Characterization of photoreceivers for LISA F Guzman Cervantes, J Livas, R Silverberg, E Buchanan, R Stebbins NASA Goddard Space Flight Center, Code 663, 8800 Greenbelt Road, Greenbelt, MD 20771, USA. E-mail: [email protected] Abstract. LISA will use quadrant photoreceivers as front-end devices for the phasemeter measuring the motion of drag-free test masses in both angular orientation and separation. We have set up a laboratory testbed for the characterization of photoreceivers. Some of the limiting noise sources have been identified and their contribution has been either measured or determined from the measured data. We have built a photoreceiver with a 0.5 mm diameter quadrant photodiode with an equivalent input noise of better than 1.8 pA/ Hz below 20 MHz and a 3 dB bandwidth of 34 MHz. PALS numbers: 04.80.Nn, 07.60.-j, 07.87.+v, 85.60.-q, 85.60.Gz, 85.60.Dw, 85.60.Bt, 95.55.-n 1. Introduction The Laser Interferometer Space Antenna (LISA) is a planned gravitational wave observatory in the frequency range of 0.1 mHz-100 mHz that consists of three spacecraft separated by 5 million km in an equilateral triangle whose center follows the Earth in a heliocentric orbit with an orbital phase offset of 20 degrees. Gravitational waves will be measured as distance fluctuations between test masses moving along geodetic trajectories that are located in different spacecraft. LISA will require low power ultra- low noise photoreceivers for precision inter-spacecraft heterodyne laser interferometry. Quadrant photoreceivers will be used to measure the test mass motion with a sensitivity of 8 nrad/ Hz in angular orientation and 10 pm/ Hz in displacement over the frequency range of 0.1 mHz-100 mHz F11. The laser beam at the transmitting spacecraft will have a diameter of approximately 40 cm and an output laser power at the telescope of the order of I W. Given the laser beam propagation over 5 x 109 rn and accounting for losses on the beam path, from the remote optical signal approximately 50 pW will be detected on the entire quadrant photoreceiver. LISA will use heterodyne laser interferometry ('see Figure 1) for the inter-spacecraft displacement measurement. The incoming weak signal will optically interfere with a stronger local oscillator PLO. The combined signal Characterization of photoreceivers for LISA 2 P(t) measured at the photoreceiver can be expressed as P(t) = Pr^^^ +2 PSZy cos (Aw t + VPLO Pnc: DC power PLo T 4c; heterodyne signal where Acv is the frequency difference between the interfering laser beams (heterodyne frequency), and :p is the interferometer phase containing the gravitational wave information. Both ports of the beamsplitter will be measured by quadrant detectors. Their combined information can also be used for common-mode rejection of laser amplitude noise. The main task of the photoreceiver development is to maintain nearly shot-noise limited performance over a measurement bandwidth from 3-20 XII4z. This frequency range is driven by the Doppler induced frequency variations of the optical beat note signal due to the LISA constellation armlength changes, given by the orbits of each spacecraft. The local oscillator power PLO can be adjusted, according to the required E^ _t mW Local Oscillator pe, -too r Photoreceiver #2 incoming signal Cf ^^ Z G / 2yT,.O t,[ x cos(Ord)+ P_ Qu—a dIm dmet DecItAor P= f=stn * H,^x Pbotoreedwr #1 ° P,_0 + 2yP,^,, Fj cos(Aq. )+ P,$ Quad detector + G iph— s P ' P U amplifiers Figure 1. Descriptive diagram of laser heterodyne interferometric Figure 2. Topology and noise detection. model of photoreceiver TIA. photoreceiver performance. In order to reduce power consumption and temperature gradients at the optical bench due to heat spots at the photoreceivers, we aim for a, low-noise wide-bandwidth photoreceiver development operating at low PLO levels. Using 0.5 mW local oscillator optical power on the entire photoreceiver, and assuming a responsivity p of 0.7 Ar W for InGaAs photodiodes at a laser wavelength of 1064 nm, the shot-noise can be computed as iSN iSzv = 2epPDO ^t 10 pA/' Hz. (2) Allocating 30% of the shot-noise level — 3 pA j I4z — to the input current noise contribution of a quadrant photoreceiver, and considering this is the quadrature sum of the current noise of the individual quadrants, we derive an input current noise goal of 1.5 pA/tit H7 for the single-quadrant photoreceiver transimpedance amplifier (TIA). Characterization of photoreceivers for LISA 3 2. Photodetector transimpedance amplifier We have chosen a conventional DC-coupled TIA topology with a single ultra-low noise/ wide-bandwidth operational amplifier (op-amp), as shown in Figure 2. 2.1. Noise model For the TIA topology shown in Figure 2. two main input current noise sources have been identified in the electronics: • Johnson noise (Q) from feedback resistor R f: (3) Z`'_ R FL where k is the Boltzmann's constant, and T is the temperature (in Kelvin). • Op-amp noise properties: The current in and voltage en noise properties of the op-amp contribute to the total TIA input current noise. — The op-amp current noise ti,. sums directly to the TIA input. — The op-amp voltage noise en translates to current noise at the TIA input (f) over the input and feedback impedances as iTIA R f CT iTIA(f) = n. I + (^ R )2 (4) f where f is the frequency, and CT is the total circuit capacitance photodiode capacitance CT = Cd +Cf + Cop + Cs, (5) including the photodiode capacitance Cd, feedback impedance C f, op-amp common-mode input capacitance Cam„ and stray capacitances C,, from the board, components and packaging. The bandwidth Blfl of thPe phot oreceiver can be estimated as l C 811% — r (6) — 27RfCT, where GBTVP is the gain-bandwidth product of the operational amplifier. The total TIA input current noise In,,i,e(f) model can be expressed as (r) I r, .,P(.f) _ ? + iTrA(.f) - iITF(.f)fi', where is the normalized TIA transfer function, iTIA(f) is a frequency 1I TF(f) { dependent component of the input current noise (see Equation 4). and iT is the quadrature sum of various contributors that can be approximated by neglecting their frequency dependency for modeling purposes. For example, the expected current noise iT in the photoreceiver shown in Figure 2. can be computed as iT =V r + i T + id, (8) Characterization of photoreceivers for LISA 4 where i„ is the op-amp current noise, i i is the Johnson noise of the feedback resistor R f (see Equation 3), and id is the shot-noise from the photodiode dark current. It can be seen from Equation 5 that the photodiode capacitance and the op-amp common-mode input capacitance are crucial factors in the total noise budget. The challenge for the photodiode manufacture lays in achieving a minimum capacitance per unit area while maintaining high responsivity. For the TIA electronics, it is necessary to identify an op-amp with minimal common-mode input capacitance, current and voltage noise. and a gain-bandwidth product large enough to maintain the required sensitivity over the required measurement bandwidth of 3-20 MHz. 3. Prototype photoreceivers 3.1. Collaboration with industry Under a Small Business Innovation Research (SBIR) grant, the company Discovery Semiconductors has developed a large-area quadrant photodiode (QPD) of 1 mm diameter and a quadrant capacitance of 2.5 pF when reverse-biased at 5 V. A first fully integrated quadrant photoreceiver (Figure 3: QPD + TIA electronics) performs with an equivalent input current noise of less than 3.2 pAI Hz below 20 MHz [2] . The characteristics of this prototype quadrant, photoreceiver are: • Diameter of 1 mm with a 20 pm inter-quadrant gap. • Individual quadrant capacitance Cd = 2.5 pF. • Dark current: 140 nA. • TIA characteristics: - feedback impedance: R f = 51 kQ, Cf = 0.1 pF. - op-amp ADA481 7: en = 4 nVJ Hz, in = 2.5 fA/ Hz, C,, =1.4 pF. Discovery Semiconductors has been awarded a second stage grant to further develop quadrant photoreceivers. Given the successful development of a large-area low- capacitance QPD in the first step, the next stage will be focused on the noise reduction of the electronics, e.g. by integrating op-amps with better noise properties and studying alternative TIA topologies. We expect to receive additional devices with lower noise electronics at a later date. 3.2. Laboratory prototypes Working in parallel with Discovery Semiconductors to try to understand the noise and bandwidth trade-offs in more detail, we have identified the ultra-low noise/high- bandwidth op-amp EL5135 from Intersil [31 with the following nominal noise properties: e„ = 1.5 nV/ Hz, 17z = 0.9 p Ai Hz, Cep =1 pF. tVe have designed a TIA, as shown in Figure 2, with a feedback impedance R f - 40 kS Cf = 0.1 pF. and an expected bandwidth of 40 _MHz (according to Equation 6). We LISA 5 Characterization of photoreeeivers for f C = O.IpF Cd= 2.4pF ^^--^ Rt= 40k S2 Vout Rt=40kQ = Vm Figure 3. Photograph of a proto- Figure 4. Schematics of TIA type quadrant photoreceiver man- mock-up board for noise urea- ufactured by Discovery Semicon- surements and frequency response ductors. measurements. have built two different prototype boards to test the noise properties of a TIA with the EL5135 op-amp: • GAP500Q photoreceiver board: we have chosen the commercially available QPD GAP500Q from GPD Optoelectronics [4] with a diameter of 0.5 mm. When reverse-biased at 5 V, this device has a, nominal quadrant capacitance = 2.0 pF Cd and a dark current of 2.0 nA, according to the manufacturer. The idea is to operate the TIA electronics with a photodiode that approximates the per- quadrant capacitance and package parasitic capacitance of the larger area Discovery Semiconductors detector. Discovery Semiconductors has the capability to work with electronics in die form, whereas our investigations are limited to packaged parts. • Mock-up TIA board: we have built a board for controlled noise investigations of the TIA performance, shown in Figure 4. This board has two inputs: (i) input 1: an input capacitor (2.4 pF) of similar quadrant capacitance is used to replace the photodiode. For noise measurements, this input can be grounded while maintaining input 2 open. (ii) input 2: this is used to measure the expected photoreceiver transfer function (TF) by injecting a, signal (maintaining input 1 open), and scaling it accordingly by the feedback gain (40k). The equivalent input current, noise can be obtained, by dividing the output voltage noise by the scaled transfer function. The GAP500Q photodiode was reverse-biased with a battery power supply at 5 V. and the op-amps in both circuits were driven with a power supply at ±5 V. 4. Performance measurements of prototype photoreeeivers We operated the photoreceiver using only one quadrant of the CAP500Q QPD with the EL5135 op-amp for the TIA electronics. The photoreceiver output voltage noise 1<r (f ) Characterization of photoreceivers for LISA 6 is given by 17,(1f) - TF(f) yl SN + ^DN(f) (9) where iSN is the photocurrent shot-noise of the incident light. TF(f) is the photoreceiver transfer function, and (f) is the input current noise of the TIA electronics. Operating iDN under dark conditions, the photoreceiver output voltage noise VDN (f) is given by VDN(f) = TF'(f) - ZDN(f )^ (10) By dividing Equations 9 and 10, we obtain that the input current noise of the TIA electronics can be computed as [6] ^_^ zsN iD:v(f) = 2-1 (11) (f VDNtf For equivalent input current noise measurements, we used a light-emitting diode (LED) at a center wavelength of 1050 nm (±50 nm) [5] as shot-noise-limited light source. We V j)) measured the GAP500Q photoreceiver output voltage noise with ( " and without (VDN (f)) LED light, operating at two different optical power levels of 90µW and 60µW that yielded equal input current noise levels iDN ). We also measured the output voltage noise and the transfer function (TF(f )) of our mock-up TIA board (see Figure 4). Analogously to Equation 10, the input current noise can be computed by referring the output voltage noise to the input dividing by the transfer function (scaled by the photoreceiver feedback gain: 40k). Figure 4 shows the obtained noise measurement results. The GAP500Q photoreceiver reaches a level of about 1.5 pA/ Hz up to —10 MHz, increasing at higher frequencies. It exceeds the noise goal by approximately 2010 (1.8 pA/ Hz) at 20 MHz. The mock-up TIA circuit meets our noise goal over the entire bandwidth (3-20 MHz), however, it shows noise in excess than expected from the model. At lower frequencies the equivalent input noise is determined by excess current noise (iT: assumed to have no frequency dependence, Equation 8), while at higher frequencies, the increasing slope is dominated by the op-amp voltage noise swing across the total circuit capacitance dependent on (iT1A: frequency, Equation 4). NVe. run a set of measurements in order to determine some of the involved unknowns: (i) op-amp voltage noise (c,,,): we measured the op-amp voltage noise on a separate sample of the EL5135. by driving the op-amp as a voltage follower with grounded input. A 10x amplifier in series with the op-amp output was necessary for a voltage noise measurement above the spectrum analyzer noise floor. The voltage noise level measured was e,, = 2.1 nVl Hz at 10 i1IHz. which is higher than the expected 1.5 11 r` Hz. (ii) photodiode and feedback capacitances (Cd. C f ): using an LCR-bridge impedance measurement instrument. we measured the photodiode quadrant capacitance Cd on a separate sample of the GAP500Q to be 3.2 pF with a 5 V reversed bias, which is higher than the nominal 2 pF. NVe also measured the capacitor Cd of the mock-up Characterization of photoreceivers for LISA 7 3.0 GAP500Q photoreceiver (EL5135) --------- N Mock-Up TIA (EL5135) nominal noise model 7 2.5 FIT GAP500Q photoreceiver FIT Mock-Up TIA goal 1.5 pA/ti'Hz a^ 0 2.0 C V' E C a^ 1.5 U Q 1.0 C a^ m 0.5 aa^ 0 1 2 3 4 5 6 7 8910 20 30 frequency [MHz] Figure 5. Input current noise measurements of photoreceiver prototypes. The dashed trace is the photoreceiver with one quadrant of the GAP500Q QPD and the EL5135 op-amp TIA. The solid trace is the mock-up test board (see Figure 4). The dashed- dotted trace is the photoreceiver noise model for a TIA design with an EL5135 op-amp and a quadrant capacitance of 2.5 pF (Equations 7) . The traces with crosses and circles show the corresponding photoreceiver noise models using parameter values obtained j from a fit to the data. `the thick solid traced is our TIA input current noise goal of 1.5 pA Hz in the measurement band 3-20 MHz. board and the feedback capacitor Cf to be 2.2 pF (nominally 2.4 pF) and 0.1 pF, respectively. These noise properties are higher than nominal and account for part of the excess noise. A direct measurement of the op-amp current noise in,, the op-amp input capacitance Cop, and the stray capacitances C, of the circuit involve the development of dedicated electronic boards (currently on-going) for well-controlled measurements. This is planned to be conducted at a later stage. However, it is possible to obtain an estimate of these values by fitting them as parameters of the noise model (Equations 7 and 8) to the two measured data sets. The noise level difference (offset) in the data of the CAP500Q photoreceiver and the mock-up TIA is an indicator of a significant excess current noise contribution. i.y. present in the photovoltaic measurement and not in the measurement of the mock-up :TIA. This <°an also be included into the fit by considering the following Characterization of photo receivers for LISA 8 non-frequency dependent contributions iT (Equation 8) for each case: CAP500Q photoreceiver : iTID _ Alin f iJ i,d iX (12) Mock — up TIA : iT IU _ din iJ (13) The capacitance values Cd and C f are assumed to be known from the LCR-bridge measurements. We also assume similar op-amp and board noise properties (en,, i'. Cop + Cs) for the two circuits. From the fit, we obtained an op-amp current noise of i„ ti l.1pAj Hz (about 20% higher than nominal 0.9pA/ Hz) and a combined stray plus op-amp input capacitance Cop + Cs ;:t 1.3 pF (1 pF nominal Cop). We also fit a common op-amp voltage noise for the two data sets to be en ^ 1.9 nV f Hz, which is comparable (within < 101c) to the independent measurement (2.1 nV/ Hz), but about 25% higher than nominal (1.5 nV f Hz). Table 1 summarizes the current best estimates (CBE) of the photoreceiver noise properties. The excess current noise parameter } CBE nominal Cd [pF] 3.2 2.0 j en, [nV Hz] 1.9 1.5 in, [pA j Hz] 1.1 0.9 C,P -?- CS [pF] 1.0 1.3 ix [pA/ Hz] 0.7 - Table 1. Noise parameters: comparison between nominal values and current best estimates (CBE). contribution, ix, present in the CAP500Q photoreceiver data was determined to be of the order of ix ;^t 0.7 pA/ Hz. We have reversed-biased the photodiode with a battery power supply, therefore, fluctuations of the bias voltage translating to excess current noise are considered unlikely. Additional tests are required to determine the origin of this contribution. 5. Conclusions and Outlook We have presented the results of noise measurements conducted on different photoreceiver prototypes. The measurements showed approximately 20% noise in excess of our goal between 10 20 'vIHz. Direct measurements of the op-amp voltage noise and the reverse-biased QPD quadrant capacitance evidenced noise levels higher than nominal. accounting for part of the excess noise at higher frequencies. By fitting the Characterization of photoreceivers for LISA 9 parameters of the noise model to the data, we obtained estimates for the combined stray plus op-amp input capacitance and the op-amp current noise i ,, which was determined to be approximately 20% higher than nominal. Significant excess current noise (507c of total) ix was determined between photovoltaic (GAP500Q photoreceiver) and electronic (mock-up TIA) noise measurements. Additional testing is required to determine its origin. The measured photoreceiver performance is of the order of 1.5 pA f Hz below I0 MHz, increasing up to I.S pA/ Hz at 20 4Hz with a 3 dB bandwidth of 34 MHz. However, the mock-up TIA performs at a level of 1.35 pA/ Hz below 20 MHz (10% higher than expected from the nominal model) with a measured 3 dB bandwidth of 38 MHz. This suggests a potentially better performance of a real photoreceiver possible with the current TIA design, depending upon clarification and, if viable, mitigation of the excess current noise ix. In addition, as following steps we plan to conduct spatial scanning of the photodiode surfaces, measurement of inter-quadrant cross-talk, and differential wavefront sensing angle measurements. 6. Acknowledgements This research was supported in part by NASA contract ATFP07-0127. F. Guzmdn Cervantes is supported by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center, administered by Oak Ridge Associated Universities (ORAU) through a contract with NASA. '%e thank A. Joshi and S. Datta for stimulating discussions. References [l] Jennrich O, LISA technology and instrumentation, Class. Quantum Gray... 26 (2009). [2]Joshi A, Rue J, and Datta S, Low-Noise Large-Area Quad Photoreceivers Based on Low-Capacitance Quad InGaAs Photodiodes, IEEE Photonics Technology Letters, Vol.21, No.21 (2009). [3]Datasheet of Intersil device EL5135: http: //www. intersil. com/data/fn/fn7383.pdf [4]Datasheet of GPD Optoelectonics device GAP500Q: http://www.gpd-ir.com/ [5]Datasheet of THORLABS device LED1050E: http://www.thorlabs.com/Thorcat/16300/ 16388-SOl.pdf [61 Diekinann C, Phasenstabilisierung und -auslesung fur LISA, Diploma Thesis. Leibniz Universitat Hannover. Germany (2008).