Integrated fiber optical receiver reducing the gap to the quantum limit

Experimental results of a single-photon avalanche diode (SPAD) based optical fiber receiver integrated in 0.35 µm PIN-photodiode CMOS technology are presented. To cope with the parasitic effects of SPADs an array of four receivers is implemented. The SPADs consist of a multiplication zone and a separate thick absorption zone to achieve a high photon detection probability (PDP). In addition cascoded quenchers allow to use a quenching voltage of twice the usual supply voltage, i.e. 6.6 V instead of 3.3 V, in order to increase the PDP further. Measurements result in sensitivities of −55.7 dBm at a data rate of 50 Mbit/s and −51.6 dBm at 100 Mbit/s for a wavelength of 635 nm and a bit-error ratio of 2 × 10−3, which is sufficient to perform error correction. These sensitivities are better than those of linear-mode APD receivers integrated in the same CMOS technology. These results are a major advance towards direct detection optical receivers working close to the quantum limit.


Integrated fiber optical receiver reducing the gap to the quantum limit
Horst Zimmermann*, Bernhard Steindl, Michael Hofbauer, Reinhard Enne

I. Quantum limit and sensitivity
The quantum limit follows from the Poisson statistics where m is the average number of events and pm(k) is the probability that k events happen when in average m events occur.
For a receiver with one photodiode and a bit error rate (BER) of 10 -9 (For such a low BER usually no error correction is necessary.) the probability that a "0" is detected has to be smaller than 10 -9 when a logical "1" is sent, when the quantum efficiency of the detector is 100%. According to (1), 21 photons have to be sent in average for a "1". For a BER of less than 2×10 -3 at least 7 photons are needed.
Due to the parasitic effects (dark count rate, afterpulsing probability 5.1%, optical crosstalk probability OCP 2.3%) of an SPAD a logical "1" can be detected although a logical "0" was sent. The most critical effect is, when in two SPADs an afterpulse occurs in the same bit period, leading to a BER of about 2.5×10 -3 . Another critical event is when an SPAD shows an afterpulse and causes an optical crosstalk (APP-OCP: 5.1×10 -2 × 2.3×10 -2 ) in a neighboring SPAD, leading to a probability of about 1.2×10 -3 . Because there are dark counts in addition, a receiver consisting of two SPADs possessing the mentioned parasitic properties is not sufficient in order to be able to perform error correction, where a BER of less than 2×10 -3 is necessary. A receiver with three SPADs would lead to a BER of larger than 1.3×10 -4 (The worst combination of errors comes from an SPAD APP of 5.1%, when an afterpulse in each of the three SPADs occurs in the same bit, leading to a probability of (5.1×10 -2 )³=1.3×10 -4 . Because the error probabilities from other combinations like APP-APP-OCP, APP-OCP-OCP, DCR-APP-APP, DCR-APP-OCP and so on have to be added, we assumed that three 2 SPADs will not be sufficient also because of additional errors due to jitter for instance. The probability of APP 4 , however, is 6.3×10 -6 , leaving enough room to the BER limit of 2×10 -3 also when considering the other combinations. Therefore we designed a receiver with four SPADs. The experiments indeed showed that four SPADs are necessary for a low enough BER. As a consequence a low-enough BER of a "0" will increase the average number of sent photons for a "1" by a factor equal to the number of necessary SPADs, i. e. by a factor of 4 for the receiver introduced here.
The average optical power Popt corresponding to the number of photons can be calculated according where ℎ is the photon energy and B is the data rate in s -1 .
The sensitivity is defined as the average optical power which is necessary to achieve a certain BER.

II. Thin SPAD versus thick SPAD, capacitance and avalanche charge
Many SPADs integrated in CMOS were reported, which have a thin combined absorption and multiplication region at a p+/n-well junction or at a p+/deep-n-well junction S1,S2,S3,S4,S5 . Fig. S1 compares these thin SPADs with the thick SPAD investigated here.
The thickness of the space-charge region within the n-well or deep n-well in these thin SPADs (see right part of Fig. S1) is in the order of only 1µm. In 0.13µm CMOS, the thickness of the space-charge region was only 0.3µm. S5 Charge carriers photogenerated in the p-substrate below the (deep) nwell do not reach the multiplication region (because the (deep) n-well is connected to a positive bias voltage) and cannot start an avalanche process. Therefore the photon detection probability of thin SPADs for red is rather low and their junction capacitance is rather large.
The thick SPAD (see left part of Fig. S1) possesses a space-charge region with a thickness of 12µm for absorption of more photons in the red spectral range. The electrons photogenerated in the thick 3 absorption zone drift upwards to the multiplication zone and can trigger the avalanche process there leading to a larger PDP for red and near-infrared light than of the thin SPADs. Charge carriers photogenerated in the substrate below the (deep) n-well of the thin SPAD do not reach the multiplication zone and do not trigger an avalanche. whereas the thin SPAD uses a thin combined multiplication/absorption zone.
Recent work S6 implemented a thicker multiplication region, which however still was limited by the penetration depth of the deep n-well in 0.18µm CMOS technology. Nevertheless at 11V excess bias, an impressive PDP of 43% for 600nm, DCR of 1.5cps/µm² and an APP of 7.2% (for 300ns dead time) were reported. S6 A thicker epitaxial structure was used for an SPAD with a PDP of 62.2% to 64.8% at 610nm and at an excess bias of 5V S7,S8 . DCR of best SPADs was 0.6cps/µm² and mean DCR density was 7.6cps/µm² at an excess bias of 5V. APP was 1.63% for a dead time of 17.9ns at 5V excess bias.
However, a proprietary customized CMOS process with special n-and p-type layers was used. The capacitance was not reported.
The SPAD suggested here possesses an about 12µm thick separate absorption zone and its capacitance C is about a factor of 10 lower as that of thin SPADs. Figure S2  presented here has about a factor of 10 lower capacitance than thin SPADs formed by p+/(deep)nwell junctions. Fig. 2 and having an area of 3,750 µm².

Fig. S2. Capacitance over voltage of an SPAD with the cross-section shown in
Since the afterpulsing probability increases with the amount of charge carriers being generated in the avalanche process, because more traps can be filled by more available charge carriers, a smaller capacitance of the SPAD reduces the amount of charges, which can be captured by traps. With an active quencher the SPAD's cathode is left floating after it has been charged to Vplus. The avalanche current discharges the SPAD's capacitance C and the maximum available charge is C times Vplus. A fast quencher, however, discharges the SPAD's capacitance via the quencher and reduces therefore the amount of charge carriers within the avalanche. It can be expected that the thick SPAD shows a much lower avalanche charge Q and afterpulsing probability than thin p+/(deep-)n-well SPADs.

III. Isolation of circuits
The avalanche photodiode needs a much larger bias voltage than the circuit supply voltage. The anode of the SPAD is formed by the substrate of the complete chip and therefore has to be biased with a negative voltage compared to the circuit supply voltage. Circuits on the same chip together with the SPAD are only possible when the transistors can be isolated from this negative substrate voltage. The process used is a so-called triple-well CMOS process, which offers a deep n-well as a third well. Fig. S3 shows a cross section of the SPAD together with transistors to explain the isolation of the circuits. The deep n-well is connected to the most positive potential in the circuit, i. e. to Vplus.
In such a way the junction formed by deep n-well and p-substrate is always in reverse direction. The deep n-well possesses a punch-through voltage VPT of about 40V towards the substrate (see Fig. S3), i. e. the n-channel MOSFETs can be isolated inside a deep n-well from the negative anode 6 of the SPAD. The deep n-well is also used to increase the breakdown voltage of the n-well, in which the p-channel MOSFETs are located, towards substrate. The breakdown voltage of deep n-well towards the substrate VBD,DNW is larger than 40V (see Fig. S3) in the CMOS process used. This breakdown occurs at the edge as marked in Fig. S3. In such a way, circuits can be operated together with the thick SPAD on the same chip. These high breakdown voltages represent a clear advantage of the 0.35µm pin-photodiode CMOS process used over nanometer CMOS technologies with very limited breakdown voltages.

IV. Spectral dependence of the photon detection probability
The spectral dependence of the PDP was measured by illuminating the SPAD with a constant photon flux. This photon flux was generated by means of a tunable light source built by the Xenon light source ASB-XE-175 and the monochromator CM110, both from Spectral Products, as well as by a fiber coupled tunable optical attenuator DD-100-11 from OZOptics. The photon flux for each wavelength was calibrated by a standard Si PIN photodiode (S5971). This photodiode was cooled down to a temperature of -30°C in order to reduce its leakage current down to the femtoampere range. The PDP was then obtained by stepping the wavelength while illuminating the SPAD and by building the ratio between the pulse rate at the output of the quencher (corrected for afterpulses and dark counts) and the photon flux.
The spectral dependence of the photon detection probability (PDP) of the SPAD with the cross section of Fig. 2 for two quenching voltages Vq (breakdown voltage Vbd=25.8V) is shown in Fig. S4.
There is a ripple due to optical interference in the isolation and passivation stack of the standard 0.35µm CMOS process. In Fig. S4 additionally the PDPs measured with the 635nm laser used for the bit error measurements are indicated by markers. It can be concluded however from Fig. S4 that the PDP is largest in the red spectral range. At 850nm and for Vq=6.6V the PDP of 25% is more than three times larger than that of the thin SPAD described in ref. 10. 7 Fig. S4. Measured photon detection probability (PDP) of a SPAD reference device.

V. Dark count rate
The dark count rate at 25°C was measured at a reference SPAD having the same shape and an area of the multiplication zone of 3,750µm² (as depicted in Fig. 2) in dependence on the excess bias voltage. Fig. S5 shows the obtained results. At an excess bias voltage of 3.3V the DCR is 21.5kcps (5.7cps/µm²) and at 6.6V excess bias the DCR is 35.5kcps (9.5cps/µm²). 8

Fig. S5
Measured dark count rate of a reference SPAD with 3,750µm² active area. Figure S6 depicts the measurement set-up used for the characterization of the SPAD-based receiver. The light source was stabilized at constant temperature and with a control loop using a monitor photodiode. The optical receiver was mounted on a Peltier element and kept at 25°C by a thermoelectric cooler (TEC) controller. The set-up was controlled by a PC with a Labview measurement program. After calibration the fiber was moved from the optical power meter to the SPAD receiver.