Si-based photonic quantum dots with the self-similar distributed Bragg reflectors

Thin Solid Films 519 (2011) 3295–3300

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Si-based photonic quantum dots with the self-similar distributed Bragg reflectors

San Chen a,b,⁎, Chen Cheng a, Bo Qian a, Kunji Chen a,⁎, Xiangao Zhang a, Jun Xu a, Zhongyuan Ma a,Wei Li a, Xinfan Huang a

a State Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, People's Republic of Chinab Department of Physics, Huaibei Normal University, Huaibei 235000, People's Republic of China

⁎ Corresponding authors. Tel.: +86 25 83594836; faxto be contacted at State Laboratory of Solid State MicroPhysics, Nanjing University, Nanjing 210093, People's R

E-mail addresses: chen_san@sina.com (S. Chen), kjch

0040-6090/$ – see front matter © 2010 Elsevier B.V. Aldoi:10.1016/j.tsf.2010.12.134

a b s t r a c t

Article history:Received 11 July 2010Received in revised form 15 December 2010Accepted 16 December 2010

Keywords:Conformal coverageSelf-similar microcavitiesFinite difference time domain simulation

In this letter, optical microcavities are deposited directly on mesa-patterned substrates, and three dimensionalBragg cavities are formed due to the conformal deposition process. The room temperature photoluminescencespectra of three-dimensional Braggmicrocavity exhibit a series of discrete resonant peaks. Opticalfield profiles ofcorresponding resonant peaks were given, by finite difference time domain simulation. These discrete peaksobviously show cavity resonant characteristics and optical field is mostly localized in the cavity layer. Also sizedependence of cavity modes was concluded from our experimental results.

: +86 25 83595535. S. Chen isstructures and Department ofepublic of China.en@nju.edu.cn (K. Chen).

l rights reserved.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Since the pioneering works of enhanced and inhibited spontane-ous emission in the atom–cavity systems [1–3], many interestingquantum phenomena have been demonstrated in such systems,especially in the solid state cavity ones, over the last decades. Solidstate semiconductor optical micro or nanocavities have beenintensively investigated all over the world, because of their meritslike easier fabrication and detection, accurate control of “atoms” sites,richer quantum physical meanings and potential opto-electronicdevice applications and integration. In the weak coupling regime oflight–matter interaction, spontaneous emission rate could be modi-fied [4–6]. Lower or thresholdless laser [4,5], high efficiency light-emitting diodes [7], and single photon devices [8] could be made.Exciton polaritons can be formed, in the strong coupling regime,inducing reversible process of spontaneous emission and RabiSplitting occurrence. Owing to bosonic nature of polaritons, Bose–Einstein condensation [9,10], superfluidity [11,12], and vortices [13]of exciton polaritons have been reported in experiments. The uniqueproperties of exciton polaritons, such as light emission [14],stimulated scattering [15,16], parametric amplification [17–19], lasing[10,20–22], present a better perspective in ultra-efficient polaritonemitters or lasers, fast optical switches and other quantum devices.

The preceding works mainly focus on the coupling between one-dimensional confined microcavities and excitons, and excitons could

couple to all possible photonic states with the same in-planewavevector k|| as excitons, duo to the translational invariance in thecavity plane. This inevitably leads to exciton radiative loss, totallyfeatureless spontaneous emission rate, and only partial photonic andexcitonic states could couple to polariton states. As for pillar, micro-disk, planar photonic crystal microcavities or nanocavities, photonicconfinement is partly based on total internal reflection by thediscontinuity of reflective index [23,24]. For light not satisfying totalinternal reflection conditions, it can easily leak from the sidewalls.Consequently, this leads to lower spontaneous emission couplingcoefficient β, large leakage loss, negligible modification of totalspontaneous emission rate, polaritons formed by only a small numberof photons and excitons, and so on. Moreover, the rough sidewallsinduced by etching leads to the optical scattering loss and the defectssuch as dangling bonds will be introduced during the etching process,which serve as nonradiative recombination centers to deteriorate thelight emission efficiency of active materials. All those characters ofmicrocavities mentioned above are harmful to high efficient emittersor lasers, ultra-fast optical switches, polariton Bose–Einstein conden-sation, parametric amplification, and superfluidity. Photonic crystalscould provide full band gap for perfect confinement of photons;however, there are difficulties in fabrication and arbitrary introduc-tion of defects or “atoms”. So designing a simple, feasible method, forfabricating three-dimensional confinement microcavities, becomes achallenging task.

In this paper, we present a simple method for fabricating truethree-dimension microcavities, photonic quantum dots [25,26]. Thepatterned substrates with two-dimensional arrays of micro-mesasplay an important role for sample fabrication. Owning to conformalcoverage, distributed Bragg reflectors (DBRs) could cap micro-mesas,

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which naturely forms the self-similar DBRs for three dimensionalphoton confinement. These three dimensional microcavities, showthe discrete eigenmodes as demonstrated by the room temperaturephotoluminescence (PL) spectra; the mode spacing is obviouslydependent on the lateral size. The finite difference time domainmethod is used to simulate optical field distribution of resonantmodes of our sample structures, in which obviously resonantcharacteristics could be observed, and optical field is mostly localizedin the cavity areas evidenced in the spatial field patterns.

2. Experiments

Our samples are based on all amorphous silicon nitride (a-SiN) anddeposited in conventional plasma-enhanced chemical vapor deposi-tion system. Ammonia (NH3) and silane (SiH4) gas mixtures are usedas the reaction sources and gas flux ratio R=[NH3/SiH4] is changed tocontrol the film compositions. In the deposition process, the substratetemperature and rf power are kept at 250 °C and 30 W, respectively.By controlling the N/Si composition in the films, the optical bandgapcould be tuned from 1.98 eV to 3.82 eV as well as refractive index from2.8 to 1.9, accordingly. The a-SiN film with high index (2.8) isdeposited by using gas ratio R=0.5, and the one with low index (1.9)is deposited with R=8; they are alternatively deposited to constructDBRs with 6 periods. The a-SiN luminescent layer, exhibiting a broadluminescence band with the peak at about 680 nm and band width180 nm, is prepared by using gas ratio R=2 with optical band gap2.5 eV. Due to finite width of DBR stop band, there are severalresonant modes, and we tune cavity resonant wavelength to DBRcentral ones at 720 nm at long wavelength side of the luminescentband. We fabricate micro-mesas on (100)-silicon substrates byapplying standard photo-lithography and reactive ion etching. Thesquare micro-mesas with two feature sizes 1 μm, 2 μm and the sameheight 0.5 μm were fabricated. The detailed parameters of ourmicrocavities are given in Table 1.

The as-deposited products are characterized and analyzed bytransmission electron microscopy (TEM) (JEM-200CX, 200 kV, JEOL),scanning electron microscopy (SEM) (LEO1530VP, 30 kV, Zeiss), andthe confocal microscope LabRam HR800 (HR800, Jobin-Yvon) for PLmeasurements, with the 600 l/mm grating for spectrum dispersionand the Ar+ laser with 488 nm line for excitation. Laser is focused onthe samples with a spotsize about 1 μm through the microscopeobjective lens, and light emission is coupled to Raman spectruminstrument through the same lens. In cross-section TEM samplepreparation, we first make a stack by gluing together two substratefragments, film to film, to prevent samples from being damaged, andsection them into thin wafers, approximately 0.5 mm (or less) inthickness. Mechanical pre-thinning is used to decrease the samplethickness down to several microns, and finally ion milling makesthe thickness small enough to be electron transparent (less than100 nm).

3. Results and discussion

Fig. 1(a) and (b) presents both the side and top views of Braggcavity, in which the black dash line box denotes the cavity layer. TheDBRs and cavity layer are conformally deposited on the micro-mesas;

Table 1The detailed parameters for deposited optical microcavity as well as 6 period DBRs withresonant wavelength 720 nm.

NH3/SiH4 fluxratio

Refractiveindex

Thickness(nm)

Optical gap(eV)

λ/4 α-SiHx 8 1.86 96 3.8λ/4 α-SiHy 0.5 2.8 65 2.0λ/2 α-SiHz 2 2.0 180 2.5

the DBRs on the mesas and along the mesa sidewalls provide verticaland lateral photonic confinement for the cavity. In order todemonstrate that the idea mentioned above could work, we depositthe microcavity sample on the strip-patterned substrate. Fig. 1(c)gives a cross-section TEM image normal to the strip direction, of onesample on such substrates. It is shown that the microcavity couldconformally cap on the strips. The active layer and six-period upperand bottom DBRs can be obviously distinguished from the image andthe film thickness that is quite uniform. The active layer is embeddedbetween the bottom and upper DBRs. Fig. 1(d) gives the SEM imagesof a microcavity sample by conformal deposition on 1 μm×1 μmsquare micro-mesa substrates. For samples on 1 μm×1 μm squaremicro-mesa substrates, because sidewalls of mesas are not steep, theshape is not exactly the square pillar. The top surface and sidewalls ofthe sample are rather smooth, which can improve the Q factors ofcavity modes. However, other areas are quite rough, which is causedby non-smooth substrates, introduced in the process of etching. Thequality of mesa surfaces is very important for fabricatingmicrocavitieswith high quality.

In order to detect the optical eigenmodes of microcavities, a-SiNactive layer, with broad luminescent band and central wavelength at680 nm, is used as an optical probe. The room temperature PL spectra,modulated by cavity structures, could give information about theireigenmodes. Fig. 2 gives the PL spectra of microcavities with self-similar Bragg reflectors onmesas, and the PL spectra of cavities exhibitstriking difference compared with the one-dimensional ones with asingle resonant peak, denoted by the dotted line. For a cavity on1 μm×1 μm mesas, a series of discrete resonant peaks could beobserved, and these peaks originate from the discretization of thecontinuum of photon states in the cavity, due to the transverse photonconfinement. The full width at half maximum of these peaks isestimated to be 4.7 nm, 4.1 nm, 4.3 nm, and 5 nm, which correspondsto Q quality factors 151, 170, 160, and 135. The intensity of differentoptical modes varies remarkably. This is primarily the conse-quence of the different selection rules and of the different far fieldemission patterns of the modes. With the increase of the size ofthe dots, the mode spacing is significantly decreased, due to theincrease of the cavity width. This could be observed obviouslyfrom Fig. 3, and it is indicated that the size-dependent resonantphotonic energy is quantized by introducing the transverse opticalconfinement. Also the FWHM, of modes in cavity sample withtransverse dimensions 3.5 μm, are estimated to be 2.6 nm, 2.2 nm,3.2 nm, 5.5 nm, corresponding to 275, 322, 220, and 127 of cavity Qfactors, respectively.

In these two cavity structures, the Q factors are far lower thanones of other reported cavities, such as micro-disk, micro-sphere,micro-pillar, planar microcavities and photonic crystal defectcavity. Four main channels for optical losses can be considered:(i) the material absorption in the cavity and the DBRs themselves,(ii) absorption due to defect states in the cavity, in the DBRs and atthe surface, (iii) radiation losses into vertical directions as well as(iv) radiation losses into radial directions including any scatteringdue to surface roughness. Radiation losses play a dominant role,because the measured DBRs reflectivity only reaches about 90%.Less period numbers of DBRs, fluctuation of layer thickness of DBRsand absorption can lower reflectivity and the Q factors of cavitymodes. Also radial radiation loss including waveguide mode onesinfluence the Q factors. For detecting modes as many as possible,objective lens with larger numerical aperture is used to collect PLsignals, and this inevitably results in widening of mode linewidth.So Q factors of cavity modes are underestimated. We compare Qfactors of the four lowest order modes of cavities with two sizes,The Q factors increase with cavity sizes as reported elsewhere, exceptthe third order mode. Because the forth resonant peak of PL for largercavity size consists of two near degenerate resonant peaks, this leads towidening of linewidth.

Fig. 1. (a) The side view, (b) the top view of the schematic drawing of photonic quantum dots, in which the black dash line box indicates the cavity layer; (c) the cross-section TEMimage of multilayer prepared by conformal deposition method. (d) The SEM photograph of a sample with transverse dimensions about 2.5 μm of the square shape.

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In order to understand characteristics of these resonant peaks, wesimulate mode field distribution by the time domain finite difference(FDTD) method, in which the central wavelength of both longitudinaland transverse DBRs are assumed to be the same as shown above.The width of the cavity can be estimated from the SEM photographs.For photonic quantum dots on 1 μm×1 μm square micro-mesas, thewidth of cavity is approximately 2.5 μm, and this value can beconfirmed by latter resonant peak fitting. We only give the electricfield components Exof corresponding resonant peaks, because

Fig. 2. The PL spectra of two microcavity samples with transverse dimensions 2.5 μm(the dashed line), 3.5 μm (the solid line), and the PL of planar microcavity as acomparison (the dotted line).

structure symmetry leads to degenerate modes with x and ypolarizations. In Fig. 3, field distribution of the several lowest ordermodes is given. Because structures are so complex, field patterns arecomplex and different from the ones of one-dimensional or two-dimensional microcavities. For the fundamental mode, optical fieldmainly focuses in the central area of the cavity; near the DBR region,amplitude of field rapidly decays to zero, in which green denotes theminimum value of field amplitude, and red maxima. In order todemonstrate three-dimensional confined effects, field patterns ofother two cross-section planes normal each other, namely, fielddistribution of xz and yx planes, are also given in Fig. 3(b) and (c),respectively. These cap-like self-similar DBRs could confine andlocalize optical field near cavity areas very well. From the patterns,some fine structures could be found, superposed on the profiles offield distribution, and this phenomena could attribute to reflectivephase modulation of DBR reflectors. For higher order modes, thisamplitude fluctuation becomes more distinct, because of resonantwavelength mismatch between cavity and Bragg. The field patterns ofthe corresponding higher ordermodes are also presented in Fig. 4, andstill the field is mostly localized in the cavity layer. Comparedwith thefield distribution of the fundamental mode, the one of higher ordermode tends to diffuse into the neighboring DBR areas. The order ofmodes is higher, and more field diffuse into DBR Areas. This could beevidenced from Fig. 4. Different from the fundamental mode, thehigher order modes, nodes occur and increase with order increasing,along the y axis direction. Moreover, field patterns become morecomplex, and fluctuation of field amplitude is more obvious along thex direction. In Figs. 5 and 6 field patterns of samples with transverse

Fig. 3. The spatial field distribution of fundamental mode M00, the field pattern of(a) cavity plane parallel to the substate ones (xy plane); (b) the plane normal to thesubstate ones (xz plane); (c) the plane normal to the substate ones and the xz plane(yz plane) of microcavity sample with transverse dimensions 2.5 μm.

Fig. 4. The spatial field distribution of fundamental mode (a) M02, (b) M03 and (c) M04,respectively, in the xy plane, of microcavity sample with transverse dimensions 2.5 μm.

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dimensions 1.5 μm, are also given, and show a similar profile,compared with ones of the above samples.

According to the field patterns of resonant modes and their sym-metries, the resonant wavelengths of our three-dimensional confinedmicrocavities could be expressed as

λ = λ0 1 +kxk0

� �2+

kyk0

� �2" #−1

=2 ;

where k0=2πn/λ0 denotes the wave vector of the vertical cavity, λ0 isa longitudinal resonant wavelength of cavity with lateral dimensionsbeing infinite, and kxand ky are related to the lateral dimensions. The

wave vectors of the modes are quantized, because of introducing thelateral confinement;

kx;y = mx;y + 1� �π

L:

Here mx, y could take 0, 1, 2, 3,…, which characterize the differentresonant modes. mx and my are the lateral quantum numbers, andeach indicates the number of nodes of the electric field in the givendirection. L is the lateral width of the square shaped structures. So theconfined optical modes in the microcavities could be characterized byMmx,my. It is suggested that the photon energy could be quantized in aconfined system and the luminescence shows the discrete peaks atthe eigenmodes. For resonant modes, each possesses specificsymmetry, which could be identified from the field patterns by fieldamplitude in symmetric plane. As demonstrated above, M00, M02, andM04 modes are even symmetric and M03 is odd symmetric. Thesecharacteristics of optical resonant modes are very similar to the ones

Fig. 5. The spatial field distribution of fundamental mode M00, the field pattern of(a) cavity plane parallel to the substate ones (xy plane); (b) the plane normal to thesubstate ones (xz plane); (c) the plane normal to the substate ones and the xz plane(yz plane) of microcavity sample with transverse dimensions 1.5 μm.

Fig. 6. The spatial field distribution of fundamental mode (a) M02, (b) M03 and (c) M04,respectively, in the xy plane, of microcavity sample with transverse dimensions 1.5 μm.

Fig. 7. The comparison of experimental data (circles) and calculated results (squares) ofmicrocavity samples with transverse dimensions 2.5 μm (bottom) and 3.5 μm (upper),respectively.

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of electronic states confined in the quantum dots. So these kinds ofconfined structures should be photonic correspondence of electronicquantum dots, and could be termed as photonic quantum dots.

To further confirm resonant modes and their size dependenceshown in photoluminescence spectra, we calculated four lowest orderresonant modes of microcavity samples with transverse dimensions2.5 μm and 3.5 μm, respectively, based on the above formula. Fig. 7gives the resonant wavelength of eachmode from photoluminescencespectra and corresponding theoretical values, in which the circlesindicate experimental values and the squares calculated ones. Theyagree well with each other. From the experimental and theoreticalvalues, obvious transverse dimensional dependence of mode spacingcould be identified, which presents very important similarities tocharacteristics of electronic eigenstates in quantum dots. Withincreasing of mode orders, deviation of experimental values fromtheoretical ones becomes distinguishable and field patterns are more

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complex and featureless, because of bigger mismatch between thecavity resonant wavelength and the DBR one. In our samples, no M01

mode is found,we thought that there is a smallermode spacingbetweenM00 and M01, and M00 mode pattern dominates over M01 ones.

Based on FDTD simulation, we also get the Q factors of four lowestorder modes, about 385, 352, 280, 176 for bigger size cavity, and 292,255, 217 and 150 for smaller ones. Compared with experimentalvalues of Q factors, the theoretical values are obviously higher thanexperimental ones, because our simulations are based on ideal pillarstructures and ignore absorption, thickness fluctuations of each layerand actual shapes of cavities. With increasing of mode orders, the Qfactorsmonotonously decrease, and the tendency can be evidenced bythe mode patterns. For the fundamental mode, the field is highlylocalized in the cavity area, and partly diffuses into the DBRs for higherorder modes. While for experimental values of Q factors, the firstorder mode has the highest Q factor, probably due to the smallestmismatch between operating wavelengths of cavity and DBRs. Thechanging of Q factors, with increasing of cavity sizes, shows the samebehaviors. For practical applications, the cavities should be optimized,and optical loss should be lowered, to improve the Q factors.

4. Conclusions

In summary, conformal deposition method was used to directlyfabricate three-dimensional confinement microcavities on the pat-terned substrates. The cap-like self-similar DBRs constituted three-dimensional optical confinement for our microcavities. The photo-luminescence spectra reveal a series of resonant peaks and spatialfield distribution gave direct proof that these peaks come from ourthree-dimensional Bragg cavity resonances, with the finite differencetime domain simulation. The conformal coverage provides an easyapproach to get true three-dimensional confined microcavitis on thepatterned substrates, and furthermore, this method is compatiblewith Si IC technology. This kind of photonic structures shows wellprospective for studying fundamental physics problems of strongcoupling effects between light and matter and the device applicationsuch as high efficiency light-emitting diodes, low threshold laser andeven thresholdless laser.

Acknowledgments

The authors would like to thank the support from the NationalScience Foundation of China (grant nos. 60806015 and 10974091) anda Project from Education Department of Anhui Province KJ2008B018.

References

[1] P. Goy, J.M. Raimond, M. Gross, S. Haroche, Phys. Rev. Lett. 50 (1983) 1903.[2] G. Gabrielse, H. Dehmelt, Phys. Rev. Lett. 55 (1985) 67.[3] R.G. Hulet, E.S. Hilfer, D. Kleppner, Phys. Rev. Lett. 55 (1985) 2137.[4] Y. Yamamoto, S.Machida, K. Igeta, Y.Horikoshi, in: L.Mandel, E.Wolf, J.H. Eberly (Eds.),

Coherence and Quantum Optics, Vol. VI, Plenum Press, New York, 1989, p. 1249.[5] H. Yokoyama, K. Nishi, T. Anan, H. Yamada, S.D. Brorson, E.P. Ippen, Appl. Phys.

Lett. 57 (1990) 2814.[6] G.S. Solomon, M. Pelton, Y. Yamamoto, Phys. Rev. Lett. 86 (2001) 3903.[7] M. Yamanishi, K. Watanabe, N. Jikutani, M. Ueda, Phys. Rev. Lett. 76 (1996) 3432.[8] J. Kim, O. Benson, H. Kan, Y. Yamamoto, Nature 397 (1999) 500.[9] H. Deng, G. Weihs, C. Santori, J. Bloch, Y. Yamamoto, Science 298 (2002) 199.

[10] J. Kasprzak, M. Richard, S. Kundermann, A. Bass, P. Jeambrun, J.M.J. Keeling, F.M.Marchetti, M.H. Szymańska, R. André, J.L. Staehli, V. Savona, P.B. Littlewood, B.Deveaud, L.S. Dang, Nat. Lond. 443 (2006) 409.

[11] A. Kavokin, G. Malpuech, F.P. Laussy, Phys. Lett. A 306 (2003) 187.[12] I. Carusotto, C. Ciuti, Phys. Rev. Lett. 93 (2004) 166401.[13] K.G. Lagoudakis, M. Wouters, M. Richard, A. Baas, I. Carusotto, R. André, L.S. Dang,

B. Deveaud-Plédran, Nat. Phys. 4 (2008) 706.[14] S.I. Tsintzos, N.T. Pelekanos, G. Konstantinidis, Z. Hatzopoulos, P.G. Savvidis, Nature

453 (2008) 372.[15] L.S. Dang, D. Heger, R. Andre', F. Boeuf, R. Romestain, Phys. Rev. Lett. 81 (1998) 3920.[16] P. Senellart, J. Bloch, B. Sermage, J.Y. Marzin, Phys. Rev. B 62 (2000) R16263.[17] P.G. Savvidis, J.J. Baumberg, R.M. Stevenson, M.S. Skolnick, D.M. Whittaker, J.S.

Roberts, Phys. Rev. Lett. 84 (2000) 1547.[18] C. Ciuti, P. Schwendimann, B. Deveaud, A. Quattropani, Phys. Rev. B 62 (2000) R4825.[19] M. Saba, C. Ciuti, J. Bloch, V. Thierry-Mieg, R. Andre', L.S. Dang, S. Kundermann, A.

Mura, G. Bongiovanni, J.L. Staehli, B. Deveaud, Nature 414 (2001) 731.[20] D. Porras, C. Ciuti, J.J. Baumberg, C. Tejedor, Phys. Rev. B 66 (2002) 085304.[21] G. Malpuech, A. Di Carlo, A. Kavokin, Appl. Phys. Lett. 81 (2002) 412.[22] S. Christopoulos, G. Baldssarri Höger von Högersthal, A.J.D. Grundy, P.G.

Lagoudakis, A.V. Kavokin, J.J. Baumberg, G. Christmann, R. Butté, E. Feltin, J.-F.Carlin, N. Grandjean, Phys. Rev. Lett. 98 (2007) 126405.

[23] R.E. Slusher, A.F.J. Levi, U. Mohideen, S.L. McCall, S.J. Pearton, R.A. Logan, Appl.Phys. Lett. 63 (1993) 1310.

[24] K.L. Lear, K.D. Choquette, R.P. Schneider Jr., S.P. Kilcoyne, Appl. Phys. Lett. 66(1995) 2616.

[25] J.P. Reithmaier, M. Röhner, H. Zull, F. Schäfer, A. Forchel, P.A. Knipp, T.L. Reinecke,Phys. Rev. Lett. 78 (1997) 378.

[26] T. Gutbrod, M. Bayer, A. Forchel, J.P. Reithmaier, T.L. Reinecke, S. Rudin, P.A. Knipp,Phys. Rev. B 57 (1998) 9950.