1. INTRODUCTION

While fiber optic digital transmission has been one of the principle drivers for the development of optoelectronic components, there is a growing number of applications that utilize analog links and microwave photonics [1]. These include deployment of analog optical links for video distribution in CATV services [2], replacement of point-to-point microwave links [3], and antenna remoting [4,5]. Generation of millimeter-wave frequencies using photonic technology has numerous advantages [6,7]. V-band frequencies ranging from 50 to 75 GHz are of particular interest since the Federal Communications Commission has allocated 7 GHz unlicensed spectrum (57–64 GHz) for 60 GHz band communication [8]. The light weight and compactness of fiber analog links are beneficial for shipboard or avionics systems [9,10] (where bulk is a concern). Analog optic links are also used in beam-forming networks for phased array antennas [11–13]. Local oscillator signals can be distributed to individual antennas for radio telescopes using analog optic links [14,15]. Other than applications focused on signal transmission, photonic processing of microwave signals also uses analog optics [16]. Examples include photonic delay lines [17,18], filtering [14,19–27], arbitrary waveform synthesis [28], A/D conversion [29,30], downconversion [31–34], and optoelectronic oscillators (OEOs) [35,36].

The key figures of merit for the optoelectronic devices used in these systems are, in many cases, quite different from those in digital transmission communications systems. For example, for optical modulators it is essential that $V\pi$ be as low as possible to achieve high link gain. The photodiodes used in analog optic links also have a major impact on link performance. High power handling capability of the photodiode is needed to achieve high link gain. High-speed operation of the link is impossible without photodiodes that have correspondingly large bandwidth. It is also important for the photodiodes to have high linearity in order to minimize signal distortion and maintain large spurious-free dynamic range (SFDR) [4]. However, the output power of PDs is generally limited by space-charge screening and, at very high power levels, thermal failure. The space-charge effect has its origin in the spatial distribution of the photo-generated carriers as they transit the depletion layer [37–40]. The electric field generated by the free carriers, referred to as the space-charge field, opposes the field established by ionized dopants and the applied bias voltage. As a result, at high current densities the total electric field can collapse in some portion of the depletion region. Once this happens, the carrier transit time increases significantly and the RF power output suffers from compression/saturation. Also significant at high current levels, the voltage drop across the load resistor reduces the effective bias voltage, which also pushes the photodiode toward saturation. In the following, “saturation current” will denote the photocurrent at which the RF output power is compressed by 1 dB.

To achieve high RF output power at high frequency, various photodiode structures have been developed, among which the uni-traveling carrier (UTC) structure [41–45] has demonstrated high saturation current at high frequency. In an InGaAs/InP UTC PD, photons excite carriers in an undepleted p-type InGaAs absorption layer. Since only electrons are injected into the InP drift layer, the effective transit time is shorter than for a p-i-n structure, which has both electrons and holes in the drift region, and there is minimal space-charge screening effect. The UTC structure has been modified to further reduce the space-charge effect while maintaining high bandwidth. A schematic cross section of the structure is shown in Fig. 1. By inserting an undoped InGaAs layer with an appropriate thickness between the undepleted InGaAs absorption layer and the InP drift layer, the responsivity of the UTC PD can be increased [46,47]. Of greater benefit, this layer also helps to maintain high electric field at the heterojunction interfaces, which facilitates electron transport. The RF output power can also be increased by incorporating a lightly doped charge in the depletion region [48], which predistorts the electric field to partially compensate the field change caused by the space-charge effect. Finally, adding a charge layer or “cliff” layer [49] enhances the electric field next to the absorption region, which suppresses field collapse in the depleted absorber layer. These photodiode structures have proved so successful at suppressing the space-charge effect that thermal failure has become the primary factor that limits the maximum operating current.

 

Fig. 1. Modified charge-compensated uni-traveling carrier (MUTC) photodiode with cliff layer.

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The surface temperature of a conventional backside-illuminated photodiode was measured by thermo-reflectance imaging [50]. For power dissipation of 500 mW it was found that the surface temperature can reach 500 K. An optical probe technique that measures the temperature inside the photodiode has shown that the temperature in the depletion region may be $\sim 100\mathrm{K}$ higher than the surface temperature [51]. Among the various techniques to improve thermal dissipation, flip-chip bonding has achieved the best results [50,52–56].

2. DEVICE DESIGN AND FABRICATION

Much of the work described in this paper utilized two modified uni-traveling carrier (MUTC) photodiode structures that will be designated as MUTC-LF (refers to lower frequency structure) [53] [Fig. 2(a)] and MUTC-HF (refers to higher frequency structure) [52] [Fig. 2(b)], which were designed to have bandwidths in the range of 10 to 30 GHz and 40 to 70 GHz, respectively. The bandwidth variation in each frequency range is a function of device diameter. The MUTC-LF structure was grown on semi-insulating double-side-polished InP substrates by metal-organic chemical vapor deposition. The epitaxial growth began sequentially with 200-nm-thick $n^{+}$ InP, 20 nm $n^{+}{\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$, and 900 nm $n^{+}$ InP layers. A 100 nm n-type InP layer with a doping concentration of $1\times {10}^{18}{\mathrm{cm}}^{-3}$ was then grown to reduce Si diffusion into the following 900 nm lightly doped InP drift layer. Following the InP drift layer are three transition layers, a 50 nm InP cliff layer and two 15 nm lightly doped InGaAsP layers. The ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ absorbing region consists of a 150 nm lightly doped $n^{-}$ layer that is depleted when the device is biased for operation and four undepleted, step-graded $p^{+}$ layers. The two top layers are a 100 nm $p^{+}$ InP electron blocking layer and a 50 nm $p^{+}{\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ contact layer. The function of the two 15 nm InGaAsP quaternary layers is to “smooth” the abrupt conduction band barrier at the InGaAs–InP heterojunction interface. In the p-type ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ absorbing region, the doping was graded in four steps ($2.5\times {10}^{17}{\mathrm{cm}}^{-3}$, $5.0\times {10}^{17}{\mathrm{cm}}^{-3}$, $1.0\times {10}^{18}{\mathrm{cm}}^{-3}$, and $2.0\times {10}^{18}{\mathrm{cm}}^{-3}$) in order to create a quasi-electric field that assists electron transport. In the depletion region, the 900 nm InP layer, the 150 nm depleted ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ absorbing layer, and the two InGaAsP transition layers were n-type-doped to $\sim {10}^{16}{\mathrm{cm}}^{-3}$ for the purpose of charge compensation [46]. The InP cliff layer, which is a thin InP layer n-doped to $1\times {10}^{17}{\mathrm{cm}}^{-3}$, was added between the charge-compensated ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}$ and InP layers. The layers of the two structures are the same except the thicknesses of the undepleted InGaAs absorption and InP collector layers of MUTC-HF are half those of MUTC-LF. This reduces the electron transit time for MUTC-HF but also results in decreased responsivity. The responsivities of MUTC-LF and MUTC-HF are 0.75 and 0.5 A/W, respectively.

 

Fig. 2. InGaAs–InP (a) MUTC-LF and (b) MUTC-HF photodiode structure.

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Back-illuminated double-mesa structures were fabricated by inductive coupled plasma etching. A Ti/Pt/Au metal stack was deposited as both p- and n-type contacts. Microwave contact pads and air-bridge connections to the top p-contact layer were fabricated for high-speed measurements. A 230-nm-thick ${\mathrm{SiO}}_2$ anti-reflection layer was deposited on the back of the wafer. For devices that were flip-chip bonded on high-thermal-conductivity submounts, Au bonding bumps with a diameter of 6 μm and a height of 2 μm were plated on the $p$ and $n$ contacts. The wafer was then diced into $1\mathrm{mm}\times 3\mathrm{mm}$ chips. The diced chips were flip-chip bonded to a submount having coplanar waveguide (CPW) pads using a FINEPLACER pico ma system. Figure 3 shows a schematic cross section of the flip-chip bonded photodiode.

 

Fig. 3. Schematic cross-sectional view of a photodiode flip-chip bonded on submount [56].

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A. High-Power CW Photodiodes

An optical heterodyne setup with a modulation depth close to 100% was used to measure responsivity, bandwidth, and saturation characteristics. The outputs from two distributed-feedback (DFB) lasers with slightly different wavelengths were mixed, and the beat note frequency was used as the RF source signal. Both lasers are temperature-controlled; their wavelengths are near 1544 nm at room temperature. The beat note frequency was swept by changing the temperature and thus the wavelength of one laser. For all the saturation measurements, the lensed fiber that illuminates the devices was pulled back to the position where the photocurrent decreased to approximately half the peak photocurrent in order to maintain spatially uniform illumination.

Initial work on high-power photodiodes, whether top or back illuminated, relied on thermal dissipation through the substrate, which was typically mounted on a metal heat sink or thermoelectric cooler. The MUTC structure enabled performance that was relatively immune to space-charge limitations. Figure 4 summarizes the saturation current and RF output power levels that were attained.

 

Fig. 4. Illumination configuration and summary of bandwidth, saturation current, and RF output power for various photodiode diameters.

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As stated above, higher RF output power necessitates improved thermal management. The thermal conductivity of InP is only 68 W/K.m. We have shown that significant improvement can be achieved by flip-chip bonding to submounts with higher thermal conductivity. We began with Si submounts and transitioned to AlN, and finally to diamond with thermal conductivities of 142, 280, and $\sim 1000\mathrm{W}/\mathrm{K}·\mathrm{m}$, respectively. Figure 5 shows the power density at failure versus diameter for devices that were not flip-chip bonded and those on Si, AlN, and CVD diamond. It is clear that (1) flip-chip bonding results in higher power densities and (2) the higher the thermal conductivity of the submount, the higher the power density at failure. As the diameter decreases by a factor of 2, the power density increases by $\sim 2\times$. However, the area has decreased by $4\times$ so that the total output power is lower for smaller photodiodes. Scaling to smaller diameters results, somewhat counterintuitively, in higher dc power ($\text{average photocurrent}\times \text{bias voltage}$) density at failure. This is likely due to improved thermal dissipation through the edges of the mesa [37]. Figure 6 summarizes the output power versus frequency for MUTC-LF and MUTC-HF photodiodes on diamond submounts. The output power of a 50-μm-diameter MUTC-LF device at 10 GHz is 1.86 W (without active cooling), and that for a similar device on AlN at $\sim -10°\mathrm{C}$ is 1.0 W [57]. For the devices with diameters of 40, 34, and 28 μm on diamond, the output RF powers improve 22.7% at 15 GHz, 78.4% at 20 GHz, and 35.5% at 25 GHz, respectively. For the MUTC-HF photodiodes the saturation currents and RF output powers of the 14 and 20 μm devices were 55 and 95 mA and 20.3 and 15.9 dBm, respectively.

 

Fig. 5. Power density at failure versus diameter of CC-MUTC photodiodes. The data symbols represent photodiodes that are not flip-chip bonded. Heat is dissipated through the InP substrate. The , , and data points denote devices flip-chip bonded on Si, AlN, and diamond, respectively.

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Fig. 6. RF output power versus frequency.

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Recently, Li et al. demonstrated high-speed MUTC PDs that achieved 50 mA saturation current and 9.6 dBm RF output power at 100 GHz [58]. In the epitaxial layer structure the absorber layer and drift layer thicknesses were decreased to 180 and 300 nm, respectively, for the purpose of reducing the electron transient time. To reduce the junction capacitance, photodiodes with active areas as small as $20{\mathrm{\mu m}}^2$ were fabricated. To further increase the bandwidth, a high impedance transmission line, which also incorporated the flip-chip bond pads, was implemented on the chip and the AlN submount. The characteristic impedance for this transmission line was 96 Ω and was designed to provide inductive peaking. The frequency responses of a 5-μm-diameter flip-chip bonded MUTC PD at a reverse bias of 3.5 V at 5, 10, and 15 mA average photocurrent are shown in Fig. 7. As reported in [46], at high current levels, bandwidth enhancement is observed. This is attributed to the fact that the photo-generated carriers induce an electric field in the undepleted absorber, which assists electron transport.

 

Fig. 7. Frequency responses of a 5-μm-diameter MUTC PD (the solid lines are polynomial fitting curves).

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MUTC photodiodes designed for terahertz operation have been reported by Ishibashi et al. [59]. Output power levels of $-20$ and $-30\mathrm{dBm}$ were achieved at 300 GHz and 1 THz, respectively. Using a conventional UTC photodiode, Rouvalis et al. reported 3 dB bandwidth of 170 GHz, and output power of up to $-5\mathrm{dBm}$ at 170 GHz and $-9\mathrm{dBm}$ at 200 GHz [60]. Another photodiode that has achieved high subterahertz output power is the near-ballistic uni-traveling carrier photodiodes (NBUTC-PD). A $24{\mathrm{\mu m}}^2$ NBUTC device exhibited 165 GHz 3 dB bandwidth, 18 mA saturation current, and 5.11 dBm output power at 160 GHz [61].

Some of the design aspects of the charge-compensated (CC) MUTC structure promote high power conversion efficiency. The combination of drift layer, cliff layer, and partially depleted absorption layer helps to maintain high electric field across the heterojunction interfaces, which ultimately allows more of the electric power and input optical power to be converted to RF output power. The power conversion efficiency is defined as the RF output power divided by the sum of the input optical power and the electrical power delivered to the photodiode. For a sinusoidal optical intensity envelope, which corresponds to Class A operation of an electrical amplifier, the power conversion efficiency was 42%, 37.7%, and 37% at 10, 20, 25 GHz, respectively. If the modulator is biased away from quadrature, the optical envelope is cut off or “clipped” similar to Class AB operation. For this mode, by optimizing the bias voltage of the modulator and the RF signal voltage, 60%, 52%, and 51% power conversion efficiency at 6, 8, and 10 GHz, respectively, was achieved.

B. Integrated Balanced Photodiodes

Integrated balanced detectors have also been fabricated from the MUTC-LF and MUTC-HF wafers. Similar to the discrete photodiodes, they were flip-chip bonded on diamond submounts. A balanced pair of MUTC-LF 40 μm diameter devices exhibited 8 GHz bandwidth, 320 mA photocurrent without saturation, RF output power of 1.5 W, and common-mode rejection ratio (CMMR) $>30\mathrm{dB}$ up to 11 GHz. Balanced detectors with small diameters were fabricated from the MUTC-HF wafer. The 10 μm detectors achieved bandwidth $>40\mathrm{GHz}$ and 16 dBm RF output power. The CMMR was $>40\mathrm{dB}$ to 20 GHz and 20 dB up to 45 GHz. The decrease in CMMR above 20 GHz reflected asymmetry in the photodiodes.

C. Photodiode-Antenna Integration

A high-power V-band photodiode has been integrated with a coplanar patch antenna. The MUTC-HF photodiode had 60 GHz bandwidth and output power of 16.7 dBm at 50 GHz. Figure 8(a) shows the simulated and measured return loss, S11, versus frequency for the patch antenna. The radiation pattern is illustrated by the plot of signal intensity versus angle relative to the normal at 50 GHz in Fig. 8(b). At 60 GHz the saturated output power was $\sim -6.5\mathrm{dBm}$ at $-5\mathrm{V}$ and the average photocurrent was 45 mA. Using the Friis equation, the effective radiated power (ERP) (in decibels) is defined as

 

Fig. 8. Measured and simulated (a) return loss, $S_{11}$, versus frequency and (b) relative signal intensity versus angle (at 50 GHz) for the patch antenna [62].

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D. Photodiode Arrays

The rapid drop in output power with increasing frequency in Fig. 6 indicates that it will be difficult to achieve watt-level power for frequencies $>30\mathrm{GHz}$ with single devices. A possible solution is to utilize photodiode arrays. In order to achieve high speed, it will be beneficial to use a traveling wave electrode configuration. Toward this end, $4\times 1$ arrays of MUTC-HF photodiodes have been fabricated. Figure 9 shows a top view and the electrode configuration of an array flip-chip bonded to AlN. Time-domain measurements were carried out on the array in order to characterize the CPWs and match the delay times of the diodes. Following this setup procedure, a $1\times 4$ lensed fiber array with $\sim 250\mathrm{\mu m}$ pitch was aligned to the photodiodes. The diodes were illuminated through the InP substrate. RF output powers of 26.2 and 21.0 dBm are achieved at 35 and 48 GHz, respectively, with an array of 28 μm diameter photodiodes. The saturation current was 2.5 times the saturation current of a discrete 28 μm device. At 48 GHz an array of 20-μm-diameter photodiodes achieved saturation currents 2.6 times higher than a discrete 40-μm-diameter photodiode, which has the same active area as the array, and more than three times that of a discrete 20 μm detector under the same operating conditions.

 

Fig. 9. Superimposed photo of a segment of the MUTC chip (dashed line) with four diodes (PD1–PD4) and the AlN submount with coplanar transmission line [53].

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E. Heterogeneous Integration

In the past decade, silicon-based photonic circuits have been the focus of numerous research efforts. For some applications that utilize these circuits, higher performance within the areas of low dark current, high bandwidth, high saturation current, and high linearity can be achieved by heterogeneous integration of III-V compounds with Si waveguides. Xie et al. have reported MUTC photodiodes on silicon-on-insulator (SOI) waveguides [63]. A schematic cross section of the structure is shown in Fig. 10. The fabrication process begins with dry etching of the SOI waveguides. Then, the III-V detector material dies were plasma activated and bonded at room temperature to the Si waveguide layer [64]. The III-V substrate was removed via wet chemical etching, leaving active device layers for fabrication. It should be mentioned that the RF probe pads were deposited on a 3-μm-thick SU8 layer to reduce RF loss originating from the low-resistivity Si substrate. To match the width of the active PD region (10 and 20 μm) the 2-μm-wide passive single-mode input Si waveguide was tapered over a length of 40 μm.

 

Fig. 10. Cross section of MUTC photodiode on SOI. Doping concentrations in ${\mathrm{cm}}^{-3}$ [63].

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Photodiodes with effective areas of $10\mathrm{\mu m}\times 21\mathrm{\mu m}$, $10\mathrm{\mu m}\times 35\mathrm{\mu m}$, and $20\mathrm{\mu m}\times 35\mathrm{\mu m}$ exhibited bandwidths of 48, 31, and 18 GHz, respectively. Capacitance-voltage measurements indicated that the bandwidth was primarily limited by the RC-time constant. The RF output power versus average photocurrent at room temperature (no temperature control) for different bias voltages and modulation frequencies is shown in Fig. 11. The maximum RF output powers of the $20\mathrm{\mu m}\times 35\mathrm{\mu m}$ photodiode with a 50 Ω load were 16.6, 15.8, and 13.5 dBm at 10, 20, and 30 GHz, respectively. The device exhibited 1 dB saturation current of 60 mA at 30 GHz. The maximum output RF power of the $10\mathrm{\mu m}\times 35\mathrm{\mu m}$ photodiode was 12 dBm at 40 GHz at $-7.5\mathrm{V}$. The maximum values of the RF output power were limited by the maximum available optical input power (for the $10\mathrm{\mu m}\times 35\mathrm{\mu m}$ device) or thermal failure under high current operation (for the $20\mathrm{\mu m}\times 35\mathrm{\mu m}$ device).

 

Fig. 11. Output RF power of waveguide photodiodes versus modulation frequency at 1.55 μm wavelength.

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F. High-Power Pulsed Operation

For some applications it is desirable to generate high-power pulses or pulsed RF signals. There have been a variety of approaches including a photonic microwave filter [65], phase modulation [66], polarization modulation [67], and a mode-locked laser and optical filter [68].

For pulsed illumination, the photodiodes can handle higher bias voltage, which enables higher output peak voltage pulses compared with CW operation since thermal dissipation becomes relatively insignificant. An erbium-doped fiber laser with pulsewidth $<80\mathrm{fs}$ and 100 MHz repetition rate was used as the optical pulse source. As the average photocurrent increased, for a fixed bias the peak voltage initially increased linearly and then began to saturate and exhibit pulse shape distortion due to the space-charge effect. By applying higher bias voltage, the space-charge effect can be mitigated with concomitant reduction in pulse shape distortion. In order to determine the maximum peak output voltage at different bias voltages, the average photocurrent was increased until the pulse completely saturated. The maximum bias voltage was limited to $-35\mathrm{V}$ owing to avalanche breakdown. For $-35\mathrm{V}$ bias, the peak output voltage and FWHM were 33.5 V and 50 ps, respectively.

Gated microwave signals that were generated using the experimental apparatus shown in Fig. 12 were also studied. A low-noise fiber laser with an optical power of 17 dBm and 1550 nm wavelength was used as the optical source. A microwave signal was modulated on the CW optical carrier by the first Mach–Zehnder modulator (MZM). A second MZM was used to gate the input RF-modulated optical signal. An erbium-doped fiber amplifier (EDFA) with maximum output power of 33 dBm was used to increase the input power level of the pulsed-RF-modulated signal. The pulsed-RF-modulated optical signal was converted to a pulsed RF signal by the high-power photodiode. The photodiode output signal was simultaneously recorded with a spectrum analyzer and with a fast sampling oscilloscope. Peak power ($P_{\text{peak}}$) was calculated using the equation $P_{\text{peak}}=P_{\text{avg}}-20\log (\tau /T)$, where $\tau$ is the pulsewidth and $T$ is the pulse period.

 

Fig. 12. Experimental setup for generation of high-power optical pulsed microwave signals.

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Figure 13(a) shows the peak power of a 1 GHz pulsed RF signal versus the average photocurrent at bias voltages from $-9$ to $-36\mathrm{V}$. The peak power increases linearly as the photocurrent increases until saturation. When the bias voltage was increased to $-36\mathrm{V}$ the maximum peak power was 41.5 dBm (14.2 W) and the corresponding average photocurrent was 21 mA. The peak power for a 10 GHz pulsed RF signal versus photocurrent is plotted in Fig. 13(b). The maximum peak power was 40 dBm (10 W) when the bias voltage was $-36\mathrm{V}$ and the average photocurrent was 20 mA.

 

Fig. 13. (a) Peak power of 1 GHz pulse signal and (b) 10 GHz pulse signal at different photocurrents and bias voltages [69].

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G. High-Linearity Photodiodes

The SFDR, an essential figure of merit for analog optical links, is defined as the ratio of the power of the fundamental frequency to the power of the next largest harmonic or intermodulation distortions above the noise floor. Unlike other performance parameters such as loss or noise figure, SFDR cannot be improved by adding pre- or post-amplification [70]. The two primary sources of nonlinearities in analog optical links are the optical modulators and the photodiodes. In order to improve the SFDR of the entire link, it is essential to reduce the nonlinearities of both components. When properly biased at the quadrature point, the harmonics and intermodulations produced by the modulators can be effectively minimized [71]. However, unlike modulators, there is not an explicit expression for the transfer function of photodiodes and the nonlinearity of photodiodes is a complicated function of reverse bias, photocurrent, and temperature [72]. Usually the linearity of photodiodes is the limiting factor for the SFDR in high-performance analog optical links, especially when the optical power is high [73]. Among all the intermodulation products and harmonics, the third-order intermodulation distortion products (IMD3) at $2f_1-f_2$ and $2f_2-f_1$ are important, because they are close to the fundamental frequencies $f_1$ and $f_2$ and thus difficult to filter, as shown in Fig. 14(a). The third-order output intercept point (OIP3) is a key figure of merit to evaluate the linearity of an analog optical link; it is defined as the extrapolated intercept point of the power of the fundamental frequency and the IMD3, assuming that the fundamental power has a perfect slope of 1 and the power of the IMD3 has a perfect slope of 3 [Fig. 14(b)]. Based on its definition, the OIP3 can be calculated from the measured fundamental power and the power of the IMD3 using the relation [73]

 

Fig. 14. (a) Schematic of fundamentals and IMD3. (b) Definition of OIP3.

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At low frequencies, photodiodes with very good linearity have been demonstrated. A dual depletion region (DDR) photodiode has been reported to have a third-order harmonic output intercept point (HOIP3) of 54 dBm at 829 MHz [74], and a partially depleted absorber (PDA) photodiode has achieved an HOIP3 of 51 dBm at 3 GHz [75], which is equivalent to OIP3 values of 49.2 and 46.2 dBm, respectively, as estimated from the cubic dependence of the third-order nonlinearity terms. For a waveguide UTC photodiode 40.9 dBm OIP3 at 1 GHz has been reported by Klamkin et al. [76]. However, the OIP3 of previously reported photodiodes exhibited significant roll-off with frequency, and thus high OIP3 has been difficult to obtain at high frequencies [77]. OIP3 values of 35 and 36 dBm at 20 GHz were reported for a UTC photodiode [78] and a charge-compensated modified uni-traveling carrier (CC-MUTC) photodiode [79], respectively. An InGaAs/InP PDA photodiode with a highly doped absorber (HD-PDA) exhibited an OIP3 of 39 dBm at 20 GHz [80].

Various measurement-based models have been developed to explain photodiode nonlinearities [80–84]. Using bias modulation the voltage-dependent responsivity has been identified as the primary factor that determines nonlinearities at low frequencies ($<3\mathrm{GHz}$). As the frequency increases, the nonlinear capacitance becomes significant and dominates [78]. In order to reduce the voltage dependence of the capacitance in MUTC photodiodes and increase OIP3 at high frequencies, Pan et al. [81] have incorporated a highly doped p-type absorber (referred to as HD-MUTC). At optimized photocurrent and bias conditions, the OIP3 of the HD-MUTC is 55 dBm at low frequencies ($<1\mathrm{GHz}$) and remains as high as 47.5 dBm at 20 GHz. Figure 15 compares the OIP3 versus the frequency of a conventional MUTC with the HD-MUTC. At low frequency the difference is small, but at 20 GHz the HD-MUTC provides 10 dB higher OIP3. The solid and dashed lines were calculated using the equivalent circuit model in [77]. The solid line only considers the voltage dependence of the capacitance, C(V). For the dashed line the current dependence, C(I), is included.

 

Fig. 15. OIP3 versus frequency for a conventional charge-compensated MUTC and an HD-MUTC. The solid line is the calculated variation for the voltage dependence of the capacitance C(V), and the dashed line includes the current-dependent capacitance C(I).

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The OIP3 of the HD-MUTC photodiodes is strongly photocurrent dependent. Figure 16 shows the variation of OIP3 with photocurrent for bias voltage in the range of $-4$ to $-8\mathrm{V}$. The peaks shift to higher photocurrent values for higher voltage and lower temperature. Fu et al. have developed a model based on voltage/current-dependent responsivity that explains the variation of OIP3 with photocurrent, bias voltage, and temperature [85]. That work predicted that grading the composition of the depleted absorber region in the MUTC structure would reduce the photocurrent dependence. Figure 17 is a schematic cross section of this type of MUTC. While this structure modification has not eliminated the photocurrent dependence of OIP3, Figs 18(a) and 18(b) show OIP2, which is defined similarly to OIP3 for the second-order intermodulation distortions, and OIP3 versus photocurrent. OIP2 at $-5$, $-6$, and $-7\mathrm{V}$ reverse bias voltage is larger than 55 dBm between 10 and 80 mA photocurrent. The maximum OIP2 is 75 dBm when the reverse bias voltage is $-5\mathrm{V}$ and the photocurrent is 38 mA, which compares favorably with published results [50]. The OIP3 at 300 MHz was measured from $-6$ to $-10\mathrm{V}$. The OIP3 of the graded-bandgap absorber MUTC device exhibits relatively flat behavior, compared with the HD-MUTC in Fig. 16. At $-6\mathrm{V}$ reverse bias voltage, OIP3 is $>45\mathrm{dBm}$ with a variation of $\sim 7\mathrm{dB}$, which is an improvement from a minimum of $\sim 33\mathrm{dBm}$ and 20 dB variation in OIP3 for the HD-MUTC.

 

Fig. 16. Dependence of OIP3 on DC photocurrent and bias voltage.

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Fig. 17. Cross section of the graded-bandgap absorber MUTC.

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Fig. 18. (a) OIP2 and (b) OIP3 of a 40-μm-diameter graded-bandgap absorber MUTC photodiode at 300 MHz at $-4$ to $-7\mathrm{V}$ reverse bias voltage.

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H. Analog Optical Links

Recently, we used a MUTC-LF PD in an analog fiber optic link that achieved high gain and low-noise figure [86]. The experimental setup is shown in Fig. 19(a). The optical source was an erbium-doped fiber laser with 23 dBm output power and an RIN of $-165\mathrm{dBc}/\mathrm{Hz}$. The continuous wave light was coupled into a Mach–Zehnder (MZ) intensity modulator with $V\pi$ of 9 V, 20 GHz bandwidth, and 3 dB insertion loss. The modulator was operated at low bias below quadrature to achieve maximum SNR [87]. An EDFA with maximum output power of 33 dBm and noise figure of 4.8 dB was used to provide $>26\mathrm{dBm}$ optical power to the photodiode in order to achieve high photocurrent. Owing to the high-power, high-linearity MUTC PD, the analog link achieved $>24.5\mathrm{dB}$ gain, $<6.9\mathrm{dB}$ noise figure, and $>120({\mathrm{dBHz}}^{2/3})$ SFDR. Figure 19(b) summarizes the measured link characteristics between 6 and 12 GHz.

 

Fig. 19. (a) Analog photonic link experimental setup. (b) Measured gain, noise figure, and SFDR [86].

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It is well known that the large gain and low-noise figure of an analog link utilizing a low-biased MZ modulator are achieved at the cost of decreased linearity [88]. This is primarily due to the fact that even-order terms in the optical electric field that are usually suppressed by biasing the MZ modulator at quadrature strongly contribute to the RF power at low bias. One approach to achieve comparable gain with a quadrature-biased modulator is the balanced analog link. Figure 20(a) shows the architecture of a 20 GHz link reported in Ref. [89]. The link consists of a matched pair of fibers that connect a quadrature-biased dual-output MZ modulator with a balanced photodiode. In each branch a high-power EDFA, a variable optical attenuator, an optical tunable filter with 1 nm bandwidth, and an optical delay line were used. The detector was a flip-chip high-power balanced MUTC-LF PD. As shown in Fig. 20(b), the link gain improved with photocurrent and reached 16.2 dB at 20 GHz when the photocurrent was 65 mA per photodiode. The noise figure was 14 dB above a 40 mA average photocurrent. It can be expected that the noise figure can be further improved by using only one EDFA followed by a high-power MZ modulator [87]. The second- and third-order SFDRs were $92.6\mathrm{dB}·{\mathrm{Hz}}^{1/2}$ and $112\mathrm{dB}·{\mathrm{Hz}}^{2/3}$, respectively.

 

Fig. 20. (a) Balanced analog photonic link. ECL, external cavity laser; PC, polarization controller; VOA, variable optical attenuator; OTF, optical tunable filter; ODL, optical delay line; HP BPD, high-power balanced photodiode; ESA, electrical spectrum analyzer. (b) Link gain and noise figure measured at 20 GHz versus average photocurrent per photodiode.

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3. CONCLUSION

As the performance of photodiodes designed for RF photonics improves, their application sphere continues to expand. Future research thrusts will include optimization of device geometry and epitaxial structure, effective optical/electrical coupling, integration with other components (e.g., antennas), heat management, and incorporation into the Si photonics platform.