Computation of Bit-Error Probabilities for Optical Receivers Using Thin Avalanche Photodiodes

The large-deviation-based asymptotic-analysis and importance-sampling methods for computing bit-error probabilities for avalanche-photodiode (APD) based optical receivers, developed by Letaief and Sadowsky [IEEE Trans. Inform. Theory, vol. 38, pp. 1162-1169, 1992], are extended to include the effect of dead space, which is significant in high-speed APDs with thin multiplication regions. It is shown that the receiver\u27s bit-error probability is reduced as the magnitude of dead space increases relative to the APD\u27s multiplication-region width. The calculated error probabilities and receiver sensitivities are also compared with those obtained from the Chernoff bound

Bit Error Rates for Ultrafast APD Based Optical Receivers: Exact and Large Deviation Based Asymptotic Approaches

Exact analysis as well as asymptotic analysis, based on large-deviation theory (LDT), are developed to compute the bit-error rate (BER) for ultrafast avalanche-photodiode (APD) based optical receivers assuming on-off keying and direct detection. The effects of intersymbol interference (ISI), resulting from the APD\u27s stochastic avalanche buildup time, as well as the APD\u27s dead space are both included in the analysis. ISI becomes a limiting factor as the transmission rate approaches the detector\u27s bandwidth, in which case the bit duration becomes comparable to APD\u27s avalanche buildup time. Further, the effect of dead space becomes significant in high-speed APDs that employ thin avalanche multiplication regions. While the exact BER analysis at the generality considered here has not been reported heretofore, the asymptotic analysis is a major generalization of that developed by Letaief and Sadowsky [IEEE Trans. Inform. Theory, vol. 38, 1992], in which the LDT was used to estimate the BER assuming APDs with an instantaneous response (negligible avalanche buildup time) and no dead space. These results are compared with those obtained using the common Gaussian approximation approach showing the inadequacy of the Guassian approximation when ISI noise has strong presence

Optimization of InP APDs for high-speed lightwave systems

Calculations based on a rigorous analytical model are carried out to optimize the width of the indium phosphide avalanche region in high-speed direct-detection avalanche photodiode-based optical receivers. The model includes the effects of intersymbol interference (ISI), tunneling current, avalanche noise, and its correlation with the stochastic avalanche duration, as well as dead space. A minimum receiver sensitivity of -28 dBm is predicted at an optimal width of 0.18 mu m and an optimal gain of approximately 13, for a 10 Gb/s communication system, assuming a Johnson noise level of 629 noise electrons per bit. The interplay among the factors controlling the optimum sensitivity is confirmed. Results show that for a given transmission speed, as the device width decreases below an optimum value, increased tunneling current outweighs avalanche noise reduction due to dead space, resulting in an increase in receiver sensitivity. As the device width increases above its optimum value, the receiver sensitivity increases as device bandwidth decreases, causing ISI to dominate avalanche noise and tunneling current shot noise

Effect of dead space on avalanche speed

The effects of dead space (the minimum distance travelled by a carrier before acquiring enough energy to impact ionize) on the current impulse response and bandwidth of an avalanche multiplication process are obtained from a numerical model that maintains a constant carrier velocity but allows for a random distribution of impact ionization path lengths. The results show that the main mechanism responsible for the increase in response time with dead space is the increase in the number of carrier groups, which qualitatively describes the length of multiplication chains. When the dead space is negligible, the bandwidth follows the behavior predicted by Emmons but decreases as dead space increase

Optimization of InP APDs for High-Speed Lightwave Systems

Calculations based on a rigorous analytical model are carried out to optimize the width of the indium phosphide avalanche region in high-speed direct-detection avalanche photodiode-based optical receivers. The model includes the effects of intersymbol interference (ISI), tunneling current, avalanche noise, and its correlation with the stochastic avalanche duration, as well as dead space. A minimum receiver sensitivity of -28 dBm is predicted at an optimal width of 0.18 mum and an optimal gain of approximately 13, for a 10 Gb/s communication system, assuming a Johnson noise level of 629 noise electrons per bit. The interplay among the factors controlling the optimum sensitivity is confirmed. Results show that for a given transmission speed, as the device width decreases below an optimum value, increased tunneling current outweighs avalanche noise reduction due to dead space, resulting in an increase in receiver sensitivity. As the device width increases above its optimum value, the receiver sensitivity increases as device bandwidth decreases, causing ISI to dominate avalanche noise and tunneling current shot noise

Error Probabilities for Optical Receivers That Employ Dynamically Biased Avalanche Photodiodes

A novel theory was recently reported for the avalanche multiplication process in avalanche photodiodes (APDs) under dynamic reverse-biasing conditions. It has been shown theoretically that the bit-synchronized, periodic modulation of the electric field in the multiplication region can offer improvements in the gain-bandwidth product by reducing intersymbol interference in optical receivers. This paper reports a rigorous formulation of the sensitivity of optical receivers that employ dynamically biased APDs. To enable the sensitivity analysis, a recurrence theory is developed to calculate the joint probability distribution function (PDF) of the stochastic gain and avalanche buildup time in APDs that are operated under dynamic biasing. It is shown that in an ideal buildup-time limited scenario, a minimum receiver sensitivity of -20 dBm is predicted at an optimal gain of approximately 47 for a 60 Gb/s communication system, compared to a minimum of 0 dBm in the static-bias case. The receiver sensitivity analysis also reveals that, as the peak-to-peak voltage of the dynamic reverse bias increases, the device optimal gain increases while maintaining a short avalanche buildup time and reduced ISI. Of course, a point of diminishing return exists in practice when the tunneling current in the multiplication region becomes dominant

Optical Communication with Semiconductor Laser Diode

Theoretical and experimental performance limits of a free-space direct detection optical communication system were studied using a semiconductor laser diode as the optical transmitter and a silicon avalanche photodiode (APD) as the receiver photodetector. Optical systems using these components are under consideration as replacements for microwave satellite communication links. Optical pulse position modulation (PPM) was chosen as the signal format. An experimental system was constructed that used an aluminum gallium arsenide semiconductor laser diode as the transmitter and a silicon avalanche photodiode photodetector. The system used Q=4 PPM signaling at a source data rate of 25 megabits per second. The PPM signal format requires regeneration of PPM slot clock and word clock waveforms in the receiver. A nearly exact computational procedure was developed to compute receiver bit error rate without using the Gaussion approximation. A transition detector slot clock recovery system using a phase lock loop was developed and implemented. A novel word clock recovery system was also developed. It was found that the results of the nearly exact computational procedure agreed well with actual measurements of receiver performance. The receiver sensitivity achieved was the closest to the quantum limit yet reported for an optical communication system of this type

Time Resolved Gain and Excess Noise Properties of InGaAs/InAlAs Avalanche Photodiodes with Cascaded Discrete Gain Layer Multiplication Regions

To predict pulse detection performance when implemented in high speed photoreceivers, temporally resolved measurements of a 10-stage InAlAs/InGaAs single carrier multiplication (SCM) avalanche photodiode (APD)\u27s avalanche response to short multi-photon laser pulses were explained using instantaneous (time resolved) pulse height statistics of the device\u27s impulse response. Numeric models of the junction carrier populations as a function of the time following injection of a primary photo-electron were used to create the probability density functions (pdfs) of the instances of the avalanche buildup process. The numeric pdfs were used to generate low frequency gain and excess noise models, which were in good agreement with analytic models of multiple discrete low-gain-stage APDs and with measured excess noise data. The numeric models were then used to generate the instantaneous and cumulative instantaneous low order statistics of the instances of the impulse response. It is shown that during the early times of the impulse response, the SCM APDs have lower excess noise than the pseudo-DC measurements and the common APDmodels used to describe them. The methods of determining the time resolved low order statistics of APDs are described and the importance of using time-resolved models of APDgain and noise is discussed

Low-Photon Detection Using InGaAs/InAlAs and InAs Avalanche Photodiodes

Single-photon avalanche photodiodes (SPADs) based on the InGaAs/InAlAs material system are designed, fabricated, and characterised for 1550 nm light detection. The two designed wafers reduce the electric field across the InGaAs absorber to a minimum in order to minimise dark current. The first wafer is designed to punch-through at the point of high breakdown probability (above breakdown voltage), while the second is designed to punch-through just under breakdown voltage. The first wafer is found to be unsuitable for single-photon counting due to an uncharacteristically fast rise in dark count rate, likely caused by the onset of punch-through during breakdown. Low photon levels are detected using diodes fabricated from the second wafer, however the diodes were found to not fully punch-through, preventing single-photon counting. Peak laser pulse detection probabilities at 150 K were 73, 71, and 46 % for 100, 30, and 10 photons, respectively. At room temperature, pulse detection probabilities were 39, 35, and 30% for the respective photon levels. This informs future SPAD designs; crucially that full punch-through must occur before breakdown voltage. A simulation model for the sensitivity of electron APDs (e-APDs) is developed and applied to InAs e-APD based optical receivers. The model simulates bit-error rate (BER), and captures the effects of inter-symbol interference (ISI), dark current, current impulse duration, avalanche gain, and amplifier noise. With a target BER of 10 −12 , the receivers’ sensitivities were -30.6, -22.7, and -19.2 dBm for 10, 25, and 40 Gb/s data rates. The simulated InAs APDs offer improvements over existing InAlAs APDs at 10 and 25 Gb/s, however SOA-PIN based receivers outperform both types of APD for 40 Gb/s for 1550 nm operation. Utilising the newly developed e-APD sensitivity model, and a previously developed sensitivity model for standard APDs, simulations are performed comparing InAs, InAlAs, and InP based optical receivers. The simulations utilise a common parameter set where appropriate, allowing for a direct comparison between the three avalanche materials for high-speed operation. Simulated InAs APDs achieved the best performance for 10 Gb/s operation (-29.4 dBm for InAlAs), while the simulated InAlAs APDs were found to perform better at 25 and 40 Gb/s, achieving a sensitivity of -23.5 and -21.0 dBm, respectively. InP APDs showed sensitivities of -27.9, -22.5, and -19.9 dBm, for 10, 25, and 40 Gb/s operation, respectively. These simulations demonstrate significant performance benefits to replacing InP with InAlAs as an APD avalanche region. Additional simulations of InAs APDs were performed, exploring how to further optimise InAs based optical receivers