IEEE JOURNAL IEEE OF ELECTRONICS,QUANTUM VOL. QE-22, NO. 9, SEPTEMBER 1986 1887 -, Spectra, Dynamics

Y. ARAKAWA, MEMBER, IEEE, AND A. YARIV, FELLOW, IEEE

(Invited Paper)

Abstract-We discuss a number of theoretical and experimental is- ness. The (per unit energy and area) of sues in quantum well lasers with emphasis on the basic behavior of the such confined in a SQW structure is given by gain, the field spectrum, and the modulation dynamics. It is revealed that the use of quantum well structures results in improvement of these properties and brings several new concepts to optical devices. where H[x],m,, fi, and E, are the Heaviside function, the I. INTRODUCTION effective mass of electrons, Planck’s constant (h)divided by 27r, and the quantized of electrons in the HE ability to fabricate single quantum well (SQW) nth subband of the QW, respectively. When the barriers Tand multiple quantum well (MQW) deviceshas given are sufficiently high and thebarrier thickness is suffi- rise to new optical and electronic devices as well as to ciently large, E, is equal to new physical phenomena [l]. Since the first investigation of optical properties in quantum wells by Dingle et al., (nnh)’ E, = - [2] the application of quantumwell structures to semicon- 2rn,L; (2) ductor diodes [3], [4] has received considerable at- tention because of physical interest as well as its superior where L, is the thickness of the QW. characteristics, such as low threshold current density [5], If we use a MQW structure instead of the SQW, the [6], low temperature dependence of threshold current[7]- density of states is modified. When barrier layers between wells are thick enough, each well independent. In this [9], lasing wavelength tunability, and excellent dynamic is properties[lo]-[12]. By controllingthe width of the case, the densityof states is just N times density of states quantumwells, one can modify theelectron and hole of electrons in an SQW. wavefunctions, which leads to the modification of mate- m rial parameters. This results in improvements of the laser characteristics, as well as introduction of new concepts to semiconductor optical devices. where N is the number of QW’s. On the other hand,if the In this paper, we describe the basic properties of the barrier is sufficiently thin or itsbarrier height is small with emphasison its dynamicand enough so that coupling between adjacent wells is sub- spectral properties as well as gain characteristics. We also stantial, the quantized energy levels are no longer degen- discuss new deviceconcepts including a Q-switched erate, and each single well level splits into N different quantum well laser [13] and a laser [9], energy levels. In this case, the density of states -(perunit [lo]. energy and area) is expressed by mN 11. GAIN AND THRESHOLD CURRENT A. Density of States In a quantum well (QW) structure, a series of energy where (k = 1, * * , N) arethe energy levels which levels and associatedsubbands are formed due to the split from a single well energy level. Kroemer et al. [ 141 quantization of electrons in the directionof the QW thick- and Yariv et al. [15] analyticallyestimated the energy broadening due to this coupling. The coupling is impor- tant forobtaining a uniform carrierdistribution in the Manuscript received January 5, 1986; revised April 11, 1986. This work MQW structure. However, strong coupling leads to the was supported by theU.S. Air Force Office of Scientific Research, the U.S. smearing of the configuration of the density of states and Office of Naval Research, the I.T.T. Corporation, and the Japan Society a resulting reduction in the two-dimensional character of for the Promotion of Science. Y. Arakawa is with the California Institute of Technology, Pasadena, the wells. We can characterize the smearing due to cou- CA 91125, on leave from the Instituteof Industrial Science, University of pling by A E ( = max enk - min E,~). This A E corresponds Tokyo, Minato-ku, Tokyo 106, Japan. to the degreeto which the smearing in the density of states A. Yariv is with the California Institute of Technology, Pasadena, CA 91 125. occurs. Since the tunneling time 7, of electrons through a IEEE Log Number 8609366. barrier is on the order of Tz/AE, the following relations 0018-9197/86/0900-1887$01.00 0 1986 IEEE are required for obtaining good uniformity of carrier con- velocity, and Eg is the bandgap. Although the possibility centration and maintaining the two-dimensional proper- of the transition with no k-selection rule [19] and a vio- ties [14]: lation of the An = 0 selection rule have been discussed, we will adopt the formula with k-selection rule with An hlr, << AE( =h/r,) << h/rin (5) = 0 selection rule. where r, is the carrier recombination time at lasing and In QW structures, it was observed by Kobayashi et al. rinis the intraband relaxation time (i.e., T2 time). The first [27] that the internal gain depends on the polarization of inequality indicates that the tunneling time for uniform the light. Asada et al. [28] and Yamanishi et al. [29] dis- carrier distribution should be much smaller than the re- cussed this phenomenon using the k * p perturbation combination time. The second one implies that the smear- method developed by Kane [30]. For instance, IMn,jl:ve ing due to the coupling should be much smaller than the for the TE mode (polarized parallel to the layers) due to smearing due to the carrier relaxation effects. A locali- an -heavy hole transition is given by zation effect in two slightly asymmetric wells is also dis- cussed by Lang et al. [16] and Yariv et al. [15]. In order l~n,hIE= IWI:ve (1 + E/(E~~- 4,)) (8) to simplify the discussion in this paper, we assume that the coupling in an MQW is weak enough that the density where IMol:v, is the square of the dipole matrix element of states can be described by (3). of conventional (DH) lasers and is approximately equal to 1.33 moEg. For more precise dis- B. Linear Gain cussion on this matrix element, nonparabolicity and an- Thegain properties in QW lasershave been investi- isotropy of valence band should be considered, which is gated using different theoretical treatments [17]-[23]. The discussed elsewhere. The calculated results shown below main features of the gain properties in QW lasers are the are, however, on the basis of the above simple model. gain flattening effect, dependence on the number and the The quasi-Fermi energy levels eFc and eFUin a laser are thickness of the QW's and the anisotropy of the momen- determined by both the charge neutrality condition and tum matrix element.When the recombination is domi- the condition that the modal gain gmod(E)=r,(E) where nated by the band-to-band radiativeprocess [24], [25], I' is the optical confinement factor) at the photon energy the linear bulk gain derived underk-selection rule is given El for the laser oscillation is equal to the total losses atoral as follows: by [261 gmod(El) = rg(E) = Oltotal = TICY,,+ (1 - r) CY,,+ L-' In (UR) (9)

om where cyac, CY,,,R, and L are the loss in the active region, the loss in the cladding layers, the reflectivity, and the cavity length, respectively. - f"(E7JJ) W(E,E) Lie. (7) Oncethe Fermi energy levels are fixed, the injected The bulk gain is the gain exercised by an electromagnetic current density J is determined by the following equation: fieldif it were completely confined to the QW (i.e., a confinement factor of unity). E is the photon energy, j designates either light holes (1) or heavy holes (h),p,kd, is the reduced density of states which is defined by pied, = ((pen)-' + (pLn)-')-', pi, is the density of states of light holes (j = I) or heavy holes (j = h), and f, (f,) is the quasiFermi-Dirac distribution function for electrons The optical confinement factor I' depends strongly on (holes) in the conduction band (the valence band) with the the structure. If we use the separate confinement struc- Fermi-energy efC (E&). Ec,, and E;,, are equal to (m,& + ture,can be expressed approximately by the following &"E + m&,,)/{m, + mi) and (m,eJ,,- m,E + miecn)/(rn, simple formulas [ 111 : + d;),respectively, where mi and EL,, are the effective Lz mass and theenergy level of the nth subband of light holes r = 0.3~- (1 1) (j = I) or heavy holes (j= h). xZ(E,n) is the imaginary LO part of the susceptibility and gY"(E, E) is the susceptibility where N is the number of QW's, Lo is equal to 1000 A, of each electron-heavy hole pair (or electron-light hole and the following structure is assumed; the MQW laser pair) in the nth subband and is given by has Gao.7sAlo.25Asbarriers and Ga0,7sA10.2sA~waveguide layers, and the dimension of the waveguide layers is de- termined so that the total thickness, including QW's, bar- riers,and waveguide layers, is equalto 2000 A. The where nr is the refractive index of the active layer, e is cladding layersare made of p-Gao,,AlO,,As and n- the electron charge, mo is the mass electrons, c is the light Ga0,6Alo.4As.In the following calculation, we will ignore ARAKAWAAND YARIV: QUANTUM WELL LASERS 1889

-- 80 - 3 60 E m z 40 17a _I na 0 20 5

0 100 200 300 400 500 CURRENT DENSITY (A/cm2) (EF = EF-EF") t- t,, , I I (a) (b) 50 70 io0 200 5oc Fig. 1. (a) The modal gain gmod(=rg) as a function of the injected current WELL THICKNESS (A) density with various number of quantum wells N. The thickness of each quantum well is assumedto be 100 A. (b) An illustration which explains Fig. 2. The threshold current as a function of the quantum well thickness how the gain flattening effect occurs with the increase of the Fermi en- with various totalloss CY loss. The number of quantum wells is optimized ergy levels. so that the threshold current is minimum. nonradiative effects such as the Auger recombination and imum with N = 1. On the other hand, if cytotal = 20 cn-', the intervalence band effect [31]-[34]. the threshold current with N = 1 is larger than that of If thecarrier density, hence the quasi-Fermi energy N = 2. At higher values of cytOtalwhich call for larger laser level, in each QW is the same, the modal gain with N modal gain, a larger number of wells is needed. When QW's, grfIod(El),is given by cytotal is 50 cm-', a five-well structure (N = 5) will have the lowest threshold current. g:od(El ) = NgKZ '@l) (12) Fig. 2 shows the threshold current as a function of the where E! is the lasing photon energy. But, this, of course, QW thickness for various cytotal. In this .calculation, the happens at number of QW's is optimized for each QE thickness so that the threshold current is minimum. The results indi- JN = NJ(N=~) (13) cate that the threshold current of thinner QW lasers (Lz = or, stated in words, the modal gain available from N QW's 50-100 A) is much lower than that of thicker QW lasers. is N times that of an SQW and is obtained at a current We also notice that the threshold current is minimized with density which is N times that of an SQW laser. Fig. l(a) L, = 60 A when cyloss is low (aloss= 10-30 cm-'). This shows the calculated modal gain gEd(El)as a function of is mainly due to the fact that the current for transparency the injected current density in a QW laser with N QW's (gain equals to zero) is minimized atthe thickness of on the basis of (12) and (13). We notice a very marked L, = 60 in the case of N = 1 and also due to the fact flattening ("saturation") of the gain at high injected cur- that the optimum N in QW lasers with each thickness is 1 rents, especially in an SQW (N = l). This gain flattening in the case of low cytotalfor thin QW structures. effect is due to the step-like shape of the density of states functions, and the fact that once the quasi-Fermi energy C. Experiment levelspenetrate into the conduction band and valence Many experiments on GaAsIGaAlAs QW laser [5], [7], band, which happens at high injected currents, the prod- [36]-[43], hGaAsP/InP QW lasers [44]-[47], InGaAlAs uct &d(E)( fc - fu), which determines the gain, becomes QW lasers [48], and AlGaSb QW lasers [49] have been a constant and no longer increases with the current. This reported. Fuji et al. [5] reported a very low threshold cur- is illustrated in Fig. l(b). This flattening effect was evi- rent densityas low as175 A/cm2 with 480pm cavity denced recently by Arakawa et al. [35] in a systematic length in a GaAdAlGaAs GRIN-SCH SQW laser. This measurement of the threshold current of high-quality demonstrates the realization of high gain with lower spon- GRIN-SCH (graded index waveguide-separate confine- taneousemission rate owing to thestep-like density of ment heterostructure)SQW lasers of different cavity states. length. They observed the jump of the lasing wavelength sulting in a red shift of the excitonic absorption energy. with the decreaseof the cavity length from the wavelength The band discontinuities prevent the ionization of the ex- corresponding to ri = 1 transition to the wavelength cor- citon,allowing excitonic resonances to be observed at responding to n = 2 transition, which demonstrates the room temperature with large applied fields (> lo5 V/cm). existence of discrete quantized energy levels. The concept of the size effect modulation proposed by Owing to this gain flattening effect, there exits an op- Yamanishi et al. [74] ais0 utilizes the application of elec- timum number of QW's for minimizing the threshold cur- tric field. This causes the spatial of the electron distribu- rent for a given total loss cytotal. From Fig. l(a), we see tion and hole distribution in a well, which leads to the that, for low losses, the injected threshold currentis min- modulation of the matrix elements. 1890 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-22, KO. 9, SEPTEMBER 1986

row far field is a result of increased lateral coherencepro- duced by uniformly distributed and phase-locked filaments.

111. DIFFERENTIALGAIN AND MODULATIONBANDWIDTH E IOOO- - A. Relaxation Oscillation Frequency and Differential Gain

c The directmodulation of a semiconductor laser has been a subject of active research for the past 20 years [51]- 3 600- 0 [55]. Experiments have shown the existence of a reso- nance peak in the modulation response. In the early stage of thesemiconductor laser development, the principal concern was in optimizingstructures for realizing low threshold currents and high quantum efficiencies. With the increasing sophistication of the laser and the maturing of the technology, their high-speed dynamic characteristics

CURRENT [mA] became a subject of increasing importance. Many efforts have been devoted to realizing a wide bandwidth in con- Fig. 3. The light output power versus injection current under pulsed con- dition of a 100 pm wide and 480 pm broad area GaAsiAlGaAs GRIN- ventional DH semiconductor lasers by changing the laser SCH laser (400 ns, 25 Hz). geometry. Another approach is to modify the basic ma- terial properties through the useof QW structures. In this section, we discuss the possibility of the improvement of these characteristics. The relaxation oscillation corner frequency f, gives the useful direct modulation bandwidth of a semiconductor laser. The simple rate equation for laser dynamics can be described as follows:

Fig. 4. The far-field pattern parallel to the injection plane of a 100 pm wide broad area GaAsiAlGaAs GRIN-SCH laserat I = 1 .21th.The mea- sured full width at half maximum is 0.8" which is quite close to the diffraction limit of 0.4". where P is the photon density, /3 is the spontaneous emis- Recently, in MBE-grown broad area GaAdAlGaAs sion coefficient into the lasing mode, r, is the carrier life- GRIN-SCH SQW lasers, a quantum efficiency around 70 time, J(t) (cmP2)is the injected current density, n is the percent with a single far-field lobe as narrow as 0.8" has carrier concentration, and g(n, El)(cmW2) is the bulk gain, been achieved by Larsson et al. [50]. Fig. 3 shows the while I'g(n, El) is the modal gain as a function of the measured light output power versus injection current un- carrier density n at the lasing photon energy El. To em- der pulsed condition (400 ns, 25 Hz) using calibrated Si phasize the dependence of the gain on carrier concentra- photodiodes and filters. The threshold current is 110 mA, tion, we denote the gain as g(E, n) hereafter. When we which corresponds to a threshold current density of 230 discuss the carrier density in QW structures, we usually A/cm2. The maximum output power of 1.35 W from one use the two-dimensional density (per cm2). However,the mirror was limited by the available current from current proper "bookkeeping" of photons and carriers requires source. The high external quantum efficiency is a com- that n stand for carrier density per unit volume. The re- bined result of the low threshold current density and the laxation resonance frequency f, is determined by a small- high differential quantum efficiency of 84 percent. This signal analysis of (14) and (15). The result can simply be can be explained in terms of the step-like density of states expressed by [53] associated with the quasi-two-dimensional structureof the SQW,enhanced carrier and optical confinement inthe GRIN region, and optimized growth conditions. The in- ternal loss estimated by measuring the differential quan- tum efficiency of the lasers with various cavity length is where Po is the stationary photon density in the cavity and as low as 1.8 cm-'.Fig. 4 shows the far-field pattern g'(El , n) is the differential gain (i.e., g'(E, n) = dg(E, parallel to the junction plane for a 100 pm wide laser at n)ldn). This result suggests several ways to improve f, : 1 = 1.21th where &h is the threshold current. The measured larger g'(El, n), smaller rp, and larger Po. The reduction full width at half maximum (FWHM) is 0.8", to be com- of rp and the increase of Po are realized with the use of pared to the diffraction limit of 0.4". This extremely nar- short cavity lasers [53] and window-type lasers [54]. To ARAKAWAAND YARIV: QUANTUM WELL LASERS 1891

I I I I1 I L, = 50i1 fl I l------

LASER

6DH LASER

u40 60 80 100 120 FERMI ENERGY E~ (rneV) 0- 0- 50 70 100 200 500 Fig. 5. The differential gain as a function of the conduction band quasi- WELL THICKNESS (A) Fermi energy level in a conventional double heterostructure laser and a quantum well laser with 50 A well thickness. Fig. 6. The relaxation resonance frequency in a quantum well laser as a function of the well thickness. The number of quantum wells and quan- tum wires is optimized for each quantum well thickness. increase g‘(El, n), operation at low temperatures [55]and the use of coupled cavity lasers [56] have been consid- ered. than ey. Therefore, the largest g’(El, n) and the fastest modulation speeds are achieved for the cases (N The basic quantum mechanical expression for g’(E, n) MQW 2 2). Fig. 6 shows the calculated as a function of Lz (the suggests yet another way to increase g’(E, n): changing f, QW width); atotalis assumed to be 50 cm-’. At each L,, the electron density of states with the use of QW’s [lo], the number of wells is optimized andf, is normalized by [ 113. Since the gain g(E, n) is proportional to the imagi- nary part xl(E, n), as shown in (6), g’(E, n) can be ex- f, of a conventional DH laser (i.e., L, -+ 03). The results suggest that by optimizing N, can be enhanced by a pressed by the following equation: f, factor of two in thin QW lasers. 3. Experiment Theenhancement of fr was experimentally demon- It is easily seen from this equation that the density of states strated by Uomi et al. [57]. They used an MQW laser plays an important role in determining the properties of with a self-aligned structure grownby MOCVD and mea- g’(E, n) as well as g(E, n). The step-like density of states sured the relaxation oscillation observed in the transient narrows the gain spectrum compared to that in the bulk characteristics without dc bias at room temperature. fr was material, which leads to an increase of g’(E, n). measured as a function of (PIP,) where P is the output Fig. 5 showsthe calculated differential gain g’(E,, power and PC is the power for catastrophic optical dam- n(eF,)) for a conventional DH laser and a QW laser as a age. It was found thatf, of the MQW laser is about twice function of the conduction band quasi-Fermi energy level as large as that of a DH laser with the same structure. eFc (measured from the lowest subband energy level). The They estimated the modulation frequency to be 11 GHz thicknessof the QW structures is equalto 50 A. The near the catastrophic optical damage limit. This experi- quasi-Fermi energy level for the holes is determined by mental result supports the above theoretical calculations. the charge neutrality condition. The result predicts an en- Iwamura et al. [58] measured the longitudinal mode be- hancement of g‘(E, n) for the QW active layer. Note that havior in MQW lasers under modulation, and they ob- since g’(El, n) is a bulk parameter, it is independent of tained a result which suggest that the narrower gain spec- the number of QW’s. trum of an MQW laser causes fewer longitudinal modes This figure also shows that g’(E,, n) depends strongly under modulation. on eF, (i.e., necessary excitation for laser oscillation).The IV. SPECTRALNOISE PROPERTIES Fermi energy dependence of g’(El, n) implies that there is an optimum number N of QW’s in a laser structure A. Spectral Linewidth which causes the largest enhancement off, . To see this, Recently, the subject of semiconductor laser noise has consider, again, the threshold condition for lasing in (9). received considerable attention. The deviation of conven- For simplicity, we ignore. the dependence of aYtotaion the tional DH lasernoise characteristics from well-estab- structure.Since the gain is a monotonically increasing lished norms was demonstrated by Fleming et al. [59]. function of eFc, the required eFc for laser oscillation de- They found that the linewidth varies inverselywith output creases monotonically with theincrease of N. Conse- power, as predicted by the modified Schawlow-Townes quently, there exits an optimum N for realizing epcax,de- formula. The coefficient of the power dependence, how- fined to yield the maximum g’(El, n). It is easily shown ever, was significantly larger than predicted by the for- that the eFc at lasing threshold for N = 1 is much larger mula. Thisdiscrepancy was explained physically by 1892 JOURNAL IEEE OF ELECTRONICS,QUANTUM VOL. QE-22, NO. 9, SEPTEMBER 1986

QUANTUM WELLLASER

f>- -2 71 I

$1 I I, w -4 4 Jz 40 60 80 100 120 011 I I I I FERMI ENERGY cF (meV) 50 70 100 200 500 WELL THICKNESS (A) Fig. 7. The linewidth enhancement factor 01 as a function of the conduc- tion band quasi-Fermi energy level in a conventional double heterostruc- Fig. 8. The spectral linewidth in a quantum well laser as a function of the ture laser and a quantum well laser with 50 A well thickness. well thickness. The numberof quantum wells is optimized for each quan- tum well thickness. Henry [60], and a new theory was developed by Vahala et aZ. [61], [62]. They showed that the expected broaden- The denominator of (19) is proportional to g'(El, n). Therefore, from the results of the previous section, an in- ing enhancement is a factor (1 + CY') where CY is named the linewidth enhancement factor. The basic explanation crease of the denominator canbe expected with the use of is that phase fluctuations can result from index variations QW's. The numerator in (19), however, is also enhanced during relaxation oscillations after a spontaneous event, in QW structures. Therefore, it is difficult to predict the as well as by direct spontaneous emission events. For re- behavior of CY in these structures without numerical cal- ducing the linewidth, the use of an external mirror, cou- culations. Fig. 7 gives a calculation of CY as a function of pled cavity laser, and distributed feedback laser havebeen eFc for conventional DH lasers and QW lasers. In this fig- investigated. Another approach forreducing the linewidth ure, the thickness of the QW's is equal to 50 A. These is to modify the density of states. In this section, we in- calculation indicate first that CY depends strongly on eFC(or dicate how the linewidth (ora) is reduced through the use equivalently, on the levelof injection which is determined of QW structures [lo]-[12], [63]. by optical gain required for laser oscillation), its magni- The spectrallinewidth Av can be expressed by [60], tude decreasing for larger eFc. (This result has been ob- [611, ~41 served experimentally for conventional DH lasers [65].) Second, this reduction of la1 with increasing excitation is u,hvl?, R n larger in QW lasers than inconventional DH lasers. Av = rn sp (1 + CY2) TP Therefore, a smaller number of QW's leads to a smaller value of ICY( because a laser with a smaller number of QW's requires higherFermi energy levels for a given modal gain. R,, u,, hv, I?, g, nsp,and P are the mirror loss, the group The linewidth Av also contains the spontaneous emis- velocity of light, the photon energy, the optical confine- sion factor nspwhich decreases monotonically with the increase of eFCand converges to 1. This n is the ratio of ment factor, the bulk gain at threshold, the spontaneous sp emission factor, and the laser output power, respectively. the spontaneous emission rate into the lasmg mode to the xR(E, n) is the real part of the complex susceptibility and rate and is given by

(22) If the energy broadening due to the intraband relaxation (21) is extremely small, we can approximate nSpat the photon a reflects the strong amplitude-phase coupling of the energy El by lasing field in a semiconductor laser resulting from the 1 highly detuned optical gain spectrum. Equation (18) in- nsp = (23) dicates that Av depends on the electronic density of states 1 - exp ((El - E~,+ eFC)/kT)' through CY and nsp. As shown in this equation, nspis a monotonically decreas- ARAKAWAAND YARIV: QUANTUM WELL LASERS 1893 ing function of E~,.Therefore, for a fixed loss (Le., Fg is constant), it is advantageous to operate with a high eFCto attain a reduction in Av. With regard to the number of QW’s, this means that, in contrast to f, , the SQW active layer is the optimum choice for phase noise reduction. Fig. 8 gives the minimum attainable Av as a function of L, with various aloss.We notice that Av is reduced great9 for a thin active layer. Av is minimum around L, = 80 A because there is the current region in which a of L, = 80 is smaller than that of L, = 50 in the case of cyloss = 10 cm-’. Since the value Av for a DH laser (0.1 Frn active layer) is calculated to be 60 MHzImW with atOtal = 30 cm-’ , Av can be substantially reduced with a thin QW structure by a factor of & compared to Av for DH lasers. For all L,, Av increases monotonically when the number of QW’s increases.

B. Experiments Recently, Ogasawara et al. [66] measured the a param- eter ofMQW lasers experimentally. The active layer con- sisted of four 40 thick GaAs wells and four 50 A thick Al0,,Gao.,As barriers.They measured the change in (b) aXR(El, n)/anand aXr(El, n)/anseparately. aXR(El, n)/an Fig. 9. (a) Perspective view of the two-segment quantum well laser. The lengths of the amplifier section I, and the modulator section Z2 were 250 is measured from the wavelength shift of a Fabry-Perot and 50 pm, respectively. (b) The associated energy band diagram of the mode with pulsed current injection below threshold and active layer. 8xI(El,n)/an is measured from the depth of modulation in thespontaneous emission intensity. Although their The band discontinuities prevent the ionization of the ex- measurement is not a direct measurement and the mea- citon,allowing excitonic resonancesto be observed at sured a is obtained below threshold, their result supports room temperature with large appliedfields (> lo5 V/cm). our prediction. Their experimentsuggests that a of a QW The concept of the size effect modulation proposed by laser is smaller by a factor of 4 compared to that of a Yamanishi et al. [74] also utilizes the applicationof elec- conventional DH laser with the same carrier concentra- tric field. This causesthe spatial displacement of the elec- tion. tron distribution and hole distribution in a well, which leads to the modulation of the matrix elements. V. NEW OPTICALDEVICES USING QUANTUM WELLS A. New Optical Devices Using QW Structures B. Q Switching in an MQW Laser with an Internal Loss As discussed above, the QW laser is a promising light Modulation source for various applications, and considerable effort has Picosecondpulse generation technology in semicon- been devoted to developing high-quality QW lasers. In ductorlaser diodes is importantfor high-speed optical addition, other new optical devices based on QW struc- communication systems 1751-[83]. In Q-switching lasers, tures havebeen proposed and demonstrated. These in- in contrast to mode-locked lasers, no external mirror is clude optical modulators [67], [68], optical bistable de- needed [80], [81] and lower modulation power isrequired vices [69], tunable p-i-n QW [70], [71], compared to gain switching systems [82], [83]. Recently, size effect modulationlight sources 1741, Q-switching effective activeQ switching was successfully demon- laser light sources [9], andmodulation-doped detectors strated by Arakawa et al. [13] in a GaAsIAlGaAs MQW [72], [73]. The first three devices utilize thequantum- laser with an intracavity monolithic electroabsorption loss confined Stark effects [84], [85] described as follows. The modulator.The physical phenomena utilized are the room-temperature absorption spectrum of MQW displays quantum confined in the modulation section enhanced absorption at the band edge, witha double- and the enhanced carrier-induced band shrinkage effect peaked structure caused by excitons whose binding en- [86] in the section. Optical pulses as nar- ergyis enhanced by thetwo-dimensional confinement. row as 18.6 ps full width at half maximum (FWHM), as- When an electric field is applied to the QW’s perpendic- suming a Gaussian waveform, are generated. ular to the layers, the exciton absorption peak shifts to Fig. 9(a) illustrates the two-segment MQW laser con- lower energy. This effect is much larger than the Franz- sisting of an optical amplifier section and an electroab- Keldysh effect seen in bulkmaterials. The dominant sorption loss modulator section. The device structure was mechanism is the decrease in confinement energies, re- grown by molecular beam epitaxy. Theassociated energy sulting in a red shift of the excitonic absorption energy. band diagram is shown in Fig. 9(b). A 5 pm wide sepa- 1894 IEEEJOURNAL OF QUANTUMELECTRONICS, VOL. QE-22, NO. 9, SEPTEMBER 1986

QUANTUM WELL QUANTUM,WIRE QUANTUEf BOX

BARRIER

30 -40 0 40 E0 1-P(€1 I-PE --Pel DELAY TIME T (psec) QUANTUMWELL QUANTUMWIRE QUANTUM BOX Fig.10. Intensity autocorelation trace obtained from second widht 1.5 GHz modulation frequency and 0 V bias. The cur- rent injected into the optical amplifier section is 170 mA. Fig. 11. (a) Illustration of the active layer with a multiquantum well struc- ture, a multiquantum wire structure, and a multiquantum box structure, (b) Density of states of electrons in a DH structure, a multiquantumwell structure, a multiquantum wire structure, and a multiquantum box struc- ration was selectively etched in the p+-GaAs between the ture. two segments for electrical isolation. The lengths of the amplifier section Il and the modulator section Z2 were 250 and 50 pm, respectively. maximum repetition rate which still leads to regular pulse In the amplifier section, the carrier-induced band shift generation is 5.2 GHz. occurs. This effect is enhanced in MQW lasers compared VI. QUANTUMWIRE AND QUANTUMBox LASERSAND to conventional DH lasers, resulting in a decrease of the THEIR EXPERIMENTAL DEMONSTRATION lasing photon energy by about 17 meV [86] compared to the absorption edge. Therefore, with no electronic field, A. Concepts of Quantum Wire Laser and Quantum Box the absorption loss is small at the lasing photon energy, Laser which results in extremely large loss changes induced by The QW structure has proved to be very promising for the application of an electrical field with the quantum- application to semiconductor lasers, which is due mainly confined Stark effects to the modulation section. to the two-dimensional properties of the carriers [9]. Ar- Q switching was obtained by applying both a dc bias akawa et aZ. [9] proposed the concept of quantum wire voltage vb and a microwave signal to the modulator. Fig. lasers or quantum box lasers with, respectively, a one- 10 shows an intensity autocorrelation trace obtained from dimensional or/and a zero-dimensional electronic system. the second harmonic generation under thecondition of 1.5 They predicted a reduction in the temperature dependence GHz modulation frequency and vb = 0. The autocorre- of the threshold current due to the peaked structure of the lation FWHM is 26.3 ps, which corresponds to a pulse density of states. In addition, the gain characteristics [87] full width at half maximum AT^,^ of 18.6 ps if a Gaussian and the dynamic properties were also investigated [lo]. waveform is assumed. Although Petroff tried to fabricate quantum wire struc- The efficient Q switching in the two-segment MQW tures [88], no satisfactory quantum wire structure has been laser results from the following mechanisms. In the Q- fabricated for optical devices or electronic devices[89] to switching regime, a large loss change and a high differ- date. Another approach for realizing the one- or two-di- ential gain (the derivative of the gain with respect to car- mensional effects experimentally is the use of magnetic rier concentration) will lead to a narrow pulse width. In fields [9], [90]-[95]. One-dimensional electronic systems this device, a large loss changeis realized with the quan- can be formed by placing a conventional DH laser in a tum-confined Stark effect in the modulatorsection and the high . If we place a quantum well laser in band shrinkage effect in the optical amplifier section. On a high magnetic field so that the quantum well plane is the other hand, a high differential gain is also expected in perpendicular to the field, a zero-dimensional electronic the quasi-two-dimensional electronic system in an MQW system is realized. In this section, we discuss the possible structure [ 101, [ 111. Thus, by the use of an MQW struc- properties obtained in quantum wire lasers and quantum ture, the two-segment lasersatisfies both requirements for box lasers theoretically and then demonstrate these effects the generation of narrow optical pulses. in high magnetic field experiments. The modulation frequency response (i.e., repetition Fig. 1l(a) shows simple illustrations of the active layer rate) of the laser was also measured. We observed the in multiquantum well, multiquantum wire, and multi- fundamental spectrum as well as harmonic spectrum lines quantum box lasers. By making such multidimensional in the spectrum analyzer display.At the present stage, the microstructures, the freedom of the carrier motion is re- ARAKAWA AND YARIV: QUANTUM WELLLASERS 1895

?i z I,, I 23

33sLL-[L 8- 2

z i 0.. 2 -j -2 01; - a 2 I- - ;-L J

~~~~ a -z B J 0 I1 I 1 Z 50 70 100 200 500 40 60 80 100 120 QUANTUM DIMENSIONS FERMI ENERGY eF (meV) IL ,LJ (a) Fig. 12. The differential gain and a as a function of the conduction band Fig. 13. The relaxation resonance frequency and the linewidth in a quan- quasi-Fermi energy level in a quantum wire laser with 50A quantum tum wire laser as a function of the wire thickness. The number of quan- dimensions. tum wells and quantum wires is optimized at each quantum well thick- ness. duced to one or zero. The density of states of electrons in these structures is expressed as a! in a quantum wire laseris not as enhanced andis almost constant in the whole range. The second curve in Fig. 13 shows Av as a function of the thickness of the quantum wells. This indicates that a! is reduced with the decrease for the quantum wire laser (24) of the thickness. The a! parameter of quantum box lasers should be noted. If we can ignore higher subbands' effect, the density of states is a 6 function-like. Therefore, the photon energy for the quantum box laser (25) with the maximum gain coincides with the energy levels, where q, E,, and Ek are the quantized energy levels of a which leads to the disappearance of the detuning and the quantum wire laser and a quantum box laser. As shown realpart of thecomplex susceptibility becomeszero. in Fig. 1l(b), the density of states has a more peaked Consequently, a! is expected to be extremely small in a structure with the decrease of the dimensionality. This quantum box laser with a simultaneous improvement of leads to a change in thegain profile, a reduction of thresh- 5. old current density, and a reduction of the temperature dependence of the threshold current.Furthermore, im- B. Magnetic Field Experiment provements of the dynamic properties are also expected. A quasi-quantum wire effect in a semiconductor laser The narrower gain profile due to the peaked density of can be realized through the use of high magnetic fields states leads to a high differential gain. One curve in Fig. [8], [SI, in which case electrons can move freely only in 12 shows the differential gain as a function of the Fermi the direction of the magnetic field. The motion of such energy level for quantum wire lasers. A comparison of electrons is quantized in the two transverse directions (x, this figure to Fig. 5 reveals two important results. One is y), forming a series of Landau energy subbands. The den- that a higher differential gain can beobtained with the use sity of states for the system P,(E) can be expressed as of quantum wire structures. The second one is that the 312 m dependence of the differential gain on the Fermi energy 1 PC(€) = (Aw3 @) (26) level is enhanced for quantum wire lasers compared to j=o JC - (j + +) hoc quantum well lasers. A higher differential gain, therefore, is obtained in a quantum wire laser with a large number where w, and mC are the cyclotron corner frequency and of quantum wires, and the sensitivity of the differential the effective mass of electrons. When Tzu, is large enough gain to the number is more enhanced for quantum wire (i.e., the B field is large enough), only the first Landau lasers compared to the quantum well lasers. subband is occupied, resulting in a true one-dimensional One curve in Fig. 13 shows the fi as a function of the electronic system. In the actual system, the carrier relax- dimension of the quantum wires. In this calculation, it is ation effect should also be considered. assumed that the two quantum dimensions are equal and Fig. 14 shows the measured spectral linewidth at. 190 that the number of quantum wires is optimized for each K for various magnetic fields (B = 0, 11, 16, 19 tesla) as quantum dimension. This result indicates that fr is en- afunction of thereciprocal mode power 1/P 1941. A hanced by a factor of 3 with the use of thin quantum wires GaAlAs buried heterostructure lasergrown by liquid phase compared tothe conventional DH. The spectral properties epitaxy was operated in a stationary magnetic field of up of the quantum wire laser are also improved. The second to 19 tesla at 190 K. The test laser (an ORTEL Corpora- curve in Fig. 12 shows the dependence of a! on the Fermi tion experimental model) has a 0.15 pmactive region energy level. As shown in this figure, the dependence of thickness, 3 pm stripe width, and was 300 pm long. As 1896 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-22, NO. 9, SEPTEMBER 1986

h N I T=R T. 5 & 8- v T = 190K OTESLA z ,E- W E!= 20 TESLA 3 300 0 u I6- B=I I TESLA E= I6 TESL! B= 19 TESLA 200

IO0 012345 SQUARE R30T OF OUTPLT POWER no ! ARBITRAqY UNITS) INVERSE POWER (RELATIVE UNIT) Fig. 15. The measured relaxation resonance frequency asa function of the Fig. 14. The measured spectral linewidth as a function of the reciprocal square root of output power (in relative units) for magnetic fields of B = 0, 20 tesla at room temperature. of output power (in relative units) for magnetic fields of B = 0, 11, 16, and 19 tesla at 190 K. I , 1 shown in the figure, the measuredlinewidth for each mag- netic field varies linearly with the reciprocal mode power. Such a variation indicates that the linewidth results from quantum broadening (spontaneous emission). The exper- imental results indicatethat this power-dependent line- width is substantially reduced with theincrease of the magnetic field. At 19 tesla, the linewidth decreases by a factor of 0.6 compared to the linewidth without a mag- netic field.This improvement of the power-dependent linewidth is believed to be due mainly to quantum wire effects through the formation of a quasi-one-dimensional electronic system as discussed above. MAGNETIC FILED TESLA) One importantdifference between ‘‘true” quantum wire (b) structures and the quasi-quantum wires due to magnetic Fig. 16. (a)Electron motions confined by thequantum well potential as fields is that the optical confinement factor for true quan- well as Lorentzian force, being in zero-dimensional electronic states. (b) tum wire structures can be controlled by varying the num- Experimental results of the wavelength shift of the spontaneous emission ber of quantum wires. Theoretical predictions indicate that spectrum as a function of the pulsed magnetic field up to 30 tesla. a higher Fermi energy level for laser oscillation leads to lower (Y and nSp[7]. Therefore, in the true quantum wire GaAlAs quantum well laser in a high magnetic field. If a case, it should be possible to decrease nSpand a by re- magnetic field is appliedperpendicular to the quantum ducing the number of quantum wires while maintaining well plane as shown in Fig. 16(a], electrons are confined the one-dimensional electronic properties. This would al- by the quantum well potential as well as the Lorentzian low one to reap the benefits of quantum wires in terms of force, being in zero-dimensional electronic states. In this smaller a’s without paying a penalty in nsp. The overall case, the density of states is described by the following reduction of linewidth AV would then be much larger than formula: demonstrated here. frwas also measured at room temperature [93]. Fig. 15 shows the measured fr with and without a magnetic field of 20 tesla as a function of the square root of the output power Po. Open circles (B = 0) and closed circle (B = 20 tesla) indicate the measured fr . The straight lines in the figure aredrawn by theleast square error method. The evidenceof the formation of the full quantized effects Since, as shown in (16), fris proportional to fro, frshould was obtained by measuring anistropic properties of the lie on a straight line. The variation of the slope of this spectral shift with the increase of the magnetic field. If a line will mainly reflect the change in differential gain g’ magnetic field is applied parallel to the QW plane, the which has resulted from the applications of the magnetic cyclotron motion isinterrupted by the QW potentials. field. We notice thatf, with B = 20 tesla is enhanced 1.4 Therefore, as long as the magnetic field is not extremely times compared to fr with B = 0. From this change, we strong, the spectral peak shift is suppressed. On the other can estimate that g’ (B = 20 tesla) is 1.9 times larger than hand, with the perpendicular magnetic field, the spectral g’ (B = 0). peak shift occurs towards a shorter wavelength through Quantum box effects (i.e., full quantization) were also the increase of the Landau energy level. Fig. 16(b) is the investigated by Arakawa et al. [95] by placing a GaAs/ experimental results of the wavelength shift of the spon- ARAKAWA AND YARIV:QUANTUM WELL LASERS 1897 taneousemission spectrum as a function of the pulsed P. T. Landsberg. M. S. Abrahams, and M. Olsinski, “Evidence of magnetic field up to 30 tesla. The results clearly indicate no k-selection in gain spectra of quantum well AlGaAs laser diodes,” ZEEE J. Quantum Electron., vol. QE-21, pp. 24-28, 1985. the anisotropic properties, which is the evidence of the N. K. Dutta, “Calculated threshold current of GaAs quantum well formation of the zero-dimensional electron states. lasers,” J. Appl. Phys., vol. 53, pp. 7211-7214, 1982. -, “Currentinjection in multiquantumwell lasers,” ZEEE J. Quantum Electron., vol. QE-19, pp. 794-797, 1983. VII. CONCLUSIONS M. Yamada, S. Ogita, M. Yamagishi, and K. Tabata, “Anisotropy We have discussed a number of interesting theoretical and broadening of optical gain in a GaAsiAlGaAs multiquantum-well laser,” ZEEE J. Quantum Electron., vol. QE-21, pp. 640-645, 1985. and experimental results of quantum well lasers with em- M. Yamada, K. Tabata, S. Ogita, and M. Yamagishi, “Calculation phasis on the basic physical phenomena involved in the of lasing gainand threshold current in GaAsAlGaAs mutiquantum gain, the spectral fields, and the modulation response. The well lasers,” Trans. ZECEJapan, vol. E68, pp. 102-108, 1984. Y. Arakawa, H. Sakaki, M. Nishioka, J. Yoshino, and T. 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with quantum wire effects-Spectral properties of GaAlAs double het- extended his speciality to optical device research. His current research in- erostructure lasers,” Appl. Phys. Lett., vol. 48, pp. 384-386, 1986. cludes dynamic and noise properties of quantum well lasers, basic inves- 1951 Y.Arakawa, H. Sakaki, M. N. Nishioka, H. Okamoto, and N. Miura, tigation of quantum wire and quantum box lasers using high magnetic fields, “Spontaneous emission characteristics of quantum well lasers in and fabrication of new optical devices using quantum well structures. From strong magnetic fields-An approach to quantum box light source,” 1984 to 1986, he was Visiting Scientist at the California Institute of Tech- Japan. J. Appl. Phys., vol. 22, pp.L804-L806, 1985. nology, Pasadena, doing research in collaboration with Professor A. Yariv. In 1980 Dr. Arakawa was awarded the Niwa Memorial Prize. In 1981 and 1983, he was also awarded the Excellent Paper Award andthe Young Scientist Award, respectively, from Institute of Electronics and Commu- nication Engineers of Japan. He is a member of the Institute of Electronics Yasuhiko Arakawa (S’77-M’80) was born in Ai- and Communication Engineers of Japan and the Japan Society of Applied chi Prefecture, Japan, on November 26, 1952. He Physics. receivedthe B.S., M.S., and Ph.D.degrees in electrical engineering from the University of To- kyo, Tokyo, Japan, in 1975, 1977, and 1980, re- spectively. In the graduate school, he conducted research on opticalcommunication theory. In 1980,he joined the Institute of Industrial Science, Univer- sity of Tokyo, as anAssistant Professor andis Arnnon Yariv (S’56-M’59-F’70), for a photograph and biography, see p. currently an Associate Professor. After 1980, he 448 of the March 1986 issue of this JOURNAL.