Chapter 4. High Power Distributed Photodetectors for RF Photonic Applications. Sagi Mathai and Ming C. Wu

Transcription

1 Chapter 4 High Power Distributed Photodetectors for RF Photonic Applications Sagi Mathai and Ming C. Wu Electrical Engineering and Computer Sciences and Berkeley Sensors and Actuators Center University of California, Berkeley I. Introduction Photodetector linearity is of paramount importance in external intensity modulated direct detection (IMDD) analog fiber-optic links, especially at high optical illumination. This realization creates a demand for high bandwidth, high saturation current photodetectors. Applications that benefit from high performance photodetectors include antenna remoting, fiber-radio, and terahertz signal generation by photomixing. The system level benefits of high current photodetectors may be seen by plotting the RF Gain (G RF ), noise figure (NF), and spurious free dynamic range (SFDR) versus photocurrent for a hypothetical external IMDD link. The curves in Figure 4. clearly demonstrate the benefits of high current photodetectors. As the photocurrent increases so does the link performance until laser relative intensity noise (RIN) dominates the noise floor. Link performance may be further improved by utilizing balanced detection, in which case, laser RIN is suppressed. Shot noise limited performance is achieved and excess laser power, or equivalent photocurrent, may be employed to dramatically improve G RF, NF, and SFDR simultaneously. [Figure 4. (a) (b) (c) near here]

2 Space charge effects and thermal runaway are the primary factors limiting photodetector high power operation []. Large photocurrent density in the absorption regions can screen the applied electric field leading to a lowering of the photo-generated carrier velocity, and ultimately, complete collapse of the applied electric field [2]. Consequently, RF photoresponse decreases and nonlinearities generated by the photodetector start to degrade the system dynamic range. High photocurrent density also causes excessive Joule heating (bias voltage photocurrent) of the absorption region leading to thermally activated dark current runaway [3], which eventually results in catastrophic photodiode failure. Dark current and the effective barrier height for dark current flow are the fundamental device parameters involved in thermal runaway [4]. Photodetectors with low dark currents and high effective barriers have been found to sustain larger amounts of Joule heating before catastrophic failure. For example, metal-semiconductor-metal (MSM) photodetectors have much lower effective barriers than p-i-n diodes, and consequently, MSMs fail at 700 K [5] whereas p-i-n junctions can withstand temperatures up to 900 K [4]. It should also be mentioned that device fabrication induced damages, such as poor surface passivation and plasma induced damage, can increase the dark current and contribute to premature device failure. These issues are especially problematic in lumped element photodetectors, operating under high power illumination, that rely on a small absorption volume (~0 μm 3 ) to achieve high bandwidth. An intuitive approach to mitigate space charge effects and thermal runaway is to distribute the photogenerated carriers over an enlarged absorption volume. First suggested in [6] by Taylor, the traveling wave concept applied to photodetectors has received considerable attention due to its ability to distribute photogenerated carriers over a large absorption volume without succumbing to RC speed limitations found in lumped element devices. By embedding the photodetector in a transmission line, the photodiode 2

3 capacitance is absorbed by the transmission line s distributed admittance, while the load impedance associated with the lumped element device RC is de-embedded. Hybrid [7, 8] and monolithic [9-6] implementations have been demonstrated. Most monolithic implementations are a variation of the p-i-n waveguide photodetector (WGPD) [7, 8] with the transmission line terminated at the input by a matched impedance. As shown in Figure 4.2, two types have been demonstrated: () continuous and (2) distributed. The continuous type is normally referred to as the traveling wave photodetector (TWPD), while the distributed type is referred to as the velocity matched distributed photodetector (VMDP). In a TWPD, the absorption region spans the entire length of the microwave transmission line. Due to excessive capacitive loading from the thin intrinsic absorption layer, the characteristic line impedance is lower than 50 Ω, and the microwave phase velocity is much lower than the optical group velocity (typically 30% lower). This velocity mismatch can limit the bandwidth due to phase walk-off between the optical and electrical signals. Consequently, TWPD are kept short to mitigate the effects of velocity mismatch. In VMDPs, the absorption length is divided among discrete transit time limited photodiodes periodically placed along a transmission line. The separation between diodes is used to dilute the capacitive loading on the transmission line and simultaneously achieve 50 Ω impedance and velocity matching. Consequently, the photocurrents from each photodiode are coherently added along the transmission line. [Figure 4.2 (a) and (b) near here] This chapter reviews the research our group has performed in the area of high speed high power distributed photodetectors. Section II develops a transmission line modeling tool to 3

4 design distributed photodetectors. Section III presents our experimental work on VMDPs, including balanced VMDPs. Section IV presents a means to increase the saturation photocurrent in VMDPs by using parallel optical feed. Section V addresses the issue of backward traveling wave cancellation, and Section VI summarizes the review. II. Transmission Line Model Design Tool The frequency response of distributed photodetectors may be calculated using the ABCD transfer matrix approach [9]. An equivalent circuit for the transmission line is shown in Figure 4.3. It consists of an array of unit cells comprising a section of transmission line with length Δ and a photodidode. The photodiodes are represented using a Norton equivalent circuit comprised of a series resistance, R S, and capacitance, C j, shunted by an effective current source, i eff. [Figure 4.3 (a) and (b) near here] The Norton equivalent photocurrent feeding the transmission line is related to the photocurrent generated in a single photodiode, i ph, by the following expression: i eff = + jω R s C j i ph Equation The ABCD matrix for the transmission line segment of length Δ is written in terms of its characteristic line impedance, Z, and propagation constant, γ, while the ABCD matrix for the photodiode can be written in terms of an admittance, Y. 4

5 5 ( ) ( ) ( ) ( ) cosh sinh sinh cosh Δ Δ Δ Δ = γ γ γ γ Z Z M Equation 2 = 0 2 Y M Equation 3 j s C j R Y ω + = Equation 4 The voltage and currents at the terminals of the unit cell may now be evaluated iteratively using: ( ) t o n eff n n n n F n j i I V M M I V Δ + = β exp 0, 2 Equation 5 β o, n, and F t are the optical propagation constant, unit cell index (n [0,N]), and normalized transit time frequency response [20], respectively. The relationships between V N, I N and V 0, I 0 are obtained from Equation 5 by setting i eff to zero and assuming input termination impedance, Z T. The homogeneous solutions, N N I V,, are obtained by setting V 0, I 0 to zero. ( ) 0 2 ' ' V Z M M M I V I V T N N N N N + = Equation 6 N is the total number of diodes. The total solution is obtained by superposition [4]. To investigate the effect of periodic loading on the transmission line, consider the simple case of a lossless transmission line. When the spacing between photodiodes is small compared to the microwave wavelength on the transmission line (<λ/0), it may be considered electrically

6 smooth. In this case, the loaded microwave phase velocity and characteristic impedance are modified by the photodiode admittance or an effective capacitance, C eff. v L = C TL C + Δ eff L TL Equation 7 LTL Z = Equation 8 L Ceff CTL + Δ C eff = jω Rs + C j Equation 9 Note that the capacitive loading can be tailored to achieve simultaneous velocity and impedance matching. If the transmission line loss is negligible, the bandwidth of the VMDP is essentially limited by the intrinsic speed of a single photodetector in the array. III. Velocity Matched Distributed Photodetectors In the VMDP, photodiodes evanescently coupled to an underlying passive optical waveguide, periodically feed a transmission line. A unique advantage of the VMDP lies in its flexibility in optimizing the optical waveguide, photodiode, and microwave transmission line independently. The optical waveguide can be designed with a large mode size for low fiberto-waveguide coupling loss and left undoped to minimize free-carrier absorption. The photodiodes can be optimized for high speed (as in conventional ultrafast photodiodes), and low optical confinement in the absorber for high saturation current. Impedance and velocity matching can be incorporated in the transmission line design, as well as low microwave propagation loss. The distributed design also mitigates thermally induced catastrophic failure 6

7 due to thermal runaway [5]. The VMDP concept is so flexible that numerous types of photodiode structures have been incorporated: MSM [9, 4], Schottky [2], p-i-n [22], and the uni-traveling carrier photodiode (UTC-PD) [3]. In our group, we demonstrated MSM based VMDPs on GaAs [4] and InP [0] material systems, but switched to p-i-n structures as they are less susceptible to thermal runaway and able to achieve much higher saturation current [22]. A crucial issue in VMDPs is the photocurrent distribution along the photodiode array. To characterize the distribution, VMDPs with split electrical contacts to each photodiode were fabricated. Figure 4.4 describes the photocurrent distribution among four photodiodes along an array. When the fiber-to-waveguide alignment was optimized for maximum responsivity, the responsivity was maximum, but the photocurrent distribution and linear current (22 ma) were poor. By optimizing the alignment to photodiodes farther away from the input waveguide facet, lower responsivity but much higher linear photocurrents (Figure 4.5) were possible. The best compromise was achieved by optimizing the alignment to the third photodiode. 35 GHz bandwidth and 45 ma linear DC photocurrent were achieved. At higher photocurrent (55 ma), the waveguide input facet experienced catastrophic failure, while the p-i-n photodiodes remained operational [22]. [Figure 4.4 near here] [Figure 4.5 near here] An important development in microwave photonics was the introduction of high power balanced photodetectors for common mode optical noise (laser RIN and added amplified spontaneous emission noises) suppression. Shot noise limited performance was demonstrated 7

8 with a hybrid balanced detector built with commercially available low frequency photodetectors [23]. For high bandwidth operation, monolithic devices are required. Figure 4.6 shows the schematic and equivalent circuit of a monolithically integrated balanced photodetector based on the VMDP concept. It consists of a pair of parallel optical waveguides periodically coupled to high speed p-i-n photodiodes and a coplanar waveguide (CPW) transmission line with 50 Ω loaded characteristic impedance. Balanced mode is set by applying the reverse bias voltage between the ground electrodes of the CPW. [Figure 4.6 near here] Figure 4.7 reports record high common mode rejection ratio (CMRR) of more than 37 db from a few na to 3 ma and laser RIN suppression of more than 40 db from a few MHz to 8 GHz [22]. For comparison, in a balanced photodetector, 3 ma is equivalent to 62 ma in standard photodiodes. [Figure 4.7 (a) and (b) near here] IV. Parallel Optical Feed Photodetectors The first photodiode in VMDPs and the input facet of continuous TWPD usually generate the highest photocurrent density (per unit length) in the entire photodetector, and therefore, failure occurs at the first photodiode or input facet, respectively. Techniques to improve the uniform distribution of photocurrent density include: tailoring the optical confinement factor in the absorber [24], employing electro-absorptive active materials to independently control the absorption coefficient in the propagation direction [2], and splitting the optical power 8

9 equally among an array of discrete photodiodes using optical fiber delay lines[7]. Among these, parallel optical feed is the most direct avenue to achieve uniform photocurrent density. The VMDP concept is quite compatible with parallel optical feed. A schematic of a parallel fed VMDP (PF-VMDP) is shown in Figure 4.8. It utilizes a N multi-mode interference (MMI) optical power splitter [25], an array of high-speed photodiodes, a coplanar strip (CPS) microwave transmission line, and an on-chip 50 Ω thin film resistor. [Figure 4.8 near here] We fabricated PF-VMDPs with MSM [26] and p-i-n photodiodes[27]. Although the responsivity is limited by the absorption volume in each individual photodiode, higher saturation current can be achieved by increasing the MMI splitting ratio. Figure 4.9 shows DC linearity measurements on two PF-VMDPs employing identical MSM photodiodes but different MMI splitting ratios. The device with 4 MMI saturates at 3.5 ma, while in the 8 case, linearity is maintained until device failure at 20. ma [28]. The maximum linear photocurrent can be further increased by increasing the splitting ratio and optimizing the MMI excess loss. [Figure 4.9 near here] PF-VMDP implemented with p-i-n photodiodes showed even higher linear response. Referring to Figure 4.0, the DC photocurrent and detected RF power at 0 GHz are linear up to 52.2 ma and 9 dbm, respectively, without device failure. In this experiment, the available optical power limited the maximum photocurrent and RF power [27]. 9

10 [Figure 4.0 (a) and (b) near here] Although the saturation photocurrent can be increased by increasing the optical power splitting ratio, the quantum efficiency in PF-VMPD is limited by the length of the individual photodiodes. Index matching layers (Figure 4.) have been proposed as a means to increase the responsivity and reduce the length of waveguide coupled lumped element photodetectors [29]. By varying the matching layer material composition and extension in front of the photodiode, the absorption profile can be tailored to improve the linearity of the device without sacrificing bandwidth [30]. [Figure 4. near here] Figure 4.2 compares the frequency response and RF response at 20 GHz for two detectors (A and B) with different matching layer extensions (A = 8 μm and B = 8 μm). Detectors A and B had identical RC limited bandwidths of 30 GHz, but detector B exhibited nearly an order of magnitude improvement in RF response at 20 GHz [30]. [Figure 4.2 (a) and (b) near here] V. Backward Wave Cancellation A fundamental issue for traveling wave devices is the backward propagating wave illustrated in Figure 4.3. Without input termination matched to the line impedance, the backward wave, reflected at the open input termination, can destructively interfere with the forward propagating wave to limit the bandwidth. 0

11 [Figure 4.3 (a) and (b) near here] To improve the bandwidth, an impedance matched to the line impedance may be employed, but at the expense of efficiency. This point is illustrated experimentally in Figure 4.4 for a TWPD with and without 50 Ω input termination [3]. With 50 Ω input termination, the RF response drops by 6 db, while the bandwidth broadens by a few gigahertz. High speed operation without sacrificing responsivity can be obtained by backward wave cancellation (BWC) using a multi-section transmission line, originally proposed by Ginzton for distributed amplification in traveling wave tubes [32]. [Figure 4.4 near here] A schematic of our multi-section traveling wave distributed photodetector (MS-TWDP) and its equivalent circuit is shown in Figure 4.5. Much like the VMDP, it consists of a passive optical waveguide loaded with an array of photodiodes represented by current sources. Similar structures have been proposed in [5]. The forward traveling photocurrents are coherently combined on a multi-section transmission line, while the backward traveling photocurrents are eliminated. The impedance mismatch between adjacent sections causes a negative reflection coefficient, Γ, such that the reflected photocurrent, Γ I, cancels the backward propagating photocurrent, β I 2. [Figure 4.5 (a) and (b) near here] For example, between sections and 2, the following condition must be satisfied.

12 Γ I + β I 0 Equation 0 2 = By applying a similar condition at each node between transmission line segments a general condition for the line impedance can be derived. Z n+ Z n n+ j= = n i= I I j i Equation Z n, Z n+, and I i are the impedances of sections n and n+ (n increasing from the input end) and the photocurrent generated by the i th photodiode, respectively. For the case of equal photocurrent contributions from each photodiode, the relation simplifies to Z and Z n are the line impedance of the input and n th sections, respectively [33]. Z =, where n Z n Initially, we demonstrated BWC for unequally distributed photocurrents [3], but later employed photodiode arrays with uniform photocurrent distribution [33]. Figure 4.6 compares the frequency response of a standard distributed TWPD with a continuous CPS to that of a MS-TWDP. The low frequency roll-off was due to the measurement equipment and not the photodetectors. In each case, the optical waveguides, total absorption volume, and responsivity (~ 0.25 A/W) were nearly identical. In the continuous CPS case, the efficiency reduced by 6 db while the bandwidth increased by more than a factor 2 when the input was terminated with the line impedance. In the MS-TWDP, less than 2 db reduction in efficiency was seen with input termination, which indicates that db of photocurrent flowed toward the input. More importantly, the bandwidth of MS-TWDP was comparable to the terminated continuous CPS version but with a 6 db response improvement [3]. 2

13 [Figure 4.6 near here] An SEM of a MS-TWDP with uniform photocurrent distribution is given in Figure 4.7. The widths of the coplanar lines and separation between ground and signal were adjusted to obtain the desired impedances of 50, 75, and 50 Ω in the three sections. The waveguide design employed index matching layers to optimize the absorption profile in each photodiode for high linearity, while the lengths of the photodiodes were adjusted for uniform photocurrent generation. [Figure 4.7 near here] Referring to Figure 4.8, the measured 3 db bandwidth without input termination was 38 GHz, 2.5 times higher than the round-trip bandwidth limit of 5 GHz confirming successful BWC. Also notice the steep roll-off beyond the 3 db bandwidth, much steeper than the typical RC roll-off in lumped element devices, which is indicative of multi-section transmission line designs. The db compression point at 40 GHz is -5 dbm, at which point failure occurs due to thermally induced interconnect metal breakage at the first photodiode. Consequently, the responsivity dropped by 30%, but the MS-TWDP remained operational. With thicker metals and improved heat sinking, much higher linear RF power can be achieved [33, 34]. [Figure 4.8 (a) and (b) near here] VI. Conclusion 3

14 High power, broadband, impedance matched photodetectors are crucial components in high performance external IMDD analog fiber-optic links. If high saturation power photodetectors are available, excess laser power can be utilized to simultaneously improve RF gain, noise figure, and spurious free dynamic range. The VMDP concept provides the flexibility to design photodetectors with the potential to meet these challenges. Our toolbox for implementing high performance VMDPs include a traveling wave transmission line model (ABCD matrix approach), clever optical waveguide designs (evanescent coupling and matching layers), multiple architectures (serial and parallel optical feed), and microwave techniques (backward wave cancellation). By selecting the best methods from our toolbox, and more recent advances in photodiode epitaxial layer design and heat sinking [34], the VMDP concept has the potential to make an even greater impact on RF photonic systems. 4

15 References [] K. J. Williams and R. D. Esman, "Design considerations for high-current photodetectors," Journal of Lightwave Technology, vol. 7, pp , 999. [2] K. Kato, "Ultrawide-band/high-frequency photodetectors," IEEE Transactions on Microwave Theory and Techniques, vol. 47, pp , 999. [3] J. S. Paslaski, P. C. Chen, J. S. Chen, C. M. Gee, and N. Bar-Chaim, "High-power microwave photodiode for improving performance of rf fiber optic links," presented at SPIE - The International Society for Optical Engineering, 996. [4] M. S. Islam, T. Jung, T. Itoh, M. C. Wu, A. Nespola, D. L. Sivco, and A. Y. Cho, "High power and highly linear monolithically integrated distributed balanced photodetectors," Journal of Lightwave Technology, vol. 20, pp , [5] A. Nespola, T. Chau, M. Pirola, M. C. Wu, G. Ghione, and C. U. Naldi, "Failure analysis of traveling wave MSM distributed photodetectors," presented at International Electron Devices Meeting, 998. [6] H. F. Taylor, O. Eknoyan, C. S. Park, K. N. Choi, and K. Chang, "Traveling wave photodetectors," presented at SPIE - The International Society for Optical Engineering, 990. [7] C. L. Goldsmith, G. A. Magel, and R. J. Baca, "Principles and performance of traveling-wave photodetector arrays," IEEE Transactions on Microwave Theory and Techniques, vol. 45, pp , 997. [8] H. H. Hashim and S. Iezekiel, "Traveling-wave microwave fiber-optic links," IEEE Transactions on Microwave Theory and Techniques, vol. 54, pp. 95-8, [9] E. H. Bottcher, H. Pfitzenmaier, E. Droge, S. Kollakowski, A. Strittmatter, D. Bimberg, and R. Steingruber, "Distributed waveguide-integrated InGaAs MSM 5

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17 [7] K. Kato, A. Kozen, Y. Muramoto, Y. Itaya, T. Nagatsuma, and M. Yaita, "0-GHz, 50%-efficiency mushroom-mesa waveguide p-i-n photodiode for a.55-μm wavelength," IEEE Photonics Technology Letters, vol. 6, pp. 79-2, 994. [8] A. R. Williams, A. L. Kellner, X. S. Jiang, and P. K. L. Yu, "InGaAs/InP waveguide photodetector with high saturation intensity," Electronics Letters, vol. 28, pp , 992. [9] D. M. Pozar, Microwave Engineering, 2nd ed: John Wiley & Sons, Inc., 998. [20] J. E. Bowers and C. A. Burrus, Jr., "Ultrawide-band long-wavelength p-i-n photodetectors," Journal of Lightwave Technology, vol. LT-5, pp , 987. [2] M. P. Nesnidal, A. C. Davidson, G. R. Emmel, R. A. Marsland, and M. C. Wu, "Efficient, reliable, high-power VMDPs for linear fiber optic signal transmission," presented at PSAA-0, Monterey, CA, USA, [22] M. S. Islam, S. Murthy, T. Itoh, M. C. Wu, D. Novak, R. B. Waterhouse, D. L. Sivco, and A. Y. Cho, "Velocity-matched distributed photodetectors and balanced photodetectors with p-i-n photodiodes," IEEE Transactions on Microwave Theory and Techniques, vol. 49, pp , 200. [23] K. J. Williams and R. D. Esman, "Optically amplified downconverting link with shotnoise-limited performance," IEEE Photonics Technology Letters, vol. 8, pp , 996. [24] S. Jasmin, N. Vodjdani, J. C. Renaud, and A. Enard, "Diluted- and distributedabsorption microwave waveguide photodiodes for high efficiency and high power," IEEE Transactions on Microwave Theory and Techniques, vol. 45, pp , 997. [25] R. M. Jenkins, R. W. J. Devereux, and J. M. Heaton, "Waveguide beam splitters and recombiners based on multimode propagation phenomena," Optics Letters, vol. 7, pp. 99-3,

18 [26] S. Murthy, T. Jung, T. Chau, M. C. Wu, D. L. Sivco, and A. Y. Cho, "A novel parallelly-fed traveling wave photodetector with integrated MMI power splitter," presented at Optical Fiber Communication Conference, [27] S. Murthy, M. C. Wu, D. Sivco, and A. Y. Cho, "Parallel feed traveling wave distributed pin photodetectors with integrated MMI couplers," Electronics Letters, vol. 38, pp , [28] S. Murthy, T. Jung, C. Tai, M. C. Wu, D. L. Sivco, and A. Y. Cho, "A novel monolithic distributed traveling-wave photodetector with parallel optical feed," IEEE Photonics Technology Letters, vol. 2, pp. 68-3, [29] R. J. Deri and O. Wada, "Impedance matching for enhanced waveguide/photodetector integration," Applied Physics Letters, vol. 55, pp , 989. [30] S. Murthy, T. Jung, M. C. Wu, Z. Wang, and W. Hsin, "Linearity improvement in photodetectors by using index-matching layer extensions," presented at 5th Annual Meeting of the IEEE Lasers and Electro-Optics Society, [3] S. Murthy, T. Jung, M. C. Wu, D. L. Sivco, and A. Y. Cho, "Traveling wave distributed photodetectors with backward wave cancellation for improved AC efficiency," Electronics Letters, vol. 38, pp , [32] E. L. Ginzton, W. R. Hewlett, J. H. Jasberg, and J. D. Noe, "Distributed amplification," Proc. I.R.E., vol. 36, pp , 948. [33] S. Murthy, K. Seong-Jin, T. Jung, W. Zhi-Zhi, H. Wei, T. Itoh, and M. C. Wu, "Backward-wave cancellation in distributed traveling-wave photodetectors," Journal of Lightwave Technology, vol. 2, pp , [34] N. Duan, X. Wang, N. Li, H. D. Liu, and J. C. Campbell, "Thermal Analysis of High- Power InGaA-InP Photodiodes," IEEE Journal of Quantum Electronics, vol. 42, pp. 255,

19 Figure 4.: Simulated performance of an external intensity modulated direct detection analog link, with and without balanced detection, in terms of (a) RF gain (b) noise figure, and (c) spurious free dynamic range. (Vπ=6 V, ηpd=0.9, Link Loss=-5 db, RIN=-65 dbc/hz, and 50 Ohm matched impedance) Figure 4.2: Physical layout of a (a) TWPD and (b) VMDP. In the TWPD, the transmission line spans the entire length of the photodiode, while in the case of the VMDP, photodiodes are periodically arrayed along the transmission line. Figure 4.3: Equivalent circuit representations of the (a) distributed photodetector and (b) a single photodiode Figure 4.4: Measured responsivity of individual photodiodes in a split contact VMDP with the input fiber alignment optimized for maximum photoresponse from the (a) entire VMDP, (b) 2 nd, (c) 3 rd, and (d) 4 th photodiode [22]. Figure 4.5: Total photocurrent versus optical input power when the fiber-to-waveguide alignment was optimized for maximum responsivity in a VMDP with a continuous transmission line, and to the 2 nd and 3 rd photodiodes in a split contact VMDP [22]. Figure 4.6: Schematic diagram and equivalent circuit of the balanced VMDP [22]. Figure 4.7: Record high (a) CMRR versus photocurrent and (b) broadband laser RIN suppression in a balanced VMDP [22]. 9

20 Figure 4.8: Schematic diagram of the PF-VMDP. Figure 4.9: DC linearity measurements on MSM based PF-VMDP. Higher MMI splitting ratio results in higher saturation current [28]. Figure 4.0: P-i-n based PF-VMDP (a) DC saturation current measurement and (b) RF linearity at 0 GHz [27]. Figure 4.: Waveguide coupled photodiode epitaxial layer design with an index matching layer. Figure 4.2: (a) Frequency response and (b) RF response at 20 GHz for photodetectors with different index matching layer extension (Detector A = 8 μm, and Detector B = 8 μm) [30]. Figure 4.3: Illustration of backward and forward waves generated by photodiodes along a VMDP with (a) open input termination and (b) matched termination. Figure 4.4: Effect of input termination on the frequency response of TWPD [33]. Figure 4.5: Schematic of the (a) MS-TWDP and (b) its equivalent circuit. The arrows indicate forward and backward wave current flow [33]. Figure 4.6: Experimental demonstration of bandwidth and efficiency improvement using BWC in MS-TWDP. The MS-TWDP achieves similar bandwidth to the standard distributed TWPD without sacrificing efficiency [3]. 20

21 Figure 4.7: SEM of a fabricated MS-TWDP with three p-i-n photodiodes and a three section CPS line. The impedances needed for BWC at each section are indicated on the respective transmission line segments [33]. Figure 4.8: RF performance of a MS-TWDP. (a) Frequency response (3 db bandwidth equal to 38 GHz) and (b) linearity measurements at 40 GHz [33]. 2

22 Figure G RF (db) Photocurrent (ma) (a) NF (db) 40 Conventional 20 Balanced Photocurrent (ma) (b) 22

23 30 Balanced SFDR (dbxhz 2/3 ) 0 90 Conventional Photocurrent (ma) (c) Figure 4.2 I ph P opt (a) I ph P opt (b) Figure

24 I 0 I I 2 I N- I N Z T V 0 V V 2 V N- V N Z L M M 2 (a) R s C j i eff (b) Figure 4.4 Responsivity (A/W) A/W 0.39A/W 0.36A/W 0.30A/W a b Alignment optimized to VMDP 2nd PD 3rd PD 4th PD c d Photodiode Number Figure

25 mA R=0.36A/W Photocurrent (ma) mA R=0.42A/W 35mA R=0.39A/W Alignment optimized VMDP 0 2 nd PD 3 rd PD Input Power (mw) Figure 4.6 CPW Optical waveguide Microwave Output Optical Input Figure

26 50 45 CMRR (db) Photocurrent (ma) (a) 20 0 Single PD Balanced VMDP RF Power (dbm) dB Frequency (GHz) (b) Figure

27 50Ω termination Microwave Transmission Line MMI Power Splitter Photodiodes Optical Input Substrate Figure 4.9 Photocurrent (ma) Device with x4 Splitter Device with x8 Splitter Device Failure Optical Power (mw) Figure

28 60 Photocurrent (ma) Optical Power (mw) (a) 20 0GHz output power (dbm) Average optical input (dbm) (b) Figure 4. Matching Layer Extension Photodiode Index Matching Layer Passive Waveguide 28

29 Figure 4.2 (a) (b) Figure

30 Load Open Input Termination (a) Load Matched Termination (b) Figure 4.4 Normalized Response (db) Input end unterminated Input end terminated with 50Ω Frequency (GHz) Figure

31 p-i-n Diodes Optical Waveguide Substrate Coplanar Strip Waveguides with Tapered Impedances (a) ΓI ( Γ ) I βi 2 ( β ) I 2 I I I 2 3 Load Z Z 2 Z 3 (b) Figure MS-TWDP - input open MS-TWDP input 200 Ω Response (db) SS-TWDP input open SS-TWDP input 50 Ω Frequency (GHz) Figure 4.7 3

32 To Load Optical Waveguide p-i-n Photodiodes Input Facet 50Ω CPS 75Ω CPS 50Ω CPS Figure 4.8 Calibrated Response (db) Frequency (GHz) (a) 32

33 0 x RF power at 40GHz (dbm) Metal Interconnect Failure Bias at -2V Bias at -3V Input Optical Power (dbm) (b) 33