Carrier dynamics under two- and single-photon excitation in bulk GaN
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Phys. Status Solidi B 249, No. 3, 503–506 (2012) / DOI 10.1002/pssb.201100307
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basic solid state physics
,1 1,2 2 ¨ zgu¨r2, and Hadis Morkoc¸2 ¨ mit O Patrik Sˇcˇajev* , Ke˛stutis Jarasˇiu¯nas , Serdal Okur , U
1 2
Institute of Applied Research, Vilnius University, Saule˙tekio Ave. 9 – III, Vilnius 10222, Lithuania Department of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond, VA 23284, USA
Received 5 July 2011, revised 28 August 2011, accepted 2 November 2011 Published online 29 December 2011 Keywords diffusion, free-carrier absorption, GaN, photoluminescence, recombination, transient gratings, two photon absorption * Corresponding
author: e-mail
[email protected], Phone: þ370 5 2366036, Fax: þ370 5 2366037
Carrier diffusion and recombination features in freestanding 200 mm thick GaN were studied using light-induced transient grating, time-resolved free-carrier absorption, and photoluminescence techniques. Under two-photon excitation (527 nm, 8 ps), in-plane carrier diffusion paved the way for determining the hole and ambipolar carrier diffusion coefficients (Dh ¼ 0.8 and Da ¼ 1.6 cm2/s) and their temperature dependence. The nearly inverse correlation between the diffusivity and carrier lifetime in the 80–800 K range was ascribed to nonradiative
carrier recombination at the extended defects. Very low density of dislocations, in mid-105 cm2, provided extremely long lifetime values, up to 40 ns at 300 K and 120 ns at 800 K. Under single-photon excitation (267 nm, 100 fs), the initial very fast transient of photoluminescence decay at 3.4 eV was described by carrier diffusion normal to the surface, reabsorption of emission, and surface recombination. The nonequilibrium processes in the entire 80–800 K range can be reliably analyzed by a free electron–hole model.
ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1 Introduction Carrier dynamics in GaN is typically investigated under carrier injection by femtosecond or picosecond laser pulses at wavelengths above the bandgap Eg. The high absorption coefficient results in a 50–100 nm thick photoexcited layer (e.g., at 267 or 355 nm). Subsequent spatial redistribution of the carriers by diffusion from the surface into the bulk, trapping at surface states, radiative and nonradiative recombination rates were treated as critical parameters contributing to the fast initial decay of already thermalized carriers. The fast transients with few nanoseconds decay times were observed in GaN heterostructures grown by metalorganic chemical vapor deposition on various substrates as well as in hydride vapor phase epitaxy (HVPE) crystals using time-resolved photoluminescence (TRPL), picosecond light-induced transient grating (LITG), and a variety of other techniques [1–4]. In this paper, we combined single- and two-photon excitation in bulk GaN by utilizing a range of complementary optical techniques to determine the critical parameters for modeling the fast transients observed in photoluminescence (PL). Two-photon (2P) carrier injection at wavelengths below Eg was found advantageous for investigating the nonradiative recombination and carrier transport
processes in the bulk of the sample at moderate excess carrier densities (from 1015 to 1017 cm3). The electronic delay of probe beam enabled monitoring of the free-carrier absorption (FCA) decay up to a 3 ms [5]. The in-plane LITG technique allowed the determination of minority and bipolar carrier diffusion coefficients. These data were used to analyze PL decay for single-photon (1P) excitation in the same GaN crystal, taking into account the surface, diffusion, and bulk contributions to the instantaneous PL signal. 2 Samples and techniques For this study, we investigated excess carrier dynamics in d ¼ 200 mm thick HVPE-grown GaN (electron concentration and mobility are n0 ¼ 1.3 1016 cm3 and mn ¼ 1200 cm2/Vs, respectively [6]) under 2P excitation conditions (using 8 ps pulses at 527 nm from a neodymium-doped yttrium lithium fluoride laser, Nd:YLF) and under 1P excitation (using 100 fs pulses at 267 nm from a frequency tripled Ti-Sapphire laser or 7 ps pulses at 351 nm from Nd:YLF laser). The thickness of the photoexcited region under 2P excitation was estimated using the determined 2P-absorption coefficient b which 1 ¼ 80–100 mm led to a penetration depth of a1 2P (b P0) ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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P. Sˇcˇajev et al.: Carrier dynamics in bulk GaN
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γ = 3.4
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β =13 cm/GW -17 2 σeh=(2.5±0.5)×10 cm
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10 γ = 3.9
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Diffraction efficiency
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3 Results and discussion FCA decay at 2P injection conditions exhibited single exponential kinetics in the 80– 800 K range and led to tR 40 ns at room temperature (RT) (Fig. 1b). The lifetime was found to be independent of the excess carrier density in the range of DN ¼ 3 1016–5 1017 cm3. Consequently, the contribution of radiative carrier recombination to the total carrier lifetime 1/tR ¼ 1/tRad þ 1/tnRad was negligible [1/tRad ¼ BN ¼ (200– 500 ns)1 using a range of effective radiative recombination coefficients of B ¼ 2–5 1011 cm3 s1 representing both excitonic and free carrier recombination and N ¼ 1017 cm3] and revealed the nonradiative origin of decay (tR ¼ 40 ns ¼ tnRad). We note that the dependence of tR on temperature followed the power law tR / T1.15 from 80 to
-1
10
γ=
at P0 ¼ 1 GW/cm2 power density. This is some 100– 1000 times higher when compared to the 1P injection case (a1 1P 100 nm with diffusion-expanded photoexcited region to a few micrometers [4]). LITG [4] and FCA [5] techniques were used to monitor the spatial and temporal carrier dynamics. These techniques enabled us to examine the changes in refractive index, Dn, and absorption coefficient, Da, at wavelengths far below Eg (at 1053 nm), which are well described by the Drude– Lorentz theory through the simple relationships: Dn ¼ nehDN and Da ¼ sehN, where DN is the nonequilibrium carrier density, neh is the refractive index change per one electron– hole pair in cm3, and seh is the FCA cross-section [4, 5]. Spatial modulation of Dn with grating period L (i.e., recording of a transient free-carrier grating) was realized for carrier injection by the light interference pattern. Diffraction efficiency of an IR probe beam (at 1053 nm) on the grating, h(t) / DN2(x,0)exp(2t/tG), provided a decay rate 1/tG ¼ 1/tD þ 1/tR, composed of the diffusive decay time tD ¼ L2/(4p2Da), where Da is the ambipolar diffusion coefficient and tR is the recombination time. Carrier lifetimes longer than 10 ns were determined from FCA, monitoring the probe beam differential transmission ln (T0/T(t)) ¼ Da(t)d. Electrical delay of the probe beam enabled determination of tR values up to 10 ms [5]. The linear dependence Da ¼ sehDN was used to determine the free electron–hole absorption cross-section, seh, from the measured value of Da for a given DN and the twophoton absorption coefficient, b. The two-photon excitation was confirmed by a nearly quadratic increase of differential transmission (DT / I01:9 ) associated with the nonlinear carrier generation rate DN / I02 . The grating diffraction efficiency, h, increased twice steeper than the DT with excitation fluence (h / I03:8 ). The calibrated DT and h signals (see Fig. 1a) provided seh ¼ 2.5 1017 cm2 at 1053 nm and a two-photon absorption coefficient of b ¼ 13 cm/GW at 527 nm. For the TRPL measurements, the decay transients were detected by a UV sensitive streak camera system at excess carrier density in the range 1016 to 1018 cm3 (estimated at the very surface of GaN at the end of the excitation pulse).
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Figure 1 (online color at: www.pss-b.com) (a) Dependences of light-induced diffraction efficiency and differential transmission on excitation energy density I0 in bulk HVPE GaN under two-photon carrier injection at 527 nm. (b) Temperature dependence of carrier lifetime and bipolar diffusion coefficient at injected carrier density DN 1017 cm3. Points—experimental data, dashed lines—linear fits in the log–log plot, providing slopes g.
800 K, thus indicating its genesis being different from the exciton radiative decay in GaN, tex / T3/2 in the T ¼ 80– 300 K range [1, 3]. The determined long tR value validated the condition tR tD and allowed determination of the D value from the LITG diffusive decay time measured for small grating periods (2–3 mm). The Da values were determined at various injected carrier densities and sample temperatures. At 2P excitation conditions, holes and electrons with equal densities were created. Therefore, the Dember field between the mobile carriers ensured the regime of bipolar diffusion with an ambipolar diffusion coefficient Da ¼ (n0 þ DNn þ DNp)DnDp / [(n0 þ DNn)Dn þ DNpDp] (indices n and p refer to electrons and holes, respectively). Assuming that hole mobility is much smaller than that of electrons, the moderate excitation regime (DNn ¼ DNp ¼ 1017 cm3 n0) provided an ambipolar diffusion coefficient of Da 2Dp ¼ 1.6 cm2/s (Fig. 1b). Consequently, for low excitations (DNn ¼ DNp ¼ 1015 cm3 < n0) the hole diffusion coefficient was determined to be Da Dp ¼ 0.8 cm2/s. www.pss-b.com
Original Paper Phys. Status Solidi B 249, No. 3 (2012)
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A fitting of Da(T) dependence provided n0 ¼ 7 1015 cm3 at RT. The temperature dependence of Da is consistent with typical scattering by acoustic and optical phonons for T > 150 K. At lower temperatures, the impurity scattering as well as the spatial bandgap renormalization [7] hindered carrier diffusion and thus resulted in slightly lower Da values. The determined valued of tR and Da led to a carrier diffusion length of LD ¼ 2.5 mm, being the largest reported up to now for GaN at RT. The observed inverse correlation between the tR(T) and Da(T) dependences exhibits features of surface recombination. Note that when the carriers are created inside the thick crystal of thickness d, their surface lifetime tS is dependent on the rate at which carriers diffuse from the bulk to the surface (tdiff / d2/Da) and recombine there tsurf / d/S (S is the surface recombination velocity) [5]. In our case, the estimations for the studied 200 mm-thick layer provided tdiff 100 ms which is far from reality. Therefore, diffusion to the internal boundaries of GaN hexagonal grains (assumed to be cylinders of radius rc for simplicity) must be considered. Using this model wherein tS ¼ tinter þ tdiff ¼ p1/2rc/S1 þ p3/2r2c /Da [8], the fit of the measured tR value at RT (Fig. 1b) provided rc ¼ 3.6 mm and an effective interface recombination velocity of S1 ¼ 9500 cm/s at RT. Thus, the extended defects (dislocations) and associated point defects near the grain boundaries must be effective centers of nonradiative recombination for the carriers reaching them by diffusion. TRPL kinetics at 1P excitation provided very fast initial decay transients which only after 1 ns became nearly exponential with a 1.5 ns decay time (Fig. 2), still being much faster as compared to 40 ns decay time in 2P case (see Fig. 1b). A deeper analysis of the PL kinetics was undertaken with help of the numerical solution [4, 5] of the continuity equation, assuming carrier injection by 100 fs pulse at
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4 Conclusions Complementary study of carrier dynamics in a high quality bulk GaN under two- and single-photon excitation conditions has shown that nonequilibrium recombination and diffusion processes in the entire 80–800 K range and moderate excitations (from 1015 to 1017 cm3) can be reliably explained by a free electron–hole model. The diffusion was shown to be critical in bulk recombination, the analysis of which led to the determination of diffusion-limited nonradiative recombination values from 10 to 120 ns. The subnanosecond PL decay transients revealed carrier diffusion, surface recombination and PL emission reabsorption processes, thus masking access to intrinsic recombination processes. The analysis indicates that the radiative lifetime is still longer than the nonradiative one even in this high-quality bulk GaN crystal.
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Acknowledgements The research was sponsored by TAP Project No.5/2011 and the Baltic-American Freedom foundation.
0.5
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Figure 2 (online color at: www.pss-b.com) RT PL decay at few emission wavelengths (see inset) at 1P carrier injection. The best fits for TRPL in spectral regions 1, 4 were obtained using reabsorption coefficients of 7000, 400 cm1, correspondingly. www.pss-b.com
267 nm, a boundary condition at the front surface [5] and above described density dependent D value: @N(z,t)/@t ¼ D(N)52N(z,t) N(z,t)/tR BN2(z,t) þ G(z,t), where G(z,t) is the carrier generation rate. For calculation of the PL signal, the intensity of the measured signal was integrated over the excited layer thickness by taking into account reabsorption of light emission at the short wavelength wing [3, 4]. It was found that the initial fast decay within the first 100–500 ps has its genesis in the carrier diffusion away from the surface deeper into the sample which distributes the carriers into 1 mm depth within 1 ns and thus reduces their peak density by an order of magnitude (from 1017 cm3 at the end of laser pulse to 1016 cm3 at 1 ns). The impact of PL emission reabsorption becomes more pronounced for t > 1 ns and particularly for the shorter wavelengths. In the whole range of observed decay (2 ns), the impact of radiative recombination to the measured effective PL decay time was negligible, thus preventing its direct determination and deeper insight into the origin of PL (i.e., excitonic or free-carrier recombination). A contribution of the surface recombination is also important, and fitting of the data revealed S ¼ 1.1 104 cm/s. We note that the LITG decay modeling at 1P excitation (351 nm) also revealed the impact of surface recombination, and the fitting provided the S ¼ 3 104 cm1 value. The difference in S values may be caused by S increasing with injection [1, 5]. Large S value might be influenced by chemical mechanical polishing and subsequent long-term surface self-oxidation.
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ß 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
P. Sˇcˇajev et al.: Carrier dynamics in bulk GaN
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