Electrical Properties of Multi P-N Junction Devices

IEEE TRANSACTIONSIEEE ON ED-29,ELECTRONDEVICES,VOL. NO. 6, JUNE 1982 977

[ 151 J. G. Nash and J. W. Holm-Kennedy, “Effect of electron-electron [23] P. N. Swartztrauber and R. Sweet, “Efficient fortran subprograms scattering on hot-electron repopulation in n-Si at 77”K,” Phys. forthe solution of elliptic partial differential equations,” Na- Rev. B, vol. 16, p. 2834, 1977. tionalCenter for Atmospheric Res.,Tech. NoteTN/IA-109, [ 161 J V. Faricelli, “Physics of large-signal response of short-channel 1975. MESFET’s,” M.S. thesis, Cornell Univ., Ithaca, NY, 1980. [24] R. W. Hockney,“POT4-A fast direct Poisson solverfor the [ 171K. Blotekjaer, “Transport equations for two-valleysemiconduc- rectangle allowing some mixed boundary conditions and internal tors,’’ IEEE Trans. Electron Devices, vol. ED-17, p. 38, 1970. electrodes,” IBM Res. Rep., RC-2870. [18] M. S. Shur,“Influence of non-uniformfield distribution on [25] D. L. Scharfetter and H.K. Gummel, “Large signal analysis of a frequency limits of GaAs field-effect transistors,” Electron Lett., siliconRead diodeoscillator,” IEEE Trans. ElectronDevices, vol. 12, p. 615, 1976. VO~.ED-16, p. 64, 1969. [ 191 C. Jacoboni et al., “A review of some charge transport properties [26] M. Reiser,“Large scale numerical simulation in semiconductor of silicon,” Solid-state Electron., vol. 20, p. 77, 1977. device modeling,” Computing Methods in Applied Mathematics [20] P. M. Smith, M. Inoue,and J. Frey,“Electron velocity in Si and Engineering, vol. 1, p. 17. and GaAs at very high electric fields,” J. Appl. Phys., vol. 37, p. [27] J. Ruch, “Electron dynamics in short channel field effect transis- 797, 1980. tors,” IEEE Trans. Electron Devices, vol. ED-19, p. 652, 1912. [21] T. J. Maloney, “Non-equilibrium electron transport in compound [28] R. C. Eden and B. M. Welch, “GaAs digital integrated circuits for semiconductors,” Ph.D, dissertation,Cornell Univ., Ithaca, NY, ultra-high speed LSI/VLSI,” in VLSI: Fundamentals and Applica- 1977. tions, D. F. Barbe, Ed. Berlin, Germany: Springer-Verlag, 1980. [22] S. Kratzer,“Computer simulations of electrontransport in [29] T. Wada and J. Frey, “Physicalbasis of short-channel MESFET GaAs,” M.S. thesis, Cornell Univ., Ithaca, NY, 1978. operation,”IEEE J. Solid-State Circuits, vol. SC-14, p. 398,1979.

Electrical Properties of Multi p-n Junction Devices

JOSEPH KATZ, SHLOMO MARGALIT, AND AMNON YARIV, FELLOW, IEEE

Abstract-The electrical properties of multi p-n junction devices are devices as injection lasers has also been reported, but no analy- analyzed. It is found that this type of device possesses bistable charac- sisof the electrical properties of such structures has been teristicssimilar tothat of aShockley diode and thus provides an published. alternativerealization of devices forswitching applications. The inherently greater current gains involved in the operations of such a de- This paper analyzes the electrical properties of semiconduc- viceyield in princ,iplehigher breakover voltages andhigher holding tor devices consisting of many layers of alternating p- and currents.Furthermore, the incorporation of heterostructuresin this n-type.Incorporation of heterostructures in these devices device introduces a new degree of freedom in tailoring their switching makes the design of their characteristics more flexible due to characteristics.Multi p-n heterojunction devices operatingas SCR the introduction of the additional degreeof freedom of the lasers were fabricated, and the experimental results are presented, energy band gap difference. It is foundthat such devices provide an alternative for realizing bistable switching charac- I. INTRODUCTION teristics. Compared to switching devices fabricated from sili- INCE THEIR introduction,the Shockleydiode [l] and con, GaAsdevices are lesssensitive to high temperatures Sother related deviceshave foundmany applications in because of their larger band gap and are inherently faster be- switching and regulating circuits [2] . Recently the operation cause of their shorter carrier lifetime. Since the common-base of Shockley diodes which function also as AlGaAs injection current gainof thetransistors that model thesedevices (see lasers has been demonstrated [3]. Operation of both homo- next section) is distributed among all the regions of the struc- structure [4] and heterostructure [5] multi p-n GaAs-GaAlAs ture,different switching conditions are obtained. Mainly it is foundthat it takes more gain to perform the switching, Manuscriptreceived November 16,1981; revised February 3, 1982. which results in an increase in the breakover voltages and in Thiswork was supported in part by the Jet Propulsion Laboratory, the holding currents. California Institute of Technology, under NASA Contract NAS7-100, the Office of Naval Research and the National Science Foundation. The outline of this paper is as follows: In Section 11, a quali- J. Katz is with the Jet Propulsion Laboratory, California Institute of tative analysisof multi p-n devices,based on an extended Technology, Pasadena, CA 91109. transistormodel, is carried out. The results of this analysis S. Margalit and A. Yariv are with the Department of Electrical Engi- neeringand Applied Physics, California Institute of Technology, show that such structures have bistable characteristics similar Pasadena. CA 9 1125. to those of aShockley diode. Sections I11 and IV analyze

0018-9383/82/0600-0977$00.75 0 1982 IEEE 978 IEEE TRANSACTIONS ON ELECTRON DEVICES, VQL. ED-29, NO. 6, JUNE 1982

(a) (b) (c) Fig. 1. Transistor model of a (p-n), device. (a) Schematic structure of the device. (b) Decomposition of the device into individual transistors. (c) Equivalent circuit of the device. quantitatively the device in its two stable states: the forward ing matrix equation. A is given by blocking (“OFF ”) and the forward conducting (“ON”) states, r- - 1000 000 00-100 respectively, Finally, Section V describes the fabrication pro- cedure and the experimental results of several types of such 1-1-10 000 000 00 devices, and compares the experimental results with the theo- -CY,OlO 010 000 00 retical calculations. 0-100 010 00000 11. MODIFIED TRANSISTORMODEL FOR 0 001-1-10 000 00 MULTI p-n STRUCTURES 0 OO-a2010 000 00 Consider a structure consisting of 2m layers of alternating 0 0-10101 010 00 p- and n-type, which is denoted by (p-n),. In this structure the ith junction separates the ithand the (it 1)th layer. 0 000 001-1-10 00 By a directextension of thetwo-transistor model for the 0 000 00-cu3010 00 SCR, one can analyze the structure using a more complicated 0 00-1 000-100 01 transistor network. An example of a (p-n), structure is shown in Fig. 1. Generally, it takes a 2 X (m - 1) transistor network 0 000 000 001-1-1 to describe a (p-n), structure. The 3 X 2 X (m - 1) equations 0 000 000 OO-a,Ol- needed to describe thenetwork (three equations for each transistor) are (3) and Z and Idfive are given by IBj t ICj = IEi, i= 1,2,.,2(m - 1) (la)

7-l I-- -I Ici=aiI~i+Icoi, i=1,2;..,2(m- 1) (lb) IE 1 -CIGi

ICi =IB,i-1 +IE,i-2 +IG,i-1 9 i=2,4,6;**,2(m- 1) (IC) IB1 0

IC1 IC0 1 IEi = -IB,i-lIC,i-2 2 IG,i-l > i=3,5,7;-.,2m- 3 (Id) IE2 IG 1 IB2 0

I = IC2 . Idrive = IC702 IE3 IG2 where the transistors are assumed to be initially in the cutoff 0 or active region(i.e., the deviceis in the forward blocking IB3 state), Icoi is the collector to base reverse saturation current IC3 IC03 of theith transistor, ai is the common-basecurrent gain of IE4 IG 3 the ith transistor, and IG~is the current generated at the ith 0 gate of the device. The set of equations (1) can be cast in a I84 matrix form IC4- - IC04 4 Equation (2) can be solved for la = IE~with {ai} as a set of For example, the (p-n), structure is described by the follow- parameters. The particular case where IA approaches infinity KATZ et al.: MULTI p-n JUNCTION DEVICES 979

+ P Anode + P Anode ”O 7

JI - x El a8 ff’ JZ a, / J3 P‘ 0.6 - b//’ / / /’ a 1’ I c ,p’

0.4 - ,/ I‘ n‘ ’ / 6’ -bCothode -6 Cathode // (a) (b) Fig. 3. Comparisonbetween the generic characteristics of (p-n), and (p-n)zdevices. (a) (p-n), device. (b)Corresponding (p-n)~device

I’ / (regular Shockley diode).

IIIIII 23456789 electrical characteristics, Fig.3(a) depictsthe device in the rn Fig. 2. Common base current gain (a)for switching of a (p-n), device forward blocking (“OFF”) state. The crosshatched areas versus m. (a) All the transistors are identical (ai = 01). (b) All the odd represent the depletion regions of the reverse biased junctions (or all the even) numbered transistors in the model have 01 = 0.95. (J2 and J4). The junction J, is, in principle, forward biased. Shown is a neededfrom the other transistors for switching. (c) Same as in (b), but with agiven AI of 0.99. However, since thecurrent that flows throughthe deviceis very small, there is also a very small voltage drop in the region (i.e., the determinant of A equals zero) indicates theswitching between Jz and J4. Since a region with virtually no current condition.Inspection of thematrix A in (2) shows the and voltage has a little effect on the device, to the external following: world the device appears basically as if‘it had thestructure 1) (p-n)m structures, with m 2 2, cannot possess more than depicted in Fig. 3(b), which is a device. Inthe forward twostable states. This is deducedfrom thefact that for a conducting (“ON”) state, all the internal regions in the (p-n), given structure, only one set of {acui},at most, yields 1, +. 00. device are in saturation, which is the same situation as in the 2) The conditionfor switching changes, depending on the (p-n)z device. Of course, the quantitative analysis is different structure parameters. Some of the results are shown in Fig. 2. for the twocases, as will be seen in sections which follow. In Fig. 2(a) all the transistors are equal; in Fig. 2(b) all the odd 111. SOLUTION OF DIFFUSIONEQUATION IN THE (or all the even) numbered transistors in the model have (Y = FORWARDBLOCKING (“OFF”) STATE 0.95, and Fig. 2(c) is the same as Fig, 2(b) but with a given a = 0.99. In Fig. 2(b) and 2(c) shown in the a needed from In this section the (p-n), structure in the forward blocking theother transistors for switching. It isclearly seen that as state is analyzed.In this section and in thenext one, the m increases, the device must have more gain in order to possess indexes on the various parameters refer to either the junctions two stable states. Structures with insufficient gain remain in (e.g., voltages, depletion region recombinationcurrents) or the forward blocking state, and when the applied voltageis to the layers between thejunctions (e.g., diffusion lengths, increased they eventually undergoeither avalanche or zener widthsof the layers). Theminority-carrier distribution in breakdown. One simple explicit expression is obtained for the the forward blocking (“OFF”) state is shown in Fig. 4. All the case where all thetransistors have the same gain, i.e., a1 = even numbered junctions arereverse biased so thattheir minority-carrierconcentrations are effectively zero.The az = , * . , a. Inthis case switching occurs in a (p-n), structure when equationfor the current density through the reversebiased junctions is &=I--1 m J=JZz‘ =MZi[JG,Zcui+Jp,Zi+l(W) -t Jn,Zi(o)l 3 i= 1,2;..,(m- 1). (5) For m = 2 we get the well known result for the SCR (a1 = a2 = 0.5). Mzi is the avalanche multiplication in the depletion region As a final remark, it is interesting to note that the above of the 2ith junction, which, for GaAs, is the same for both analysiscan be also carried outfor multi p-n structures in electrons and holes and can be approximated by thefollowing which the first layer and the last layer are of the same type empirical formula [6, p. 3311 : (e.g., a p-n-p-n-p structure). In this case it is found that the device behavior does not show bistability, and thus itis similar to that of a transistor. It seems that all generic types of one port low frequency low field semiconductor devices are de- where VBD,~~is the breakdown voltage of the 2ith p-n junc- scribed by one of the following structures: p (or n), p-n, p-n-p tion and c is an empirical constant, JG,~~is the current density (or n-p-n) and p-n-p-n. generated in the depletion regionof the 2ith junction (e.g., Fig. 3 helps to explain this fact. In particular, it describes thermal or light generation) which can-to the first order- why both (p-n), and (p-n);,devices have the samebasic be approximated as a constant. Jp,2i+l(W) is the holedif- 980 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-29, NO. 6, JUNE 1982

fusion current density entering the junction from the left and where JRO and NE are empirical constants. In the following is given by calculations it will be assumed that NE = 2, which is a good approximation forpractical devices [6, p. 102-1041. Since thecurrent is the same throughoutthe device, the current densities through the even and odd numberedjunc- tions can be equated, so the current densityis given by where A = qJkT and Vi is the voltage across the ith junction

and Jn,zi(0), theelectron diffusion currentdensity entering the junction from the right,is given by

AV2it1 - where J=J;zitl(e 1, ’Js,zi+l tJRO,ziti emitl/~3 i=O, 1,2;.. ,(m- 1) (13)

where Jp,2i+l (0) is the hole diffusion current density entering the junction from the right, J,,zi+2(W) is the electron diffusion current density entering the junction from the left, Jsp npo, W,, D,, L, and pno, W,, D,, L, are theequilibrium and Jsn are as defined before in (8) and (10) concentration of the minority carriers, the width, the diffusion coefficient and the diffusion length of the minority carriers in the appropriatep and n regions, respectively. The advantage of using heterostructuresin the multi p-n devices can be understood from (8) and (10). Since thein- trinsic carrier concentration ni in a material is proportional to exp (- Eg12kT) where Eg is a band gap, and since, for a (1 5) given doping level, theminority-carrier concentration (i.e., and J~o,~i+~is the recombination currefit constantof the npo or pno) is proportional to n;, the diffusion currents and (2i t 1)th junction. hence the current gains a of thetransistors that model the Note that for i = 0, Jp(0) = 0, and for i = m - 1, Jn(Wp) = 0, device can be modifiedindependently of the doping levels. since it can be assumed that the diffusion currents in the two Thus it is possible to achieve low a transistors in devices with extreme layers are negligible,e.g., these layers are AlGaAs thinlayers, i.e., to increase the breakover voltage without layers with high Al contents, and thus their values of npo and sacrificing its temporal response. pno are much lower than those of GaAs, because of the differ- The odd numbered junctions are slightly forward biased, so ences in theband gap energies. theeffect of thedepletion region recombinationcurrents Using (5) to (13), a closed form expression for theJ-V curve must be included. These currents can be approximated by of the device can be obtained in the following way.For a [6, pp. 102-1041 given value of J, (1 3) is a quadratic in KATZ et al.: MULTI p-n JUNCTION DEVICES 981

-x

Fig. 5. Minority-carrier distribution across a (p-n), device in the forward conducting (“ON”) state.

Once a solution is obtained for all the odd numbered junc- resulting diffusionequations of theentire structure canbe tions, (6) can be solved for written in the form Vi, i=2,4, - - ,(m - 2) Bu+Ew=J (1 6) using (5) and (7) to (10). The sumof all of thejunction where voltages thus obtained is the total voltage Vacross the device, corresponding to the assumed value of J. The particular form of the resulting expressions is quitecomplicated, but the calculations are straightforward, as described above. The im- portant parameter J-V curve in the “OFF” state is the breakover voltage (VBo),which is defined in the same way as for the Shockley diode. At this point dV/d = 0. As the current is further increased, the voltageacross the device decreases. This is a negative resistance [dV/dJ< 01 regionand thus unstable, leading to the “ON” state. In this new situation the assumption aboutthe junction voltages are no longer valid, and new calculations needto be done. Thebreakover voltage of the(p-n), deviceis the sameas ,Avzrn -112 -1‘I the voltage across (m- 1) Shockley diodes operating in series. This is because thestructure consists of distinctsections, and each isolated between two reverse biased junctions at which 1 the carrier concentration is virtually zero (see Fig. 4). Thus is seen that by increasing m devices can be found with higher -1 breakover voltages. J= . .

1 IV. SOLUTIONOF THE DIFFUSIONEQUATION IN THE FORWARDCONDUCTING (“ON”) STATE The matrix E, given by In the forward conducting state all the junctions are forward biased J&l -Jsn2

I Vil >> kT/q, i = 1,2, * - * , (2m - 1) i.e., all thetransistors that model the device are insaturation. B = This is similar to the behavior of the common Shockley diode inthe “ON” state.The distribution of theminority-carrier concentration in thisstate is shown in Fig. 5. (Notethe change of sign in the notation for theeven numbered junction voltages; now all thejunctions are forward biased). The 982 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-29, NO. 6, JUNE 1982

TABLE I PARAMETERSOF A (p-n)7 STRUCTURE

1 n 0.4 0.1 1.5 2 P 0.0 3 0.2 3 n 0.1 0.1 0.8 4 P 0.0 3 0.2 5 n 0.1 0.1 0.8 6 P 0.0 3 0.2 7 n 0. I 0.1 0.8 8 P 0.0 3 0.2 9 n 0.1 0.1 0.8 10 P 0.0 3 0.2 11 n 0.1 0.1 0.8 12 P 0.0 3 0.2 13 n 0.1 0.1 0.8 14 P 0.4 1 1.5 15 P+ 0.0 - 10 1.0 0.4 I-0 i n TABLE I1 PARAMETERSOF A (p-n)s STRUCTURE .Is

A1 Layer Doping Width 23456T89101lI213 Number Type Contents Concentration Layer Number (X) x 1018 Lcrn-31 [uml (b) 1 n 0.4 0.1 1.5 Fig. “ON” state characteristics of the (p-n), device describedin 2 P 0.0 3 0.25 6. 3 n 0.1 0.1 0.5 Table I. (a) Excess minority carriers. (b) Recombination current 4 P 0.1 0.1 0.5 distribution in the various regions. 5 n 0.0 3 0.25 6 P 0.1 0.1 1.0 7 n 0.0 3 0.25 8 P 0.1 0.1 1.0 9 n 0.0 3 0.25 ‘E 10 P 0.4 1 1.5 3 2.4~10‘~ 11 P+ 0.0 = 10 1.0 z P containsthe diffusion contribution to thetotal current and

JROl 0 0

0 JR02 0 c= . JR03 0 (2 1) ...... 0 ‘JRO,2rn -1 contains the depletion region recombination contribution to to total current. Jsp,i, Jsn, i, J2i and J~oiare given in (8), (lo), (1 5) and (1 l), respectively. Also

J$, i = Jsp, i CO~( wn,JLp, i) and 89

Jzn, i = Jsn, cash (wp,i/Ln, i>. i (b) II The derivation of (16) to (21) is based on solving the diffu- Fig. 7. “ON” state characteristics of the (p-n)s device describedin sionequation in each region separatelyand arranging the Table 11. (a) Excess minority carriers. (b) Recombination current individual solutions with the appropriate indexing. distribution in the various regions. Several calculated results for the devices described in Tables I and I1 are shown in Figs. 6 and 7, respectively. Part (a) of across the device. As will be discussed in Section V, it is some- these figures showsthe distribution of the excess minority timesdesirable to have as uniform distribution in the GaAs carriers across the devices. The distribution across the (p-n)5 regions when possible. When designing a structure for a par- device is much more balanced than in the (p-n), device. This ticular carrier profile, the parameters at our disposal are the fact is alsoclearly demonstrated in part(b) of thefigures, number of the layers, their types and widths, and the doping whichshows thedistribution of the recombination current concentration. All these parameters appear in the solution of KATZ et al.: MULTI p-n JUNCTION DEVICES 983

m Fig. 8. Calculated dependence of the holding current density (JH) on the number of layers in the device. (a) W, = Wp= 0.5 pm. (b) W, = W, = 1 pm. the diffusion equation, and thus can affect the performance of the device. Theholding current of the device (i.e.,the minimum forward currentwhich is required to sustainthe “ON” state) can be estimated in the following way. We know that if the current is reduced below the holding value, the device exhibits negative resistanceand is unstable.This leads to the “OFF” state described in the preceding section, so the value of J for Fig. 9. Dependence of the I-V curve of (p-n), devices on the A1 con. tents (x) in the waveguide layers. (a) x = 0.1. (b) x = 0.2. (c) x = 0.4 which dV/dJ = 0 is theholding current density (JH). This (no bistability). parametercan be foundby solving (16) numerically. Cal- culated dependence of JH on several parameters is shown in Fig. 8. In Fig. 8(a) the width of all the layers is 0.5 pm, and tualgrowth wafer. The dopants used were Ge (p-type), Sn in Fig. 8(b) the width of all the layers is 1 pm. The device (n-type, forregionswithNo 5 1 X 10l8 ~m-~)and Te (n-type, consists of (m - 1) p-n sections of GaAs sandwiched between for regions withND 2 1 X 10” ~m-~). two layersof high Al contents AlGaAs. As expected,the Devices testedonly for electrical parameters were etched holding current density increases with increasing the number down to a 100 X 100 pm2 mesas, while devices which oper- of the p-n sections of the device, with increasing the widths ated also as injection lasers were etched down to a 100 pm of the layers and with increasing the doping levels. The basic mesa in one direction and cleaved to m300 pm length in the cause forthis increase is theneed to replenishrecombined perpendicular direction. carriers in more and more regions while still maintaining all Cr-Au was used on the p-type contact and AuGe/Au (with thelayers in saturation. Because of the basic exponential a post-deposition alloying at 360°C) was used for the n-type dependence between the current and the voltage in p-n devices, contact. the increase in the holding current with increasing the number The first typesof devices tested were (p-n),structures of sections in the device is larger than the corresponding in- whose order and type of layers, dimensions and doping (but crease in the breakover voltages. not the Al contents (x)) are described in Table I. In particular, It should be notedthat the above analysis can be easily the dependence of the I-V curve of the structure on the Al extended to any arbitrary structure, not necessarily one which contents (x) in thelayers between the GaAs regions were consists of alternating p and y1 regions (e.g., p-p-n-n . . . ). investigated. Curves of devices with x = 0.1, 0.2, and 0.4 are shown in Fig. 9. When the Al contents is too high, the current V. FABRICATION PROCEDUREAND EXPERIMENTAL gain of the p-n-p transistors in the device model (these are the RESULTS transistorswhich have the n-AlGaAs layers as their base regions) becomes too small to maintain the device in the “ON” Thelayered structures ofAlGaAs describedin this paper state. For x = 0.4 even reductionin the number of layers, were grown by liquid phase epitaxy at 800°C. Parameters of e.g., (p-nk is not enough. In this case the obtained I-Vcurve two typical device structures (e.g., layerstypes, widths, is that ofa transistor in avalanche. The calculatedcarriers doping) are described in Tables I and 11. Since the number of distribution in the device is shown in Fig. 6(a) for x = 0.1. solutionchambers in the graphite boat is smaller thanthe The carrier concentration is found to be highest in the upper required number of layers in the structure, the periodic parts GaAs region,with fewer carriersin the subsequent regions. of the structure were grown by moving the slide-bar of the Thisresult was qualitatively verified inthe following way. boat in both directionsbetween the solutions. In that case, Instead of etching the devices into the 100 X 100 pmZ mesas, two “dummy” wafers were used, one on each side of the ac- they were etchedonly in onedirection and cleaved inthe 9 84 IEEE TRANSACTIONSELECTRON ON DEVICES, VOL. ED-29, NO. 6,1982 JUNE

ofrecombination currents in thedifferent active regions is uniform to within 10 percent. The breakover voltage (V&) of the device is 9 V. Devices with breakover voltages of more than35 V were also observed. The valueof VBO in each particular device also depends on the amount of leaking due to imperfections.The holding current density (JH) is about 1.5 A cm-2, Lasers made of the (p-n)S devices had threshold current density of about 13 kA cm-2, which is comparable to conventional large optical cavity lasers of thesame dimensions. More details on the optical characteristics of multi p-n structures can be found in [5] [7].

VI. CONCLUSIONS The electrical properties of multi p-n junction devices (both homostructures and heterostructures) were analyzed. By using a modified transistor model it was found that devices of this type possess bistablecharacteristics similar tothat of a Shockleydiode, and thus they are potentiallysuitable for switchingapplications. Among theseapplications are semiconductor controlled rectifiers with higher breakover voltages and potentially shorter switching times, semiconductor laser Fig. 10. I-V curve of a device (horizontal scale: 1 V/div;vertical devices which also have intrinsicelectrical switching capa- scale: 0.1 mA/div). bilities,and large opticalcavity lasers with multiple active regions. Quantitative analysis indicated thatthe inherently otherdimension (with lengths about 300 pm)thus forming greatercurrent gains involved inthe operation of such a the commonFabri-Perot cavity of semiconductorinjection device yield higher breakover voltages and higher holding lasers. Below the lasing thresholdcurrent of the device, the currents.Experimental results verified the basic generic distribution of the amount of light emitted from each GaAs characteristicsand showed a good fit with the calculated (“active”) region via the spontaneous emission, which is pro- performance. portional to the carrier concentration in it, was observed to be in agreementwith Fig. 6(b). As thecurrent was furtherin- REFERENCES creased, it was found that at, or slightly above the threshold [ 11 J. L. Moll etal., “p-n-p-n transistor switches,” Proc. IRE, vol. (Jth 5.5 kA - cm-2) onlythe upper active region is lasing, 44, pp. 1174-1182,1956. while all theother active regions emitted only spontaneous [2] F. E. Gentry etal., Semiconductor Controlled Rectifiers. Engle- wood Cliffs, NJ: PrenticeHall, 1964. emission.Only when the current was raised to about 1.4 X [3] C. P. Lee etal., “Barrier-controlled low-thresholdp-n-p-n GaAs Ith did the next active region lase. ’ heterostructure laser,” Appl.Phys. Lett., vol. 30,pp. 535-538, 1977. Devices of asecond type were grownwith the goal of [4] W. F. Kosonoclcy, R. H. Comely,and I. J. Hegyi, “Multilayer equalizingthe carrier distribution in all the GaAs layersof GaAs injection laser,” IEEE J. QuantumElectron., vol. QE-4, the device so that the light emitted will be more evenly dis- pp. 175-179,1968. [5] J. Katz et al., “Large optical cavityAlGaAs lasers with multiple tributed, Theparameters resultingtheof structure active regions,”J. Appl. Phys., vol. 51, pp. 4038-4041, 1980. are described in Table 11, and its typical I-V curve is shown [6] S. M. Sze, Physics of SemiconductorDevices. New York: Wiley- in Fig. 10. Thecalculated results on this structure are given Interscience, 1969, pp. 102-104, 331. [7] P. Yeh, A Yariv, and C. S. Hong, “Electromagneticpropagation in Fig.- 6. From Fig.- 6(b).. it is seen that most of the carriers in periodic stratified media. I. Generaltheory,” J. Opt.Soc. (42 percent) recombine in the active regions, and the level Am&., vol. 67, pp. 428-438, 1977.