Optimal cavity design for lowthresholdcurrentdensity

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2 2 radiation is likely to overlap the broadband emission. At present, there is no ... Optimal cavity design for low-threshold-current-density operation of double-.
Optimal cavity design for lowthresholdcurrentdensity operation of double heterojunction diode lasers Dan Botez Citation: Appl. Phys. Lett. 35, 57 (1979); doi: 10.1063/1.90908 View online: http://dx.doi.org/10.1063/1.90908 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v35/i1 Published by the AIP Publishing LLC.

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shifted to the red ofthe nl L I2. emission, the RR 'X excimer 2 2 radiation is likely to overlap the broadband emission. At present, there is no direct evidence for such radiation, but it should be noted that the theoretically predicted In L n2. 2

2

emission was never determined experimentally either. Triatomic excimer radiation introduces a further uncertainty to all rate constants deduced from high-pressure experiments. Very recently, the broadband emission in XeF has been lased in two very different experiments. In the first, the presence of electrons which could mix the In2. and n2. states was 2 2 avoided by photolyzing XeF2 9; but a second experiment also obtained lasing using discharge pumping. 10 Since the gain cross section on the 1112.-n2. transition is about 0.33 of that in 2 2 the presumed n L I2. broadband transition, it is possible to 2 2 extract energy on both transitions for a sufficiently high

fluence. The same comment also applied to XeCI, should the broadband ever be lased. For XeCI, the peak gain cross section for the III L n2. and n L I2. transitions are nearly the 2 2 2 2 same.

IP.J. Hay and T.H. Dunning, Jr., J. Chern. Phys. 66,1306 (1977). 'P.J. Hay and T.H. Dunning, Jr., J. Chern. Phys. 69, 2209 (1978). 3D. Kligler, H.H. Nakano, D.L. Huestis, N.K. Eishel, R.M. Hill, and C.K. Rhodes, Appl. Phys. Lett. 33, 39 (1978). 'H.C. Brashears and D.W. Setser, Appl. Phys. Lett. 33, 821 (1978). 'H.J. Kolts and D.W. Setser, J. Phys. Chern. 82,1766 (1978). 'D.W. Setser, Third Quarterly Progress Report, DOE, 1978. 'J.G. Eden and S.K. Searles, Appl. Phys. Lett. 30,287 (1977). SM. Rokni, J.A. Mangano, J.H. Jacob, and J.e. Hsia, IEEE J. Quantum Electron. QE-14, 464 (1978). • 'W.K. Bischel, H.H. Nakano, DJ. Eckstrom, R.M. Hill, and D.L. Huestis, and D.C. Lorentz (unpublished). lOR. Burnham (unpublished).

Optimal cavity design for low-threshold-current-density operation of doubleheterojunction diode lasers Dan Botez RCA Laboratories, Prince/on, New Jersey 08540

(Received 16 March 1979; accepted for publication 26 April 1979) A simple and accurate closed-form expression for the threshold-current density J th in the symmetric DH structure is presented. The novel expression allows analytical solutions for do, the active-layer thickness corresponding to minimum threshold-current density. Optimization of the cavity thickness for minimum J th is presented for wide variations in cavity length (100-500 J.lm and facet reflectivity values. The analytical formulas are applied to the AIGaAs/GaAs system and extended to the InGaAsP/lnP system. By using previously published experimental results, a linear gain-current relationship is estimated for InGaAsP (X = 1.2; 1.3 J.lm); and thus it is found that do should vary between 0.12 and 0.20J.lm as the cavity parameters (length and facet reflectivity) change; and that minimum,Jth values should be comparable to the ones for AIGaAs lasers. PACS numbers: 42.55.Px, 73.40.Lq Double-heterojunction lasers have been analyzed by many workers. 1-4 Since it is often desirable to use low-current lasers, it is helpful to optimize the laser cavity for the minimum threshold-current density J th • For this purpose, one usually plots J th -vs-cavity-thickness 5 d curves, which necessitate tedious numerical calculations. We present here an accurate analytical approximation for the threshold-current density of broad-area devices, which in tum allows, for the first time, the derivation of a relationship linking the lasing cavity parameters (i.e., internal and external losses, thickness, wavelength, and transverse dielectric step) at the minimum J th value. The optimization formulas are directly applied to the GaAs-AIGaAs system, and a preliminary extension to InP-InGaAsP lasers also is presented. The optimizations cover the range of practical device lengths (100500 J.lm) and device facet reflectivity values, in contrast to previous calculations, which were limited to long devices with uncoated facets. 5-7 All formulas are derived for symmetric DH structures operating in the TEo mode. The threshold-current density for broad-area devices is 57

Appl. Phys. Lett. 35(1). 1 July 1979

commonly expressed as 1,2

= (/3'TJ) - I [aod + (d Ir)Gth ] , with Gth = a + (1/L) In(1/R).

J th

j

(la)

Here, 'TJ is the laser internal efficiency at threshold, r is the radiation confinement factor, 1.2,8 G th is the mode gain at threshold, a j is the internal cavity loss, 1,2 L is the cavity length, R = (R 1R 2) 112 is the geometrical mean of the facet reflectivities, and f3 and a o are material- and temperaturedependent parameters expressing a linear dependence between the (unsaturated) gain g and the current density J9: g = f3(TfJ Id) - ao'

(lb)

Expression (1a) is obtained from Eq. (lb) by applying the lasing condition: Gth = rgth · (2) Current leakage, interfacial recombination, and radiation scattering losses are neglected in the above formulas. Expression (1 a) has proved useful in describing the operation of various semicond uctor lasers. 1,2,4 However, since r is not an

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@ 1979 American Institute of Physics

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explicit function of the cavity parameters, one must determine J th from point-by-point numerical calculations. Recently, we have shown 10 that r can be approximated very accurately (maximum error: - 1.5%) by using a simple formula:

+ D 2)

r~D 2/(2

with

1500.------------------, GoAs - I A1GoiAs

),"09~m,n,"359

.A!c 014

0.2

D = 21r(d I A, )(n~ _ n~) 112. 0.4

(3) Here, A, is th vacuum wavelength, n I and n 2 are the bulk refractive indices of the active layer and cladding layers, respectively, and D is the normalized waveguide thickness. II By using the approximation formula (3) for r in Eq. (la), one obtains J th ~

-

1 (

7]/3

d (a o + Gth )

+ -1

A, 2Gth

) 2

d 2~(ni - n 2 )

.

(4)

Here, for the first time, an analytical expression for J th is presented simply as the sum of two asymptotic limits: a term that is linear in d, which dominates for large cavity thicknesses, and a lid term which dominates for small cavity thicknesses. The sum of these two terms accounts directly for the existence of a minimum threshold-current density, as commonly observed. 1-6 We should add that the expression for the low-thickness asymptote is a direct result of the fact that the optical confinement factor r is a strong function of A, and.:in = n l - n2 as d-->-O. 10 From Eq. (4) one can easily solve for the cavity thickness corresponding to the minimum J th value: A, (2Gth )112 do = 21r(n~ - n~) 1/2 Gth + a o

Do = (

or

2Gth )112, Gth + a o

(5)

where Do is the normalized guide thickness for minimum J th . The minimum value of the threshold-current density is then: (6)

r ':::

Go As - (AIGaIAs

10 pm in planar DH structures). We note that J lh does not vary by more than 10% over a thickness region as wide as do. A dashed curve is plotted for 1.5do as an arbitrary upper limit of a minimum J lh region. To determine a lower limit is not easy since, as d decreases, carrier leakage across the heteroboundaries (especially in the Lin = 0.14 case), 1-3 interfacial recombination, and scattering due to active-layer-thickness variations 15 can drastically increase J lh • Figure 2 displays optimization curves which, to the best of our knowledge, have not been previously considered. Here, by using Eq. (8), we plot the variation of do for several values of Lin as the threshold mode gain Gth takes values between 30 and 130 cm - 1. It is seen that in going from long to short devices (i.e., small to large values of Gth ) the value of d almost doubles. Also shown in Fig. 2 are values of do o ' 1ca 1cu 1atlOns ' 4-6 obtained by other workers from numenca and experiment. 4--6 The agreement to our curves is good, the slight discrepancies being due mainly to those workers' use of a 180-cm - I value for a o (from early calculations by Stern). 16 Devices with large Gth values (i.e., short length and/or antireftective coatings) trade low-threshold-currentdensity values for high external quantum efficiencies and

>~3 V>

z

OJ

o

,... z

OJ

N""'~

~B2

:;'0

~--'

-0 ~r -V>

-'",

""0:r ,...

L

~- ----------

,...> u

'""'" "-

-- --

8n.0.27 (),=1.3}'m)

",I

_-

do

ACTIVE LAYER THICKNESS. d (A)

FIG. 3. Effective threshold-current density versus active-layer thickness for AIGaAs lasers (A. = 0.85 /lm and..::ln = 0.2; 0.3) and InGaAsP lasers [A. = 1.3 /lm and..::ln = 0.27 (Ref. 20)]. All curves are plotted for a threshold mode gain value of SO cm - 1. For InGaAsP we use the gain-current relationship: g (cm - 1) = 4O(1]J /d)-35 (see text for derivation). 59

short photon lifetimes. The latter are especially important for high-frequency (GHz) applications. All formulas are plotted for...l. = 0.9 pm (GaAs active layer), but one can extend their use to the more practical region...l. = 0.80-0.85 pm, (see Fig. 3 for...l. = 0.85 pm) since the gain-current relationship (lb) is not expected to change in any significant way. An interesting application of the J th formula (4) is to InGaAsP/lnP DH lasers. The only uncertainty is in the use of a gain-current relationship. However, there is experimental evidence that a linear gain-current relation can be used for InGaAsP. 17-19 Some indication of the values for {3 and ao can be obtained by applying Eq. (4) to the experimental data by Nahory and Pollack 17 (...l. = 1.25 pm). We obtain a good fit for: J lh = 4.75d + 0.15/d, which implies, via Eq. (4), that Glh /1/{3 = 3 kA/cm 2 and aol1/{3 = 1.75 kA/cm 2. (Experimentally determined step index values 20 Lin were used.) The authors 17 report relatively low external quantum efficiencies and values of Jth / d (at large d) higher than the ones obtained by Yamamoto et al. 21 for similar structures. Their data thus point to low internal efficiencies and high internal losses. Assuming 1/ ~ 50% and a i a; 30 cm - 1 we estimate{3~40 cmpmlkA and a o ::::;35 cm - I. A{3 value (at 1.25 pm) comparable to the GaAs one is in agreement with other workers' experimental results. 19 With the above estimated values for {3 and ao and experimentally determined step index values for InGaAsP / InP in the 1.2-1 ,35-pm region, 20 we find that do should vary between 0.12 and 0.2 pm as Gth takes values between 20 and 130 cm - 1. For comparison, we plot in Fig. 3 1/Jlh -vs-d curves for AIGaAs (...l. = 0.85 pm and Lin = 0.2;0.3) and InGaAsP (...l. = 1.3 pm and Lin = 0.27 2~, for the same Glh value: 50 cm - I. Mainly as a result of quite different a o 's, the two systems differ in the values for do [i.e., 0.075 pm for AIGaAs versus 0.16 pm for InGaAsP, from Eq. (5)] and in the slopes of the 1/Jth curves at large values of d [see Eq. (4)]. By contrast, the threshold-current-density minima should be comparable for the two systems [see Eq. (6)], which is . mdeed t h e case accord'mg to recent resuIts. 22-24 In conclusion, we present in this letter simple explicit expressions for the threshold-current-density of broad-area diode lasers and the conditions for 10W-Jlh diode operation when the cavity parameters vary over wide ranges. The formulas are applied to the AIGaAs DH system and extended to the InGaAsP/lnP DH system, and the significance of the results is discussed. These analytical approximations should prove useful in device design and allow a better physical understanding of device behavior. The author acknowledges helpful discussion with H. Kressel, G.H. Olsen, and c.J. Nuese.

Appl. Phys. Lett .• Vol. 35, No.1, 1 July 1979

IH. Kresse! and J.K. Butler, Semiconductor Lasers and Heterojunction LED's (Academic, New York, 1977). 'H.C. Casey, Jr. and M.B. Panish, Heterostructure Lasers (Academic, New York, 1978). IG.H.B. Thompson, G.D. Henshall, J.E.A. Whiteaway, and P.A. Kirkby, J. Appl. Phys. 47, 1501 (1976). 'N. Chinone, H. Nakashima, I. Ikushima, and R. Ito, Appl. Opt. 17, 3!1 (1978). 'H. Kresse! and M. Ettenberg, J. Appl. Phys.47, 3533 (1976). Dan Botez

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'R,D. Dupuis and P.O. Dapkus, Appl. Phys. Lett. 32,473 (1978). 'RC. Casey, Jr., J. Appl. Phys. 49, 3684 (1978). 'F. Stern, Radiative Recombination in Semiconductors (Dunod Cie., Paris, 1965), p. 165. 'F. Stern, J. Appl. Phys. 47,5382 (1976). iOD. Botez, J. Quantum Electron. QE-14, 230 (1978). "W.W. Anderson, J. Quantum Electron. QE-l, 228 (1965). "B.W. Hakki and T.L. Paoli, J. Appl. Phys. 46,1299 (1975). "G.D. Henshall, Appl. Phys. Lett. 31, 205 (1977). '40. Botez and P.S. Zory, Appl. Phys. Lett. 32, 261 (1978), "G,H.B. Thompson, P.A, Kirkby, and J.E.A. Whiteaway, IEEE J. Quantum Electron. QE-ll, 481 (1975). "F. Stern, J'-Quantum Electron, QE-9, 290 (1973). "R,E. Nahory and M.A. Pollack, Electron. Lett, 14, 727 (1978).

"I,J, Hsieh, Appl. Phys. Lett, 28, 283 (1976). "J,J, Hsieh (private communication), lOG,H. Olsen (private communication). "T. Yamamoto, K, Sakai, S. Akiba, and y, Suematsu, IEEE J. Quantum Electron. QE-14, 95 (\978). "J.J. Hsieh, IEDM Conference Proceedings (IEEE, Washington, D.C., 1978), p. 628, "J.1. Coleman, P,W. Foy, R.B. Zetterstrom, S. Sumski, RC. Casey, Jr., and G.A. Rozgonyi, GaAs and Related Compounds, S1. Louis 1978 Institute ofPhys. Conf. Series No, 45 (Institute of Physics, London, '1978): Chap,S, p.380, "G.R Olsen, C.I. Nuese, and M, Ettenberg, Appl. Phys. Lett. 34, 262 (\979).

Range-resolved measurements of atmospheric ozone using a differentialabsorption CO2 laser radar Kazuhiro Asai, Toshikazu Itabe, and Takashi Igarashi Radio Research Laboratories, Ministry of Posts and Telecommunications, Koganei, Tokyo 187, Japan

(Received 4 January 1979; accepted for publication 26 April 1979) A 9.4-,...m CO z laser radar was used to obtain ozone measurements in the atmosphere with the differential-absorption method. Concentrations of ozone were measured in the horizontal interval from 0.5 to 2 km with 3OO-m range resolution. The measurement uncertainty varied from about ±15 ppb at 0.5 km to about ±40 ppb at 1.5 km. Experimental results showed good agreement between the ozone concentrations measured with the laser radar and those measured by point monitors at various sites. PACS numbers: 42.68.Db, 42.60.By, 06.70.Dn, 92.60.Sz The differential-absorption laser radar (DIAL) is considered to be the most sensitive system for the remote measurements of rare gases in the ambient atmosphere. I This technique has been applied mainly in the ultraviolet and visible region. 2,6 Murray et al. extended this technique to the infrared spectral region to obtain measurements of atmospheric water vapor with a lO-Jlm pulsed CO 2 laser. 7 Other authors have made remote measurements of atmospheric ozone with optical laser techniques in the ultraviolet region. 8.9 Ozone has also a strong absorption band in the infrared region, the wavelength of which is centered about 9.6 Jlm. In this region, the measurements of ozone have been made by long-path absorption techniques using a cw CO 2 laser. 10, II This letter reports the results of remote measurements of the atmospheric ozone with differential-absorption 9-J.lm CO 2 laser radar.

Figure 1 shows a block diagram of the DIAL system. The laser used in the experiments is a grating-tuned TEA CO2 pulse laser. The laser wavelengths are electrically tuned by a piezoelectric transducer. Details of the performance characteristics of the DIAL system are given in Table I. Scattered laser light is focused onto a HgCdTe detector in the focal plane of the receiving mirror. The received signals are amplified, filtered, and digitized to a minicomputer. The minicomputer processes the signals for on-line data reduction and produces a punched-tape output for off-line analysis, For the differential-absorption technique, a careful selection of the laser line is required to avoid interference from other gaseous species. H 20 and CO 2 in the ambient atmosphere are the important interference species in the measurement of ozone. We used the P (14) line in the (00·1-02"0) band TABLE L Parameters of CO 2 laser radar. Transmitter (TEA CO2 laser)

Receiver

Output energy Pulse width Beam divergence Repetition rate Telescope diameter Field of view HgCdTe detector

DO

Size Time constant Absorption coefficients a P(14) line (0.1 ppm) P(24} line FIG. I. Block diagram of the differential-absorption CO 2 laser radar. 60

Appl. Phys. Lett. 35(1), 1 July 1979

5.5 J 100 nsec (FWHM) 3 mrad (FWHM) I Hz 30cm 4.5 mrad (FWHM) 1 X 10 19 cm Hz 1I2/W 2x2mm 0.5 J1.sec

0.125 km 0.OO8km -

I I

')From Ref. 10.

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