Carrier pinning by mode fluctuations in diodes J. O’Gorman AT&T Bell Laboratories, Murray Hill, New Jersey 07974 S. L. Chuang Department of Computer and Electrical Engineering, University of Illinois at Urbana-Champaign, 1406 W. Green Street, Urbana, Illinois 61801 A. F. J. Levi AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (Received 27 August 1992; accepted for publication 28 January 1993) We show that fluctuations into cavity modes give rise to substantial subthreshold carrier pinning in laser diodes. These fluctuations, which extract a current Ifl from the device, play an increasingly important role with increasing temperature.

Recently we reported that photons fluctuating into trical contact to the back of the n-type InP substrate allows cavity modes of a at subthreshold drive current collection of nonguided light generated in the active region. contribute to the temperature dependence of the device.’ As-cleaved devices lase at wavelength A= 1.31 pm with We also demonstrated that, contrary to popular belief, Au- room temperature threshold currents in the range 9 mA ger recombination does not play a dominant role in deter-

1454 Appl. Phys. Lett. 62 (13), 29 March IQ93 0003-6951/93/131454-03fiO6.00 0 1993 American institute of Physics 1454

Downloaded 27 Jul 2001 to 128.125.104.79. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp 10 LED -l- = 25°C 100 I =20mA t

1 50

P =- 0 a cl I EXPERIMENTAL t I

-100 I I t 850 900 950 1000 PHOTON ENERGY, ho (meV) PHOTON ENERGY, fiw (meV)

LED 04 FIG. 2. Experimental and theoretical TE-polarized gain spectrum of a T = 25°C laser diode for injection current Z=20 mA at temperature T=328 K n=344x1018cms (55 %) . This comparison provides an estimation of carrier density n= 1.7 = 2’46 x 1 O’* cm9 x IO’* cm....3. From n we obtain &I$= -26.3 meV and given Z$=956.8 = 1:89x 1Oi8 cm4 meV, we obtain E,=930.5 meV. The inset shows the Fabry-Perot mod- = 1.41 x lOi cm9 ulated emission spectrum for facet light. = 0.74 x 1Oi8 cmd

The window light intensity L W is proportional to the spontaneous emission rate per unit volume per unit energy interval R,,(4iw) multiplied by the volume of the cavity, wld, and a factor which accounts for free carrier absorption afC in the n-type substrate of thickness dr We may write 81 900 1000 1100 1200 1300 PHOTON ENERGY, hw (meV) L “= fiuRspwIdA w exp ( - af,d,) he, (1) where be is the energy resolution of the spectrometer and FIG. 3. (a) Measured ratio of TE-polarized facet and unpolarized win- A w is the window aperture function. Gain as a function of dow LED light, LF/Lw, corrected for free carrier absorption in the sub- photon energy, &, is calculated from the spontaneous strate. Injection currents are Z=50, 20, 10, 5, 2 mA at temperature T=298 K (25 “C). (b) Theoretical results for experimental conditions in emission spectrum making use of the relationship4 (a). Carrier density for the corresponding current in sequence in (a) is indicated.

‘11 -exp B(&- Au> ]R,,(fiw), (2) As may be seen, apart from low-energy scattering or Ur- where P=l/kBT, c is the speed of light, and ng is the bath band tailing effects8’9 our theoretical model agrees refractive index. R,, is calculated taking into account con- well with experiment. Using this model, we determine the duction band non-parabolicity and the presence of both carrier density from the overall gain spectrum and the heavy- and light-hole valence bands.’ transparency energy E,=$ j- AEg+ A., where A& The facet light intensity experiences gain or loss de- =- 1’3 is the approximate carrier induced band gap scribed by an amplification factor [exp(g’Z) - 1]/g’L6 shrincge,” {=2.2X lo-’ meV cm, and Ap is the differ- Hence, ence between the chemical potential pu, for the conduction band and ph for the valance band, measured from the band edges. Furthermore, the value of Et, is independently con- ln ($)=ln ( ‘exp($~-ll)+ln ($)+a&. firmed by using a wavelength tunable laser to measure the photon energy at which net gain is zero.” (3) In Fig. 3 (a) we show the results of plotting the natural In this expression AF is the aperture function for the facet logarithm of the ratio of facet light to window light for and gain, g’, includes the influence of the conlinement fac- various LED injection currents. Figure 3(b) gives results tor.5 From a logarithmic plot of LF/L w, we determine the of calculating this ratio using our gain model. The agree- transparency energy Et, which we then use to extract the ment between experiment and model is very good consid- carrier concentration n using our gain model. ering the lack of reported data on the interband matrix For the laser diode we independently measure gain elements for InGaAsP materials. Here we take a linear spectra over a wide energy range using the Hakki-Paoli interpolation using the Ep (energy equivalent interband method.7 Typical results of doing this are shown in Fig. 2. momentum matrix element) values of InAs, InP, GaAs,

1455 Appl. Phys. Let, Vol. 62, No. 13, 29 March 1993 O’Gorman, Chuang, and Levi 1455

Downloaded 27 Jul 2001 to 128.125.104.79. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp In Fig. 4 we show carrier density n vs current for LD and LED for two different temperatures. It is apparent from the data that carrier pinning in the LED is both less substantial and less temperature sensitive than in the LD. Photons fluctuating into cavity modes of the laser cause carrier density to be pinned more effectively than in the corresponding LED device. Thus, to reach lasing thresh- old, it is necessary to provide an extra current 1h to over- come the effects of this pinning. We define I& as the dif- ference in drive current between LED and LD to reach the laser diode’s threshold carrier density, Q,. Scrutiny of Fig. 4 shows that lfh accounts for almost half the LD threshold current, Ith. 4t elevated temperatures carrier density at threshold increases so that the relative importance of fluc- r4(tt,=9.;mA , , , tuations is enhanced and IFh increases. Naturally, such sub- threshold fluctuations act as a feedback mechanism which cause laser threshold current Ith to increase with increasing temperature. 10 20 30 40 50 t50 The above results imply that Ifl plays an important role CURRENT, I (mA) in determining the temperature dependence of threshold current in long wavelength laser diodes. Presumably, it is necessary to use multimode rate equationsi3’i4 to approxi- (b) mately take into account the temperature dependence of 3.0 I’. In addition to photon mode fluctuations, any such cal- T culation must correctly deal with amplified spontaneous El emission and the carrier density dependence of the fraction 2 2.5 0 of spontaneous emission coupling into a given mode. x We thank E. J. Flynn for providing the devices used in c 2.0 this work and K. Wecht for antireflection coating the laser if diodes. S.L.C. thanks AT&T Bell Laboratories and GNR v, 5 1.5 (Grant No. NOOO14-90-J-1821) for their support. cl ‘J. O’Gorman, A. F. J. Levi, S. Schmitt-Rink, T. Tanbun-Ek, D. E E 1.0 L.Coblentz, and R. A. Logan, Appl. Phys. Lett. 60, 157 (1992). *J. G’Gorman, A. F. J. Levi, T. Tanbun-Ek, D. L. Coblentz, and R. A. Logan, Appl. Phys. Lett. 60, 1058 ( 1992). ‘Y. Zou, J. S. Osinski, P. Grodzinski, P. D. Dapkus, W. Rideout, W. F. Sharfln, and F. D. Crawford, Appl. Phys. Lett. 62, 175 (1993). 4H. Haug and S. Schmitt-Rink, Prog. Quantum Electron. 9, 13 (1984). ‘S. L. Chuang, J. O’Gorman, and A. F. J. Levi (unpublished). ‘E. 0. Gobel, in GaZnAsPAlloy Semiconductors, edited by T. P. Peanall CURRENT, I (mA) (Wiley, New York, 1982), Chap. 13. ‘B. W. Hakki and T. L. Paoli, J. Appl. Phys. 46, 1299 (1975). FIG. 4. Carrier density for LED and LD as a function of injection cur- *M. Yamanishi and Y. Lee, IEEE Quantum Electron. QE-23, 367 rent determined from experiment and theory. In (a) temperature is (1987). T=298 K (25X!), laser diode threshold current is 1e,=9.7 mA, and 9G. D. Mahan, Phys. Rev. 145, 602 (1966). lf,,=4 mA and in (b) temperature is T=328 K (55 “C), laser diode “B Sermage, D. S. Chemla, D. Sivco, and A. Y. Cho, IEEE J. Quantum threshold current is I,,,-21.5 mA, and I$= 10 mA. Electron. QE-22, 774 (1986). ” P. A. Andrekson, N. A. Olsson, T. Tanbun-Ek, R. A. Logan, D. Coblentz, and H. Temkin, Electron. Lett. 28, 171 (1992). and Gap.” It can be seen from Figs. 2 and 3 that there is “P. Lawaetz, Phys. Rev. B 4, 3460 (1971). a sharp decrease in gain near the transparency energy Et,. 13T. P. Lee, C. A. Burrus, J. A. Copeland, A. G. Dentai, and D. Marcuse, IEEE J. Quantum Electron. QE-18, 1101 (1982). This behavior, when combined with our band structure 14J. Lee and M. 0. Vassell, IEEE J. Quantum Electron. QE-28, 624 calculation, allows an estimation of carrier density. (1992).

1456 Appl. Phys. Lett., Vol. 62, No. 13, 29 March 1993 O’Gorman, Chuang, and Levi 1456

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