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Dynamics and gain in highly-excited InGaN MQWs
Current Applied Physics 2 (2002) 321–326 www.elsevier.com/locate/cap
Dynamics and gain in highly-excited InGaN MQWs q R.A. Taylor
a,*
, K. Kyhm a, J.D. Smith a, J.H. Rice a, J.F. Ryan a, T. Someya b, Y. Arakawa b
a
b
Clarendon Laboratory, University of Oxford, Parks Road, Oxford UK, OX1 3PU Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8558, Japan Received 8 May 2002; accepted 25 May 2002
Abstract The Kerr gate technique is used to time-resolve the gain in an In0:02 Ga0:98 N/In0:16 Ga0:84 N multiple quantum well sample. A new way of analyzing the data in such a variable stripe length method gain experiment is used to analyze both the time-integrated and timeresolved spectra. We confirm that the stripe length dependence of the gain in the multiple quantum wells under nanosecond excitation is caused by the change of the chemical potential along the excited stripe due to the interaction of the carrier and photon densities, and the gain threshold density is estimated. A trial function assuming a Lorentzian line shape for the stripe length dependence of the gain is compared with the edge emission intensity. This is found to fit very well with our data, even beyond the saturation region. Furthermore, we have extended the investigation to examine the dynamics of the emission and gain. These measurements suggest that the photoexcited carriers must localize (possibly at indium-rich sites) before strong stimulated emission is seen. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 78.45.þh; 71.35.Ee; 78.66.Fd; 78.55.-m Keywords: Time-resolved gain; InGaN; Kerr gate
1. Introduction The realization of Inx Ga1x N blue, green, and yellow light-emitting diodes (LEDs) [1] and the demonstration of a long lived CW blue InGaN quantum well laser diode [2] has led to a great deal of interest in the physical properties of GaN-based semiconductors. Although a high quantum efficiency has been seen in these devices, the physics of optical gain and stimulated emission has not been resolved. The primary mechanism responsible for stimulated emission in InGaN MQWs depends on the degree of electron/hole localization in the InGaN active layer, which is determined mainly by the mean Inmole fraction (i.e. the In/Ga distribution) [3–6]. Analysis of gain spectra is very useful in understanding the
q
Original version presented at QTSM and QFS ’02 (multilateral symposium between the Korean Academy of Science and Technology and the Foreign Academies), Yonsei University, Seoul, Korea, 8–10 May 2002. * Corresponding author. Tel.: +44-1865-272230; fax: +44-1865272400. E-mail address: [email protected] (R.A. Taylor).
mechanism responsible for stimulated emission, and the variable stripe length method (VSLM) is commonly used for this purpose [7]. Conventional analysis has been limited to short stripe length regimes ( 6 50 lm) as it has proved difficult to find appropriate fitting functions [8]. In this paper, we present a way of analyzing the VSLM data [15] that allows us to deduce a stripe length dependent gain for longer stripe lengths. Initial measurements were made with 10 ns long pump pulses, where the laser pulse is much longer than the lifetime of the carriers (800 ps). We have extended this analysis by time-resolving the emission at different stripe lengths, enabling us to measure the buildup and decay of the gain and carrier density following excitation by 125 fs light pulses. The dynamics and gain under such short pulse excitation are quite different from those seen with the 10 ns pulses, where carrier scattering, recombination and localization are found to play a major role. 2. Experimental technique The sample was grown on a sapphire substrate by atmospheric pressure metalorganic chemical vapor
1567-1739/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 1 5 6 7 - 1 7 3 9 ( 0 2 ) 0 0 1 1 8 - 9
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deposition. Initially a 3.0 lm GaN buffer layer was grown on the sapphire, followed by a multiple quantum well consisting of 30 In0:16 Ga0:84 N quantum wells of thickness separated by 41 A thick In0:02 Ga0:98 N 24 A barriers. For the initial gain measurements, a 10 Hz Q-switched Nd:YAG laser was used as the excitation source, producing 6 ns pulses at a wavelength of 355 nm. The laser beam was spatially filtered to produce a uniform stripe 50 lm wide with a mean excitation power of 9.2 mW. The sample was mounted in a cryostat at 4 K. The exciting beam was focused onto the edge of the sample, and the length of the excited stripe was varied by moving the whole stripe image along the sample. The edge emission spectrum was detected by a CCD camera mounted on a 0.25 m spectrometer, and the surface emission was also measured to obtain the photoluminescence spectrum. Photoluminescence excitation (PLE) measurements were also made in order to determine the absorption edge using a frequency-doubled modelocked Ti:sapphire laser. For the time-resolved measurements, the edge emission from the sample passed through crossed polarizers between which a cell of CS2 was placed. This cell was pumped by a train of 125 fs duration 100 lJ laser pulses derived from an amplified Ti:sapphire laser [16]. The Kerr rotation induced in the cell lasts for 1 ps and allows luminescence to be transmitted through the polarizers. This has the advantage of enabling a complete emission spectrum to be collected with a 1 ps time resolution. Thus the build-up of the edge emission for various excitation stripe lengths can be determined. The sample was excited at 3.6 eV by 125 fs pulses from an optical parametric amplifier, pumped by the same amplified Ti:sapphire laser, at a repetition frequency of 1 kHz. The pump beam was focused into a 25 lm wide stripe, whose length could be controlled between 0 and 400 lm. A conventional variable stripe gain experiment was also performed using these short pulses.
and this gives the gain spectrum by fitting the stripe length dependent edge emission intensity. Despite the fact that this model can only be applied to very short stripe lengths, Eq. (2) has been used and applied widely. As the stripe length increases, considerable deviation from the exponential behaviour has been noted because the gain saturates and it is even possible for negative gain (absorption) to appear [8]. These effects cannot be explained using this simple model (nor considered when the gain spectrum is measured). This is a severe limitation, where only data taken in the short stripe length regime is valid. Attempts to include gain saturation effects have so far failed [8,13]. We have adopted a different approach whereby we deduce the gain spectrum by applying differential Eq. (1) directly to the data, rather than fitting with an approximate analytical solution, dIðhx; LÞ Jspon X dL Iðhx; LÞ Iðhx; LÞ dIðhx; LÞ dL ’ þ CðLÞ: Iðhx; LÞ
gðhx; LÞ ¼
ð3Þ
In Eq. (3), the first term can be measured experimentally by dividing the derivative of the edge emission intensity for the stripe length by the edge emission intensity. Given that the edge emission intensity grows superlinearly as the stripe length increases ( P 40 lm) and the small solid angle (X) due to the stripe geometry, the contribution of the second term is expected to be very small and cause offsets of the gain spectra for different stripe lengths. This was indeed found to be the case in our experiment, enabling the calculation of gain spectra for different stripe lengths by subtracting these small offsets
3. Long pulse gain measurements In the variable stripe length geometry, the emission is amplified as it passes through the excited volume towards the edge of the sample. The dependence of the edge emission on the stripe length L is given by dIðhx; LÞ ¼ gð hx; LÞ Ið hx; LÞ þ Jspon X; dL
ð1Þ
where gð hx; LÞ, Jspon and X are the gain coefficient, the spontaneous emission density, and the solid angle along the stripe relatively. Assuming the gain coefficient to be independent of the stripe length, a solution to Eq. (1) is Iedge ð hx; LÞ ¼
Jspon X gðhxÞL ðe 1Þ; gð hxÞ
ð2Þ
Fig. 1. (a) Comparison of gain spectra for different stripe lengths at 4 K and (b) corresponding edge emission spectra at 4 K, and a front surface PL spectrum taken under the same excitation conditions.
R.A. Taylor et al. / Current Applied Physics 2 (2002) 321–326
(taken from a point well below the emission spectrum for each stripe length). The net gain spectra for different stripe lengths are shown in Fig. 1(a), and the corresponding edge emission spectra are shown in Fig. 1(b) for comparison. Both sets of spectra exhibit a red shift. The gain spectrum intensity decreases with increasing stripe length, whilst the intensity of the edge emission increases. It is also apparent from the figure that the width of the gain spectrum reduces as the stripe length increases. These phenomena can be understood by an inhomogeneous electron–hole pair distribution and a reduction in the effective chemical potential along the excited stripe due to the interaction of the carrier and photon densities [9]. The effective chemical potential lðneh ; T eh Þ for each stripe length can be deduced by measuring the width of the gain spectrum at zero gain. The corresponding electron–hole pair density in the quantum well structure can also be calculated [14] by using Eq. (4) with a carrier temperature of 217 K deduced from the high-energy tail of the PL spectra at comparable densities, meh kB T eh eh ln½1 þ el=kB T ; h2 p me mh ¼ e ; T eh ¼ 217 K: m þ mh
neh ¼ meh
ð4Þ
The inhomogeneous electron–hole pair distribution density is shown in Fig. 2(a). As the stripe length increases, both the electron–hole pair density and the effective chemical potential decrease. This reduction of the effective chemical potential is due to the interaction of the carrier and photon densities [9], and results in a decrease in the intensity of the gain spectrum. If the effective chemical potential energy becomes lower than corresponding photon energy, then emission at short wavelengths cannot be amplified and absorption results, i.e. negative gain. Although the total edge emission in-
Fig. 2. (a) Chemical potential and electron–hole pair density distribution along the stripe deduced from Fig. 1(a) using a carrier temperature of 217 K. (b) Peak gains versus the corresponding electron–hole pair density.
323
tensity increases due to an increase of the photon density as the stripe length increases, the intensity of short wavelength emission decreases due to the change of gain into absorption. As a result, the short wavelength emission is saturated more rapidly than that at longer wavelengths, resulting in a red shift of the edge emission. The red shift of the gain peak can be understood in the same way; arising from a reduction in the effective chemical potential as the stripe length is increased. In Fig. 2(b) we estimate the threshold carrier density of the stimulated emission, nth ¼ 1:00 0:27 1016 m2 , by fitting the gain peak energy as a function of the corresponding electron–hole pair density using [10], gmax ðnÞ ¼ g0 ð1 þ lnðn=n0 ÞÞ;
nth ¼ n0 e1 :
ð5Þ
This value is comparable with the theoretical threshold carrier density of nth ¼ 2:30 1016 m2 at room temperature for an InGaN multiple quantum well laser [11], and gives us an upper limit for the Mott density. The primary mechanism responsible for stimulated emission in InGaN MQWs depends on the degree of localization in the InGaN active layer. With an Incontent of 30% it has been reported that this mechanism is the deep localization of excitons (or carriers) originating from In-rich regions acting as quantum dots, the energy of which is found to be 500 meV below the lowest quantized exciton level [3]. However, with 10% [3] and 18% [4] In-content, delocalized states of electron–hole
Fig. 3. (a) Open circles show the edge emission intensity as a function of the stripe length at 3.14 eV. The solid curves correspond to three different fitting functions as detailed in the text ((1), Eq. (1); (2), [13]; (3), Eq. (6)). (b) Gain distribution along the stripe for different energies deduced from Fig. 1(a).
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pairs become the dominant mechanism for the stimulated emission. In Fig. 1(b), a photoluminescence spectrum is presented for comparison with the edge emission spectra. We found that there is no shift of the peak photoluminescence energy when the excitation density is varied over a wide range. This fact supports the assertion that photoluminescence in our sample may be attributed to weak localization effects ( 6 30 meV) due to potential fluctuations in the sample. At high carrier densities, these localized states are saturated, and nearly delocalized states of electron–hole pairs contribute to the optical gain [4]. A plot of the edge emission intensity versus stripe length at an energy of 3.14 eV is shown in Fig. 3(a). The emission intensity increases exponentially for short stripe lengths, then enters a region where the intensity dependence is linear. Eventually, the intensity saturates for long stripe lengths, and even decreases. The initial exponential growth of the emission intensity can be fitted with the simple amplification model of Eq. (1), but beyond this region, large deviations occur. It is therefore essential that gain saturation effects should be included in the analysis. When considering Eq. (1), various model functions for the intensity dependence of the gain coefficient allowing for gain saturation have been proposed [12,13], gðhx; IÞ ¼
g0 ð hxÞ ; ð1 þ I=Is Þa
ð6Þ
gð hx; IÞ ¼
g0 ðhxÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð1 þ I=I0 Þ 1 þ I=Is
ð7Þ
In Eq. (6), a is either 1 or 0.5 in the case of the homogeneous and inhomogeneous broadening [12]. I0 and Is are the interband and intraband saturation intensities respectively. Danker [13] (Eq. (7)) considers non-linear effects as well. In Fig. 3(a), Eq. (2) shows that this model is a better description than Eq. (1), but works best only in the intermediate stripe length regime, around 100 lm. Neither of the above two models work well in both the short and intermediate stripe length regimes, and fail completely in the long stripe region, where negative gain occurs. In contrast to the above models we find that the dependence of the gain on stripe length is the critical factor in understanding saturation effects rather than the intensity dependence. Mathematically, if the intensity dependent gain is considered, then the emission intensity rather than the stripe length should be the variable used when solving differential equation (1), and this makes difficult to solve Eq. (1) in general. Fig. 3(b) shows the gain distribution along the stripe for different energies deduced from Fig. 1(a). As mentioned above, the gain decreases as the stripe length increases due to the reduction of the effective chemical potential, which results from the inhomogeneous electron–hole distribution. We approximate the stripe length dependence of the gain
by fitting the data with a Lorentzian function (Eq. (8)). This yields an analytic solution of Eq. (3), c1 gðhx; LÞ ¼ 2 þ c4 ; ð8Þ 2 ðc2 ðL L0 Þ þ c23 Þ " Iðhx; LÞ ¼ c6 þ c5 exp c4 ðL L0 Þ þ
0Þ c1 tan1 ½c2 ðLL c3
c2 c3
# : ð9Þ
Eq. (8) provides a much better fit to the stripe length dependence of the edge emission intensity, and indeed follows the curve into the negative gain region. 4. Time-resolved gain measurements In order to attempt to understand the growth of the gain after excitation, we have extended the above measurements into the time-resolved domain. Previous timeresolved work on gain in a range of III–V semiconductor systems [3,17–19] have relied on up-conversion or pumpprobe techniques for their time resolution. The Kerr gate technique employed here has the advantage of large signal levels and good time resolution, enabling a detailed study of time-resolved edge emission to be undertaken. Fig. 4(a) shows the time-integrated edge emission spectra taken under pulsed excitation. These are clearly
Fig. 4. (a) Edge emission intensity at 4 K for various stripe lengths under excitation by 125 fs pulses. Note the red shift of the peak with increasing stripe length, and the emergence of a second peak at 3.2 eV. (b) Gain spectra calculated by the method described in the text from the above edge emission data.
R.A. Taylor et al. / Current Applied Physics 2 (2002) 321–326
similar to those seen under long pulse excitation, with the peak showing a pronounced red shift of 20 meV with increasing stripe length. One interesting feature, however, which is not seen in the earlier data is the emergence of a second emission peak at 3.2 eV for longer stripe lengths. The corresponding gain spectra are shown in Fig. 4(b), where the width of the gain spectrum suggests that the chemical potential has a maximum value of 22 meV for this excitation density. Analysis of the time-resolved edge emission and gain data is at a preliminary stage, however many features seen at different stripe lengths are present at a stripe length of 290 lm. Consequently, we display in Figs. 5 and 6 the time-resolved edge emission and gain at early times during the risetime of the emission and at later times as the stimulated emission begins to decay, for this stripe length. The data show that for long stripes the emission exhibits a risetime of 6 ps, and a pronounced red shift in the peak of over 50 meV within the first 15 ps after excitation. After 20 ps, as the carrier density in the electron–hole plasma produced drops due to stimulated emission, the emission then begins to blue shift, although the peak never recovers its original energy before the emission has decayed into the noise level of our system. For short (20 lm) stripe lengths, the emission begins promptly at 3.25 eV, followed by a red shift of over 100 meV into a second, well-defined peak corre-
325
Fig. 6. (a) Time-resolved edge emission spectra measured using the Kerr gate at later times for a stripe length of 290 lm. Note the rise of a second peak at 3.22 eV at 20 ps after excitation. (b) Transient gain spectra at later times calculated from the above edge emission data.
sponding to that seen at longer stripe lengths. This may be an indication that the photoexcited carriers must localize (possibly at indium-rich sites) before strong stimulated emission is seen. Fig. 5(a) shows that for a 290 lm long stripe the edge emission shows a rapid red shift within the first 10 ps from 3.22 to 3.16 eV. The corresponding gain shifts from 3.16 eV at 2 ps to 3.13 eV at 10 ps. By 22 ps, as shown in Fig. 6(a) and (b), the edge emission reaches its maximum red shift at 3.14 eV, whilst the gain remains fixed at an energy of 3.13 eV but drops from a peak value of 0.065 lm1 . An interesting feature of the data is that the edge emission increases in intensity at 3.22 eV between 18 and 22 ps after excitation, with a reasonably large gain emerging that red shifts rapidly. It is unclear at present what the cause of this feature might be, although it is clearly present to varying degrees at all stripe lengths. Indeed for short stripes the emission at 3.22 eV rises before that at 3.15 eV, and may well evidence for carriers localizing initially at sites with only slightly greater indium concentration, with the carriers transferring to deeper localized states at later times. Fig. 5. (a) Time-resolved edge emission spectra measured using the Kerr gate at early times for a stripe length of 290 lm. (b) Transient gain spectra at early times calculated from the above edge emission data.
5. Conclusions In conclusion, we have shown that it is possible to measure the gain spectrum for the different stripe lengths
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using the VSLM technique over a wide range of stripe lengths. We have confirmed that the stripe length dependence of the gain is caused by a change in the chemical potential along the excited stripe due to the interaction of the carrier and photon densities, and a gain threshold density has been estimated. Our analysis provides not only the gain distribution along the stripe, as shown in Fig. 3(b), but also the stripe length-dependent gain spectra (Fig. 1(a)) using the whole stripe length regime. We also found that it is possible to use a Lorentzian function to model the edge emission intensity for stripe lengths beyond the saturation region. We have also shown that nearly delocalized electron–hole pairs from the lowest confined level are responsible for the gain in our In0:02 Ga0:98 N/In0:16 Ga0:84 N MQW sample. This result is consistent with recent reports [3–6] on samples with relatively low (<16%) In-content. In an extension to this long pulse work we have made measurements of the time-resolved gain as a function of stripe length. It is clear from a preliminary analysis that the interplay of carrier relaxation, scattering and localization is much more complex in this excitation regime. We see the edge emission red shift during the early part of the emission, followed by a blue shift as the carrier density drops due to recombination by stimulated emission. The risetime is a strong function of the stripe length, where photon transit times for longer stripes become important.
Acknowledgements We would like to thank A.J. Turberfield, D.N. Sharp and E. Dedman for technical assistance.
References [1] S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, S. Nagahama, Jpn. J. Appl. Phys. 34 (1995) L797. [2] S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, K. Chocho, Appl. Phys. Lett. 72 (1998) 2014. [3] Y. Kawakami, Y. Narukawa, K. Omae, S. Fujita, Appl. Phys. Lett. 77 (2000) 2151. [4] G. Mohs, T. Aoki, R. Shimano, M. Gonokami, S. Nakamura, Solid State Commun. 108 (1998) 105. [5] Y. Narukawa, Y. Kawakami, Sz. Fujita, Sg. Fujita, Phys. Rev. B 55 (1997) R1938. [6] Y. Narukawa, Y. Kawakami, Sg. Fujita, Phys. Rev. B 59 (1999) 10283. [7] K.L. Shaklee, R.E. Nahory, R.F. Leheny, J. Lumin. 7 (1973) 284. [8] G. Mohs, T. Aoki, M. Nagai, R. Shimano, M. Gonokami, S. Nakamura, Solid State Commun. 104 (1997) 643. [9] H. Kalt, M. Umlauff, M. Kraushaar, M. Scholl, J. Sollner, M. Heuken, J. Cryst. Growth 184/185 (1998) 627. [10] S.L. Chuang, in: Physics of Optoelectronic Devices, Wiley Series, New York, 1995, p. 430. [11] G.G. Zegrya, N.A. Gun’ko, Semiconductors 32 (1998) 749. [12] W.W. Rigrod, J. Appl. Phys. 34 (1963) 2602. [13] Y. Danker, Solid State Commun. 93 (1995) 707. [14] H. Haug, S.W. Koch, in: Quantum theory of the optical and electronic properties of semiconductors, World Scientific, Singapore, 1991, p. 91. [15] K. Kyhm, R.A. Taylor, J.F. Ryan, T. Someya, Y. Arakawa, Appl. Phys. Lett. 79 (2001) 3434. [16] J. Takeda, H. Jinnouchi, S. Kurita, Y.F. Chen, T. Yao, in: N. Miura, T. Ando (Eds.), Proc. 25th ICPS, Springer, Berlin, 2001, p. 1549. [17] C. Lingk, G. von Plessen, J. Feldmann, K. Stock, M. Arzberger, G. B€ ohm, M.C. Amann, G. Abstreiter, Appl. Phys. Lett. 76 (2000) 3507. [18] P. Michler, U. Neukirch, K. Wundke, J. Gutowski, M. Behringer, D. Hommel, H. G€ undler, K. Henneberger, Phys. Status Sol. B 206 (1998) 399. [19] J. Wang, H.C. Schweizer, IEEE J. Sel. Top. Quant. Elect. 3 (1997) 218.
Dynamics and gain in highly-excited InGaN MQWs q R.A. Taylor
a,*
, K. Kyhm a, J.D. Smith a, J.H. Rice a, J.F. Ryan a, T. Someya b, Y. Arakawa b
a
b
Clarendon Laboratory, University of Oxford, Parks Road, Oxford UK, OX1 3PU Institute of Industrial Science, University of Tokyo, 7-22-1 Roppongi, Minato-ku, Tokyo 106-8558, Japan Received 8 May 2002; accepted 25 May 2002
Abstract The Kerr gate technique is used to time-resolve the gain in an In0:02 Ga0:98 N/In0:16 Ga0:84 N multiple quantum well sample. A new way of analyzing the data in such a variable stripe length method gain experiment is used to analyze both the time-integrated and timeresolved spectra. We confirm that the stripe length dependence of the gain in the multiple quantum wells under nanosecond excitation is caused by the change of the chemical potential along the excited stripe due to the interaction of the carrier and photon densities, and the gain threshold density is estimated. A trial function assuming a Lorentzian line shape for the stripe length dependence of the gain is compared with the edge emission intensity. This is found to fit very well with our data, even beyond the saturation region. Furthermore, we have extended the investigation to examine the dynamics of the emission and gain. These measurements suggest that the photoexcited carriers must localize (possibly at indium-rich sites) before strong stimulated emission is seen. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 78.45.þh; 71.35.Ee; 78.66.Fd; 78.55.-m Keywords: Time-resolved gain; InGaN; Kerr gate
1. Introduction The realization of Inx Ga1x N blue, green, and yellow light-emitting diodes (LEDs) [1] and the demonstration of a long lived CW blue InGaN quantum well laser diode [2] has led to a great deal of interest in the physical properties of GaN-based semiconductors. Although a high quantum efficiency has been seen in these devices, the physics of optical gain and stimulated emission has not been resolved. The primary mechanism responsible for stimulated emission in InGaN MQWs depends on the degree of electron/hole localization in the InGaN active layer, which is determined mainly by the mean Inmole fraction (i.e. the In/Ga distribution) [3–6]. Analysis of gain spectra is very useful in understanding the
q
Original version presented at QTSM and QFS ’02 (multilateral symposium between the Korean Academy of Science and Technology and the Foreign Academies), Yonsei University, Seoul, Korea, 8–10 May 2002. * Corresponding author. Tel.: +44-1865-272230; fax: +44-1865272400. E-mail address: [email protected] (R.A. Taylor).
mechanism responsible for stimulated emission, and the variable stripe length method (VSLM) is commonly used for this purpose [7]. Conventional analysis has been limited to short stripe length regimes ( 6 50 lm) as it has proved difficult to find appropriate fitting functions [8]. In this paper, we present a way of analyzing the VSLM data [15] that allows us to deduce a stripe length dependent gain for longer stripe lengths. Initial measurements were made with 10 ns long pump pulses, where the laser pulse is much longer than the lifetime of the carriers (800 ps). We have extended this analysis by time-resolving the emission at different stripe lengths, enabling us to measure the buildup and decay of the gain and carrier density following excitation by 125 fs light pulses. The dynamics and gain under such short pulse excitation are quite different from those seen with the 10 ns pulses, where carrier scattering, recombination and localization are found to play a major role. 2. Experimental technique The sample was grown on a sapphire substrate by atmospheric pressure metalorganic chemical vapor
1567-1739/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 1 5 6 7 - 1 7 3 9 ( 0 2 ) 0 0 1 1 8 - 9
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R.A. Taylor et al. / Current Applied Physics 2 (2002) 321–326
deposition. Initially a 3.0 lm GaN buffer layer was grown on the sapphire, followed by a multiple quantum well consisting of 30 In0:16 Ga0:84 N quantum wells of thickness separated by 41 A thick In0:02 Ga0:98 N 24 A barriers. For the initial gain measurements, a 10 Hz Q-switched Nd:YAG laser was used as the excitation source, producing 6 ns pulses at a wavelength of 355 nm. The laser beam was spatially filtered to produce a uniform stripe 50 lm wide with a mean excitation power of 9.2 mW. The sample was mounted in a cryostat at 4 K. The exciting beam was focused onto the edge of the sample, and the length of the excited stripe was varied by moving the whole stripe image along the sample. The edge emission spectrum was detected by a CCD camera mounted on a 0.25 m spectrometer, and the surface emission was also measured to obtain the photoluminescence spectrum. Photoluminescence excitation (PLE) measurements were also made in order to determine the absorption edge using a frequency-doubled modelocked Ti:sapphire laser. For the time-resolved measurements, the edge emission from the sample passed through crossed polarizers between which a cell of CS2 was placed. This cell was pumped by a train of 125 fs duration 100 lJ laser pulses derived from an amplified Ti:sapphire laser [16]. The Kerr rotation induced in the cell lasts for 1 ps and allows luminescence to be transmitted through the polarizers. This has the advantage of enabling a complete emission spectrum to be collected with a 1 ps time resolution. Thus the build-up of the edge emission for various excitation stripe lengths can be determined. The sample was excited at 3.6 eV by 125 fs pulses from an optical parametric amplifier, pumped by the same amplified Ti:sapphire laser, at a repetition frequency of 1 kHz. The pump beam was focused into a 25 lm wide stripe, whose length could be controlled between 0 and 400 lm. A conventional variable stripe gain experiment was also performed using these short pulses.
and this gives the gain spectrum by fitting the stripe length dependent edge emission intensity. Despite the fact that this model can only be applied to very short stripe lengths, Eq. (2) has been used and applied widely. As the stripe length increases, considerable deviation from the exponential behaviour has been noted because the gain saturates and it is even possible for negative gain (absorption) to appear [8]. These effects cannot be explained using this simple model (nor considered when the gain spectrum is measured). This is a severe limitation, where only data taken in the short stripe length regime is valid. Attempts to include gain saturation effects have so far failed [8,13]. We have adopted a different approach whereby we deduce the gain spectrum by applying differential Eq. (1) directly to the data, rather than fitting with an approximate analytical solution, dIðhx; LÞ Jspon X dL Iðhx; LÞ Iðhx; LÞ dIðhx; LÞ dL ’ þ CðLÞ: Iðhx; LÞ
gðhx; LÞ ¼
ð3Þ
In Eq. (3), the first term can be measured experimentally by dividing the derivative of the edge emission intensity for the stripe length by the edge emission intensity. Given that the edge emission intensity grows superlinearly as the stripe length increases ( P 40 lm) and the small solid angle (X) due to the stripe geometry, the contribution of the second term is expected to be very small and cause offsets of the gain spectra for different stripe lengths. This was indeed found to be the case in our experiment, enabling the calculation of gain spectra for different stripe lengths by subtracting these small offsets
3. Long pulse gain measurements In the variable stripe length geometry, the emission is amplified as it passes through the excited volume towards the edge of the sample. The dependence of the edge emission on the stripe length L is given by dIðhx; LÞ ¼ gð hx; LÞ Ið hx; LÞ þ Jspon X; dL
ð1Þ
where gð hx; LÞ, Jspon and X are the gain coefficient, the spontaneous emission density, and the solid angle along the stripe relatively. Assuming the gain coefficient to be independent of the stripe length, a solution to Eq. (1) is Iedge ð hx; LÞ ¼
Jspon X gðhxÞL ðe 1Þ; gð hxÞ
ð2Þ
Fig. 1. (a) Comparison of gain spectra for different stripe lengths at 4 K and (b) corresponding edge emission spectra at 4 K, and a front surface PL spectrum taken under the same excitation conditions.
R.A. Taylor et al. / Current Applied Physics 2 (2002) 321–326
(taken from a point well below the emission spectrum for each stripe length). The net gain spectra for different stripe lengths are shown in Fig. 1(a), and the corresponding edge emission spectra are shown in Fig. 1(b) for comparison. Both sets of spectra exhibit a red shift. The gain spectrum intensity decreases with increasing stripe length, whilst the intensity of the edge emission increases. It is also apparent from the figure that the width of the gain spectrum reduces as the stripe length increases. These phenomena can be understood by an inhomogeneous electron–hole pair distribution and a reduction in the effective chemical potential along the excited stripe due to the interaction of the carrier and photon densities [9]. The effective chemical potential lðneh ; T eh Þ for each stripe length can be deduced by measuring the width of the gain spectrum at zero gain. The corresponding electron–hole pair density in the quantum well structure can also be calculated [14] by using Eq. (4) with a carrier temperature of 217 K deduced from the high-energy tail of the PL spectra at comparable densities, meh kB T eh eh ln½1 þ el=kB T ; h2 p me mh ¼ e ; T eh ¼ 217 K: m þ mh
neh ¼ meh
ð4Þ
The inhomogeneous electron–hole pair distribution density is shown in Fig. 2(a). As the stripe length increases, both the electron–hole pair density and the effective chemical potential decrease. This reduction of the effective chemical potential is due to the interaction of the carrier and photon densities [9], and results in a decrease in the intensity of the gain spectrum. If the effective chemical potential energy becomes lower than corresponding photon energy, then emission at short wavelengths cannot be amplified and absorption results, i.e. negative gain. Although the total edge emission in-
Fig. 2. (a) Chemical potential and electron–hole pair density distribution along the stripe deduced from Fig. 1(a) using a carrier temperature of 217 K. (b) Peak gains versus the corresponding electron–hole pair density.
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tensity increases due to an increase of the photon density as the stripe length increases, the intensity of short wavelength emission decreases due to the change of gain into absorption. As a result, the short wavelength emission is saturated more rapidly than that at longer wavelengths, resulting in a red shift of the edge emission. The red shift of the gain peak can be understood in the same way; arising from a reduction in the effective chemical potential as the stripe length is increased. In Fig. 2(b) we estimate the threshold carrier density of the stimulated emission, nth ¼ 1:00 0:27 1016 m2 , by fitting the gain peak energy as a function of the corresponding electron–hole pair density using [10], gmax ðnÞ ¼ g0 ð1 þ lnðn=n0 ÞÞ;
nth ¼ n0 e1 :
ð5Þ
This value is comparable with the theoretical threshold carrier density of nth ¼ 2:30 1016 m2 at room temperature for an InGaN multiple quantum well laser [11], and gives us an upper limit for the Mott density. The primary mechanism responsible for stimulated emission in InGaN MQWs depends on the degree of localization in the InGaN active layer. With an Incontent of 30% it has been reported that this mechanism is the deep localization of excitons (or carriers) originating from In-rich regions acting as quantum dots, the energy of which is found to be 500 meV below the lowest quantized exciton level [3]. However, with 10% [3] and 18% [4] In-content, delocalized states of electron–hole
Fig. 3. (a) Open circles show the edge emission intensity as a function of the stripe length at 3.14 eV. The solid curves correspond to three different fitting functions as detailed in the text ((1), Eq. (1); (2), [13]; (3), Eq. (6)). (b) Gain distribution along the stripe for different energies deduced from Fig. 1(a).
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pairs become the dominant mechanism for the stimulated emission. In Fig. 1(b), a photoluminescence spectrum is presented for comparison with the edge emission spectra. We found that there is no shift of the peak photoluminescence energy when the excitation density is varied over a wide range. This fact supports the assertion that photoluminescence in our sample may be attributed to weak localization effects ( 6 30 meV) due to potential fluctuations in the sample. At high carrier densities, these localized states are saturated, and nearly delocalized states of electron–hole pairs contribute to the optical gain [4]. A plot of the edge emission intensity versus stripe length at an energy of 3.14 eV is shown in Fig. 3(a). The emission intensity increases exponentially for short stripe lengths, then enters a region where the intensity dependence is linear. Eventually, the intensity saturates for long stripe lengths, and even decreases. The initial exponential growth of the emission intensity can be fitted with the simple amplification model of Eq. (1), but beyond this region, large deviations occur. It is therefore essential that gain saturation effects should be included in the analysis. When considering Eq. (1), various model functions for the intensity dependence of the gain coefficient allowing for gain saturation have been proposed [12,13], gðhx; IÞ ¼
g0 ð hxÞ ; ð1 þ I=Is Þa
ð6Þ
gð hx; IÞ ¼
g0 ðhxÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð1 þ I=I0 Þ 1 þ I=Is
ð7Þ
In Eq. (6), a is either 1 or 0.5 in the case of the homogeneous and inhomogeneous broadening [12]. I0 and Is are the interband and intraband saturation intensities respectively. Danker [13] (Eq. (7)) considers non-linear effects as well. In Fig. 3(a), Eq. (2) shows that this model is a better description than Eq. (1), but works best only in the intermediate stripe length regime, around 100 lm. Neither of the above two models work well in both the short and intermediate stripe length regimes, and fail completely in the long stripe region, where negative gain occurs. In contrast to the above models we find that the dependence of the gain on stripe length is the critical factor in understanding saturation effects rather than the intensity dependence. Mathematically, if the intensity dependent gain is considered, then the emission intensity rather than the stripe length should be the variable used when solving differential equation (1), and this makes difficult to solve Eq. (1) in general. Fig. 3(b) shows the gain distribution along the stripe for different energies deduced from Fig. 1(a). As mentioned above, the gain decreases as the stripe length increases due to the reduction of the effective chemical potential, which results from the inhomogeneous electron–hole distribution. We approximate the stripe length dependence of the gain
by fitting the data with a Lorentzian function (Eq. (8)). This yields an analytic solution of Eq. (3), c1 gðhx; LÞ ¼ 2 þ c4 ; ð8Þ 2 ðc2 ðL L0 Þ þ c23 Þ " Iðhx; LÞ ¼ c6 þ c5 exp c4 ðL L0 Þ þ
0Þ c1 tan1 ½c2 ðLL c3
c2 c3
# : ð9Þ
Eq. (8) provides a much better fit to the stripe length dependence of the edge emission intensity, and indeed follows the curve into the negative gain region. 4. Time-resolved gain measurements In order to attempt to understand the growth of the gain after excitation, we have extended the above measurements into the time-resolved domain. Previous timeresolved work on gain in a range of III–V semiconductor systems [3,17–19] have relied on up-conversion or pumpprobe techniques for their time resolution. The Kerr gate technique employed here has the advantage of large signal levels and good time resolution, enabling a detailed study of time-resolved edge emission to be undertaken. Fig. 4(a) shows the time-integrated edge emission spectra taken under pulsed excitation. These are clearly
Fig. 4. (a) Edge emission intensity at 4 K for various stripe lengths under excitation by 125 fs pulses. Note the red shift of the peak with increasing stripe length, and the emergence of a second peak at 3.2 eV. (b) Gain spectra calculated by the method described in the text from the above edge emission data.
R.A. Taylor et al. / Current Applied Physics 2 (2002) 321–326
similar to those seen under long pulse excitation, with the peak showing a pronounced red shift of 20 meV with increasing stripe length. One interesting feature, however, which is not seen in the earlier data is the emergence of a second emission peak at 3.2 eV for longer stripe lengths. The corresponding gain spectra are shown in Fig. 4(b), where the width of the gain spectrum suggests that the chemical potential has a maximum value of 22 meV for this excitation density. Analysis of the time-resolved edge emission and gain data is at a preliminary stage, however many features seen at different stripe lengths are present at a stripe length of 290 lm. Consequently, we display in Figs. 5 and 6 the time-resolved edge emission and gain at early times during the risetime of the emission and at later times as the stimulated emission begins to decay, for this stripe length. The data show that for long stripes the emission exhibits a risetime of 6 ps, and a pronounced red shift in the peak of over 50 meV within the first 15 ps after excitation. After 20 ps, as the carrier density in the electron–hole plasma produced drops due to stimulated emission, the emission then begins to blue shift, although the peak never recovers its original energy before the emission has decayed into the noise level of our system. For short (20 lm) stripe lengths, the emission begins promptly at 3.25 eV, followed by a red shift of over 100 meV into a second, well-defined peak corre-
325
Fig. 6. (a) Time-resolved edge emission spectra measured using the Kerr gate at later times for a stripe length of 290 lm. Note the rise of a second peak at 3.22 eV at 20 ps after excitation. (b) Transient gain spectra at later times calculated from the above edge emission data.
sponding to that seen at longer stripe lengths. This may be an indication that the photoexcited carriers must localize (possibly at indium-rich sites) before strong stimulated emission is seen. Fig. 5(a) shows that for a 290 lm long stripe the edge emission shows a rapid red shift within the first 10 ps from 3.22 to 3.16 eV. The corresponding gain shifts from 3.16 eV at 2 ps to 3.13 eV at 10 ps. By 22 ps, as shown in Fig. 6(a) and (b), the edge emission reaches its maximum red shift at 3.14 eV, whilst the gain remains fixed at an energy of 3.13 eV but drops from a peak value of 0.065 lm1 . An interesting feature of the data is that the edge emission increases in intensity at 3.22 eV between 18 and 22 ps after excitation, with a reasonably large gain emerging that red shifts rapidly. It is unclear at present what the cause of this feature might be, although it is clearly present to varying degrees at all stripe lengths. Indeed for short stripes the emission at 3.22 eV rises before that at 3.15 eV, and may well evidence for carriers localizing initially at sites with only slightly greater indium concentration, with the carriers transferring to deeper localized states at later times. Fig. 5. (a) Time-resolved edge emission spectra measured using the Kerr gate at early times for a stripe length of 290 lm. (b) Transient gain spectra at early times calculated from the above edge emission data.
5. Conclusions In conclusion, we have shown that it is possible to measure the gain spectrum for the different stripe lengths
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using the VSLM technique over a wide range of stripe lengths. We have confirmed that the stripe length dependence of the gain is caused by a change in the chemical potential along the excited stripe due to the interaction of the carrier and photon densities, and a gain threshold density has been estimated. Our analysis provides not only the gain distribution along the stripe, as shown in Fig. 3(b), but also the stripe length-dependent gain spectra (Fig. 1(a)) using the whole stripe length regime. We also found that it is possible to use a Lorentzian function to model the edge emission intensity for stripe lengths beyond the saturation region. We have also shown that nearly delocalized electron–hole pairs from the lowest confined level are responsible for the gain in our In0:02 Ga0:98 N/In0:16 Ga0:84 N MQW sample. This result is consistent with recent reports [3–6] on samples with relatively low (<16%) In-content. In an extension to this long pulse work we have made measurements of the time-resolved gain as a function of stripe length. It is clear from a preliminary analysis that the interplay of carrier relaxation, scattering and localization is much more complex in this excitation regime. We see the edge emission red shift during the early part of the emission, followed by a blue shift as the carrier density drops due to recombination by stimulated emission. The risetime is a strong function of the stripe length, where photon transit times for longer stripes become important.
Acknowledgements We would like to thank A.J. Turberfield, D.N. Sharp and E. Dedman for technical assistance.
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