Interwell carrier transport in InGaN/(In)GaN multiple quantum wells Free

Active regions of GaN-based light emitting diodes (LEDs) and laser diodes are often formed from several, up to eight, quantum wells (QWs).¹ Using multiple QWs (MQWs) instead of a single well is potentially advantageous, because for the same output power, it would allow reducing the carrier density in the QWs and diminish the detrimental effect of Auger recombination. To achieve these benefits, a uniform carrier distribution between QWs is required. However, for InGaN/GaN MQW devices emitting in the blue and especially in green spectral regions, this requirement may be difficult to realize because of the strong hole confinement and slow transport. Simulations suggest that only one or two QWs located closest to the p-side of an InGaN/GaN LED structure substantially contribute to the overall light emission or lasing.^2,3

In spite of the importance of the interwell (IW) carrier transport and the uniform carrier distribution for the device performance, experimental investigations of these effects have been scarce. So far, they have been limited to steady-state optical measurements. David et al. have suggested that emission in blue-emitting LEDs with an MQW active region primarily takes place from just one QW on the p-side of the structure.⁴ Their conclusion has been based on electroluminescence (EL) measurements and simulations, and is attributed to an inefficient hole transfer between the QWs. A similar conclusion has been drawn from the comparison of EL and photoluminescence (PL) measurements.⁵ Studies of LED structures with QWs emitting at different wavelengths have produced controversial results. Some works have suggested that the IW hole transport is the limiting effect,⁶ while in others the electron transport has been found to be critical.⁷ Here, one should note that the mentioned steady-state optical studies are rather indirect and do not provide data on the dynamics of the IW carrier distribution. An investigation of IW transport dynamics should help to explore the relevance of different transport mechanisms, contribute to a better understanding of the limitations of typical MQW structures, and suggest ways to their improvement.

In this work, such measurements have been performed by time-resolved PL using an optical marker technique. This method has previously been successfully used to study carrier transport in GaAs- and InP-based MQW structures and superlattices,^8–10 but surprisingly, has not yet been applied to nitride MQWs. The experimental approach is based on the measurement of PL dynamics from regions with different band gaps located at different positions of a heterostructure. The schematics of a structure used in our experiments are presented in Fig. 1. The IW transport of carriers, primarily excited in the top GaN cap layer, has been traced by monitoring PL rise at the emission wavelength of the deeper detector quantum well (DQW).

The experiments were performed on six different MQW structures grown on a c-plane sapphire substrate and consisting of a 6 μm buffer layer, a DQW, a region with a number of uniform QWs called transport QWs (TQWs), and a 100 nm GaN cap layer. The thickness of the QWs was 3 nm and the nominal In content in the TQWs and DQW was 12% and 18%, respectively. Room temperature peak wavelengths for the TQWs and DQWs were in the region of 420–430 and 460–480 nm. Structures with a different number of TQWs and barrier parameters were examined (Table I). The samples were not intentionally doped with the majority electron concentration of about 1 × 10¹⁷ cm⁻³.

The properties of IW carrier transport were evaluated by measuring time-resolved and time-integrated PL at TQW and DQW emission wavelengths. PL was excited by third harmonic pulses from a self-mode-locking Ti:sapphire laser with a pulse duration of 200 fs, a pulse repetition frequency of 80 MHz and a central wavelength of 260 nm. To measure long PL transients, the pulse repetition rate was reduced to 4 MHz with an acousto-optic pulse picker. Short PL transients were recorded with a spectrometer–streak camera system (time resolution: 5 ps); to measure the long ones, a time-correlated single photon counter (temporal response: 50 ps) was used. In the latter case, the appropriate spectral region was selected with band pass filters. Most of the carriers were excited in the GaN cap layer since for 260 nm excitation the absorption length is 50 nm. The pulse energy was 25 pJ, which corresponds to the photoexcited carrier density in the GaN layer just after a pulse of about 5 × 10¹⁷ cm⁻³. Carrier concentration in the TQWs shortly after the excitation was of the order of 1 × 10¹⁹ cm⁻³ (see an evaluation of the capture efficiency below). It is comparable to that in an operating LED making our results relevant for device modeling. The photoexcited carrier density was much larger than the background doping. In such a case, the overall IW carrier transport is determined by the slower holes.⁹ The transport measurements were performed in the 150–350 K temperature range.

Figure 2 shows the time-integrated PL spectra of several samples. The short and long wavelength peaks correspond to transitions in the TQWs and the DQW, respectively. The TQW PL is prevalent for structures with the GaN barriers. For the InGaN barrier structure, the spectrum is dominated by the DQW PL peak suggesting a much more efficient carrier transfer across the TQWs. The transport efficiency, however, cannot be directly determined from the intensity of the time-integrated PL peaks, because the transport and detector QWs may have different internal quantum efficiencies (IQE). Time-resolved measurements must be performed.

In addition to the QW PL, PL at the GaN band gap with a decay time of 45 ps has been observed. Since bulk GaN experiences much longer PL decay times of hundreds of picoseconds,^11,12 the short decay time should primarily be assigned to the carrier transfer to the TQWs. The TQW PL rise time was similar to that of the GaN decay.

DQW PL transients for five samples are presented in Fig. 3. The PL rise contains a fast and a slow component, more clearly revealed for the GaN barrier structures. The fast component with a rise time limited by the resolution of the measurement systems originates from carriers excited directly in the DQW and adjacent barriers (see Fig. 1). The slow component, in the nanosecond range, reflects the carrier transport to the DQW from the GaN cap layer via TQWs. Remarkably, the slow component is not observed in the transients of structures with thick barriers and 8 TQWs (not shown) explicitly demonstrating that in these structures carriers excited in the cap layer do not reach the DQW.

First, let us discuss the IW transport mechanism. The possible processes are ballistic transport over the QWs, tunneling, and thermionic transport. In the latter case, the transport takes place via subsequent events of carrier capture into and emission out of the QWs. The electron and hole capture into nitride QWs is very fast, of the order of sub-picoseconds.¹³ Hence, if the thermionic transport time is in a 100 ps to ns range, the thermionic emission can be safely viewed as the limiting factor. Previous research has shown that for electrons, different transport mechanisms, depending on the structure and experimental conditions, may be dominant.^14–18 In this work, as mentioned above, we address the transport of holes.

The key difference between the ballistic transport, tunneling, and thermionic transport is their temperature dependence. With increasing temperature, the phonon occupation number and the carrier–optical phonon scattering rate increase, decreasing mean free path. This reduces the probability for a carrier to traverse a QW ballistically without being captured. Consequently, the contribution of the ballistic transport to the IW carrier transfer would reduce with increasing temperature, reducing the intensity of ballistic transport-related DQW PL. The tunneling time is temperature independent¹⁹ and should not influence neither the temperature dependence of the IW transport time nor the transport-related PL intensity. Meanwhile, the thermionic emission time $τth$ decreases with temperature exponentially speeding up the IW transport. In the quasi-classical picture, the thermionic emission time is expressed as²⁰ 

where $mw*$ is the effective mass in the QW, $Lw$ is the QW width, and $ΔE$ is the energy barrier for a carrier to overcome.

DQW PL transients at different temperatures for the InGaN barrier sample are shown in Fig. 4. The slow rise time component starts to appear at 180 K when heating up from 150 K. With increasing temperature, its relative weight increases and the rise time shortens. The time-integrated intensity of the DQW also increases. For the structures with GaN barriers, the effect becomes distinct at temperatures >250 K (not shown).

To extract the PL rise and decay times, the transients were fitted with an empirical equation that describes the rise and decay with single-exponential functions

Here, $τr$ and $τd$ are the rise and decay times, respectively, and A is a proportionality constant.

The rise time dependence on temperature for the thin barrier and InGaN barrier samples is shown in Fig. 5. With increasing temperature, the rise times decrease exponentially, confirming that the IW transport is governed by the thermionic emission (see the above discussion). An Arrhenius type plot allows extracting activation energies, which for the 3 TQW, thin barrier and InGaN barrier samples are 220, 200 and 70 meV, respectively.

When evaluating the energy barrier for the thermionic emission, one should bear in mind that in nitride QWs, a carrier, to reach the next QW, should overcome not just the confinement energy ΔE_QW (inset to Fig. 4), but also the potential change in the barrier $ΔEb$ induced by the electric field due to the polarization discontinuity between the barrier and the QW. ΔE_QW can be evaluated from the PL spectra. Assuming the valence band offset of 0.3 for the band gap difference between the barrier and QW layers,²¹ ΔE_QW for the 3 TQW and thin barrier samples is 150 and 170 meV, respectively. Band structure calculations performed self-consistently solving one-dimensional Poisson and Schrödinger equations show that $ΔEb$ is about 100 meV, resulting in an effective barrier of 250–270 meV for the thermionic emission $ΔEeff=ΔEQW+ΔEb$⁠.

The $ΔEeff$ values for the samples with GaN barriers are slightly larger than the obtained activation energies. This discrepancy can be explained by several phenomena that would effectively reduce the barrier height for the thermionic emission: a partial screening of the electric field in the QWs by photoexcited carriers, thermal carrier distribution, and Fowler-Nordheim tunneling. The latter effect should be more pronounced for the thin barrier sample with a sharper barrier potential tilt and could explain why the hole transfer time per well (Table I) is slightly shorter in the thin GaN barrier structure compared to medium GaN barrier structure.

For the InGaN barrier structure, $ΔEQW≈100$ meV and $ΔEeff≈150$ meV. The latter quantity is much higher than the obtained activation energy of 70 meV. This large discrepancy cannot be explained by the arguments provided for the GaN barrier samples. Possibly, the additional reduction of the barrier for the thermionic emission is related to alloy composition fluctuations in the InGaN barriers. Percolation transport in InGaN QWs via localized states has been shown to play an important role for electrons.^16,22,23 Our experiments suggest that this mechanism is also relevant for holes. One should note, however, that in spite of the low effective barrier, the PL peaks in the GaN and InGaN barrier samples are similar in terms of shape and linewidth indicating that the lowered barriers in the InGaN barrier structure do not affect the quantum confinement and the optical quality of the QWs.

To compare the transport times for structures with a different number of TQWs, we use a parameter “transport time per QW” that is obtained by dividing the DQW PL rise time by the number of TQWs. Such transport times per TQW are presented in Table I. They vary from 0.3 ns for the InGaN barrier to 1.3 ns for the GaN barrier samples. Surprisingly, when calculated using Eq. (2) with the effective hole mass of 1.4 m₀,²⁴ the thermionic emission times are one to two orders of magnitude shorter, from 2 to 200 ps. Such a discrepancy between the experimental data and the semi-classical model, however, is not unique to InGaN/(In)GaN QWs. A similar difference between experimental data and the model has also been observed in GaAs/AlGaAs QWs as well.²⁵ It has been suggested that the model of Eq. (1) does not provide adequate quantitative results for narrow QWs.²⁶ The exponential dependence of the emission time on temperature, however, is intact in all models.

With increasing temperature, the time-integrated DQW PL intensity increases as well. This demonstrates that not only the carrier transfer rate becomes faster but also the number of carriers that reach the DQW is increasing. In the evaluation of this effect, one should bear in mind that the time-integrated PL intensity depends not only on the concentration of the electron-hole pairs or excitons N but also on the IQE (η) in the DQW, $IPL(T)∝N(T)η(T)$⁠. To estimate $η(T)$⁠, and subsequently $N(T)$⁠, we performed time-resolved PL measurements in the 4–340 K temperature range using resonant (430 nm) carrier excitation directly into the DQW. Radiative (⁠$τR$⁠) and nonradiative (⁠$τNR$⁠) recombination times were evaluated following the procedure described in Refs. 27 and 28. To evaluate the IQE, the relation $η=τNR/(τR+τNR)$ was used.

The temperature dependence on the relative carrier number in the DQW for the thin barrier structure is shown in Fig. 4. Except for the highest temperatures, the dependence is exponential. The slope provides an activation energy of 200 meV, which is similar to the one obtained from the DQW PL rise times. This is an independent confirmation that the carrier transfer to the DQW is indeed governed by the thermionic emission. Deviation from the exponential dependence at T > 300 K occurs due to an increased rate of nonradiative recombination in the TQWs, which limits the number of carriers available for the IW transport.

After measuring the transfer times and establishing the transport mechanism, it is natural to try evaluating the fraction of photoexcited carriers that reach the DQW. This value could serve as an indication of the uniformity of the IW carrier distribution in an MQW active region without the DQW. This is especially important for the samples with GaN barriers for which most of the carriers remain in the TQWs.

For a uniform IW carrier distribution, not all the carriers should be transported to the DQW but just 1/4 of them for the 3 TQW structure with four QWs in total and 1/6 for the 5 TQW and thin barrier structures with six QWs. To estimate the fraction of photoexcited carriers in the DQW, one could compare PL intensities for the TQW and DQW PL peaks. Such a comparison, however, is indirect and may be misleading because of the different IQE of the transport and detector QWs. Instead, in the evaluation of the fraction of carriers transported to the DQW, we make use of the double peak structure of the DQW transients, clearly seen for the 3 TQW, 5 TQW and thin barrier structures (Fig. 4).

As mentioned, the initial sharp rise of the PL transients originates from carriers generated directly in the DQW and adjacent barriers. The subsequent slow rise is due to carriers arriving via the IW transport. Intensities of these two peaks of the transients reflect the number of carriers that reach the DQW via the two pathways (see Fig. 1). The intensity ratio for these two peaks can then be compared to the ratio of the number of carriers generated directly in the vicinity of the DQW and in the transport region.

To estimate the carrier collection to the DQW via the two channels, one should make several approximations. First, since the carrier capture to the QWs is fast and efficient, we assume that “directly generated carriers” include carriers excited in the DQW as well as the ones generated in half of the barrier between the last TQW and the DQW and in the buffer. The fraction of directly generated carriers can be evaluated from the widths of different heterostructure layers and the corresponding absorption coefficients. The estimation shows that the directly generated carriers amount to 0.05 of the total carrier number for the 3 TQW and thin barrier structures and 0.04 for the 5 TQWs. On the other hand, the “transport carriers” include carriers excited in the TQW region and, primarily, in the GaN cap layer. The fraction of transport carriers is more difficult to assess since some of the carriers excited in the cap layer would not proceed toward the TQWs but would be captured by the surface states. The thickness d from which the carriers would end up in the surface states can be estimated from the relation $d=Sτs$⁠, where S = 1.1 × 10⁴ cm/s (Ref. 11) is the surface recombination velocity in GaN and τ_s – carrier lifetime before their capture to the surface states. Using PL decay time at the GaN band gap energy for τ_s, the estimation provides d = 5 nm. Hence, carriers excited in the remaining 95 nm of the cap layer are assumed to be captured by the TQWs. With these assumptions, the uniform IW carrier distribution would be reached if the DQW was 0.21 for the 3 TQW and 0.14 for the 5 TQW and thin barrier structures. The ratio between the transport and directly generated carriers would then be 4.2, 3.5, and 2.8 for the 3 TQW, thin barrier and 5 TQW structures, respectively.

These values should be compared to the experimentally determined ratios of 2.3, 1.5, and 1.0. It follows that only 20%, 14%, and 7% of the carriers are generated in the cap layer and the TQW region reaches the DQW. This is about 2–4 times smaller than expected for a uniform IW carrier distribution. One should note that here we ignore the role of the DQW as a carrier sink which might enhance the transfer process. Without the DQW, nonuniformity of the IW carrier distribution in the GaN barrier structures would be even larger.

In conclusion, by means of time-resolved PL measurements on InGaN/(In)GaN QW structures with a marker well, we have determined that the interwell carrier transport is governed by the thermionic emission of holes. For structures with GaN barriers, the IW carrier transfer to the DQW is inefficient. For wide barriers and 8 TQWs, the carriers excited in the cap layer do not reach the detector well at all. Even for the 3 TQW structure, the number of transported carriers was too low to ensure a uniform interwell carrier distribution. The IW transport, however, became much more efficient when In_0.05Ga_0.95N barriers were used. In the InGaN barrier structure, the IW transport time per well decreased by a factor of four and the hole thermionic emission energy from 200 meV to 70 meV. This suggests that, in addition to the reduced barrier height for the thermionic emission, the percolation transport may also play a role. Hence, introducing a small fraction of In into GaN barriers might be a promising pathway toward efficient high power InGaN LEDs.

Research at KTH was financially supported by the Swedish Energy Agency (Contract No. 45390-1). Work at UCSB was supported by the Solid State Lighting and Energy Electronics Center (SSLEEC), the DOE SSL Program through Award No. DE-EE0008204 (J. Chaddock Program Manager), and the Simons Foundation through Award No. 601952.