Dynamics of nonequilibrium carrier decay in AlGaN epitaxial layers with high aluminum content

Tanuj Saxena; Michael Shur; Saulius Nargelas; Žydrūnas Podlipskas; Ramūnas Aleksiejūnas; Gintautas Tamulaitis; Max Shatalov; Jinwei Yang; Remis Gaska

doi:10.1364/OE.23.019646

1. Introduction

The improved structural quality of AlGaN alloys and device designs has considerably enhanced the efficiency of deep UV light-emitting diodes (LEDs) [1,2]. The high emission efficiency in AlGaN devices with high dislocation densities (>10⁸ cm⁻²) [1] is usually attributed to compositional and/or well width fluctuations in the quantum wells [3–5]. These fluctuations lead to carrier localization and reduce the probability of their diffusion to the point or extended defects responsible for the nonradiative recombination. Therefore, the widely used simplistic ABC model [6], which is quite successful for describing the free carrier dynamics in binary GaN, fails to properly account for the effects of radiative and non-radiative recombination in ternary InGaN and AlGaN compounds [3,4,7–11].

Several studies of the temperature dependence of photoluminescence (PL) band peak position showed that nonequilibrium carriers in AlGaN propagate in a double-scaled potential profile [10,12], which had been suggested first to interpret the results obtained for AlInGaN [13]. According to this model, the potential profile for electrons and a symmetric profile in real space for holes have regions with a lower average potential (accumulation regions), where the potential is randomly modulated on a smaller spatial scale. This model is supported by the study of the spatial distribution of the PL intensity using the Scanning Near Field Optical Microscopy (SNOM) technique [14].

The improvement of the light emission efficiency under electrical injection is the key issue in the further development of the AlGaN-based UV LEDs. However, spectroscopy under photoexcitation is a more flexible technique to study the mechanisms of radiative and nonradiative carrier recombination that are the key processes governing the emission efficiency in AlGaN epilayers and heterostructures employed in UV LEDs. PL spectroscopy is usually used to study the results of the studies of the carrier dynamics in AlGaN epilayers and MQWs [3,4,7–11].

The relationship between the PL signal and carrier density depends on the rates of radiative and nonradiative recombination channels. The light-induced transient grating (LITG) technique [15] allows for the direct determination of relationship between the carrier density and the observed PL signal. In this work, we compared the results obtained by time-resolved photoluminescence (TRPL) and LITG techniques to reveal the influence of carrier localization on the carrier dynamics in AlGaN epilayers.

This dynamics depends on the structural quality of the epilayers. We studied four samples with different structural quality. The results presented in this paper are obtained from two different samples with the highest and the lowest dislocation densities among the AlGaN samples with similar aluminum content under study.

2. Experimental

Two n-Al_0.6Ga_0.4N epilayers grown on sapphire substrates by migration enhanced metal organic chemical vapor deposition (MEMOCVD^®) were selected for this study. The samples had similar aluminum content but different threading dislocation densities (TDD) of approximately 2–5 × 10⁸ cm⁻² and 2–5 × 10⁹ cm⁻² for the low dislocation density (LDD) high-dislocation density (HDD) sample, respectively. Fitting the temperature dependence of PL band peak position under quasi-steady-state excitation with the empirical formula suggested by Eliseev et al. [16] yielded the potential fluctuation dispersion of approximately 50 meV in both samples under study.

The carrier dynamics was investigated using time-resolved photoluminescence (TRPL) and light-induced transient grating (LITG) techniques with picosecond time resolution limited by excitation laser pulse duration. For the TRPL measurements, the excitation source was the fifth harmonic (213 nm) of a mode-locked Nd:YAG laser having a pulse width of 30 ps and operating at a repetition rate of 10 Hz. The excitation beam was focused into a spot of 480 μm in diameter. The excitation energy density varied from 3 to 300 μJ/cm². Assuming the absorption coefficient of 10⁵ cm⁻¹, the corresponding range of the initial carrier density was between 3 × 10¹⁷ cm⁻³ and 3 × 10¹⁹ cm⁻³. The highest excitation was chosen to be well below the threshold for permanent optical damage in AlGaN [17]. The PL was collected in the front-surface configuration, dispersed using a Chromex imaging spectrograph and detected by a Hamamatsu streak camera with a time resolution of 20 ps.

In the LITG experiments, the interference pattern of two 30 ps–long laser pulses at the wavelength of 213 nm (hv = 5.8 eV) induced a spatially modulated nonequilibrium carrier distribution $N (x) = N_{0} + Δ N \cos (2 π x / Λ)$ with period Λ. According to the Drude-Lorentz model, the refractive index change due to the carrier density modulation can be expressed by [15]

Δ n (x) = Δ N (x) n_{e h} = - \frac{e^{2}}{2 n_{0} ω^{2} ε_{0}} Δ N (x) [\frac{1}{m_{e}} + \frac{1}{m_{h}}]

where

Δ N

is the density of the optically excited carriers, ω is the angular frequency of the probe light,

n_{0}

is the refractive index of the unexcited material,

ε_{0}

is the static dielectric permittivity in F/m, and

n_{e h}

is the change in the refractive index due to one electron-hole pair per unit volume. Note that the electron contribution dominates in the refractive index modulation, since usually

m_{e} < m_{h}

. The decay of the transient carrier grating was monitored by the diffraction of a delayed probe beam at 1064 nm (in the transparency region of the sample under study). The diffraction efficiency, i.e. the ratio between the intensities of the diffracted and transmitted parts of the probe beam, is proportional to the square of the nonequilibrium carrier density integrated over the excited depth:

η \propto Δ n {(t)}^{2} \propto {[\int Δ N (z, t) d z]}^{2}

[15]. Thus, the carrier density is explicitly linked with the diffraction efficiency. The grating decays due to carrier recombination and diffusion with time constant

τ_{G} = {(1 / τ_{R} + 1 / τ_{D})}^{- 1}

, where

τ_{R}

and

τ_{D} = Λ^{2} / 4 π^{2} D

are the carrier lifetime and diffusive decay time depending on the ambipolar diffusion coefficient D and the grating period Λ. The results presented in this paper are obtained at Λ value of 7.7 µm, large enough for diffusion to be neglected (

τ_{D} > τ_{R}

), so that

τ_{G} \approx τ_{R}

.

3. Results and discussion

Figure 1 compares the decay of the PL intensity after a short pulse excitation and the decay of carrier density obtained from the transient grating efficiency decay in LITG at similar excitation conditions for the LDD and HDD samples. At any excitation pulse energy, the PL in the HDD sample decays exponentially approximately by three orders of magnitude and has a slow decay component with a time constant substantially exceeding the time range covered in our experiments. In the LDD sample, the fast decay component occurs at high excitation pulse energy, in addition to the exponential and slow decay components. The carrier density decay proceeds initially at the same rate as the PL decay but reaches the slow decay stage at considerably higher carrier density than in the PL decay. The coincidence of carrier density and PL decay rates at the initial decay stage shows that the luminescence is directly proportional to the carrier density. Such a linear radiative recombination is expected for electrons and holes predominantly localized at the same location in real space and moving together as an exciton; however, the direct proportionality of the luminescence intensity on carrier density is observed at the initial relaxation stage after high excitation pulse energy in the LDD sample, when the carrier density decay proceeds nonexponentially. The slow component in the LITG efficiency decays with the effective time exceeding the range covered in our experiments and can be interpreted by carrier capture to strongly localized states. Meanwhile, after the carrier density decay enters the slow decay mode, the PL decays at the same rate up to several nanoseconds. In the HDD sample, a slow decay mode is also observed for the PL intensity (at the intensity level lower by three orders of magnitude than the peak intensity after excitation).

Fig. 1 Decay of PL intensity after short pulse excitation (dashed lines) and the carrier density obtained from LITG experiments (solid lines) at similar initial carrier densities (indicated).

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Additionally, the analysis of the time evolution of PL spectra yields information on the slow decaying PL component. Figure 2 shows the time evolution of the spectra for the two samples. Each spectrum is integrated over 0.5 ns. The PL spectrum of the LDD sample consists of one broad band. The band redshifts within the first 2 ns after the excitation and remains at the same spectral position at longer delays (see Fig. 3). This behavior can be explained by a faster recombination of the free carriers emitting on the high-energy side of the PL band and by the exciton relaxation down to deeper localized states initially after excitation and further exciton recombination in the relaxed and thermalized system of the localized excitons. The initial red shift of the PL band was not observed for the HDD sample. Instead, the band exhibited a strong red shift and considerable broadening after approximately 2 ns delay. This behavior could result from the change in the recombination mechanism. The red shift by 110 meV and a slow decay indicate that this low-energy emission band might be caused by donor to valence band recombination. This band was not observed for the LDD sample, where the density of the localized states involved in the low-energy emission is presumably lower.

Fig. 2 Time evolution of photoluminescence spectra in two samples with high (HDD) and low (LDD) dislocation densities after excitation at initial carrier density of 3 × 10¹⁹ cm⁻³.

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Fig. 3 Evolution of TRPL peak position as a function of delay from the excitation pulse at initial carrier density of 3 × 10¹⁹ cm⁻³.

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The main features of the carrier density dynamics after a short-pulse excitation could be described by a set of three coupled rate equations for the densities of non-equilibrium free electrons $Δ n$ and holes $p$ and electrons and holes localized as pairs like excitons $n_{e x}$ . Some experimental results indicate that the carriers are localized in such pairs [18,19].

\frac{d Δ n}{d t} = - \frac{Δ n}{τ_{n e}} - B (n_{0} + Δ n) p - γ_{d o w n} (n_{0} + Δ n) p + γ_{u p} n_{e x}

\frac{d p}{d t} = - \frac{p}{τ_{n p}} - B (n_{0} + Δ n) p - γ_{d o w n} (n_{0} + Δ n) p + γ_{u p} n_{e x}

\frac{d n_{e x}}{d t} = γ_{d o w n} (n_{0} + Δ n) p - \frac{n_{e x}}{τ_{r a d}} - \frac{n_{e x}}{τ_{n r a d}} - γ_{u p} n_{e x}

Here we neglect the equilibrium hole concentration, which is negligible in n-type or intrinsic wide band gap semiconductors. The set of equations is strongly simplified, since the localization strength is different for individual excitons, and the rates for their different capture and escape as well as radiative and nonradiative lifetimes are represented here by single effective values $γ_{d o w n}$ , $γ_{u p}$ , $τ_{r a d}$ and $τ_{n r a d}$ respectively. In the first two equations, the first term describes the nonradiative decay with the lifetimes $τ_{n e}$ and $τ_{n p}$ , which can differ due to different thermal velocities and rates of capture of electrons and holes by the nonradiative recombination centers. The second term describes the radiative recombination with bimolecular recombination coefficient B. The last two terms describe the relaxation of free carriers into localized (excitonic) states and the escape from the localized states with corresponding rate coefficients. Equation (4) has two recombination terms with characteristic time constants of radiative and nonradiative recombination: $τ_{r a d}$ , $τ_{n r a d}$ .

The initial conditions can be written as: $p (0) = p_{p g}$ , $Δ n (0) = n_{p g}$ and $n_{e x} (0) = 0$ , where $n_{p g} = p_{p g}$ are the photogenerated nonequilibrium electron and hole densities. The luminescence contributions from radiative recombination of excitons and free carriers spectrally overlap due to large band gap fluctuations and, correspondingly, large band widths. The PL intensity can be expressed as

I_{L} \propto \frac{n_{e x}}{τ_{r a d}} + B (n_{0} + Δ n) p \approx \frac{n_{e x}}{τ_{r a d}} + B n_{0} Δ n + B Δ n^{2}

Figure 4(a) presents the emission rates described by the three terms in Eq. (5), which were calculated after solving the set of Eqs. (2)-(4) by using the following parameters: $B = 10^{- 10} {cm}^{3} /s$ , $τ_{n e} = τ_{p e} = 0.36 ns$ , $γ_{d o w n} = 5 \times 10^{- 10} {cm}^{3} /s$ , $γ_{u p} = 0.07 ns$ , $τ_{r a d} = 0.7 ns$ , $τ_{n r a d} = 5 ns$ . The value $n_{0} = 3 \times 10^{18} {cm}^{-3}$ , obtained using Hall measurements on the sample under study, was used in the calculation. The calculation results exhibited only weak sensitivity for variation in the ratio of the initial densities of free and localized carriers used as the initial conditions for a fixed density of the photogenerated carriers. For the results presented in Fig. 4, $n_{p g} = p_{p g} = 10^{19} {cm}^{-3}$ and $n_{e x} (0) = 0$ were used.

Fig. 4 (a) Recombination rates, described by first (black line), second (red), and third (blue) terms in Eq. (5), and (b) comparison of the PL intensity decay (black curve) and the decay of free electron density (red) calculated by solving Eqs. (2)-(4) and using Eq. (5).

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Figure 4(b) presents the comparison of the PL intensity decay and the decay of the free electron density. Both decay curves are normalized to their initial values. The contribution of holes and localized carriers to the LITG efficiency used to extract the carrier density decay experimentally is considerably smaller than that of electrons, since the contribution is inversely proportional to the effective mass (see Eq. (1)). Thus, the calculated free carrier density is selected for the comparison. As seen in Fig. 4(b), the solution of the simple set of rate Eqs. (2)–(4) with a reasonable set of rate coefficients can explain the coincidence in the decay rates of PL intensity and the free carrier density after intense short-pulse excitation when the density of the free carriers is substantial in comparison to the density of localized carriers (excitons). The faster decay of the PL intensity due to bimolecular recombination is partly compensated by increasing contribution of exciton emission, which is enhanced by relaxation of free electrons and holes to the excitonic (localized) states.

The third stage of the LITG signal decay is rather flat on the time scale in our experiments. As discussed above, this is an evidence that we have carriers trapped in the states below the band gap. Note that the number of the trapped carriers can be rather significant. Their contribution to the LITG signal is considerably smaller than that of the free carriers, since the localization can be roughly accounted for in Eq. (1) as an increase in effective mass. In addition, the observed very slow relaxation of LITG efficiency points to a large activation energy of the trapped carriers and, consequently, to a low thermal escape rate. The insignificant slow decay component in PL kinetics indicates that the trapped carriers do not contribute to the radiative recombination; therefore, their capture results in decreasing the densities of free carriers and optically active excitons (weakly localized carriers). The importance of this channel for the carrier dynamics depends on the density of the trapping centers. The capture to the trapping centers might also have a considerable impact on the luminescence efficiency measured after a short pulse excitation: the captured carriers are lost for luminescence because they recombine either nonradiatively or with very long recombination time substantially exceeding the measurement time in our experiments.

Figure 5 (a) presents the PL efficiency as a function of carrier density. The corresponding lifetimes are plotted in Fig. 5 (b). The lifetimes were estimated in the initial part of the PL intensity decay, as illustrated in Fig. 6.

Fig. 5 Photoluminescence efficiency (a) and fast decay lifetime (b) as functions of the density of carriers generated by 30 ps long pulse excitation in HDD and LDD samples at 300 K.

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Fig. 6 Photoluminescence decay kinetics at different density of carriers generated by 30 ps long pulse excitation in HDD and LDD samples at 300 K (dashed lines). Straight lines indicate the approximations used to extract the lifetimes presented in Fig. 5.

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For the sample LDD, the PL efficiency slightly increases with increasing initial carrier density generated by a short pulse of photoexcitation and remains nearly constant at elevated carrier densities up to 3 × 10¹⁹ cm⁻³, in spite of the decreasing carrier lifetime. This behavior is consistent with an increasing contribution of the radiative bimolecular recombination, which makes the lifetime shorter but increases the efficiency of the radiative recombination.

The increase in PL efficiency at increasing initial carrier density is substantially more pronounced in the HDD sample. In contrast to the behavior of the LDD sample, this increase in efficiency is followed by a substantial increase in the carrier lifetime. It is reasonable to assume that the saturation of the nonradiative recombination centers is one of the effects causing the increase in the carrier lifetimes and PL efficiency.

4. Conclusion

In conclusion, we show that the PL of Al_0.6Ga_0.4N epitaxial layers after short-pulse excitation decays at the same rate as the carrier density even at carrier densities when the contribution of free carriers to the PL intensity via bimolecular recombination is significant. As shown by model calculations, this behavior is a result of partial compensation of the decay of the PL intensity due to bimolecular recombination by increasing contribution of the linear radiative recombination enhanced by the relaxation of the free carriers to the localized states. The LITG and TRPL experiments show that the carriers are also captured at the states well below the band gap. The carriers at these states have lifetime exceeding the time scale in our experiments (tens of nanoseconds) and their radiative recombination occurs via different mechanism than the recombination of weakly localized electron and hole (exciton) and results in a broad redshifted band. Capture of carriers to these centers might have substantial influence on the internal quantum efficiency.

Acknowledgments

The work at VU was funded by the European Social Fund under the Global Grant measure project VP1-3.1-ŠMM-07-K-02-014. The work at RPI was supported primarily by the Army Research Laboratory (Program Manager Dr. Meredith Reed).

References and links

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Dynamics of nonequilibrium carrier decay in AlGaN epitaxial layers with high aluminum content

Abstract

1. Introduction

2. Experimental

3. Results and discussion

4. Conclusion

Acknowledgments

References and links

Cited By

Figures (6)

Equations (5)

Optics Express