- Email: [email protected]
High-Q factor single mode circular photonic crystal nano-resonator
Superlattices and Microstructures 43 (2008) 507–511 www.elsevier.com/locate/superlattices
High-Q factor single mode circular photonic crystal nano-resonator V. Errico, A. Salhi, C. Giordano, M. De Giorgi, A. Passaseo, M. De Vittorio ∗ National Nanotechnology Laboratory (NNL) of CNR-INFM, Distretto Tecnologico - ISUFI, Universit`a del Salento, via per Arnesano n.16, 73100 Lecce, Italy Available online 14 September 2007
Abstract In this work, the analysis, fabrication and optical characterization of a two-dimensional circular photonic crystal (2D-CPC) nano-resonator based on an air/GaAs/air slab waveguide are presented. Four InAs/InGaAs quantum dots (QDs) stacked layers emitting around 1300 nm at room temperature were embedded in a GaAs waveguide layer grown on an Al0.7 Ga0.3 As layer and GaAs substrate. The patterning of the structure and the membrane release were achieved by using electron beam lithography, ICP plasma etching and selective wet etching of the AlGaAs sacrificial layer. The micro-luminescence spectrum recorded from the fabricated nano-cavity shows a narrow optical transition at the resonance wavelength of about 1282 nm with a FWHM ˚ and more than 2000, respectively. and Q-factor of 6.2 A c 2007 Elsevier Ltd. All rights reserved.
Keywords: Nano-cavity; Quantum dot; Photonic crystal
1. Introduction Electromagnetic resonant cavities, which trap light within a finite volume, are essential components for the fabrication of high efficiency photonic devices such as ultra small optical filters, single-photon sources [1,2] and low-threshold lasers [3]. In a micro-cavity and in weak coupling regimes, according to the Purcell factor relationship [4], an increase in the Q-factor and a reduction of the modal volume Vmode lead to a strong enhancement of the spontaneous ∗ Corresponding author. Tel.: +39 0832 298200; fax: +39 0832 298237.
E-mail address: [email protected] (M. De Vittorio). c 2007 Elsevier Ltd. All rights reserved. 0749-6036/$ - see front matter doi:10.1016/j.spmi.2007.06.013
508
V. Errico et al. / Superlattices and Microstructures 43 (2008) 507–511
emission. High Q-factor DBR micropillars and microtoroids, based on total internal reflection (TIR), have been demonstrated in the last few years [5,6], but the scaling down of TIR devices is very difficult to achieve, since optical leakages arise when shrinking their size, which dramatically affect their Q-factor. Two-dimensional photonic crystal technology (2D-PC) offers a way to achieve both high Q-factor and small modal volume micro- and nano-cavities. Indeed, photonic crystals allow the fabrication of very efficient devices, and the scaling down of the sizes can be performed without significant loss in performances. Several architectures of micro-cavities based on 2D-PC technology have been proposed in the literature and impressive results in terms of ultra high Q-factors and small modal volumes have been demonstrated in the last few years. Indeed, theoretical Q-factors of several millions have been predicted through passive structures excited by means of PC waveguides [7,8], whereas active microresonators with Q-factors on the order of hundred thousand have been proposed [9]. The experimental Q-factor is significantly reduced by several losses and imperfections of the fabrication process [8] or carrier dynamics and thermal heating in the PC slab [9]. Most of the proposed architectures rely on triangular and square photonic crystal lattices, whose symmetry makes them easier to design and simulate. In these PC geometries, micro-cavities and bends have either 120◦ , typical of hexagonal shapes [10], (Fig. 1(a)) or 90◦ abrupt angles, which tend to support localized bound states and prevent the fabrication of pure circular micro-cavities or smooth whispering gallery devices. A different approach to achieve smooth and circular bends is based on circular photonic crystals (CPC) (Fig. 1(b)). If the Bragg condition is fulfilled, CPC geometries can also exhibit a photonic band-gap, and different CPC architectures have been theoretically proposed in the literature for micro- and nano-cavities and compact whispering gallery devices [11,12]. These theoretical results and our calculations suggest that the circular approach exhibits a better matching of the mode inside small sized cavity volumes, especially for whispering gallery PC devices. In this paper, we report on the design, fabrication and optical characterization of a membrane CPC micro-cavity based on a air/GaAs/air slab waveguide, embedding InAs/InGaAs QDs emitting around 1300 nm at room temperature. 2. Results and discussion In order to predict the behaviour of 2D-CPC vertical nano-cavity and to finely tune the cavity resonance around the QDs emission, micro-cavities with different geometric parameters have been simulated by using a 3D finite difference time domain (FDTD) method. A time-impulsive source was launched inside the cavity and the resonance spectrum was obtained by Fourier analysis. Our designed CPC nano-cavity is reported in Fig. 1(b), and it consists of air-holes in a GaAs material along circular concentric lines. We defined the period a of the CPC as the periodicity between the concentric circular lines. In our nano-cavity, the air-holes along every circular line have the same radius except for the inner air-holes around the central defect region (black circles in Fig. 1(b)). These inner air-holes, according to the results shown in the literature [8,9,13] have been reduced in size and radially shifted in order to optimize the cavity emission, avoiding abrupt changes of the cavity mode field. According to our computational results, the wavelength resonance of the nano-cavity is a function of the inner ri /a and outer ro /a ratios [14], where ri and ro are the radius of the inner and outer air-holes respectively. Depending on the chosen parameters, it is possible either to
V. Errico et al. / Superlattices and Microstructures 43 (2008) 507–511
509
Fig. 1. Different cavity lattice designs: (a) triangular lattice PC cavities with 120◦ abrupt bends which tend to support localized bound states; and (b) circular photonic crystal lattice (CPC) structures, which are theoretically expected to exhibit a photonic band-gap and can better support whispering gallery modes.
reduce the effect of fluctuations in the geometrical parameters of the cavity or to shift and tune the nano-cavity resonance wavelength over a desired spectral range. The heterostructure was grown on a GaAs bulk material by using molecular beam epitaxy (MBE), and it consists of a 2 µm thick Al0.7 Ga0.3 As sacrificial layer covered by a 200 nm thick GaAs waveguide layer, embedding four layers of InAs/InGaAs QDs. The QD density in each layer was approximately 3.2 × 1010 cm−2 , and the photoluminescence spectrum of the sample at room temperature shows a QDs ground state emission peak at 1288 nm with a full-width at half maximum (FWHM) of around 28 meV. In our structure the spectral range of interest is centered around 1.3 µm, the low-attenuation spectral window for fiber optic communications, which corresponds to the ground state emission of the embedded InAs QDs layers. The 2D-CPC pattern was defined by an EBL process carried out by a Raith150 lithography system on a 300 nm thick ZEP 520A, a positive tone electron beam resists. In order to achieve smoother and circular air-holes and faster exposure, the EBL system was used in circular mode. In this way, every circular air-hole was exposed by the deflection of the beam along concentric circles. Proximity error correction (PEC) was also applied [15], thus avoiding variations in air-holes size across the device. The ZEP 520A resist, exposed by a 38 µC/cm2 dose at an acceleration voltage of 20 kV, was developed by dipping the sample in ZED-N50 and rinsing in isopropyl-alcohol (IPA). The pattern was transferred from the resist to the underlying heterostructure by an ICP process carried out by a STS ICP system with a SiCl4 /He (16 sccm/4 sccm) mixture. This dry etch transferred the photonic crystal cavity pattern through the waveguide layer and into the sacrificial layer. After dry-etch, the sample was rinsed in ZDMAC in order to remove the ZEP residual layer. The final step was the complete removal of the underlying sacrificial Al0.7 Ga0.3 As layer in order to realize the 2D-CPC membrane nano-cavity. This target was achieved by using a HF:H2 O (1:10) wet etching at room temperature through both the photonic crystal air-holes and four trenches disposed around the nano-cavity structure in order to facilitate the reaction products removal. The final result of the fabrication procedure is shown in Fig. 2, where the black regions correspond to the dry-etched zone and the brighter regions around the CPC structure correspond to the suspended area created by the wet etching process of the AlGaAs sacrificial layer. The fabricated nano-cavity has a period a = 350 nm, inner air-holes ratio ri /a = 0.24 and outer air-holes ratio ro /a = 0.33. µ-Photo luminescence measurements were made by using an Argon Ion laser as excitation pump at a wavelength of 514 nm and InGaAs Optical Multichannel Analizer (OMA) for spectrum
510
V. Errico et al. / Superlattices and Microstructures 43 (2008) 507–511
Fig. 2. SEM image of the fabricated nano-cavity using circular photonic crystal lattice.
Fig. 3. Infrared emission from the nano-cavity measured by µ-photo luminescence setup.
measurement. Fig. 3 shows the micro-luminescence spectrum recorded from the central area of the device. A sharp peak has been measured at the wavelength centred around 1280 nm which corresponds to the inhomogeneously broadened quantum dot ground state emission. The full ˚ and more than 2000, width at half maximum of the device (FWHM) and Q-factor are 6.2 A respectively. These preliminary results are in good agreement with numerical calculation by the FDTD method, which show that the resonance peak wavelength can be finely tuned by only changing the diameter either of the inner or outer air-hole radii. Moreover, preliminary simulations show that the design and fabrication of hybrid circular/triangular photonic crystal lattices could be a very promising way to achieve high efficiency micro- and nano-cavities and whispering gallery devices for both active and passive photonic crystal applications. 3. Conclusion In summary, a high-quality factor InAs/InGaAs QDs membrane circular photonic crystal single mode nano-resonator has been simulated and fabricated. The spectral response of the active circular nano-cavity has been simulated by using a three dimensional Finite-Difference
V. Errico et al. / Superlattices and Microstructures 43 (2008) 507–511
511
Time-Domain method as a function of both the inner and outer r/a ratios of the photonic crystal structure. Good agreement between simulations and experimental results has been achieved with a single sharp resonance at the wavelength of about 1282 nm and FWHM and with Q-factor of ˚ and more than 2000, respectively. 6.2 A Acknowledgements This work has been funded by the project PRIN 2005 “Fabbricazione di nanosensori a cristallo fotonico bidimensionale” and by “FIRB 2004 - Hub di ricerca italo-giapponese sulle nanotecnologie”. The authors gratefully thank Gianmichele Epifani, Paolo Cazzato, Diego Mangiullo and Gianvito De Iaco for their expert technical help. References [1] D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, J. Vuˇckovi´c, Phys. Rev. Lett. 95 (2005) 013904. [2] W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, T.-M. Hsu, Phys. Rev. Lett. 96 (2006) 117401. [3] T. Yoshie, M. Loncar, A. Scherer, Y. Qiu, Appl. Phys. Lett. 84 (18) (2004) 3543–3545. [4] E.M. Purcell, Phys. Rev. 69 (1946) 681. [5] S. Reitzenstein, A. Bazhenov, A. Gorbunov, C. Hofmann, S. M¨unch, A. L¨offler, M. Kamp, J.P. Reithmaier, V.D. Kulakovskii, A. Forchel, Appl. Phys. Lett. 89 (2006) 051107. [6] A. Armani, D. Armani, S. Spillane, K. Vahala, APS March Meeting (2006) abstr #Y16.005. [7] E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, T. Watanabe, Appl. Phys. Lett. 88 (2006) 041112. [8] T. Asano, B.S. Song, Y. Akahane, S. Noda, IEEE J. Sel. Topics Quantum Electr. 12 (6) (2006). [9] K. Nozaki, T. Baba, Appl. Phys. Lett. 88 (2006) 211101. [10] J. Scheuer, A. Yariv, Phys. Rev. E (2004) 70. [11] J. Zarbakash, V. Rinnerbauer, K. Hingerl, Proc. IEEE ICTON (2006). [12] D. Chang, J. Scheuer, A. Yariv, Opt. Soc. Am. 13 (23) (2005) 9272. [13] M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, H.-Y. Ryu, OSA Optics Express 12 (8) (2004) 1551. [14] V. Errico, T. Stomeo, A. Salhi, M. De Giorgi, A. Passaseo, M. De Vittorio, Microelectron. Eng. 84 (2007) 1570–1573. [15] K. Hennessy, C. Reese, A. Badolato, C.F. Wang, A. Imamoglu, P.-M. Petroff, E. Hu, J. Vac. Sci. Technol. B 21 (6) (2003) 2918.
High-Q factor single mode circular photonic crystal nano-resonator V. Errico, A. Salhi, C. Giordano, M. De Giorgi, A. Passaseo, M. De Vittorio ∗ National Nanotechnology Laboratory (NNL) of CNR-INFM, Distretto Tecnologico - ISUFI, Universit`a del Salento, via per Arnesano n.16, 73100 Lecce, Italy Available online 14 September 2007
Abstract In this work, the analysis, fabrication and optical characterization of a two-dimensional circular photonic crystal (2D-CPC) nano-resonator based on an air/GaAs/air slab waveguide are presented. Four InAs/InGaAs quantum dots (QDs) stacked layers emitting around 1300 nm at room temperature were embedded in a GaAs waveguide layer grown on an Al0.7 Ga0.3 As layer and GaAs substrate. The patterning of the structure and the membrane release were achieved by using electron beam lithography, ICP plasma etching and selective wet etching of the AlGaAs sacrificial layer. The micro-luminescence spectrum recorded from the fabricated nano-cavity shows a narrow optical transition at the resonance wavelength of about 1282 nm with a FWHM ˚ and more than 2000, respectively. and Q-factor of 6.2 A c 2007 Elsevier Ltd. All rights reserved.
Keywords: Nano-cavity; Quantum dot; Photonic crystal
1. Introduction Electromagnetic resonant cavities, which trap light within a finite volume, are essential components for the fabrication of high efficiency photonic devices such as ultra small optical filters, single-photon sources [1,2] and low-threshold lasers [3]. In a micro-cavity and in weak coupling regimes, according to the Purcell factor relationship [4], an increase in the Q-factor and a reduction of the modal volume Vmode lead to a strong enhancement of the spontaneous ∗ Corresponding author. Tel.: +39 0832 298200; fax: +39 0832 298237.
E-mail address: [email protected] (M. De Vittorio). c 2007 Elsevier Ltd. All rights reserved. 0749-6036/$ - see front matter doi:10.1016/j.spmi.2007.06.013
508
V. Errico et al. / Superlattices and Microstructures 43 (2008) 507–511
emission. High Q-factor DBR micropillars and microtoroids, based on total internal reflection (TIR), have been demonstrated in the last few years [5,6], but the scaling down of TIR devices is very difficult to achieve, since optical leakages arise when shrinking their size, which dramatically affect their Q-factor. Two-dimensional photonic crystal technology (2D-PC) offers a way to achieve both high Q-factor and small modal volume micro- and nano-cavities. Indeed, photonic crystals allow the fabrication of very efficient devices, and the scaling down of the sizes can be performed without significant loss in performances. Several architectures of micro-cavities based on 2D-PC technology have been proposed in the literature and impressive results in terms of ultra high Q-factors and small modal volumes have been demonstrated in the last few years. Indeed, theoretical Q-factors of several millions have been predicted through passive structures excited by means of PC waveguides [7,8], whereas active microresonators with Q-factors on the order of hundred thousand have been proposed [9]. The experimental Q-factor is significantly reduced by several losses and imperfections of the fabrication process [8] or carrier dynamics and thermal heating in the PC slab [9]. Most of the proposed architectures rely on triangular and square photonic crystal lattices, whose symmetry makes them easier to design and simulate. In these PC geometries, micro-cavities and bends have either 120◦ , typical of hexagonal shapes [10], (Fig. 1(a)) or 90◦ abrupt angles, which tend to support localized bound states and prevent the fabrication of pure circular micro-cavities or smooth whispering gallery devices. A different approach to achieve smooth and circular bends is based on circular photonic crystals (CPC) (Fig. 1(b)). If the Bragg condition is fulfilled, CPC geometries can also exhibit a photonic band-gap, and different CPC architectures have been theoretically proposed in the literature for micro- and nano-cavities and compact whispering gallery devices [11,12]. These theoretical results and our calculations suggest that the circular approach exhibits a better matching of the mode inside small sized cavity volumes, especially for whispering gallery PC devices. In this paper, we report on the design, fabrication and optical characterization of a membrane CPC micro-cavity based on a air/GaAs/air slab waveguide, embedding InAs/InGaAs QDs emitting around 1300 nm at room temperature. 2. Results and discussion In order to predict the behaviour of 2D-CPC vertical nano-cavity and to finely tune the cavity resonance around the QDs emission, micro-cavities with different geometric parameters have been simulated by using a 3D finite difference time domain (FDTD) method. A time-impulsive source was launched inside the cavity and the resonance spectrum was obtained by Fourier analysis. Our designed CPC nano-cavity is reported in Fig. 1(b), and it consists of air-holes in a GaAs material along circular concentric lines. We defined the period a of the CPC as the periodicity between the concentric circular lines. In our nano-cavity, the air-holes along every circular line have the same radius except for the inner air-holes around the central defect region (black circles in Fig. 1(b)). These inner air-holes, according to the results shown in the literature [8,9,13] have been reduced in size and radially shifted in order to optimize the cavity emission, avoiding abrupt changes of the cavity mode field. According to our computational results, the wavelength resonance of the nano-cavity is a function of the inner ri /a and outer ro /a ratios [14], where ri and ro are the radius of the inner and outer air-holes respectively. Depending on the chosen parameters, it is possible either to
V. Errico et al. / Superlattices and Microstructures 43 (2008) 507–511
509
Fig. 1. Different cavity lattice designs: (a) triangular lattice PC cavities with 120◦ abrupt bends which tend to support localized bound states; and (b) circular photonic crystal lattice (CPC) structures, which are theoretically expected to exhibit a photonic band-gap and can better support whispering gallery modes.
reduce the effect of fluctuations in the geometrical parameters of the cavity or to shift and tune the nano-cavity resonance wavelength over a desired spectral range. The heterostructure was grown on a GaAs bulk material by using molecular beam epitaxy (MBE), and it consists of a 2 µm thick Al0.7 Ga0.3 As sacrificial layer covered by a 200 nm thick GaAs waveguide layer, embedding four layers of InAs/InGaAs QDs. The QD density in each layer was approximately 3.2 × 1010 cm−2 , and the photoluminescence spectrum of the sample at room temperature shows a QDs ground state emission peak at 1288 nm with a full-width at half maximum (FWHM) of around 28 meV. In our structure the spectral range of interest is centered around 1.3 µm, the low-attenuation spectral window for fiber optic communications, which corresponds to the ground state emission of the embedded InAs QDs layers. The 2D-CPC pattern was defined by an EBL process carried out by a Raith150 lithography system on a 300 nm thick ZEP 520A, a positive tone electron beam resists. In order to achieve smoother and circular air-holes and faster exposure, the EBL system was used in circular mode. In this way, every circular air-hole was exposed by the deflection of the beam along concentric circles. Proximity error correction (PEC) was also applied [15], thus avoiding variations in air-holes size across the device. The ZEP 520A resist, exposed by a 38 µC/cm2 dose at an acceleration voltage of 20 kV, was developed by dipping the sample in ZED-N50 and rinsing in isopropyl-alcohol (IPA). The pattern was transferred from the resist to the underlying heterostructure by an ICP process carried out by a STS ICP system with a SiCl4 /He (16 sccm/4 sccm) mixture. This dry etch transferred the photonic crystal cavity pattern through the waveguide layer and into the sacrificial layer. After dry-etch, the sample was rinsed in ZDMAC in order to remove the ZEP residual layer. The final step was the complete removal of the underlying sacrificial Al0.7 Ga0.3 As layer in order to realize the 2D-CPC membrane nano-cavity. This target was achieved by using a HF:H2 O (1:10) wet etching at room temperature through both the photonic crystal air-holes and four trenches disposed around the nano-cavity structure in order to facilitate the reaction products removal. The final result of the fabrication procedure is shown in Fig. 2, where the black regions correspond to the dry-etched zone and the brighter regions around the CPC structure correspond to the suspended area created by the wet etching process of the AlGaAs sacrificial layer. The fabricated nano-cavity has a period a = 350 nm, inner air-holes ratio ri /a = 0.24 and outer air-holes ratio ro /a = 0.33. µ-Photo luminescence measurements were made by using an Argon Ion laser as excitation pump at a wavelength of 514 nm and InGaAs Optical Multichannel Analizer (OMA) for spectrum
510
V. Errico et al. / Superlattices and Microstructures 43 (2008) 507–511
Fig. 2. SEM image of the fabricated nano-cavity using circular photonic crystal lattice.
Fig. 3. Infrared emission from the nano-cavity measured by µ-photo luminescence setup.
measurement. Fig. 3 shows the micro-luminescence spectrum recorded from the central area of the device. A sharp peak has been measured at the wavelength centred around 1280 nm which corresponds to the inhomogeneously broadened quantum dot ground state emission. The full ˚ and more than 2000, width at half maximum of the device (FWHM) and Q-factor are 6.2 A respectively. These preliminary results are in good agreement with numerical calculation by the FDTD method, which show that the resonance peak wavelength can be finely tuned by only changing the diameter either of the inner or outer air-hole radii. Moreover, preliminary simulations show that the design and fabrication of hybrid circular/triangular photonic crystal lattices could be a very promising way to achieve high efficiency micro- and nano-cavities and whispering gallery devices for both active and passive photonic crystal applications. 3. Conclusion In summary, a high-quality factor InAs/InGaAs QDs membrane circular photonic crystal single mode nano-resonator has been simulated and fabricated. The spectral response of the active circular nano-cavity has been simulated by using a three dimensional Finite-Difference
V. Errico et al. / Superlattices and Microstructures 43 (2008) 507–511
511
Time-Domain method as a function of both the inner and outer r/a ratios of the photonic crystal structure. Good agreement between simulations and experimental results has been achieved with a single sharp resonance at the wavelength of about 1282 nm and FWHM and with Q-factor of ˚ and more than 2000, respectively. 6.2 A Acknowledgements This work has been funded by the project PRIN 2005 “Fabbricazione di nanosensori a cristallo fotonico bidimensionale” and by “FIRB 2004 - Hub di ricerca italo-giapponese sulle nanotecnologie”. The authors gratefully thank Gianmichele Epifani, Paolo Cazzato, Diego Mangiullo and Gianvito De Iaco for their expert technical help. References [1] D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, J. Vuˇckovi´c, Phys. Rev. Lett. 95 (2005) 013904. [2] W.-H. Chang, W.-Y. Chen, H.-S. Chang, T.-P. Hsieh, J.-I. Chyi, T.-M. Hsu, Phys. Rev. Lett. 96 (2006) 117401. [3] T. Yoshie, M. Loncar, A. Scherer, Y. Qiu, Appl. Phys. Lett. 84 (18) (2004) 3543–3545. [4] E.M. Purcell, Phys. Rev. 69 (1946) 681. [5] S. Reitzenstein, A. Bazhenov, A. Gorbunov, C. Hofmann, S. M¨unch, A. L¨offler, M. Kamp, J.P. Reithmaier, V.D. Kulakovskii, A. Forchel, Appl. Phys. Lett. 89 (2006) 051107. [6] A. Armani, D. Armani, S. Spillane, K. Vahala, APS March Meeting (2006) abstr #Y16.005. [7] E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, T. Watanabe, Appl. Phys. Lett. 88 (2006) 041112. [8] T. Asano, B.S. Song, Y. Akahane, S. Noda, IEEE J. Sel. Topics Quantum Electr. 12 (6) (2006). [9] K. Nozaki, T. Baba, Appl. Phys. Lett. 88 (2006) 211101. [10] J. Scheuer, A. Yariv, Phys. Rev. E (2004) 70. [11] J. Zarbakash, V. Rinnerbauer, K. Hingerl, Proc. IEEE ICTON (2006). [12] D. Chang, J. Scheuer, A. Yariv, Opt. Soc. Am. 13 (23) (2005) 9272. [13] M. Notomi, A. Shinya, S. Mitsugi, E. Kuramochi, H.-Y. Ryu, OSA Optics Express 12 (8) (2004) 1551. [14] V. Errico, T. Stomeo, A. Salhi, M. De Giorgi, A. Passaseo, M. De Vittorio, Microelectron. Eng. 84 (2007) 1570–1573. [15] K. Hennessy, C. Reese, A. Badolato, C.F. Wang, A. Imamoglu, P.-M. Petroff, E. Hu, J. Vac. Sci. Technol. B 21 (6) (2003) 2918.