Turnoff characteristics of bistable laser diodeAkihisa Tomita, Tomoji Terakado, and Akira Suzuki Citation: Journal of Applied Physics 59, 1839 (1986); doi: 10.1063/1.336409 View online: http://dx.doi.org/10.1063/1.336409 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/59/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Temperature persistent bistability and threshold switching in a single barrier heterostructure hotelectron diode J. Appl. Phys. 80, 3376 (1996); 10.1063/1.363251 Analysis of optical polarization bistability in transversemagneticwaveinjected semiconductor lasers J. Appl. Phys. 67, 2223 (1990); 10.1063/1.345535 Optoelectronic measurement of picosecond turnon delay in InGaAsP laser diodes Appl. Phys. Lett. 54, 2622 (1989); 10.1063/1.101040 Bistability in twomode semiconductor lasers via gain saturation Appl. Phys. Lett. 51, 1392 (1987); 10.1063/1.98686 Polarization bistability in semiconductor laser: Rate equation analysis Appl. Phys. Lett. 50, 1406 (1987); 10.1063/1.97835

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Turn-off characteristics of bistable ~aser diode Akihisa Tomita, Tomoji Terakado, and Akira Suzuki Opto-Electronics Research Laboratory, NEC Corporation 1-1, Miyazaki 4-chome, Miyamae-ku, Kawasaki, Kanagawa 213, Japan

(Received 2 August 1985; accepted for publication 12 November 1985)

Turn-off characteristics for tandem-electrode bistable laser diodes (bistable LD's) were analyzed both experimentally and theoretically. A long tail in the light output waveform was observed when the turn-off injection current was near the switch-down current. Rate equations were solved with adiabatic approximation and gave a good explanation indicating that the tail was due to the relatively slow recovery of the saturable absorber. The analysis also showed that the turn-off time for bistable LD's can be reduced to that for ordinary laser diodes, with sufficiently small injection current. Subnanosecond operation for bistable LD's was found possible under optimal turn-off injection current.

I. INTRODUCTION

Recently, optical bistability in semiconductors has been intensively studied because of its promised applications to optical communication and optical computing. I However, most of the optical bistable systems previously reported did not have sufficient operating speed. GaAs/ AIGaAs multiple quantum-well structures, for example, were reported2 as having a relatively slow turn-off time of 20 ns or much long­er, while they can be turned on with subnanosecond input pulses.

On the other hand, a bistable laser diode (bistable LD) is expected to have different dynamic behavior from other optical bistable systems because of its threshold characteris­tics as a laser. A bistable LD with a saturable absorber in the

METAL p-lnGaAsP

..,..-----+-------'-..... 1 p-InP

(0)

(b)

p-lnP

n-lnP p-InP p-InP InGaAsP

n-InP n-lnP

n-InP (toloc:kl p-InP p-InP InGaAsP (ac:flvel n-lnP n-InP (subsfra,.)

FIG. I. (a) Artist's view of a bistable laser diode, (b) cross section ofloss region.

laser cavity was first proposed by Lasher,3 and optical bista­bility was observed for both GaAs and InGaAsP laser di­odes.4-6 Several papers have been published on the dynamic behavior of bistable LD's; however, no investigations have been reported regarding turn-off characteristics for bistable LD's. High-speed operation of bistable LD's has not been fully discussed.

In this paper, we report the turn-off characteristics for bistable LD's. Experiments reveal that the bistable LD is turned from the on state to the off state after a delay time (turn-off time) which is critically dependent on the turn-off injection current amplitude. We discuss the turn-off charac­teristics for the bistable LO's using rate equations and pres­ent an interpretation of the experiment. Rate equations are reduced to a single equation by eliminating fast varying var­iables. The turn-off characteristics are governed by the dy­namic behavior of the saturable absorber. Analysis using rate equations shows that the turn-offtime can be reduced to the fall-off time for ordinary laser diodes.

II. EXPERIMENT

Figure 1 shows a sketch of the tandem-electrode bistable LD used in the experiments. It consists of two gain regions (1 and 2) with separated p-contact electrodes and a loss region between them. As shown in Fig. 1 (b), an n-lnP cur­rent blocking layer is overgrown on the active stripe mesa of the double channel-planar buried heterostructure (DC­PBH) in the loss region. The loss region acts as a saturable absorber and plays a main role in achieving optical bistabil­ity.

The fabrication process is almost the same as that for an ordinary DC-PBH laser diode. 7 After a double heterostruc­ture wafer is grown with the first liquid-phase-epitaxy (LPE) growth process, about a 2-,um-wide center mesa stripe is formed between a pair of channels made by chemical etching. The channels are narrowed in the loss region so that a current blocking layer can be grown on the top of the center mesa stripe in the second LPE growth process. In the loss region,p-InGaAsP contact layer is etched o1l'to isolate the two gain regions electrically. The resistance between the sep­arated contact electrodes is measured to be 100 n.

Forward currents are injected into both of the gain re­gions. Hysteresis characteristics are controlled by changing

1839 J. Appl. Phys. 59 (6), 15 March 1986 0021-8979/86/061839-04$02.40 © 1986 American Institute of Physics 1839

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10

I-::> 0..5 I-::> o l­I (9

.-l

o

8 S - L D (25°C)

II: 45mA

Idown 50 Iup 100 CURRENT 12 [m A 1

FIG. 2. Static Iigbt-current characteristics for bistable 1aser diode, with con­stant current injected into gain region I.

currents 1\ and 12 injected into gain regions 1 and 2, respec­tively. Typical1ight output is shown in Fig. 2 as a function of 12 with constant current II 45 rnA, clear hysteresis is ob­served. Switch-up current Iup is 63 rnA and switch-down current I down is 28 rnA.

Turn-off characteristics are measured under constant current 1\ = 45 rnA and pulse current 12 = Ib + I up , where Ib is dc bias current and Ip is pulse current with 67-rnA peak amplitude. Thus, turn-on injection current into gain region 2 is Ib + 67 mA and turn-off injection current is lb' Current pulse fall time is 0.3 ns. The light output signal pulse for the bistable LD is detected by aGe-avalanche photodiode and viewed with a sampling oscilloscope. Total system resolu­tion is about 0.4 ns.

Bistable LD turn-off characteristics have a strong de­pendence on Ib , as shown in Fig. 3. When Ibis smaller than 5 mA, light intensity falls adruptly in less than 1 ns. Turn-off time becomes much longer when Ib gets closer toI down = 28 mAo For example, the turn-off time is 3 ns whenIb is 20 mA, but it reaches more than 15 ns when Ib is 27.5 rnA. At that time, the light output has a curious waveform with a long tail. after falling immediately to about a third of the initial light intensity.

IU. THEORY AND DISCUSSION

Bistable LD dynamics are well d.escribed by tbe coupled rate equations.s For simplicity, we assume that the bistable LD consists of two regions, a gain region and a loss region, with carrier densities of n and m, respectively. Neglecting spontaneous emission, rate equations for n, m, and photon density N are as follows

dn n -= ---g(n - no)N +P, (1) dt 1"g

dm -= dt

m - - - a(m - mo)N,

1"a

(2)

dN = [g(n - no) + oem - mol - r]N, (3) dt

1840 J. Appl. Phys., Vol. 59, No.6, 15 March 1966

Ib= 5mA

tI, =1 6 tl2=067

FIG. 3. Observed response of the bistable laser diode to current pulses with different bias current Ib values,lb is the injection current in the olfstate. a 1

and a 2 are unsaturated gains forturn-on and tum-olf, respectively, calculat­ed with a = 0.3(/1 + 12 ) - 0.5 and normalized by switch-down unsaturat­ed gain ao.

where P is pumping rate, and where 1"g and Ta are carrier lifetimes in the gain region and the loss region, respectively, and r is the reciprocal photon lifetime. The reciprocal. pho­ton lifetime is defined by (coin,) [arc + log( 1/R )/L J, us­ing light velocity Co, refractive index nn free-carrier absorp­tion coefficient arc, cavity reflectivity R, and cavity length L. The reciprocal photon lifetime is of the order of 101O_1O" s -\ . Constants g and 0 are differential gain coefficients in the gain region and the loss region, respectively, and no and mo are constants.

Let us consider the turn-off response for a bistable LD. The pumping rate is initiaUy PI above the switch-down pumping rate Po and fallis to P2 (P2 < Po) stepwise at time t = O. The carriers in the gain region decay immediately after t = 0, owing to stimulated emission, and so do the pho­tons because of their short lifetime. On the other hand, the carriers in the loss region decay much more slowly, with their lifetime of a few nanosecond.s, because they do not ex­perience stimulated emission. Since the carrier density in the gain region and photon density vary much faster than the carrier density in the loss region, they are assumed to be in the steady state at every point of the slowly varying carrier density in the loss region. Thus, the system is described with the carrier density in the loss region, the slowest variable. Eliminatingn andN adiabatically, i.e., dN Idt = Oin Eq. (1) and dnldt = 0 in Eq. (2). the rate eq[uations are reduced to

Tomita, Terakado, and Suzuki 1840

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>-I- 1.0

(f)

Z w I-Z ~0.5

l-I t!)

...J o 0

5

10

f3 ; I , r; 0.1 To ; 3.6 ns a, <1.60.

0./00

I 0.60 2 0.80 3 0.90 4 0.95 5 0.99

15

TIME 20

(ns )

FIG. 4. Calculated tum-off response for a bistable laser diode with different unsaturated gain 2 values in the off state. fJ is the unsaturated loss in the loss region normalized by reciprocal photon lifetime, T. is the lifetime of carriers in the loss region, and r = gTIl/OT.,

dA = _1_ (1 - y)A 2 + (1 - Y - a2 + pylA + py (4) dt yTa l+A

where the variables are normalized by r as absorption loss A = a(mo - m)/r, unsaturated gain a j =g(P;Tg - no)/r with pumping rate Pi (i = 0, 1, 2), and unsaturated loss P = a molr, Parameter y is defined by y = gT g I aT a' which corresponds to the saturation parameter ratio for the loss region to the gain region. Equation (4) is easily integrated,

t + C = Ta (log [ (1 - y)A 2 2(1 - y)

+ (l-y-a2 +Py)A +Pyl

+ 2(1-y+a2 -py)

.,fI5

arctan , X 2(1- y)A + 1- y-a2 +py)

~-D (5)

where parameter D is determined by D = (1 - Y - a2 + py)2 - 4{3y (1 - y), which is negative,

when a 2 is smaller than a o = 1 - Y + py + 2~Py( 1 - y) . Integral constant C is obtained by substituting t = 0 and A = A I into Eq. (5). Initial loss value A I is obtained from the steady-state solution for Eqs. (1 )-( 3), with pumping rate PI' By solving Eq. (5) for A, photon density Nis calculated with

N=_l (~-:l), gTg 1 +A

(6)

where we use adiabatic approximation again for N in Eq. (1) and for n in Eq. (2). Since A is an increasing function of time t, photon density N decreases as time increases. However, N must remain zero, once a 21 (1 + A) - 1 < 0 is satisfied be­cause N cannot be negative [note that N = 0 is a trivial solu­tion of original rate Eqs. (0-(3)J. It is notable that light output faUs to zero immediately at time t = 0, if the turn-off pumping rate is so small that a21 (I + A 1) - 1 is negative. Critical unsaturated gain a c , defined by a c I (I + A I) - 1 = 0, decreases when initial pumping rate PI increases. This is because absorption loss in the loss region becomes more saturated. In the limiting case that P1 is infi­nite, a c becomes 0.625 ao'

1841 J. Appl. Phys., Vol. 59, No.6, 15 March 1986

""" \I)

c

~ 20

l­

LL LL o

z a: ::J I-

o

o experi ment

- theory

10

f3 = 1.0 r =0.1 To = 3.6ns

II =45mA Idown =28mA Ip =67mA

o 0

20 I down -I b (mA)

FIG. 5. Tum-off time for bistable 1aser diode as a function of I down - I •. The solid curve shows calculated values and circles are experimental mea­surement values, Variables in the figure have been defined in the text.

Figure 4 shows turn-off response for a bistable LD cal­culated with different normalized unsaturated gain. The fol­lowing parameters have been used: P = - 1.0, Y = 0.1, and Ta = 3.6 ns, so as to best fit the experiment. Initial unsaturat­ed gain a 1 and final unsaturated gain a 2 are normalized with switch-down unsaturated gain ao' The waveforms in Fig. 4 show very good agreement with the experimental results in Fig. 3. Thus, the turn-off waveforms in Fig. 3 are explained as follows. The abrupt fall at time t = 0 is due to a sudden increase in optical gain, according to the change in pumping rate from PI to P2• The long tail in t> 0 is due to slow recov­ery of the saturable absorber. The bistable LD stops lasing, when the loss becomes equal to the gain corresponding to pumping rate P2•

Quantitatively, we estimate the unsaturated gain under the experimental current conditions, using gmaJ< = 1.7 X 10-2 (loom - 1900) for l.3-,um InGaAsP laser

diode,9 where gmax is the maximum gain coefficient and 'nom

is the injection current density normalized by the active layer thickness. Unsaturated gain a is expressed by a = 0.3(/1 + 12 ) - 0.5, using active layer volume 270 ,urn X 2 ,urn X 0.2,um. Since the bistable LD used in the experiment has two gain regions which are almost the same size, we take total injection current as the sum of 11 and 12 ,

Figure 5 shows the turn-off time for a bistable LD, ca:lculat­ed as a function of I down - I b , using the expression of un­saturated gain and the current condition II = 45 rnA, Ip = 67 rnA, and I down = 28 rnA. Calculation results agree excellently with the experimentally obtained results.

IV. CONCLUSION

We have shown that the turn-off characteristics for the bistable LD is described by the fast fall down, followed by a relatively Hong tail, which is due to the slow recovery of the saturable absorber. We have also shown that turn-off time can be reduced by applying sufficiently small turn-off cur­rent. The bistable LD is shown to be operated in subnanose-

Tomita, Terakado, and Suzuki 1841

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cond time scale. Thus, the bistable LD is forseen as being a device applicable for high bit rate optical memories and log­ic.

lSee, for instance, Optical Bistability, edited by C. M. Bowden, H. M. Gibbs, and S. L. MacCall (Plenum, NY, 1984), Vol. 2.

2H. M. Gibbs, S. S. Tang, J. L. Jewell, D. A. Weinberger, K. Tai, A. C. Gossard, S. L. MacCall, A. Passner, and W. Wiegmann, Appl. Phys. Lett. 41,221 (1982).

1842 J. Appl. Phys., Vol. 59, No.6, 15 March 1986

3G. J. Lasher, Solid State Electron. 7, 707 (1964). ·C. H. Harder, K. Y. Lau, and A. Yariv, IEEE J. Quantum Electron. QE-18,1351 (1982). ~H. Kawaguchi, lEE Proc. 129, 141 (1982). 6H. Goto, K. Kobayashi, Y. Ohta, K. Nagashima, Y. Odagiri, H. Kondo, S. Suzuki, and K. Komatsu, Conference Record of IEEE Globecom (Atlanta, 1984 ), paper 26-4.

'I. Mito, M. Kitamura, K. Kobayashi, M. Seld, Y. Odagiri, H. Nishimoto, M. Yamaguchi, and K. Kobayashi, IEEE J. Lightwave Tech. LT-l, 195 (1983).

'T. L. Paoli, Appl. Phys. Lett. 34, 652 (1979). ~. E. Nahory and M. A. Pollack, Electron. Lett. 14, 727 ( 1978).

Tomita, Terakado, and Suzuki 1842

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