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Sub-bandgap linear-absorption-based photodetectors in avalanche mode in PN-diode-integrated silicon microring resonators Yu Li, Shaoqi Feng, Yu Zhang, and Andrew W. Poon* Photonic Device Laboratory, Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China *Corresponding author: [email protected] Received September 3, 2013; revised October 22, 2013; accepted November 2, 2013; posted November 4, 2013 (Doc. ID 197039); published November 27, 2013 We report a sub-bandgap linear-absorption-based photodetector in avalanche mode at 1550 nm in a PN-diodeintegrated silicon microring resonator. The photocurrent is primarily generated by the defect-state absorption introduced by the boron and phosphorous ion implantation during the PN diode formation. The responsivity is enhanced by both the cavity effect and the avalanche multiplication. We measure a responsivity of ∼72.8 mA∕W upon 8 V at cavity resonances in avalanche mode, corresponding to a gain of ∼72 relative to the responsivity of ∼1.0 mA∕W upon 3 V at cavity resonances in normal mode. Our device exhibits a 3 dB bandwidth of ∼7 GHz and an open eye diagram at 15 Gbit∕s upon 8 V. © 2013 Optical Society of America OCIS codes: (230.0230) Optical devices; (040.1345) Avalanche photodiodes (APDs); (040.5160) Photodetectors; (230.5750) Resonators. http://dx.doi.org/10.1364/OL.38.005200
Over the past few years, sub-bandgap photocurrent generation in silicon (Si) at 1550 nm has been attracting research interests for applications as power monitors in Si photonic integrated circuits. Four sub-bandgap absorption mechanisms in Si have been studied, namely, linear surface-state absorption (SSA) [1,2], linear defectstate absorption (DSA) [3–7], two-photon absorption (TPA) [8], and internal photoemission effect [9,10]. For SSA-based photodetectors (PDs), Baehr-Jones et al. [1] designed a 1.5 mm long waveguide PD to obtain a sufficiently large spatial overlap between the waveguide surfaces and the optical mode, and they obtained with a multicontact design a responsivity of 36 mA∕W upon 11 V. For DSA-based PDs, researchers have exploited various fabrication processes and ions implantation in order to controllably introduce defects in Si, including ion implantation of Si [3,6], Ar [7], and other kinds of ions. Avalanche effect in DSA-based PDs has also been demonstrated. Geis et al. [3] reported a 3 mm long Si waveguide PD with an avalanche-effect-enhanced internal quantum efficiency (IQE) of ∼10 A∕W and a 3 dB bandwidth of ∼35 GHz upon 20 V. Most recently, Ackert et al. [6] reported a 600 μm long Si waveguide PD with avalanche effect and showed a responsivity of 4.7 A∕W and a 3 dB bandwidth of 2 GHz upon 40 V. In this Letter, we report a DSA-based PD in avalanche mode at 1550 nm in a PN-diode-integrated Si microring resonator. We use the defect states in Si formed via phosphorus and boron implantations during the PNdiode formation. The key merit of this method is that it does not require additional implantation process to form defects. Our experiments reveal at cavity resonances an avalanche gain of ∼72 upon 8 V. We also examine the dynamic responses of the PD in avalanche mode. Figure 1(a) schematically shows the principles of DSA and SSA (denoted as processes A) and of avalanche effect (denoted as process B) in a Si PN diode. While DSA is due to defects in the bulk of the diode, SSA is due to the interfacial states and dangling bonds at the 0146-9592/13/235200-04$15.00/0
diode surfaces and interfaces. As the optical mode mainly spatially overlaps with the bulk of the diode, we assume DSA to be dominant compared to SSA. Figure 1(b) schematically shows the device design. The microring cavity enhances the internal field at resonance wavelengths, and thus enhances the photocurrent generation at cavity resonances. The device design follows the conventional carrier-depletion Si-microring modulator [4]. We design the racetrack microring with an arc diameter of 30 μm and an interaction length of 20 μm. The fabricated gap spacing between the bus waveguide and the microring is ∼350– ∼ 400 nm. The PN diode is integrated along most of the microring with a diode length of ∼102 μm, except for the waveguide-microring coupling region that remains undoped. The zoom-in view schematically shows the cross section of the PN-diode-integrated Si waveguide. We design the waveguide with a width of 500 nm, a height of 200 nm, and a slab thickness of 50 nm on a 3 μm thick buriedoxide layer. We design the PN junction to be 100 nm
Fig. 1. (a) Schematic of the energy band diagram of a Si PN-diode for sub-bandgap linear-absorption-based photodetection in avalanche mode. A: DSA and SSA, B: avalanche. (b) Top-view schematic of the PN-diode-integrated Si microring resonator. Zoom-in: cross-sectional view schematic of the Si waveguide, with an overlaid simulated optical mode-field intensity profile. © 2013 Optical Society of America
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offset from the waveguide center toward the N-type, with a P-doping concentration of ∼2.7 × 1018 cm−3 and an N-doping concentration of ∼4 × 1018 cm−3 . The 100 nm offset along with the adopted P − and N − concentrations allows the depletion region to be centered on the optical mode maximum. We design the P and N doped regions (both with a concentration of ∼5 × 1019 cm−3 ) for contacts to be 0.3 μm away from waveguide sidewalls. Our numerical beam-propagation-method (BPM)simulated waveguide-mode intensity profile of the transverse-electric (TE) polarization [overlaid in the zoom-in view of Fig. 1(b)] suggests that the optical mode spatial overlaps with the P and N doped regions are negligible. We fabricate the PN-diode-integrated microrings following the standard complementary metal–oxide– semiconductor nanoelectronics fabrication processes using i-line (365 nm) photolithography and reactive ion etching. In order to activate the dopants and repair damages in the Si lattice after the implantations, we employ a rapid thermal annealing with a 10 s duration of 600°C preannealing process, followed by a 30 s duration of 1000°C annealing process. However, this annealing process is not optimized for introducing defects. Figure 2(a) shows the scanning-electron micrograph (SEM) of the fabricated microring resonator contacted with the groundsignal-ground metal pads. We use two identical lensed fibers to couple in/out the light. We measure the fiber-chip-fiber loss is ∼26 dB. Assuming the input/output-coupling losses are identical and the microring is nearly at the middle of the bus waveguide, we extract the loss from the input fiber to the bus waveguide right by the microring to be ∼13 dB. Figure 2(b) shows the measured TE-polarized transmission spectra around a microring resonance upon a reverse bias of 3 V (black dots) with a resonance dip at 1545.80 nm and of 7.9 V (redline) with a resonance dip at a slightly redshifted wavelength of 1545.87 nm. We estimate the optical power in the bus waveguide just in front of the microring, P bus , to be ∼0.12 mW, given a launched power of ∼2 dBm. Both the resonances exhibit a cavity quality (Q) factor of ∼3700 and an extinction
Fig. 2. (a) SEM of a fabricated device. (b) Measured optical transmission spectra upon 3 V (dots) and 7.9 V (red line). Fitted optical spectrum for 3 V (blue line). (c) Measured photocurrent spectra upon 3 V and 7.9 V. Fitted photocurrent spectrum for 3 V (blue line). (d) Measured IV curves upon 0 μW (dark), 100 μW (red line), and 500 μW (blue line) estimated optical input at 1545.8 nm. Zoom-in: IV curves from 7.9 to 8.5 V.
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ratio of ∼10 dB. We attribute the 0.07 nm redshift of the resonance wavelength to the heat generated by the photocarriers upon lattice collisions, corresponding to a temperature rise of ∼1 °C in Si. As the junction is already fully depleted upon 3 V [to be shown in Fig. 4(a)], and the photocurrent generated is only up to a few μA, any free-carrier effect can be negligible. Figure 2(c) shows the simultaneously measured photocurrent spectra. The photocurrent spectrum upon 3 V reveals a cavity-enhanced photocurrent of 0.117 μA at resonance, with ∼13-fold enhancement relative to the photocurrent obtained at an off-resonance wavelength at 1544 nm. The photocurrent enhancement is due to the internal-field buildup in the resonator. The photocurrent spectrum upon 7.9 V exhibits a peak photocurrent of 5.3 μA, which is ∼45× larger than the peak photocurrent obtained upon 3 V, with also ∼13-fold cavity enhancement. We fit both the optical transmission and photocurrent spectra following relationships derived from the transfer matrix method [11]. We assume only linear photocurrent generation given as follows: I RP res
2 κ P bus ; R −iφ tAe − 1
(1)
where I is the photocurrent generated in the microring, P res is the cavity internal power, R is the linear responsivity, κ is the complex field-amplitude coupling coefficient, t is the complex field-amplitude transmission coefficient (assuming jtj2 jκj2 1), A is the microring round-trip amplitude transmission coefficient, given by exp−αL, where L is the microring round-trip length and α is the cavity field-amplitude attenuation, φ is the round-trip phase change, given by neff L2π∕λ, where neff is the waveguide effective refractive index ( 2.65 according to the BPM calculation), and λ is the free-space wavelength. The fits suggest a κ of 0.7, an A of 0.83, a R of ∼0.33 mA∕W upon 3 V, and a R of ∼14.3 mA∕W upon 7.9 V. The fitted responsivities correspond to a quantum efficiency QE 0.8R of 0.03% upon 3 V and of 1.14% upon 7.9 V. We extract from the fits the ratio of P res at on-resonance to P res at off-resonance to be ∼13.8, which is consistent with the observed ∼13-fold cavity enhancement. We calculate the ratio of P res ∕P bus at resonance to be ∼3, using the fitted κ and A values and Eq. (1). Our analysis, therefore, suggests a ∼3× cavity enhancement of the photocurrent relative to the photocurrent generated in the waveguide. Figure 2(d) shows the measured on-resonance current–voltage (IV) curves upon P bus of ∼100 μW (red) and ∼500 μW (blue) at 1545.80 nm. The measured dark current (black) remains under 1.0 nA up to ∼7 V and significantly increases afterward. The increase indicates the onset of the avalanche effect. The inset shows the dark current reaches ∼10 μA upon 8.1 V, which is typically set as the dark current value at breakdown [12]. Below 7 V, the measured photocurrent upon 500 μW is over 2 orders of magnitude above the dark current. In the presence of the avalanche effect, the ratio of the photocurrent to the dark current drops with the bias voltage. At 8 V, the
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photocurrent-to-dark-current ratio upon 500 μW drops to ∼10. Thus, we define the avalanche-mode working region of our PD to be from 7 V to 8 V. Figure 3 shows the photocurrents versus the estimated P bus upon various reverse bias voltages. The photocurrents show linear responses to the estimated input powers. We obtain a responsivity of ∼72.8 mA∕W upon 8 V. The inset shows the range of responsivity obtained in normal mode, ranging from ∼0.7 mA∕W upon 1 V to ∼1.6 mA∕W upon 5 V. Our measured linear photoresponses in normal mode are comparable to the responsivity of ∼5.9 mA∕W upon 10 V from a DSA-based PN-diode-integrated Si microring power monitor reported by Yu et al. [4], and are around an order of magnitude higher than that from our previously demonstrated SSA-based p-i-n diode-integrated Si microring PD [2]. Thus, we attribute the observed photocurrent to a DSA-dominant process. Figure 3(b) shows the responsivity and the gain upon various reverse bias voltages. We define the gain by normalizing the responsivities to that upon 3 V, at which the PN junction is fully depleted [to be shown in Fig. 4(a)] but without significant carrier multiplication. We obtain the gain to be ∼72 upon 8 V. We fit the gain values using Miller’s formula (black line) [13], M 1 − V∕V b n −1 ;
(2)
where M is the multiplication factor (gain), V is the applied voltage, V b is the breakdown voltage, and exponent n is a constant depending on the material, the doping profile, and the operation wavelength. The fit suggests a V b of ∼8.2 V and an n of 1.7. In order to extract the linear absorption coefficient and take into account the possible photocurrents from TPA, we use a second-order polynomial function to fit the measured photocurrents at resonance upon 3 V as a function of P res , as shown in Fig. 3(c). The fit, given by IμA 0.33 mA∕WP res mW0.0038 A∕WP res mW2 , indicates that the photocurrents from TPA (∝ P 2res ) are
Fig. 3. (a) Measured photocurrents versus P bus upon various voltages. Inset: photocurrents upon 1–5 V. (b) Responsivities and gains upon various voltages. Black line: Miller’s formula fit. (c) Measured photocurrents versus P res . Black line: a second-order polynomial fit. (d) Simulated electric-field amplitude distribution of the PN diode upon 8 V.
Fig. 4. (a) Measured photoresponses upon various voltages. (b) Measured 3 dB bandwidths versus avalanche gain. (c) Measured (black) and fitted (red) S11 (c) amplitude and (d) phase upon 3 V. Inset: The circuit model of the PD. C o , Ro , capacitance and resistance of the SiO2 substrate beneath the Si layer; C j , Rj , capacitance and resistance of the junction. C pad , pad capacitance.
negligible. Thus, the photocurrents are mainly caused by linear absorption. We can extract the linear absorption coefficient from the polynomial fit, given the known TPA coefficient in Si. Following [14], we obtain the photocurrents due to linear absorption, I linear , and TPA, I TPA , as follows: Iη
q αl 1 − e−αtot Ld γP res E ph αtot
η
qβ Ld 2 2 γ P res ; 2E ph Aeff
(3)
where η is the carrier-collection efficiency for the PN diode, q is the electron charge, E ph is the photon energy, αl is the linear absorption coefficient, αtot is the total cavity power loss coefficient (≈15.3 dB∕mm, given by the fitted A value), is the TPA coefficient in Si, which has a range of ∼0.4–∼0.9 cm∕GW, Aeff is the effective crosssectional area of the waveguide (∼0.15 μm2 ), Ld is the length of the PN diode 102 μm, and γ is the optical mode spatial overlap factor with the photodiode. We assume η to be identical for I linear and I TPA . The diode depletion and diffusion regions should span the whole waveguide width, giving γ ≈ 1. Using the second-order term in Eq. (3) and the second-order polynomial fit coefficient and assuming β 0.9 cm∕GW, we calculate η to be 92%. Using the first-order term, the first-order polynomial fit coefficient and the calculated η, we extract αl to be ∼0.015 dB∕mm. We attribute the relatively large cavity loss to the subbandgap absorption, the free-carrier absorption, and the scattering losses. Given the P − ∕N − concentrations, we can estimate the free-carrier absorption loss to be ∼0.9 dB∕mm based on the Soref and Bennett’s equations [15]. We attribute the rest, namely ∼14.4 dB∕mm, to the scattering losses due to both the surface roughness and the defects. Figure 3(d) shows the simulated electric-field amplitude distribution in the waveguide upon 8 V, according to a commercial device simulation package (Silvaco). The electric-field amplitude in the depletion region
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Fig. 5. Measured eye diagrams upon 8 V at data rates of (a) 10 Gbit∕s and (b) 15 Gbit∕s.
(highlighted) exceeds 105 V∕cm, which is consistent with the typical electric-field amplitude for exciting avalanche process [16]. However, only part of the optical mode-field profile near the mode maximum [see Fig. 1(b)] is spatially overlapped with the ∼0.17 μm wide depletion region. As the avalanche effect only happens in the depletion region, the multiplication process only takes place in the center part of the waveguide. Thus, another option of increasing the responsivity via the avalanche multiplication is to increase the spatial overlap between the optical mode field and the depletion region, while optimizing the P −∕N− implantation-induced defects distribution. We measure the small-signal frequency responses of the device from 1 to 8.5 V using a 20 GHz network analyzer, as shown in Fig. 4(a). Here we use a commercial 30 GHz PD for bandwidth calibration. From 1 to 3 V, the measured 3 dB bandwidth, f 3 dB , increases from ∼5 to ∼10 GHz, which is mainly due to the increase of the photocarrier drift velocity. From 3 to 7.5 V, f 3 dB becomes saturated at ∼10 GHz, suggesting the photocarriers in the depletion region have reached the saturation velocity (∼1 × 107 cm∕s). From 7.5 to 8 V, f 3 dB drops to ∼7 GHz owing to the avalanche buildup time effect. At 8.5 V, f 3 dB drops to ∼5.3 GHz. Figure 4(b) shows the measured bandwidth as a function of the avalanche gain. The gain-bandwidth (GBW) product is ∼500 GHz upon 8 V. The f 3 dB up to the avalanche buildup delay is limited by the cavity lifetime τc , the carrier transit time τs , and the resistance–capacitance (RC) time, given as follows: 2 2 2 f −2 3 dB 2πτc τs ∕0.45 2πRC :
(4)
Given a Q 3700, we calculate τc ≈ 2.4 ps. The cavitylifetime-limited bandwidth is ∼66 GHz. Given the depletion and diffusion region widths, we estimate τs to be ∼15 ps, with ∼2 ps for the drift carriers upon saturation velocity inside the depletion region and ∼13 ps for the diffusion carriers outside the depletion region. The transit-time-limited bandwidth is ∼30 GHz. We estimate the RC time by fitting the measured S11 with a small-signal circuit model, as shown in the inset of Fig. 4(c). Figures 4(c) and 4(d) show the measured and fitted amplitude and phase responses of S11. The red lines depict the fitting curves according to the circuit model. We obtain from the fit the metal-pad capacitance C p ≈ 34 fF and the junction capacitance C j ≈30 fF. We measure a resistance of ∼125 Ω, with a load resistance of 50 Ω. We therefore obtain a RC time delay of ∼14 ps, suggesting a RC-limited bandwidth of ∼12 GHz.
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The maximum f 3 dB according to Eq. (4) is therefore ∼11 GHz. Thus, our measured f 3 dB is mainly limited by the RC delay. We note that the RC-limited bandwidth can be broadened by a few folds upon reducing the microring perimeter and the diode length to few tens of micrometers, while the responsivity is not necessarily trade off should we preserve the cavity Q. We measure the eye diagrams at 10 Gbit∕s and 15 Gbit∕s upon 8 V, as shown in Fig. 5. We use a commercial 40 Gb∕s modulator to encode the pseudorandom bit sequence signal with a pattern length of 27 − 1. We amplify the photocurrent by a 20 GHz amplifier before the oscilloscope. We use a P bus of ∼2.3 mW. The open eye diagram at 15 Gbit∕s demonstrates the device’s capability to detect at a high data rate in avalanche mode. In summary, we have demonstrated a sub-bandgap linear-absorption-based PN-diode-integrated Si microring PD in avalanche mode. Our experiments revealed an avalanche PD with a responsivity of up to ∼72.8 mA∕W upon 8 V, with the ratio of the photocurrent (upon 500 μW) to dark current of about 10. The breakdown voltage is ∼8.2 V. We demonstrated a 3 dB bandwidth of ∼7 GHz and a GBW product of ∼500 GHz upon 8 V. We measured open eye diagrams upon 15 Gbit∕s data. The avalanche PD can be used as a high-speed power monitor inside a microring resonator. We can further increase the responsivity and the bandwidth upon optimizing the P/N doping concentrations and profile, the annealing time, the optical mode spatial overlap with the depletion region, the waveguide-microring coupling, and the microring size. References 1. T. Baehr-Jones, M. Hochberg, and A. Scherer, Opt. Express 16, 1659 (2008). 2. H. Chen, X. Luo, and A. W. Poon, Appl. Phys. Lett. 95, 171111 (2009). 3. M. Geis, S. Spector, M. Grein, J. Yoon, D. Lennon, and T. Lyszczarz, Opt. Express 17, 5193 (2009). 4. H. Yu, D. Korn, M. Pantouvaki, J. Van Campenhout, K. Komorowska, P. Verheyen, G. Lepage, P. Absil, D. Hillerkuss, and L. Alloatti, Opt. Lett. 37, 4681 (2012). 5. Y. Li and A. W. Poon, in Conference on Lasers and Electrooptics: Science and Innovations (OSA, 2013). 6. J. J. Ackert, A. S. Karar, D. J. Paez, P. E. Jessop, J. C. Cartledge, and A. P. Knights, Opt. Express 21, 19530 (2013). 7. R. Grote, K. Padmaraju, B. Souhan, J. Driscoll, K. Bergman, and R. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013). 8. H. Chen and A. W. Poon, Appl. Phys. Lett. 96, 191106 (2010). 9. M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, J. Lightwave Technol. 28, 3266 (2010). 10. A. Akbari, R. N. Tait, and P. Berini, Opt. Express 18, 8505 (2010). 11. A. Yariv, Electron. Lett. 36, 321 (2000). 12. M. J. Lee and W. Y. Choi, Opt. Express 18, 24189 (2010). 13. S. L. Miller, Phys. Rev. 99, 1234 (1955). 14. S. Fathpour, K. K. Tsia, and B. Jalali, IEEE J. Quantum Electron. 43, 1211 (2007). 15. R. Soref and B. Bennett, IEEE J. Quantum Electron. 23, 123 (1987). 16. S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).
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Sub-bandgap linear-absorption-based photodetectors in avalanche mode in PN-diode-integrated silicon microring resonators Yu Li, Shaoqi Feng, Yu Zhang, and Andrew W. Poon* Photonic Device Laboratory, Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China *Corresponding author: [email protected] Received September 3, 2013; revised October 22, 2013; accepted November 2, 2013; posted November 4, 2013 (Doc. ID 197039); published November 27, 2013 We report a sub-bandgap linear-absorption-based photodetector in avalanche mode at 1550 nm in a PN-diodeintegrated silicon microring resonator. The photocurrent is primarily generated by the defect-state absorption introduced by the boron and phosphorous ion implantation during the PN diode formation. The responsivity is enhanced by both the cavity effect and the avalanche multiplication. We measure a responsivity of ∼72.8 mA∕W upon 8 V at cavity resonances in avalanche mode, corresponding to a gain of ∼72 relative to the responsivity of ∼1.0 mA∕W upon 3 V at cavity resonances in normal mode. Our device exhibits a 3 dB bandwidth of ∼7 GHz and an open eye diagram at 15 Gbit∕s upon 8 V. © 2013 Optical Society of America OCIS codes: (230.0230) Optical devices; (040.1345) Avalanche photodiodes (APDs); (040.5160) Photodetectors; (230.5750) Resonators. http://dx.doi.org/10.1364/OL.38.005200
Over the past few years, sub-bandgap photocurrent generation in silicon (Si) at 1550 nm has been attracting research interests for applications as power monitors in Si photonic integrated circuits. Four sub-bandgap absorption mechanisms in Si have been studied, namely, linear surface-state absorption (SSA) [1,2], linear defectstate absorption (DSA) [3–7], two-photon absorption (TPA) [8], and internal photoemission effect [9,10]. For SSA-based photodetectors (PDs), Baehr-Jones et al. [1] designed a 1.5 mm long waveguide PD to obtain a sufficiently large spatial overlap between the waveguide surfaces and the optical mode, and they obtained with a multicontact design a responsivity of 36 mA∕W upon 11 V. For DSA-based PDs, researchers have exploited various fabrication processes and ions implantation in order to controllably introduce defects in Si, including ion implantation of Si [3,6], Ar [7], and other kinds of ions. Avalanche effect in DSA-based PDs has also been demonstrated. Geis et al. [3] reported a 3 mm long Si waveguide PD with an avalanche-effect-enhanced internal quantum efficiency (IQE) of ∼10 A∕W and a 3 dB bandwidth of ∼35 GHz upon 20 V. Most recently, Ackert et al. [6] reported a 600 μm long Si waveguide PD with avalanche effect and showed a responsivity of 4.7 A∕W and a 3 dB bandwidth of 2 GHz upon 40 V. In this Letter, we report a DSA-based PD in avalanche mode at 1550 nm in a PN-diode-integrated Si microring resonator. We use the defect states in Si formed via phosphorus and boron implantations during the PNdiode formation. The key merit of this method is that it does not require additional implantation process to form defects. Our experiments reveal at cavity resonances an avalanche gain of ∼72 upon 8 V. We also examine the dynamic responses of the PD in avalanche mode. Figure 1(a) schematically shows the principles of DSA and SSA (denoted as processes A) and of avalanche effect (denoted as process B) in a Si PN diode. While DSA is due to defects in the bulk of the diode, SSA is due to the interfacial states and dangling bonds at the 0146-9592/13/235200-04$15.00/0
diode surfaces and interfaces. As the optical mode mainly spatially overlaps with the bulk of the diode, we assume DSA to be dominant compared to SSA. Figure 1(b) schematically shows the device design. The microring cavity enhances the internal field at resonance wavelengths, and thus enhances the photocurrent generation at cavity resonances. The device design follows the conventional carrier-depletion Si-microring modulator [4]. We design the racetrack microring with an arc diameter of 30 μm and an interaction length of 20 μm. The fabricated gap spacing between the bus waveguide and the microring is ∼350– ∼ 400 nm. The PN diode is integrated along most of the microring with a diode length of ∼102 μm, except for the waveguide-microring coupling region that remains undoped. The zoom-in view schematically shows the cross section of the PN-diode-integrated Si waveguide. We design the waveguide with a width of 500 nm, a height of 200 nm, and a slab thickness of 50 nm on a 3 μm thick buriedoxide layer. We design the PN junction to be 100 nm
Fig. 1. (a) Schematic of the energy band diagram of a Si PN-diode for sub-bandgap linear-absorption-based photodetection in avalanche mode. A: DSA and SSA, B: avalanche. (b) Top-view schematic of the PN-diode-integrated Si microring resonator. Zoom-in: cross-sectional view schematic of the Si waveguide, with an overlaid simulated optical mode-field intensity profile. © 2013 Optical Society of America
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offset from the waveguide center toward the N-type, with a P-doping concentration of ∼2.7 × 1018 cm−3 and an N-doping concentration of ∼4 × 1018 cm−3 . The 100 nm offset along with the adopted P − and N − concentrations allows the depletion region to be centered on the optical mode maximum. We design the P and N doped regions (both with a concentration of ∼5 × 1019 cm−3 ) for contacts to be 0.3 μm away from waveguide sidewalls. Our numerical beam-propagation-method (BPM)simulated waveguide-mode intensity profile of the transverse-electric (TE) polarization [overlaid in the zoom-in view of Fig. 1(b)] suggests that the optical mode spatial overlaps with the P and N doped regions are negligible. We fabricate the PN-diode-integrated microrings following the standard complementary metal–oxide– semiconductor nanoelectronics fabrication processes using i-line (365 nm) photolithography and reactive ion etching. In order to activate the dopants and repair damages in the Si lattice after the implantations, we employ a rapid thermal annealing with a 10 s duration of 600°C preannealing process, followed by a 30 s duration of 1000°C annealing process. However, this annealing process is not optimized for introducing defects. Figure 2(a) shows the scanning-electron micrograph (SEM) of the fabricated microring resonator contacted with the groundsignal-ground metal pads. We use two identical lensed fibers to couple in/out the light. We measure the fiber-chip-fiber loss is ∼26 dB. Assuming the input/output-coupling losses are identical and the microring is nearly at the middle of the bus waveguide, we extract the loss from the input fiber to the bus waveguide right by the microring to be ∼13 dB. Figure 2(b) shows the measured TE-polarized transmission spectra around a microring resonance upon a reverse bias of 3 V (black dots) with a resonance dip at 1545.80 nm and of 7.9 V (redline) with a resonance dip at a slightly redshifted wavelength of 1545.87 nm. We estimate the optical power in the bus waveguide just in front of the microring, P bus , to be ∼0.12 mW, given a launched power of ∼2 dBm. Both the resonances exhibit a cavity quality (Q) factor of ∼3700 and an extinction
Fig. 2. (a) SEM of a fabricated device. (b) Measured optical transmission spectra upon 3 V (dots) and 7.9 V (red line). Fitted optical spectrum for 3 V (blue line). (c) Measured photocurrent spectra upon 3 V and 7.9 V. Fitted photocurrent spectrum for 3 V (blue line). (d) Measured IV curves upon 0 μW (dark), 100 μW (red line), and 500 μW (blue line) estimated optical input at 1545.8 nm. Zoom-in: IV curves from 7.9 to 8.5 V.
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ratio of ∼10 dB. We attribute the 0.07 nm redshift of the resonance wavelength to the heat generated by the photocarriers upon lattice collisions, corresponding to a temperature rise of ∼1 °C in Si. As the junction is already fully depleted upon 3 V [to be shown in Fig. 4(a)], and the photocurrent generated is only up to a few μA, any free-carrier effect can be negligible. Figure 2(c) shows the simultaneously measured photocurrent spectra. The photocurrent spectrum upon 3 V reveals a cavity-enhanced photocurrent of 0.117 μA at resonance, with ∼13-fold enhancement relative to the photocurrent obtained at an off-resonance wavelength at 1544 nm. The photocurrent enhancement is due to the internal-field buildup in the resonator. The photocurrent spectrum upon 7.9 V exhibits a peak photocurrent of 5.3 μA, which is ∼45× larger than the peak photocurrent obtained upon 3 V, with also ∼13-fold cavity enhancement. We fit both the optical transmission and photocurrent spectra following relationships derived from the transfer matrix method [11]. We assume only linear photocurrent generation given as follows: I RP res
2 κ P bus ; R −iφ tAe − 1
(1)
where I is the photocurrent generated in the microring, P res is the cavity internal power, R is the linear responsivity, κ is the complex field-amplitude coupling coefficient, t is the complex field-amplitude transmission coefficient (assuming jtj2 jκj2 1), A is the microring round-trip amplitude transmission coefficient, given by exp−αL, where L is the microring round-trip length and α is the cavity field-amplitude attenuation, φ is the round-trip phase change, given by neff L2π∕λ, where neff is the waveguide effective refractive index ( 2.65 according to the BPM calculation), and λ is the free-space wavelength. The fits suggest a κ of 0.7, an A of 0.83, a R of ∼0.33 mA∕W upon 3 V, and a R of ∼14.3 mA∕W upon 7.9 V. The fitted responsivities correspond to a quantum efficiency QE 0.8R of 0.03% upon 3 V and of 1.14% upon 7.9 V. We extract from the fits the ratio of P res at on-resonance to P res at off-resonance to be ∼13.8, which is consistent with the observed ∼13-fold cavity enhancement. We calculate the ratio of P res ∕P bus at resonance to be ∼3, using the fitted κ and A values and Eq. (1). Our analysis, therefore, suggests a ∼3× cavity enhancement of the photocurrent relative to the photocurrent generated in the waveguide. Figure 2(d) shows the measured on-resonance current–voltage (IV) curves upon P bus of ∼100 μW (red) and ∼500 μW (blue) at 1545.80 nm. The measured dark current (black) remains under 1.0 nA up to ∼7 V and significantly increases afterward. The increase indicates the onset of the avalanche effect. The inset shows the dark current reaches ∼10 μA upon 8.1 V, which is typically set as the dark current value at breakdown [12]. Below 7 V, the measured photocurrent upon 500 μW is over 2 orders of magnitude above the dark current. In the presence of the avalanche effect, the ratio of the photocurrent to the dark current drops with the bias voltage. At 8 V, the
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photocurrent-to-dark-current ratio upon 500 μW drops to ∼10. Thus, we define the avalanche-mode working region of our PD to be from 7 V to 8 V. Figure 3 shows the photocurrents versus the estimated P bus upon various reverse bias voltages. The photocurrents show linear responses to the estimated input powers. We obtain a responsivity of ∼72.8 mA∕W upon 8 V. The inset shows the range of responsivity obtained in normal mode, ranging from ∼0.7 mA∕W upon 1 V to ∼1.6 mA∕W upon 5 V. Our measured linear photoresponses in normal mode are comparable to the responsivity of ∼5.9 mA∕W upon 10 V from a DSA-based PN-diode-integrated Si microring power monitor reported by Yu et al. [4], and are around an order of magnitude higher than that from our previously demonstrated SSA-based p-i-n diode-integrated Si microring PD [2]. Thus, we attribute the observed photocurrent to a DSA-dominant process. Figure 3(b) shows the responsivity and the gain upon various reverse bias voltages. We define the gain by normalizing the responsivities to that upon 3 V, at which the PN junction is fully depleted [to be shown in Fig. 4(a)] but without significant carrier multiplication. We obtain the gain to be ∼72 upon 8 V. We fit the gain values using Miller’s formula (black line) [13], M 1 − V∕V b n −1 ;
(2)
where M is the multiplication factor (gain), V is the applied voltage, V b is the breakdown voltage, and exponent n is a constant depending on the material, the doping profile, and the operation wavelength. The fit suggests a V b of ∼8.2 V and an n of 1.7. In order to extract the linear absorption coefficient and take into account the possible photocurrents from TPA, we use a second-order polynomial function to fit the measured photocurrents at resonance upon 3 V as a function of P res , as shown in Fig. 3(c). The fit, given by IμA 0.33 mA∕WP res mW0.0038 A∕WP res mW2 , indicates that the photocurrents from TPA (∝ P 2res ) are
Fig. 3. (a) Measured photocurrents versus P bus upon various voltages. Inset: photocurrents upon 1–5 V. (b) Responsivities and gains upon various voltages. Black line: Miller’s formula fit. (c) Measured photocurrents versus P res . Black line: a second-order polynomial fit. (d) Simulated electric-field amplitude distribution of the PN diode upon 8 V.
Fig. 4. (a) Measured photoresponses upon various voltages. (b) Measured 3 dB bandwidths versus avalanche gain. (c) Measured (black) and fitted (red) S11 (c) amplitude and (d) phase upon 3 V. Inset: The circuit model of the PD. C o , Ro , capacitance and resistance of the SiO2 substrate beneath the Si layer; C j , Rj , capacitance and resistance of the junction. C pad , pad capacitance.
negligible. Thus, the photocurrents are mainly caused by linear absorption. We can extract the linear absorption coefficient from the polynomial fit, given the known TPA coefficient in Si. Following [14], we obtain the photocurrents due to linear absorption, I linear , and TPA, I TPA , as follows: Iη
q αl 1 − e−αtot Ld γP res E ph αtot
η
qβ Ld 2 2 γ P res ; 2E ph Aeff
(3)
where η is the carrier-collection efficiency for the PN diode, q is the electron charge, E ph is the photon energy, αl is the linear absorption coefficient, αtot is the total cavity power loss coefficient (≈15.3 dB∕mm, given by the fitted A value), is the TPA coefficient in Si, which has a range of ∼0.4–∼0.9 cm∕GW, Aeff is the effective crosssectional area of the waveguide (∼0.15 μm2 ), Ld is the length of the PN diode 102 μm, and γ is the optical mode spatial overlap factor with the photodiode. We assume η to be identical for I linear and I TPA . The diode depletion and diffusion regions should span the whole waveguide width, giving γ ≈ 1. Using the second-order term in Eq. (3) and the second-order polynomial fit coefficient and assuming β 0.9 cm∕GW, we calculate η to be 92%. Using the first-order term, the first-order polynomial fit coefficient and the calculated η, we extract αl to be ∼0.015 dB∕mm. We attribute the relatively large cavity loss to the subbandgap absorption, the free-carrier absorption, and the scattering losses. Given the P − ∕N − concentrations, we can estimate the free-carrier absorption loss to be ∼0.9 dB∕mm based on the Soref and Bennett’s equations [15]. We attribute the rest, namely ∼14.4 dB∕mm, to the scattering losses due to both the surface roughness and the defects. Figure 3(d) shows the simulated electric-field amplitude distribution in the waveguide upon 8 V, according to a commercial device simulation package (Silvaco). The electric-field amplitude in the depletion region
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Fig. 5. Measured eye diagrams upon 8 V at data rates of (a) 10 Gbit∕s and (b) 15 Gbit∕s.
(highlighted) exceeds 105 V∕cm, which is consistent with the typical electric-field amplitude for exciting avalanche process [16]. However, only part of the optical mode-field profile near the mode maximum [see Fig. 1(b)] is spatially overlapped with the ∼0.17 μm wide depletion region. As the avalanche effect only happens in the depletion region, the multiplication process only takes place in the center part of the waveguide. Thus, another option of increasing the responsivity via the avalanche multiplication is to increase the spatial overlap between the optical mode field and the depletion region, while optimizing the P −∕N− implantation-induced defects distribution. We measure the small-signal frequency responses of the device from 1 to 8.5 V using a 20 GHz network analyzer, as shown in Fig. 4(a). Here we use a commercial 30 GHz PD for bandwidth calibration. From 1 to 3 V, the measured 3 dB bandwidth, f 3 dB , increases from ∼5 to ∼10 GHz, which is mainly due to the increase of the photocarrier drift velocity. From 3 to 7.5 V, f 3 dB becomes saturated at ∼10 GHz, suggesting the photocarriers in the depletion region have reached the saturation velocity (∼1 × 107 cm∕s). From 7.5 to 8 V, f 3 dB drops to ∼7 GHz owing to the avalanche buildup time effect. At 8.5 V, f 3 dB drops to ∼5.3 GHz. Figure 4(b) shows the measured bandwidth as a function of the avalanche gain. The gain-bandwidth (GBW) product is ∼500 GHz upon 8 V. The f 3 dB up to the avalanche buildup delay is limited by the cavity lifetime τc , the carrier transit time τs , and the resistance–capacitance (RC) time, given as follows: 2 2 2 f −2 3 dB 2πτc τs ∕0.45 2πRC :
(4)
Given a Q 3700, we calculate τc ≈ 2.4 ps. The cavitylifetime-limited bandwidth is ∼66 GHz. Given the depletion and diffusion region widths, we estimate τs to be ∼15 ps, with ∼2 ps for the drift carriers upon saturation velocity inside the depletion region and ∼13 ps for the diffusion carriers outside the depletion region. The transit-time-limited bandwidth is ∼30 GHz. We estimate the RC time by fitting the measured S11 with a small-signal circuit model, as shown in the inset of Fig. 4(c). Figures 4(c) and 4(d) show the measured and fitted amplitude and phase responses of S11. The red lines depict the fitting curves according to the circuit model. We obtain from the fit the metal-pad capacitance C p ≈ 34 fF and the junction capacitance C j ≈30 fF. We measure a resistance of ∼125 Ω, with a load resistance of 50 Ω. We therefore obtain a RC time delay of ∼14 ps, suggesting a RC-limited bandwidth of ∼12 GHz.
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The maximum f 3 dB according to Eq. (4) is therefore ∼11 GHz. Thus, our measured f 3 dB is mainly limited by the RC delay. We note that the RC-limited bandwidth can be broadened by a few folds upon reducing the microring perimeter and the diode length to few tens of micrometers, while the responsivity is not necessarily trade off should we preserve the cavity Q. We measure the eye diagrams at 10 Gbit∕s and 15 Gbit∕s upon 8 V, as shown in Fig. 5. We use a commercial 40 Gb∕s modulator to encode the pseudorandom bit sequence signal with a pattern length of 27 − 1. We amplify the photocurrent by a 20 GHz amplifier before the oscilloscope. We use a P bus of ∼2.3 mW. The open eye diagram at 15 Gbit∕s demonstrates the device’s capability to detect at a high data rate in avalanche mode. In summary, we have demonstrated a sub-bandgap linear-absorption-based PN-diode-integrated Si microring PD in avalanche mode. Our experiments revealed an avalanche PD with a responsivity of up to ∼72.8 mA∕W upon 8 V, with the ratio of the photocurrent (upon 500 μW) to dark current of about 10. The breakdown voltage is ∼8.2 V. We demonstrated a 3 dB bandwidth of ∼7 GHz and a GBW product of ∼500 GHz upon 8 V. We measured open eye diagrams upon 15 Gbit∕s data. The avalanche PD can be used as a high-speed power monitor inside a microring resonator. We can further increase the responsivity and the bandwidth upon optimizing the P/N doping concentrations and profile, the annealing time, the optical mode spatial overlap with the depletion region, the waveguide-microring coupling, and the microring size. References 1. T. Baehr-Jones, M. Hochberg, and A. Scherer, Opt. Express 16, 1659 (2008). 2. H. Chen, X. Luo, and A. W. Poon, Appl. Phys. Lett. 95, 171111 (2009). 3. M. Geis, S. Spector, M. Grein, J. Yoon, D. Lennon, and T. Lyszczarz, Opt. Express 17, 5193 (2009). 4. H. Yu, D. Korn, M. Pantouvaki, J. Van Campenhout, K. Komorowska, P. Verheyen, G. Lepage, P. Absil, D. Hillerkuss, and L. Alloatti, Opt. Lett. 37, 4681 (2012). 5. Y. Li and A. W. Poon, in Conference on Lasers and Electrooptics: Science and Innovations (OSA, 2013). 6. J. J. Ackert, A. S. Karar, D. J. Paez, P. E. Jessop, J. C. Cartledge, and A. P. Knights, Opt. Express 21, 19530 (2013). 7. R. Grote, K. Padmaraju, B. Souhan, J. Driscoll, K. Bergman, and R. Osgood, IEEE Photon. Technol. Lett. 25, 67 (2013). 8. H. Chen and A. W. Poon, Appl. Phys. Lett. 96, 191106 (2010). 9. M. Casalino, G. Coppola, M. Gioffrè, M. Iodice, L. Moretti, I. Rendina, and L. Sirleto, J. Lightwave Technol. 28, 3266 (2010). 10. A. Akbari, R. N. Tait, and P. Berini, Opt. Express 18, 8505 (2010). 11. A. Yariv, Electron. Lett. 36, 321 (2000). 12. M. J. Lee and W. Y. Choi, Opt. Express 18, 24189 (2010). 13. S. L. Miller, Phys. Rev. 99, 1234 (1955). 14. S. Fathpour, K. K. Tsia, and B. Jalali, IEEE J. Quantum Electron. 43, 1211 (2007). 15. R. Soref and B. Bennett, IEEE J. Quantum Electron. 23, 123 (1987). 16. S. M. Sze and K. K. Ng, Physics of Semiconductor Devices (Wiley, 2006).
