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4 IEEE PHOTONICS TECHNOLOGY LETERS, VOL. I, NO. 1, JANUARY 1995 Ultralow Power Optical Interconnect with Zero-Biased, Ultralow Threshold Laser-How Low a Threshold Is Low Enough? David M. Cutrer and Kam Y. Lau, Senior Member, IEEE Abstract-Ultralow threshold (Ith < 100 PA) lasers can be used in ultralow power optical interconnect, preferably in a bias-free digital optical modulation format. We show that even though optical power requirements for successful transmission may dictate that the pulse drive currentbe many times that of Ith, reducing the latter to 10-100 p A is still essential in minimizing the total driver power to the laser at multi-gigabit data rates I. INTRODUCTION INTENSE interest in recent years in ultralow threshold lasers, through a combination of quantum confined and/or microcavity VCSEL structures, was motivated mainly by their potential for optoelectronic integrated circuits (OEIC’s) due to their low electrical power requirements. Lasers with a threshold in the 100 pA range already exist [1], [ 2 ] .This threshold is small compared to the drive current above threshold needed to generate the typical required optical power for high data rate communication. It thus appears that continued research to further lower the threshold will have little impact on the laser driver requirements of the OEIC’s. We show in this paper that this is NOT true when one fully considers the switching dynamics of semiconductor lasers in an OEIC environment, particularly at high data rates. We base our analysis on the presumption that the laser is digitally modulated and zero-bias modulation format [3], [4] is used. This modulation format is highly favorable in OEIC’s since it eliminates the need for optical monitoring and feedback control of the bias point of each individual laser. This bias circuitry is a complication, particularly for VCSEL’s, that consumes both power and on-chip real estate. It is well known that zero-bias on/off switching produces data dependent tum-on delays that result in a degradation of the data. This is illustrated in Fig. 1 for the time evolution of the electron density and optical output under a pseudorandom pulse modulation. When the optical data stream is fed into a typical digital receiver, the resulting timing jitter introduces a bit-error-rate (BER) degradation. This degradation depends on the relative magnitude of the time delay compared to the bit rate. For lasers biased below threshold, the tum-on delay consists of the time for the drive current to fill the electron Manuscript received August 3, 1994; revised September 13, 1994. This work was supported in part by the NSF. D.Cutrer is supported in part by a NDSEG-ONR graduate fellowship. The authors are with the Department of EECS, Cory Hall, Box 103, University of Califomia at Berkeley, Berkeley, CA 94720 USA. IEEE Log Number 9407368. I - Time I Fig. 1. Pseudo random bit stream, the corresponding canier density in the laser, and the resulting optical bits. density up to the threshold level, plus an additional time for the photon density to build up from spontaneous emission. The variance of the time for the photon density to build up has been studied [5] and shown to be <10 ps for a wide range of drive currents. In comparison, a laser modulated in the zero-bias format typically requires a much longer time (-100 ps) to reach threshold. To model the pattem dependent switching dynamics of the laser, we assume that the tum-on delay is given simply by the time for the carrier density to reach threshold. With this assumption, it is clear that a laser with a lower threshold will require less drive current in order to achieve a certain tum-on delay, and thus reducing the power requirement for the laser driver overall. Since the tum-on delay is data dependent and is thus random, we must describe it in terms of a statistical distribution. The tum-on delay can be determined by considering the rate equation for the electron number ( n )in the active region of the laser: - d n - I ( t ) n Qnp dt e r (1) where 7 is the carrier recombination time, I ( t ) is the drive current, e is the electronic charge, Q is the optical gain coefficient, and p is the photon number in the active region. If the laser is biased below threshold, we can assume that the photon number in the cavity is approximately zero (p M 0). 1041-1 135/95$04.00 0 1995 IEEE CUTRER AND LAU: ULTRALOW POWER OPTICAL INTERCONNECT WITH ZERO-BIASED, ULTRALOW THRESHOLD LASER 5 P -11 - - -12 0.0 0.2 0.4 0.6 0.8 1.0 todto Fig. 2. Probability distributionfunction for the turn-on time of the laser for different values of q = l n ( 2 ) B ~ . SO 100 150 200 250 300 350 400 450 1, (PA) Fig. 3. Calculated BER at the receiver circuit as a function of the drive current (ITntott)he laser for different laser threshold currents. A bit rate of 1 Gb/s and a carrier lifetime of 2 ns were assumed. With this assumption, (1) can be solved for a step input current of amplitude I, at t = 0. where the approximation is valid for times small compared to T, and n; is the carrier number at t = 0. The initial carrier number in the laser n; depends on the number of “0” bits which precede the “1” bit. We see from (1) that at the end of a bit, the carrier number decays exponentially with time constant T such that: (-)iNT ni = nthexp (3) where N is the number of “ 0 bits preceding the considered bit, nth is the threshold carrier number, and T = 1/B where B is the bit rate. If the modulation current pulses follow a truly random digital pattem, the statistics of N are simply that of a geometric distribution:p ( N ) = where y = ln(2) if we take p ( N) to be a continuous distribution. Noting from Eq. (1) that I t h = n t h e / T , defining n(ton)= nth, and t o = T I t h / I m we can write: In order to quantify the requirements for drive current for satisfactory laser modulation performance, we assume that the optical pulse stream is fed into a thermal noise dominated simple photodiode receiver (5042 load) through 6 dB of optical loss (a typical number in short distance optical interconnect). We assume that the received photocurrent after equalization at the receiver has the simple form [6]. where the link efficiency ( q i n k ) includes the laser differential quantum efficiency (0.3 W/A), the link loss (6 dB), and the detector responsivity (0.5 A N ) . Standard calculations of the error rate in the presence of Gaussian noise are performed. The noise variance of the “1” bits and “0’bits are equal; however, the “1” bits are degraded by the tum-on jitter effect discussed above. Following the approach in reference [7], the bit error rate at the receiver can be expressed as: ton= to(1 - e x p ( - y ) ) . (4) Now, defining 77 = l n ( 2 ) B ~w, e can use the statistics of N to determine the distribution function of ton: ( p(ton) = -t7o7 1- - This distribution function is plotted in Fig. 2 for different values of 77. A noteworthy feature is that for 77 < 1, p(ton) is peaked around t = to, and for 77 > 1 it is peaked around t = 0. This is expected since at low bit rates the average charge in the laser is small, and hence ton M to. In comparison, at high bit rates ton M 0 since the charge does not have much decay time, and therefore remains close to the threshold value. where D is the decision level, r~ is the variance of the thermal noise, and erfc(z) is the complementary error function. For each data point the decision level (D)is numerically chosen to minimize the corresponding BER. Fig. 3 shows the calculated BER as a function of drive current to the laser (I,) for various values of I t h with a carrier lifetime of 2 ns and a bit rate of 1 Gb/s. Clearly, increasing I, improves the BER. Note that for I t h < 10 pA the power penalty is not severe; however, for I t h > 10 pA the threshold current has a large influence on the error rate. We compute the required drive current to maintain a BER of lo-’ as a function of the laser threshold current. This required drive current is used to calculate the average electrical power + consumption for the laser given by: P, = ;Im[Vo 1,201 6 IEEE PHOTONICS TECHNOLOGY LEITERS, VOL. 7, NO. 1, JANUARY 1995 power. This is expected since at high bit rates (>1 Gb/s) the carrier lifetime is long compared to the bit period, and hence has a large influence on the carrier density relaxation between bits and the corresponding time to reach threshold. It should be noted that the above results are for a specific link loss and receiver configuration. In summary, we have examined the extent to which elec- trical drive power requirements of optical transmitters can be lowered by lowering the laser threshold to the sub-100 pA level. A simple model for the BER experienced in a digital optical link employing the zero bias modulation format was used. At data rates below 1 Gb/s, there is no significant advantage to lower the laser threshold much below 100 pA, while at multigigabit rates, there is a significant advantage in 10 100 ‘Ooo reducing the laser threshold current down to the 10 pA range. Threshold Current (pA) Fig. 4. Electrical drive power required to achieve a BER = lop9 as a functionof the device threshold for different bit rates. A device tum-on voltage of 1.5 V and a series resistance of 100 0 were assumed. The solid line is for a canier lifetime of 2 ns and the dashed line is for a carrier lifetime of 4 ns. ACKNOWLEDGMENT The author wishes to thank J. Georges for his valuable discussions. where we assume VO = 1.5 V and 20 = 100 R. For drive currents in the milliampere range, the above expression is dominated by the term involving the tum-on voltage (Vo). in these low power links, the Of the laser is much more Critical than the series resistance in determining the overall power consumption. Fig. 4 shows the required electrical power as a function of threshold current for 100 Mb/s, 1 Gb/s, and 5 Gb/s. The solid and dashed curves are for carrier lifetimes of 2 ns and 4 ns, respectively. From the curves, we see that the lowest threshold which still yields a drive power advantage is approximately 100 pA for 100 Mb/s, 50 ”for Gb/s’ and lo for Gbh data rate*The desired threshold C U I ” Clearly decreases as the data rate is increased. For lar-ger data rates, the carrier density has less relaxation time between bits in more significant Panem dependent switching delays. A lower threshold device is then required to maintain satisfactory error performance for low electrical drive powers* notice that for the gigabit data rates the carrier lifetime has a significant effect on the required drive REFERENCES [ I ] T. R. Chen, L. E. Eng, B. Zhao, Y. H. Zhuang, and A. Yariv, “Strained single quantum-well InGaAs lasers with a threshold current of 0.25 mA,” Appl. Physics Lerr., vol. 63, no. 19, pp. 2621-2623, 1993. [2] T. Numai, T. Kawakami, T. Yoshikawa, M. Sugimoto, Y. Sugimoto, H. Yokoyama, K. Kasahara, and K. Asakawa, “Record low threshold current in microcavity surface-emitting laser,” Jup. J. Appl. Phys., Purr 2, vol. 32, no, pp. L1533-L1534, 1993. [3] K. Y. Lau, N. Bar-Chaim, P. L. Deny,and A. Yariv, “High-speed digital modulation of Ultralow threshold (c.1mA) GaAs single quantum well lasers without bias,” Appl. Phys. Len. ,vol. 51, no. 2, pp. 69-71, 1987. 141 T. Odagawa, K. Nakajima, K. Tanaka, H. Nobuhara, T. Inoue, N. Okazaki, and K. Wakao, “High-speed operation of strained InGaAs/InGaAsP MQW lasers under zero-bias condition,” IEEE J. Quantum Electron,, vol. 29, no. 6, pp. 1682-1686, 1993. [5] P. K. Pepeljugoski, D. M. Cutrer, and K. Y. Lau, “Parametric dependence of timing jitter in gain-switched semiconductor lasers,” Appl. Phys. Len., vol. 63, no. 26, pp. 3556-3558, 1993. [6] G. P. Agrawal and T,M. Shen, “Power penalty due to decision-time .- jitter in optical communication sv- stems..” Electron. Len.. vol. 22.. DD. 450451, ‘1986. [7] K. Schumacher and J. J. O’Reilly, “Power penalty due to jitter on optical communication systems;’ Electron. Lerr., vol. 23, no. 14, pp. 718-719, July 1987.




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