Polarization degenerate micropillars fabricated by designing elliptical oxide apertures
Morten P. Bakker, Ajit V. Barve, Alan Zhan, Larry A. Coldren, Martin P. van Exter, Dirk Bouwmeester
PPolarization degenerate micropillars fabricated by designing elliptical oxide apertures
Morten P. Bakker, Ajit V. Barve, Alan Zhan, Larry A. Coldren, Martin P. van Exter, and Dirk Bouwmeester
1, 2 Huygens-Kamerlingh Onnes Laboratory, Leiden University,P.O. Box 9504, 2300 RA Leiden, The Netherlands University of California Santa Barbara, Santa Barbara, California 93106, USA (Dated: July 16, 2018)A method for fabrication of polarization degenerate oxide apertured micropillar cavities is demon-strated. Micropillars are etched such that the size and shape of the oxide front is controlled. Thepolarization splitting in the circular micropillar cavities due to the native and strain induced bire-fringence can be compensated by elongating the oxide front in the [110] direction, thereby reducingstress in this direction. By using this technique we fabricate a polarization degenerate cavity with aquality factor of 1.7 × and a mode volume of 2 . µ m , enabling a calculated maximum Purcellfactor of 11. Quantum dots in micropillar cavities form an interest-ing platform for cavity quantum electrodynamics exper-iments in the solid state [1]. For example, the couplingbetween the spin in a singly-charged quantum dot (QD)and the polarization of a photon in the Purcell regimeholds promise for applications in hybrid quantum infor-mation processing [2]. For this purpose oxide aperturedmicropillars are attractive as they combine simple fabri-cation of voltage contacts, excellent mode-matching withexternal fields and access to the Purcell regime[3][4].An important challenge however is to obtain polar-ization degenerate cavity modes. This is an importantcondition in order to prepare entanglement between anelectron spin and the polarization of a photon [5], whichis essential for schemes as described in [2]. Several post-processing techniques have been demonstrated to tunethe polarization properties. These techniques rely on theapplication of strain mechanically [6] or on the opticalapplication of surface defects [7][8]. It is more desirableto obtain close-to polarization degenerate cavities afterthe wet oxidation processing step and thereby minimizethe need of further tuning.In this paper we demonstrate that, by systematicallyvarying the shape of the etched micropillar, the shapeof the oxide aperture can be controlled, thereby control-ling the spectral properties. Two arrays of micropillars ofwhich the diameter and ellipticity are systematically var-ied are fabricated and the optical modes are characterizedat 9.0 K. Micropillars with circular oxide fronts exhibitoptical modes with a large circular symmetry, but due tobirefringence the fundamental mode is polarization non-degenerate. However, for elliptical oxide fronts that areelongated in the [110] direction, the native birefringenceis compensated for by strain-induced birefringence andpolarization degenerate fundamental modes are obtained.The samples used in this study are grown by molec-ular beam epitaxy on a GaAs [100] substrate. Firsta planar distributed Bragg reflector (DBR) cavity isgrown which consists of a spacing layer and 26 pairsof GaAs/Al . Ga . As layers in the top mirror and 29pairs in the bottom mirror. The spacing layer consists of a λ GaAs layer, containing a layer of InAs self-assembledQDs in the center [9], and a λ Al x Ga − x As apertureregion. The oxidation aperture consists of a 10 nm AlAslayer embedded between 95 nm Al . Ga . As and 66 nmAl . Ga . As layers, providing a linearly tapered oxi-dation upon the wet oxidation. Micropillars are etchedsuch that they are connected to the bulk region via threebridges, to provide global electrical contacts, as shown inFig. 1 (a).This geometry was found to be an optimum as for twobridges the oxide front is found to be more ellipticallyshaped, while for more than three bridges the bridgesare too thin and the risk increases that the electricalconductance to the micropillar center is insufficient [10].This geometry, together with the etching process, is how-ever expected to induce in-plane anisotropic strain, whichneeds to be compensated for together with the nativebirefringence, that can be present even in perfectly cir-cular mesas.Figures 1 (b,c) schematically show that the micropillardiameter d in the [1¯10] direction and diameter d +∆ inthe [110] direction are systematically varied in a 6 × (a) (c)(b) [110]d Increasing d I n c r e a s i n g Δ [110]P-contactN-contactd+ Δ FIG. 1. (a) SEM image of a micropillar. (b) The micropillarshave diameter d and are elongated in the [110] direction by anamount +∆. (c) Systematic variations of d and ∆ are appliedover an array. a r X i v : . [ phy s i c s . op ti c s ] A p r array, with d = [29, 30, 30.5, 31, 31.5, 32, 33] µ m and∆ = [0, 0.5, 1.0, 1.5, 2.0, 2.5] µ m. Then a wet thermaloxidation procedure to form an oxide aperture is applied[11]. Finally electrical contacts to the p-doped and n-doped GaAs surrounding the QDs are fabricated.To characterize the optical properties of the confinedoptical modes, standard microphotoluminescence tech-niques are used. The sample is held in a cryostat at 9.0K and pumped using an 852 nm laser diode to exciteQD emission. We characterize the anisotropy of everymicropillar in two different ways. First of all, we mea-sure the polarization-splitting of the fundamental modeto characterize the birefringence. Second, we measure thewavelength differences between the first-order transversemodes and the fundamental mode. This transverse modesplitting is linked to the optical confinement, which canbe different in the two directions.Finally, in order to get an indication of the shape ofthe buried oxide aperture layer, which determines the op-tical confinement, a spatial reflection scan is performedat room temperature. For this, a laser with a wavelength λ = 1064 nm located outside of the DBR stopband isused, such that the reflectance depends on interfering re-flections from the top and bottom DBR mirrors. This in-terference is a function of the optical length of the spacinglayer and therefore the reflectance depends on the buriedoxide thickness [12]. The front of the oxide is clearlyvisible as a ring with a lower reflectivity. -50 0 50(GHz) P L i n t en s i t y ( a . u . ) (a) (c)(b) λ = 925.89 nm Δλ = 1.50 ± 0.15 nm [110] [110]15 µm Δν (GHz) FIG. 2. (a) PL from the fundamental Ψ mode at two orthog-onal polarizations. (b) Spatial PL scans at the wavelength ofthe fundamental mode and a wavelength interval overlappingwith both first-order modes. Wavelengths are selected usinga spectrometer. (c) Spatial reflectivity scan of a focused λ =1064 nm laser spot indicates the circular oxide front. Figure 2 shows a micropillar that was elongatedslightly, by 0.5 µ m, in the [110] direction. Due to a faster -50 0 50(GHz) P L i n t en s i t y ( a . u . ) (a) (c)(b) λ = 925.89 nm Δλ = 0.96 nm Δλ = 2.32 nm[110] [110]10 µm -50 0 50(GHz) P L i n t en s i t y ( a . u . ) (a) (c)(b) λ = 925.89 nm Δλ = 0.96 nm Δλ = 2.32 nm[110] [110]10 µm Δν (GHz) FIG. 3. (a) PL from a polarization degenerate Ψ cavitymode. (b) Spatial PL scans of the fundamental Ψ and thefirst-order Ψ and Ψ modes. (c) Spatial λ = 1064 nmreflectivity scan that indicates the oxide front is elongated inthe [110] direction. wet oxidation rate in this direction this results in a nearlycircular oxidation front as shown in Fig. 2 (c). The cir-cular symmetry is apparent as well in the spatial profilesof the confined modes in Fig. 2 (b), where the incoher-ent sum of the two first higher-order Hermite-Gaussianmodes resemble a Laguerre-Gaussian transverse modeprofile. In Fig. 2 (a) however a clear frequency split-ting between two linear orthogonal polarization modesof the fundamental mode is visible due to birefringence.Figure 3 shows an even more elliptical micropillar,elongated in the [110] direction by 2 µ m. This elon-gated shape is now also visible in the shape of the buriedoxide aperture in Fig. 3 (c). In Fig. 3 (b) clearHermite-Gaussian modes are identified that now possesa great difference between the modesplittings ∆ λ = λ − λ , owing to a difference in the amount of opti-cal confinement in orthogonal directions. We define ∆ λ to be in the [110] direction. The polarization splitting ofthe fundamental mode however is about 1 GHz, less than6% of the FWHM, indicating the birefringence has beenstrongly reduced.Figure 4 shows the result of a systematic characteriza-tion of two arrays, of which array 2 is oxidized slightlyfurther. Figure 4 (a) shows the modesplittings betweenthe fundamental and first order modes, averaged over thetwo linear polarizations. Clearly, the average modesplit-ting decreases as the size of the micropillar is increased,as expected. Figure 4 (b) shows the ratio ∆ λ / ∆ λ be-tween the modesplittings in two directions. An increasingratio ∆ λ / ∆ λ corresponds to less optical confinementin the [110] direction with respect to the [1¯10] directionwhich arises from a more elongated oxide front. Thiscorrelates with increasing ∆. Figure 4 (c) displays thepolarization splitting ∆ ν of the fundamental Ψ mode.A clear relation is visible between ∆ λ / ∆ λ and ∆ ν . (a) Δλ average Array 1 Array 2(b) Δλ / Δλ (c) Δν Increasing d I n c r e a s i n g Δ Increasing d Increasing d I n c r e a s i n g Δ Increasing d Increasing d I n c r e a s i n g Δ Increasing d FIG. 4. Colormaps indicate from two arrays: (a) theaverage modesplittings ∆ λ average between the first orderΨ / Ψ modes and the fundamental Ψ mode, (b) the ratio∆ λ / ∆ λ of the modesplittings between the Ψ / Ψ andthe Ψ modes, and (c) the polarization splitting ∆ ν of theΨ mode. Array 2 exhibits a larger average modesplittingand thus has oxidized slightly further. The dots 1 and 2 de-note the cavities displayed in Fig. 2 and Fig. 3, respectively. We qualitatively explain our findings by a modifica-tion of the birefringence under the influence of uniaxialstrain in the [110] direction [8]. Even for the almost cir-cular apertures that remains after oxidation, some uni-axial strain is expected as the oxide layer is more ex-tended in the [110] direction. This can be the result ofan anisotropy of the oxidation rate in combination withthe location of the three bridges. When the oxide frontis more elongated however we expect the strain to bereduced such that the birefringence can be fully compen-sated for.An important figure of merit of microcavities is thePurcell factor. For the cavity shown in Fig. 3 we find a Q -factor of Q ≈ . × and by following methods de-scribed in [13] we predict that a maximum Purcell factorof 11 can be achieved.We would like to remark that shape birefringencedue to anisotropic confinement is small ( < λ +∆ λ ) / (2 λ ) smaller than the shape-inducedconfinement splitting (∆ λ − ∆ λ ), which results in avalue of 0.84 GHz for the numbers mentioned in Fig. 3.In conclusion we have shown it is possible to controlthe shape of the oxide aperture by the shape of the mi-cropillar. By applying systematic variations in the etchedshapes, the strain-induced birefringence is varied and po-larization degenerate cavities are obtained. This is anappealing approach towards fabrication of polarizationdegenerate microcavities with minimal post-processingtuning techniques required.We thank Thomas Ruytenberg for experimental assis-tance. This work was supported by NSF under GrantNo. 0960331 and 0901886 and FOM-NWO Grant No.08QIP6-2. [1] S. Reitzenstein and A. Forchel, Journal of Physics D:Applied Physics , 033001+ (2010).[2] C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat,D. Ding, M. P. van Exter, and D. Bouwmeester, PhysicalReview Letters , 160503+ (2010).[3] N. G. Stoltz, M. Rakher, S. Strauf, A. Badolato,D. D. Lofgreen, P. M. Petroff, L. A. Coldren, andD. Bouwmeester, Applied Physics Letters , 031105+(2005).[4] M. T. Rakher, N. G. Stoltz, L. A. Coldren, P. M.Petroff, and D. Bouwmeester, Physical Review Letters , 097403+ (2009).[5] K. De Greve, L. Yu, P. L. McMahon, J. S. Pelc, C. M.Natarajan, N. Y. Kim, E. Abe, S. Maier, C. Schneider,M. Kamp, S. Hofling, R. H. Hadfield, A. Forchel, M. M.Fejer, and Y. Yamamoto, Nature , 421 (2012).[6] K. Panajotov, B. Nagler, G. Verschaffelt, A. Georgievski,H. Thienpont, J. Danckaert, and I. Veretennicoff, Ap-plied Physics Letters , 1590 (2000).[7] C. Bonato, D. Ding, J. Gudat, S. Thon, H. Kim, P. M.Petroff, M. P. van Exter, and D. Bouwmeester, AppliedPhysics Letters , 251104+ (2009).[8] A. K. J. van Doorn, M. P. van Exter, and J. P. Woerd-man, Applied Physics Letters , 1041 (1996).[9] P. M. Petroff, A. Lorke, and A. Imamoglu, Physics Today , 46 (2001).[10] S. Strauf, N. G. Stoltz, M. T. Rakher, L. A. Coldren,P. M. Petroff, and D. Bouwmeester, Nature Photonics , 704 (2007).[11] A. G. Baca and C. I. H. Ashby, Fabrication of GaAsDevices , Baca2005 (The Insititution of Engineering andTechnology, 2005).[12] M. P. Bakker, D. J. Suntrup, H. Snijders, T.-A. Truong,P. M. Petroff, M. P. van Exter, and D. Bouwmeester, Ap-plied Physics Letters , 101109+ (2013), bakker2013.[13] C. Bonato, J. Gudat, K. de Vries, S. M. Thon, H. Kim,P. M. Petroff, M. P. van Exter, and D. Bouwmeester,
Opt. Lett. , 4678 (2012).[14] A. W. Snyder and J. Love, Optical Waveguide Theory ,edited by Chapman (1983). [15] A. Weisshaar, J. Li, R. L. Gallawa, and I. C. Goyal,Lightwave Technology, Journal of13