Recombination lifetimes in InN films studied by time-resolved excitation-correlation spectroscopy
Horng-Chang Liu, Chia-He Hsu, Wu-Ching Chou, Wei-Kuo Chen, and Wen-Hao Chang*
Department of Electrophysics, National Chiao Tung University, Hsinchu 300, Taiwan
共Received 13 August 2009; revised manuscript received 6 October 2009; published 10 November 2009兲 Recombination dynamics in degenerate InN were investigated by means of time-resolved excitation-correlation spectroscopy. The photoluminescence decay times are determined beyond the spectral response and temporal resolution limits of conventional photon-counting detectors. Spectral and temperature dependence of decay times reveal the effects of hole localizations on the recombination mechanisms. At low temperatures, the radiative lifetimeris insensitive to temperature and significantly longer than that predicted for the radiative
band-to-band recombination, indicative of a transition dominated by the free-to-bound recombination without k conservation. Above a certain temperature determined by the electron concentration, we findr⬃T3/2, as expected for the band-to-band transition when the k-selection rule holds. We determine a lower limit for the bimolecular recombination coefficient B in InN at 300 K as 5.6⫻10−11 cm3/s.
DOI:10.1103/PhysRevB.80.193203 PACS number共s兲: 78.20.⫺e, 78.47.Cd, 78.55.⫺m
Information about the recombination dynamics and carrier lifetimes in InN are indispensable for the development of near-infrared group III-nitride devices.1 In principle, the
re-combination lifetimes can be obtained by time-resolved pho-toluminescence 共TRPL兲 measurements using either a streak camera or a fast photomultiplier tube 共PMT兲 to record PL decays. However, for high-quality InN with typical emission wavelengths in the range of 1.7– 1.9 m, the reported TRPL data are quite limited2,3 because the photon-counting-based
technique is problematic in this spectral range due to the lack of suitable photocathodes for wavelength longer than 1.7 m.4 Accordingly, some studies have turned to
em-ployee more sophisticated techniques, such as PL up conversion5,6and pump-probe differential transmission,7,8to
measure the carrier lifetimes in InN.
Excitation-correlation 共EC兲 spectroscopy is a convenient alternative to the conventional TRPL technique for the study of carrier lifetimes in semiconductor materials.9–13This
tech-nique, also known as picosecond or femtosecond EC, is based on the nonlinear dependence of PL intensity on the excitation intensity of two laser pulses with a relative time delay. By varying the delay time, the resulting time-resolved EC共TREC兲 trace can be used to determine carrier lifetimes. This technique is much easier to implement than the up-conversion technique but in principle yields the same tempo-ral resolution limited only by the laser-pulse duration. In addition, this technique is applicable to the spectral range beyond 1.7 m, which is particularly useful for the study of InN.
In this work, we investigated the recombination dynamics of n-type degenerate InN with different electron concentra-tions by using the TREC technique. The PL decay time in InN were determined. We have also performed temperature-dependent measurements to extract contributions of radiative and nonradiative lifetimes. We present here a detailed study on the influence of the carrier concentration on the hole lo-calization in the valence-band 共VB兲 tails as well as on the radiative recombination mechanisms in InN.
The sample investigated is a 300 nm InN film grown on an 1 m GaN template on sapphire共0001兲 by metalorganic chemical vapor deposition. The detailed growth conditions can be found elsewhere.14–16 Room-temperature Hall
mea-surements of the sample showed a background electron con-centration of 1.2⫻1019 cm−3. A sample with a lower
elec-tron concentration was obtained by rapid thermal annealing at 650 ° C in a N2environment for 30 s. In the annealed InN film, the Hall concentration is reduced to 3⫻1018 cm−3. In
EC measurements, a mode-locked Ti:sapphire laser deliver-ing ⬃150-fs laser pulses 共780 nm/80 MHz兲 was used as an excitation source. The laser beam was split into two beams of equal intensity to excite the sample. The two beams, with a relative interpulse time delay␥controlled by a 80-cm me-chanical stage, were modulated at different frequencies 共f1
and f2兲 and focused onto the same spot on the sample. The
resulting PL signal was collected into a 0.5 m monochro-mator and detected by a liquid-nitrogen-cooled extended In-GaAs photodiode with a cutoff wavelength at 2.1 m. The EC signal was extracted from the sum-frequency component 共f1+ f2兲 by using a lock-in amplifier. For a comparison
pur-pose, we have also measured TRPL by using a fast InGaAs PMT. The decay traces were recorded using the time-correlated single-photon-counting technique with an overall time resolution ⬃150 ps in the spectral range of 0.9– 1.65 m.
Figure 1共a兲 shows the time-integrated PL spectra for the as-grown and annealed InN samples measured at T = 12 K under an excitation power of Pex= 5 mW. The PL emission band of InN can be characterized as free-to-bound recombi-nation between the degenerate electrons in the conduction band and the photogenerated holes at the VB edge,17,18 as
schematically shown in Fig.1共b兲. The PL peak energy for the annealed InN film is lower than the as-grown sample by ⬃70 meV, due to its lower electron concentration and hence a smaller Burstein-Moss shift. The corresponding EC spectra measured without interpulse delay 共i.e.,␥= 0兲 are displayed in Fig.1共c兲. For the as-grown sample, the EC signal shows a line shape almost the same as its PL spectrum, but with a negative intensity, except a weak positive feature emerging from the high energy side. By contrast, the EC spectrum for the annealed sample consists of both negative and positive signals on the low and high energy sides, respectively.
The EC signal, SEC共ប,␥兲, detected at a given photon
energyប, is a result of the nonlinear change in PL intensity due to excitations by the two laser pulses with an interpulse PHYSICAL REVIEW B 80, 193203共2009兲
delay time ␥. It can be written as13 S
EC共ប,␥兲
= IPL共2兲共ប,␥兲−2I共1兲PL共ប兲, where IPL共1兲 and IPL共2兲 are the time-integrated PL intensity excited by one of the two beams and by both beams, respectively. For a n-type material with an electron concentration n0, the EC signal is given by
SEC共⑀,␥兲 ⬀ 1 T
冕
0 T n0共⑀兲关␦p2共t,␥兲 −␦p1共t兲兴dt + 1 T冕
0 T 关␦n1共⑀,t兲␦p2共t,␥兲 +␦n2共⑀,t,␥兲␦p1共t兲兴dt, 共1兲 where T is the laser period, ⑀⬅ប− Eg, where Eg is the energy band gap, n0共⑀兲 is the energy distribution of thede-generate electron, and␦ni共␦pi兲 with i=1,2 are the photoge-nerated electron 共hole兲 concentrations by the first pulse at t = 0 and the second pulse at t =␥, respectively. Here, we assume that the photogenerated holes are at the VB edge with a delta-function-like energy distribution so that the mea-sured PL band corresponds to the energy distribution of de-generated electrons n0共⑀兲 in the conduction band.16,17 From
Eq.共1兲, it is obvious that two major effects will contribute to EC signals. The first one is the differential absorption arising from state filling. The photocarriers generated by the first pulse make the second pulse less likely to excite as many photocarriers due to fewer available states. Therefore, the first integral in Eq.共1兲 contributes a negative EC signal be-cause ␦p2共t,␥兲⬍␦p1共t兲. The second effect, i.e., the second
integral in Eq.共1兲, is the cross recombination of the electrons ␦n1 共holes ␦p1兲 generated by the first pulse with holes ␦p2
共electrons␦n2兲 by the second pulse. Because the second
in-tegral in Eq. 共1兲 is always positive, the cross recombination
will contribute a positive EC signal. In addition, since the photogenerated electrons ␦n共⑀兲 were distributed near or above the Fermi energy ⑀F, the positive EC signal occurs only on the high energy side of the PL band. It should be noted that the positive EC signal is significant only when␦n is comparable to n0. Due to the high electron concentration
in the as-grown sample, the positive EC signal is not pro-nounced under excitation conditions used in this study. Con-versely, as shown in Fig.1共d兲, the positive EC signals for the annealed InN film can be observed when Pexⲏ1 mW, cor-responding to a photogenerated carrier density of about ␦n⬃1.2⫻1017 cm−3 Ref. 19, which is noneligible as
com-parable with the background n0.
The TREC traces for both samples recorded at the energy of EC dips as function of the delay time␥are shown in Fig. 2共a兲. Since the two beams are equal in intensity, the mea-sured TREC traces are expected to be symmetric around ␥= 0. The data can be well described by a single-exponential function Ae−兩␥兩/, yielding a decay time constant. For n-type degenerate semiconductors under low excitation conditions, the cross recombination terms in Eq. 共1兲 are negligible. If both ␦p1 and␦p2 decay exponentially with a time constant p, it can be shown from Eq.共1兲 that
SEC共⑀,␥兲 ⬀ n0共⑀兲共␦p20−␦p10兲pe−␥/p, 共2兲 where ␦pi
0
is the initial hole population created by the ith pulse. Therefore, the measured decay time from TREC 0.60 0.65 0.70 0.75 0.80 E C si gnal ( arb. uni ts) Energy ( eV ) (a) (c) (b) (d) PL EC ω g E 0( ) n ε ( , ) n t δ ε ( ) p t δ , n p 0 F ε ε 0.6 0.7 0.8 0.9 -1.0 -0.5 0.0 0.5 PL int ensi ty (a rb .unit s) As grown RTA 650o C Energy ( eV ) EC signal (arb. units) 0.1 0.2 0.5 1.0 2.0 5.0 10 Pex(mW)
FIG. 1. 共Color online兲 共a兲 The PL spectra for the investigated InN films measured at T = 12 K. 共b兲 A schematic diagram for the recombination paths in degenerate InN.共c兲 The EC spectra taken at zero delay for both samples under an excitation power of Pex= 5 mW.共d兲 The EC spectra for the annealed InN film under
different excitation powers Pex= 0.1– 10 mW. All the spectra have been normalized.
(a)
TRPL TREC RTA As grown(b)
-2000 0 2000 4000 6000 -1.0 -0.5 0.0 -500 0 500 1000 1500 EC signa ls ( arb .units ) Time ( ps ) In tens ity ( arb .uni ts ) Time ( ps ) 0.60 0.65 0.70 0.75 0.80 0.85 0 500 1000 1500 2000 2500 3000 2100 2000 1900 1800 1700 1600 1500 D ecay time ( ps ) Energy ( eV ) Wavelength ( nm )FIG. 2.共Color online兲 共a兲 TREC traces recorded at the energy of EC dips. The excitation power used is 5 mW共1 mW兲 for the as-grown 共annealed兲 sample. Solid and dotted lines are single-exponential fits. The inset shows a comparison between the TRPL and the兩SEC共␥兲兩 traces for the as-grown sample. 共b兲 Spectral depen-dence of measured decay times共E兲 together with the correspond-ing PL spectra 共dashed and dotted lines兲 for both samples. Solid lines are fitting curves.
BRIEF REPORTS PHYSICAL REVIEW B 80, 193203共2009兲
traces represents the minority-carrier lifetimes p. Because the PL decay is also determined by the minority-carrier life-timep, i.e., IPL共t兲⬀n0␦p共t兲, the decay times obtained from TREC and TRPL traces are essentially the same, as shown in the inset in Fig.2共a兲. From Eq.共2兲, it is also clear that the EC spectrum is proportional to n0共⑀兲, which reproduce the PL
spectrum, but with a negative intensity due to ␦p20⬍␦p10. In Fig.2共b兲, the spectral dependence of decay time共E兲 measured at T = 12 K are displayed. The decrease in lifetime with the increasing emission energy is a characteristic feature of carrier localizations commonly observed in disordered al-loy systems.20Similar spectral dependencies of decay time in
InN with different electron concentrations have been reported.3The localization centers have been attributed to the
VB tail states induced by the unintentionally doped n-type impurities.3,17The spectral dependence of measured lifetime can be analyzed by20,21 共E兲=r/兵1+exp关共E−E
me兲/E0兴其,
wherer is the radiative lifetime, Eme is the mobility edge, and E0 is a characteristic energy for the density of VB tail
states关⬀exp共−E/E0兲兴, which can be a measure for the
local-ization energy. As shown by solid lines in Fig.2共b兲, good fits are obtained, yielding a radiative lifetime ofr⬃0.42 ns and a localization energy of E0⬃12 meV for the as-grown InN.
For the annealed InN film, a longer radiative lifetime up to r⬃2.3 ns and a lower localization energy of E0⬃8 meV
are obtained due to its lower electron concentration. The measured E0 are quite close to the depth of VB tail states, which are estimated to be ⬃10 and ⬃6 meV for the as-grown and the annealed samples, respectively, according to the root-mean-square potential fluctuation induced by the randomly distributed ionized impurities.3,17 In Fig. 2共b兲, a
dip in共E兲 for the annealed sample is observed but its origin is not clear yet. Since the dip appears near the low-energy shoulder of the PL band, it may arise from transitions involv-ing deeper acceptor states above the VB edge.16–18
To further study the influence of the carrier localization on the radiative recombination processes, we have performed temperature-dependent TREC measurements. The measured decay timeas a function of temperature T for both samples are shown in Fig.3. The measured共T兲 consists of both the radiative 共r兲 and the nonradiative 共nr兲 components, which can be expressed as 1/= 1/r+ 1/nr. A standard way to extractrfrom the measured共T兲 is to determine the radia-tive efficiency共T兲=nr/共nr+r兲 according to the measured temperature-dependent PL intensity, by which the radiative lifetime can be determined usingr共T兲=共T兲/共T兲. In Fig.3, the deduced r共T兲 andnr共T兲 are also displayed. For the as-grown InN film, the deducedris nearly constant at tempera-tures below 140 K but above which exhibits ar⬃T3/2 de-pendence, as expected for bimolecular radiative recombination in direct band-gap semiconductors when the
k-selection rule holds.22,23 The nearly constant r for
T⬍140 K indicative of a transition without satisfying the k-selection rule, due to the localization of holes in the VB tail states. For the annealed InN film with lower n0, the effect of carrier localizations are less pronounced. We found that the temperature dependence restored to r⬃T3/2 for T⬎80 K, indicating that the radiative transition is domi-nated by the band-to-band recombination process.
Quantitatively, the bimolecular radiative recombination
coefficient B can be determined by the deduced radiative lifetime according to r= 1/Bn0. By using the expression B共T兲=B0共300/T兲3/2 and the measured Hall concentration
共1.2⫻1019 cm−3兲 for n
0to fit the deducedr共T兲 in the
high-temperature region, we obtain B0= 5.6⫻10−11 cm3/s for the
as-grown InN film. It should be mentioned that the electron concentration determined by Hall measurements could be higher than the actual concentration in InN bulk due to the presence of surface electron accumulations. Therefore, due to a lack of knowledge of the actual n0 in InN, the
deter-mined values of B can only be considered as a lower limit. For the annealed InN film with a lower electron concentra-tion, the influence of the surface electron accumulation on the Hall measurement would be more significant. In fact, if we use the same B0 and the measured Hall concentration
共3⫻1018 cm−3兲 for the annealed sample, the predicted
radia-tive lifetimes are much lower than experimental data. Nevertheless, when we modify the electron concentration to n0= 8⫻1017 cm−3for the annealed sample, a resonant fit to
experimental data can be obtained.
According to the Lasher-Stern model,22,23the bimolecular
coefficient B for the radiative band-to-band recombination is given by B = 共2兲 3/2បe2n rEg m0c3关共m e+ mh兲kBT兴3/2 EP 3 , 共3兲
where nr is the refractive index, Eg is the band-gap energy,
Epis the energy parameter of the momentum matrix element, and me共mh兲 is the electron 共hole兲 effective mass. By using the following material parameters for InN共Refs.17and24兲: Eg= 0.7 eV, Ep= 10 eV, nr= 2.9, me= 0.07m0, and mh= 0.3m0, where m0is the free-electron mass, the calculated
B at 300 K is 5.2⫻10−11 cm3/s, in good agreement with our
experimental result. However, the calculated B using Eq.共3兲 remains uncertain, due to the uncertainty of used material parameters, particularly the value of hole effective mass mh. We would also like to point out that Eq.共3兲 is derived based on transitions between nondegenerate carriers near the edges of parabolic bands. It would be less accurate for transitions
101 102 103 101 102 103 104 105 Lif et imes ( ps ) Temperature ( K ) τ r τ nr τ 3 / 2 T ∼ 3 / 2 T ∼ (a) (b) 101 102 103 Temperature ( K )
FIG. 3. 共Color online兲 The measured decay time as a function of temperature T for 共a兲 the as-grown and 共b兲 the annealed InN films. The deduced radiativer共T兲 and nonradiativenr共T兲 lifetimes are also shown. The dashed lines are calculatedr共T兲 using n0 de-termined from Hall measurements. The dotted line in共b兲 assumes n0= 8⫻1017 cm−3.
BRIEF REPORTS PHYSICAL REVIEW B 80, 193203共2009兲
involving the degenerate electrons in the conduction band with a strong nonparabolicity in such highly unintentionally doped InN films.
In summary, recombination dynamics in degenerate InN with different electron concentrations have been investigated by means of time-resolved excitation-correlation spectros-copy. The PL decay times are determined beyond the spectral response and temporal resolution limits of conventional photon-counting detectors. Spectral and temperature depen-dence of decay times reveal that the hole localization in the VB tails play a decisive role in the recombination process. At low temperatures, the radiative lifetime r is insensitive to temperature and significantly longer than that predicted for
the radiative band-to-band recombination, indicating that the PL emission from InN is dominated by the free-to-bound recombination process without k conservation. Above a cer-tain temperature determined by the carrier concentration, the temperature dependence restored tor⬃T3/2, as expected for the radiative band-to-band transitions when the k-selection rule holds. We determine a lower limit for the bimolecular recombination coefficient B in InN at 300 K as 5.6⫻10−11 cm3/s.
This work was supported in part by the program of MOE-ATU and the National Science Council of Taiwan under Grant No. NSC-97-2112-M-009-015-MY2.
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