复旦大学：《光子学器件与工艺 Photonics Devices and Technology》文献资料_Si nanocrystals microdisk array

APPLIED PHYSICS LETTERS 88, 153120(2006) Visible range whispering-gallery mode in microdisk array based on size-controlled si nanocrystals Rong-Jun Zhang, Se-Young Seo, Alexey P. Milenin, Margit Zacharias, and Ulrich Gisele Mar-Planck-Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany (Received 8 November 2005; accepted 20 March 2006: published online 13 April 2006) Microdisks based on in-plane embedded size-controlled Si nanocrystal/SiO2 superlattices (Si-NCs/SiO SLs) were mass-fabricated arranged in well-ordered arrays. The microdisks were fabricated with size irregularity of below 0.2%o over large-scale areas. Overlappin whispering-gallery modes (WGM) of the visible nanocrystalline-silicon luminescence were observed. A comparison between analytical calculation and experimental results is reported. We found that only one axial and one radial WGM exist due to their thin disk thickness and birefringence characteristic of Si-NCS/Sio2 SLs, and that the mode spacing is 15 nm and 6 nm for microdisks with a diameter of 8.8 um and 23.7 um, respectively. The advantages of such size-controlled Si-NCS/SiO, embedded in microdisk arrays for Si-based photonic application will be discussed. 2006 American Institute of Physics. [DOI: 10.1063/1.2195712 Optical microdisks, which confine light to a small modal the microdisk. The thickness of the Sio and Sio2 layers was volume by resonant recirculation with low optical loss, 3 nm and 4 nm, respectively. Finally, an additional 50 nm have received considerable attention during the past years. buffer Sio, layer was added to protect the layered structure Si-based microphotonics have been a technical challenge The total film thickness including the top/bottom Sio with respect to mass production of highly integrated photo- layers is about 310 nm. The samples were then annealed at nic devices with the help of present mature complementary 1100C for 1 h under a N2 atmosphere to realize the metal-oxide-semiconductor technique. Photonic devices Si-NCs in the Sio2 matrix based on Si are expected at least partially to functionally Optical lithography was used to pattern various struc replace the present electronic devices. As novel examples of tures. The etching processes were undertaken using sequen- Si-based integrated photonics devices, the silicon optical tial anisotropic and isotropic dry plasma etching processes modulator and silicon Raman laser have been reported Thus, while the c-CAF8790% Ar plasma chemistry was used far. In past decades, the efficient visible luminescence at to etch anisotropically through the SiO2 layer with the room temperature from silicon nanocrystals(Si-NCs)was a embedded Si-NCs, the SF plasma was used to etch isotro- focus of interest because it might lead to the development of pically the Si substrate. 4 a si-based efficient light source 5.6 rece Finally, arrays of microdisks with diameters of 8.8 um Si-NCs, and a electroluminescent field-effect device based 23. 7 um, and 48.0 um were achieved. For comparison, an on Si-NCs, were demonstrated. 7. array of microsquares with a side length of 8.8 um was also In order to further decrease the overall size of a prepared. The microdisks were arranged in a hexagonal array Si-NC-based light source, more efficient device structures with side length of 13, 28, and 55 um, depending on the size need to be adopted. One candidate for such a structure is the of the microdisks with 8.8 um, 23. 7 um, and 48.0 um di- microdisk resonator, which has an excellent o value and ameter, respectively. For the microsquare arrays, we chose a many advantages for lasing which is realized by nearly infi- square lattice arrangement, with a lattice constant of nite light circulations of whispering-gallery modes(WGMs) 12.5 um. As a result, the peripheries of microdisks or within a small volume. Even though a high-o value and microsquares were separated from their neighboring ones lasing were already observed from silica microdisks, by at least -4 um, ensuring a sufficient separation to effec little has been reported demonstrating whispering-gallery tively exclude optical coupling between microdisks or modes of the visible luminescence from si-NCs in microsquares microdisk oom-temperature photoluminescence(PL) was mea- In this letter, we present the mass fabrication of micro- sured using liquid-nitrogen-cooled charge-coupled-device disk based on Si-NCs in an arrayed structure, and the camera attached to a single monochromator. The 488 nm line observation of WGMs from them. We will show the clear of an Ar laser with a power density of 6 W/cm? was used as emergence of WGMs in microdisk arrays. excitation source. The Si-NCs/SiO, SL of an unstructured The preparation of multilayers of size-controlled part, and the arrays of microdisks or microsquares were mea- Si-NCs in Sio, matrix was reported elsewhere. As a first sured under the same conditions. All spectra were corrected step, a 50 nm buffer Sio2 layer was evaporated on Si(100) for the wavelength depending sensitivity of the measuring wafers.Then, 30 periods of the SiO, /SiO2 superlattices system. Scanning electron microscopy (SEM) was performed (SLs)were evaporated on top as the active emitting using a JSEM 6300F. Figure 1(a) shows the SEM image of an array of micro- of Optical Science and Engineering, Fudan disks with a diameter of 8.8 um. The hexagonal arrangement of the microdisks can clearly be seen. No misshaped disk was found by the SEM investigation

Visible range whispering-gallery mode in microdisk array based on size-controlled Si nanocrystals Rong-Jun Zhang,a
Se-Young Seo, Alexey P. Milenin, Margit Zacharias,b
and Ulrich Gösele Max-Planck-Institute of Microstructure Physics, Weinberg 2, 06120 Halle, Germany
Received 8 November 2005; accepted 20 March 2006; published online 13 April 2006 Microdisks based on in-plane embedded size-controlled Si nanocrystal/SiO2 superlattices
Si-NCs/SiO2 SLs were mass-fabricated arranged in well-ordered arrays. The microdisks were fabricated with size irregularity of below 0.2% over large-scale areas. Overlapping whispering-gallery modes
WGM of the visible nanocrystalline-silicon luminescence were observed. A comparison between analytical calculation and experimental results is reported. We found that only one axial and one radial WGM exist due to their thin disk thickness and birefringence characteristic of Si-NCs/SiO2 SLs, and that the mode spacing is 15 nm and 6 nm for microdisks with a diameter of 8.8
m and 23.7
m, respectively. The advantages of such size-controlled Si-NCs/SiO2 embedded in microdisk arrays for Si-based photonic application will be discussed. © 2006 American Institute of Physics. DOI: 10.1063/1.2195712 Optical microdisks, which confine light to a small modal volume by resonant recirculation with low optical loss, have received considerable attention during the past years. Si-based microphotonics have been a technical challenge with respect to mass production of highly integrated photo￾nic devices with the help of present mature complementary metal-oxide-semiconductor technique.1 Photonic devices based on Si are expected at least partially to functionally replace the present electronic devices. As novel examples of Si-based integrated photonics devices, the silicon optical modulator and silicon Raman laser have been reported so far.2–4 In past decades, the efficient visible luminescence at room temperature from silicon nanocrystals
Si-NCs was a focus of interest because it might lead to the development of a Si-based efficient light source.5,6 Recently, optical gain in Si-NCs, and a electroluminescent field-effect device based on Si-NCs, were demonstrated.7,8 In order to further decrease the overall size of a Si-NC-based light source, more efficient device structures need to be adopted. One candidate for such a structure is the microdisk resonator, which has an excellent Q value and many advantages for lasing which is realized by nearly infi- nite light circulations of whispering-gallery modes
WGMs within a small volume.9 Even though a high-Q value and lasing were already observed from silica microdisks,10,11 little has been reported demonstrating whispering-gallery modes of the visible luminescence from Si-NCs in a microdisk.12 In this letter, we present the mass fabrication of micro￾disk based on Si-NCs in an arrayed structure, and the observation of WGMs from them. We will show the clear emergence of WGMs in microdisk arrays. The preparation of multilayers of size-controlled Si-NCs in SiO2 matrix was reported elsewhere.13 As a first step, a 50 nm buffer SiO2 layer was evaporated on Si
100 wafers. Then, 30 periods of the SiOx /SiO2 superlattices
SLs were evaporated on top as the active emitting part of the microdisk. The thickness of the SiOx and SiO2 layers was 3 nm and 4 nm, respectively. Finally, an additional 50 nm buffer SiO2 layer was added to protect the layered structure. The total film thickness including the top/bottom SiO2 layers is about 310 nm. The samples were then annealed at 1100 °C for 1 h under a N2 atmosphere to realize the Si-NCs in the SiO2 matrix. Optical lithography was used to pattern various struc￾tures. The etching processes were undertaken using sequen￾tial anisotropic and isotropic dry plasma etching processes. Thus, while the c-C4F8 / 90%Ar plasma chemistry was used to etch anisotropically through the SiO2 layer with the embedded Si-NCs, the SF6 plasma was used to etch isotro￾pically the Si substrate.14 Finally, arrays of microdisks with diameters of 8.8
m, 23.7
m, and 48.0
m were achieved. For comparison, an array of microsquares with a side length of 8.8
m was also prepared. The microdisks were arranged in a hexagonal array with side length of 13, 28, and 55
m, depending on the size of the microdisks with 8.8
m, 23.7
m, and 48.0
m di￾ameter, respectively. For the microsquare arrays, we chose a square lattice arrangement, with a lattice constant of 12.5
m. As a result, the peripheries of microdisks or microsquares were separated from their neighboring ones by at least 4
m, ensuring a sufficient separation to effec￾tively exclude optical coupling between microdisks or microsquares. Room-temperature photoluminescence
PL was mea￾sured using liquid-nitrogen-cooled charge-coupled-device camera attached to a single monochromator. The 488 nm line of an Ar laser with a power density of 6 W/cm2 was used as excitation source. The Si-NCs/SiO2 SL of an unstructured part, and the arrays of microdisks or microsquares were mea￾sured under the same conditions. All spectra were corrected for the wavelength depending sensitivity of the measuring system. Scanning electron microscopy
SEM was performed using a JSEM 6300F. Figure 1
a shows the SEM image of an array of micro￾disks with a diameter of 8.8
m. The hexagonal arrangement of the microdisks can clearly be seen. No defective/ misshaped disk was found by the SEM investigation over the a Present address: Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China. b Electronic mail: zacharia@mpi-halle.de APPLIED PHYSICS LETTERS 88, 153120
2006 0003-6951/2006/8815
/153120/3/$23.00 © 2006 American Institute of Physics 88, 153120-1 Downloaded 24 Apr 2006 to 149.220.35.134. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

153120-2 Zhang et al. Appl. Phys. Lett. 88, 153120(2006 FIG. 1. SEM images of (a) the microdisk array. The microdisks are about 310 nm thick and have a diameter of 8.8 um.(b)A selected single. microdisk resonator consisting of the thin silica layer with the embedded Si-NCs/SiO, SL upon a Si post and the Si substrate. (c) Top view. Wavelength(nm) FIG. 3. WGMs emission deduced from PL measurements Inset: Compari- scanned area. In Fig. 1(b), a single microdisk is shown. The son of experimental results and predicted data for the resonant peaks via periphery of the microdisk shows a uniform undercut. The thin asymmetric trunk below the microdisk is the etched single-crystalline Si of the wafer substrate In Fig. 1(c), a of the Si-NCs, as shown in the enlarged spectra [Figs. 2(b) selected top view of one microdisk is presented(white cir- and 2(c) cular area) demonstrating the very smooth microdisk edge Such sigmoid luminescence peaks can result from the The SEM results for other diameters and for the microsquare optical interference within a film or the interference between arrays are as smooth as the presented microdisk in Fig. 1 direct luminescence from disk and its reflected luminescence Figure 2(a) compares the room-temperature PL spectra at a substrate, or can be the radial guiding mode in a of the unstructured bare film, the microdisk array, and the microstructure. However, we can exclude these possibili- microsquare array. All of the spectra show the similar lumi- ties, because they would appear in the PL spectra of the nescence profiles peaked at 800 nm which is typical ob- unstructured SL film or of the microsquare array, too served from Si-NCs with a diameter of 3 nm. While nono Instead, those narrow peaks superimposed on the spon- table features are found for the spectra of the unstructured taneous emissions of Si-NCs can be attributed to WGMs in film and the microsquare array, the spectra of the microdisk the microdisks. The spacing between two neighboring peaks array show small peaks superimposed on the luminescence is almost the same for each spectrum; and the average spac- ing decreases as the diameter of the microdisk increases These results are typically expected for WGMs of a micro- disk. Moreover, the fact that we did not observe such peaks from the microdisks with a diameter of 48.0 um(not shown) is also consistent, because here the expected spacing is C3 nm. which is too narrow to be resolved under the mea surement conditions used. Figure 3 shows the WGMs emis- sion of an array of microdisks with diameter of 8.8 um, after d of 8. 8 um can be clearly observed d of 23.7 um The WGMs within a disk can be understood by a com plete solution of the three-dimensional Maxwell equations using cylindrical coordinates. Since such a full analysis of WGMs within a microdisk is rather complicated, we tried Wavelength(nm analyze them with a rather simple model as follows: First, because the thickness of the microdisk is less than A/2neft, of8.8 um (c) dof237μm where A and neff is the vacuum wavelength and the effective refractive index of the disk, respectively, only one fundamen- al tranverse electric TE) and transverse magnetic (TM) axial mode can exist. In addition, we recently observed hat the birefringence behavior from our nc-Si/SiO2 SLs, due to the anisotropic layered film structure and the optical filling factor of the TE mode, is much higher than that of the TM mode. This fact implies that the coupling of the TE 850750 mode to microdisk is dominant over the tm mode, and it can avelength(nm Wavelength(nm be assumed that the observed modes mostly originate from FIG. 2. PL measurements of (a) a Si-NCs/SiO, SL unstructured the array of microdisks with quare length of 8.8 um and 23.7 um the Te mode. Then, we can simplify the problem to two- array of microsquares with a squ of 8.8 um.(b)Enlarged dimensional equations with a polar coordinate Based on the the array of microdisks with of 8.8 um.(c)The microdisks with solution of the two-dimensional Helmhol ield distribution r, 0)is Downloaded24Apr2006to149.220.35.134.RedistributionsubjecttoalPlicenseorcopyrightseehttp:/lapl.aiporg/apl/copyrightjsp

scanned area. In Fig. 1
b, a single microdisk is shown. The periphery of the microdisk shows a uniform undercut. The thin asymmetric trunk below the microdisk is the etched single-crystalline Si of the wafer substrate. In Fig. 1
c, a selected top view of one microdisk is presented
white cir￾cular area demonstrating the very smooth microdisk edge. The SEM results for other diameters and for the microsquare arrays are as smooth as the presented microdisk in Fig. 1. Figure 2
a compares the room-temperature PL spectra of the unstructured bare film, the microdisk array, and the microsquare array. All of the spectra show the similar lumi￾nescence profiles peaked at 800 nm which is typical ob￾served from Si-NCs with a diameter of 3 nm. While no no￾table features are found for the spectra of the unstructured film and the microsquare array, the spectra of the microdisk array show small peaks superimposed on the luminescence of the Si-NCs, as shown in the enlarged spectra Figs. 2
b and 2
c. Such sigmoid luminescence peaks can result from the optical interference within a film or the interference between direct luminescence from disk and its reflected luminescence at a substrate, or can be the radial guiding mode in a microstructure.15 However, we can exclude these possibili￾ties, because they would appear in the PL spectra of the unstructured SL film or of the microsquare array, too. Instead, those narrow peaks superimposed on the spon￾taneous emissions of Si-NCs can be attributed to WGMs in the microdisks. The spacing between two neighboring peaks is almost the same for each spectrum; and the average spac￾ing decreases as the diameter of the microdisk increases. These results are typically expected for WGMs of a micro￾disk. Moreover, the fact that we did not observe such peaks from the microdisks with a diameter of 48.0
m
not shown is also consistent, because here the expected spacing is 3 nm, which is too narrow to be resolved under the mea￾surement conditions used. Figure 3 shows the WGMs emis￾sion of an array of microdisks with diameter of 8.8
m, after deduction of Si-NCs spontaneous luminescence as back￾ground from the overall PL spectrum in Fig. 2
b. Now, the resonance peaks can be clearly observed. The WGMs within a disk can be understood by a com￾plete solution of the three-dimensional Maxwell equations using cylindrical coordinates. Since such a full analysis of WGMs within a microdisk is rather complicated, we tried to analyze them with a rather simple model as follows: First, because the thickness of the microdisk is less than / 2neff, where and neff is the vacuum wavelength and the effective refractive index of the disk, respectively, only one fundamen￾tal tranverse electric
TE and transverse magnetic
TM axial mode can exist.16,17 In addition, we recently observed that the birefringence behavior from our nc-Si/SiO2 SLs, due to the anisotropic layered film structure and the optical filling factor of the TE mode, is much higher than that of the TM mode.18 This fact implies that the coupling of the TE mode to microdisk is dominant over the TM mode, and it can be assumed that the observed modes mostly originate from the TE mode. Then, we can simplify the problem to two￾dimensional equations with a polar coordinate. Based on the solution of the two-dimensional Helmholtz equation, the field distribution
r, is16 FIG. 1. SEM images of
a the microdisk array. The microdisks are about 310 nm thick and have a diameter of 8.8
m.
b A selected single￾microdisk resonator consisting of the thin silica layer with the embedded Si-NCs/SiO2 SL upon a Si post and the Si substrate.
c Top view. FIG. 2. PL measurements of
a a Si-NCs/SiO2 SL unstructured bare film, the array of microdisks with a diameter of 8.8
m and 23.7
m, and the array of microsquares with a square length of 8.8
m.
b Enlarged view for the array of microdisks with a diameter of 8.8
m.
c The microdisks with a diameter of 23.7
m. FIG. 3. WGMs emission deduced from PL measurements. Inset: Compari￾son of experimental results and predicted data for the resonant peaks via azimuthal mode number. 153120-2 Zhang et al. Appl. Phys. Lett. 88, 153120 2006
Downloaded 24 Apr 2006 to 149.220.35.134. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

153120-3 Zhang et al. Appl. Phys. Lett. 88, 153120(2006 Mr, 0)-Jm.(2mefr r/relm (1) high-temperature anneals of amorphous SiO, (a-SiOx)films where r and 6 are polar coordinates, Jm.n are Bessel func- fabricated by chemical vapor deposition, sputtering, or ion- implantation of Si ions. This wider size distribution of mode number, respectively. Ares is the resonant wavelength. the size distribution of Si-NCs in our sls is rather For the effective refractive index neff, we used 1.60 for the Second in order to design microdisks flexibly for optimal TEO mode considering the light confinement in a slab wave- operation, independent control of the Si-NCs size and the guide. The high refractive index contrast between the film and the air, and the spatial difference between the disk diam- refractive index is required at the same time. For our eter and resonance wavelength. allow us to assume that SiO_/Sio, SLs, the Si-NC size and the refractive index can be independently controlled and designed quite well. Finally, boundary condition to be Jm.n (2 Tme R/res =0, Setting the the birefringence behavior of Sio, /SiO2 SLs film allows the tensity is almost zero at the disk radius R fact, this selective coupling of TE modes, rather than TM modes, pproximation has been successfully used in the case of he microdisk, inducing wider mode spacing semiconductor microdisks. Finally, we can find reso- In conclusion, we presented microdisk resonators which nance wavelengths of WGMs and their corresponding mode are based on size-controlled Si-NCs in a SiO, matrix. The numbers. In the case of the microdisk with a diameter of mass production of such microdisk resonators in large-scale 8.8 um, the azimuthal mode number was found to range cence of Si-NCs, were observed for the microdisk array from m=40(for Ares=950 nm) to 60(for Ares=650 nm)in Thin layer thickness and the birefring al range of Fig. 3 for the first radial mode. Experi- one to sustain only one axial and one radial mode; inducing mental peaks can be assigned to the TEOm.i modes with azi muthal modes, with a mode spacing of -15 nm, in good a rather broad mode spacing of up to 15 nm. The used pro agreement with the calculation as shown in the inset of fig cess technology for the integration of microdisks is compat 3. The second or higher orders can not be matched with the ble with planar silicon-process technology. We expect that experimental results. So, only the first-order radial modes such microdisk arrays can be applied as a base material for he TEOm. I modes, can be observed in our microdisk array integrated Si microphotonics Similarly, for the array of microdisks with a disk diameter of R.J. Z. gratefully acknowledges financial support from observed Due to the Alexander von Humboldt Foundation. S.Y.S. gratefull the absence of both higher axial modes and higher radial acknowledges financial support from the Korea Research modes, the resonance peak spacing is determined only by Foundation azimuthal modes. As a result, the mode spacing is 15 nm and ITowards the First Silicon Laser, NATO Science Series, edited by L. 6 nm. and rather broad for microdisks with a diameter of Pavesi, S Gaponenko, and L Dal Negro(Kluwer, Dordrecht, 2003) 8.8 um and 23.7 um, respectively. This fact has important 2Q F. Xu, B Schmidt, S. Pradhan, and M Lipson, Nature(London)435 implications since broader mode spacing is more advanta geous for the development of a single-line light source. 3A. S. Liu. R. Jones. L. Liao. D. Samara-Rubio. D. Rubin. O. Cohen.R. The resonant peaks in the PL spectrum result from the Nicolaescu, and M. Paniccia, Nature(London)427. 615(2004) overlapping of individual modes from each microdisk since ios, A Liu, R. Jones, O Cohen, R Nicolaescu, AFang, and M H. R PL measurements were performed by pumping several thou- sands of microdisks at the same time. Thus, the o factor, sw.L.Wilson, P F. Szajowski, andLE. Bm2/ Kovalev, alr 3) which can be evaluated from Fig 3, is mainly determined by Eichhorn, Phys. Rev. B 69,1953092004 slight irregularities in disk diameter rather than the effect of L. Pavesi, L D. Negro, C. Mazzoleni, G.Franzo, and F.Priolo,Nature the roughness of the periphery. Using higher resolved PL $R.J. Walters. G.L. Bourianoff and H.A. Atwater. Nat. Mater. 4.1 measurements with a resolution of 0 4 nm. a full width at half maximum at each resonant mode was observed to be K J Vahala, Nature(London)424 839(2003) 2 nm. Thus, the Q factor of the microdisk array was calcu T.J. Kippenberg,SM.Spillane,DK ani,and K J. Vahala, Appl lated to be around 400 for microdisks with a diameter of hys.Le.83.797(2003) 8.8 um. While this o value seems to be much smaller than x. Liu, W. Fang. Y Huang, X. H. Wu, S. T. Ho. H. Cao, and.P.H reported value for a silica-based microdisk, to the contrary, "D S Gardner and M L Brongersma, Opt. Mater. (Amsterdam, Neth.)27 this result implies the excellent mass fabrication of micro- 804(2005) disks with a size deviation of <0. 2% between each micro-M. Zacharias, J. Heitmann, R Scholz, U Kahler, M. Schmidt, and J disk, since 1%of the diameter deviation would limit the 1A. P. Milenin. C. Jamois, T Geppert,U.Gosele, and R.B.Wehrspohn overall Q factor of the microdisk array to below 80 Microelectron Eng. 81, 15 (2005). In addition to the excellent mass production and the ob- H. J. Moon, Y. T. Chough, and K. An, Phys. Rev. Lett. 85, 3161(2000) servation of WGMs of the Si-NCs microdisk array, it ISL.McCall, A.F.J. Levi,RESlusher,SJ.Pearton,and RA.Logan Si-NC/SiO, Appl. Phys. Lett. 60. 289(1992) SLs as a base material for the microdisks compared to other R. E Slusher, A F J. Levi, U. Mohideen, S L. McCall, S J. Pearton, and conventional Si-NCs methods. For microphotonic devices, ISD. Navarro- Urios. E. Riboli. M. Cazznelli, A. Chiasera N Daldosso, L. which are based on Si-NCs for active optical emission, both Pavasi, C. J. Oton, J. Heitmann, L. X. Yi, R. Scholz. and M. Zacharias the Si-NC size--which determines the luminescence prope Opt. Mater(Amsterdam, Neth. )27, 763(2005) ties. and the film refractive index- -which influences the X. Liu, W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. character of WGMs, are important parameters. However, the shang ppc Pays Ler: I4i 248 no1 p .Let.66,2932(1995 size distribution of Si-NCs is fairly broad for conventional 2J. Heitmann, F Muller, M. Zacharias, and U. Gosele, Adv. Mater(Wein- Si-NCs in a Sio, matrix, which are generally formed by heim, Ger. )17, 795(2005) Downloaded24Apr2006to149.220.35.134.RedistributionsubjecttoAlplicenseorcopyrightseehttplaplaip.orglapl/copyrightjsp

r,Jm,n
2neffr/reseim ,
1 where r and  are polar coordinates, Jm,n are Bessel func￾tions, and m and n are the azimuthal mode and the radial mode number, respectively. res is the resonant wavelength. For the effective refractive index neff, we used 1.60 for the TE0 mode considering the light confinement in a slab wave￾guide. The high refractive index contrast between the film and the air, and the spatial difference between the disk diam￾eter and resonance wavelength, allow us to assume that WGMs are strongly confined within a disk and the field in￾tensity is almost zero at the disk radius R, 19,20 setting the boundary condition to be Jm,n
2neffR/res= 0. In fact, this approximation has been successfully used in the case of semiconductor microdisks.19,20 Finally, we can find reso￾nance wavelengths of WGMs and their corresponding mode numbers. In the case of the microdisk with a diameter of 8.8
m, the azimuthal mode number was found to range from m= 40
for res= 950 nm to 60
for res= 650 nm in the spectral range of Fig. 3 for the first radial mode. Experi￾mental peaks can be assigned to the TE0m,1 modes with azi￾muthal modes, with a mode spacing of 15 nm, in good agreement with the calculation as shown in the inset of Fig. 3. The second or higher orders can not be matched with the experimental results. So, only the first-order radial modes, the TE0m,1 modes, can be observed in our microdisk array. Similarly, for the array of microdisks with a disk diameter of 23.7
m, we observed only first-order radial modes. Due to the absence of both higher axial modes and higher radial modes, the resonance peak spacing is determined only by azimuthal modes. As a result, the mode spacing is 15 nm and 6 nm, and rather broad for microdisks with a diameter of 8.8
m and 23.7
m, respectively. This fact has important implications since broader mode spacing is more advanta￾geous for the development of a single-line light source. The resonant peaks in the PL spectrum result from the overlapping of individual modes from each microdisk since PL measurements were performed by pumping several thou￾sands of microdisks at the same time. Thus, the Q factor, which can be evaluated from Fig. 3, is mainly determined by slight irregularities in disk diameter rather than the effect of the roughness of the periphery. Using higher resolved PL measurements with a resolution of 0.4 nm, a full width at half maximum at each resonant mode was observed to be 2 nm. Thus, the Q factor of the microdisk array was calcu￾lated to be around 400 for microdisks with a diameter of 8.8
m. While this Q value seems to be much smaller than reported value for a silica-based microdisk,10 to the contrary, this result implies the excellent mass fabrication of micro￾disks with a size deviation of 0.2% between each micro￾disk, since 1% of the diameter deviation would limit the overall Q factor of the microdisk array to below 80. In addition to the excellent mass production and the ob￾servation of WGMs of the Si-NCs microdisk array, it is worth noting the advantage of size-controlled Si-NC/SiO2 SLs as a base material for the microdisks compared to other conventional Si-NCs methods.21 For microphotonic devices, which are based on Si-NCs for active optical emission, both the Si-NC size—which determines the luminescence proper￾ties, and the film refractive index—which influences the character of WGMs, are important parameters. However, the size distribution of Si-NCs is fairly broad for conventional Si-NCs in a SiO2 matrix, which are generally formed by high-temperature anneals of amorphous SiOx
a-SiOx films fabricated by chemical vapor deposition, sputtering, or ion￾implantation of Si ions. This wider size distribution of Si-NCs is disadvantageous for laser applications. In contrast, the size distribution of Si-NCs in our SLs is rather narrow.13 Second in order to design microdisks flexibly for optimal operation, independent control of the Si-NCs size and the refractive index is required at the same time. For our SiOx /SiO2 SLs, the Si-NC size and the refractive index can be independently controlled and designed quite well. Finally, the birefringence behavior of SiOx /SiO2 SLs film allows the selective coupling of TE modes, rather than TM modes, to the microdisk, inducing wider mode spacing. In conclusion, we presented microdisk resonators which are based on size-controlled Si-NCs in a SiO2 matrix. The mass production of such microdisk resonators in large-scale arrays was demonstrated. WGMs, from the visible lumines￾cence of Si-NCs, were observed for the microdisk array. Thin layer thickness and the birefringence of SLs films allow one to sustain only one axial and one radial mode; inducing a rather broad mode spacing of up to 15 nm. The used pro￾cess technology for the integration of microdisks is compat￾ible with planar silicon-process technology. We expect that such microdisk arrays can be applied as a base material for integrated Si microphotonics. R.J.Z. gratefully acknowledges financial support from the Alexander von Humboldt Foundation. S.Y.S. gratefully acknowledges financial support from the Korea Research Foundation. 1 Towards the First Silicon Laser, NATO Science Series, edited by L. Pavesi, S. Gaponenko, and L. Dal Negro
Kluwer, Dordrecht, 2003. 2 Q. F. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Nature
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