phononinteraction, assuming no phonon dispersion, and has been successfully applied towards excitonic transitions in epitax-ially grown quantum dots [2, 3]. In Eq. (4), T is the sample temperature, E res ( T ) is the excitonic resonance energy, ~ ω is the phonon energy, and S is a dimensionless coupling constant. The fits shown in Fig. 3(c) were obtained withthe parameters in Table I.The phonon energies ~ ω in Table I are between the bulk GaAs transverse acoustic phonon energies at the X andL points, ~ ω T A (X) = 7 . ~ ω T A (X) = 9 . S are compatible with thosereported in refs. 2 and 3. This indicates that the sharp spectral lines correspond to excitonic QD transitions. X X X E res ( T = 0) (eV) 1 . ± . × − . ± . × − . ± . × − ~ ω (meV) 9 . ± . . ± . . ± . S . ± . . ± . . ± . , X and X with eq.(4). Errors are 95 % fit confidenceintervals (two standard deviations).[1] J.-M. G´erard and B. Gayral, J. Lightwave Tech. , 2089 (1999).[2] G. Ortner, M. Schwab, M. Bayer, R. P¨assler, S. Fafard, Z. Wasilewski, P. Hawrylak, and A. Forchel, Phys. Rev. B ,085328 (2005).[3] M. Kroner, K. M. Weiss, S. Seidl, R. J. Warburton, A. Badolato, P. M. Petroff, and K. Karrai, physica status solidi (b)246