Chapter 5 Diffusion-controlled effects of luminescence efficiency in InGaN/GaN
5.7 Nonradiative lifetime
In nonradiative recombination process, since dislocations are locally distributed, the electron-hole pairs should overcome the diffusion reaction toward the dislocations before captured by dislocations. Therefore, the nonradiative lifetime is the sum of diffusion lifetime of carriers from point A to point B and capture lifetime by dislocations. The capture lifetime can be written by SRH theory [5]: thermal velocity. Since dislocations are recognized as an efficient sink and some authors considered that nonraditaive recombination velocity at a dislocation is assumed to be infinite for minority carriers, the capture lifetime can be neglected in this work. Therefore, the nonraditaive recombination process should be
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dominated by diffusion-controlled and the nonradiative lifetime can be given by the following expression [9]:
dislocation density and diffusion coefficient. Since the diffusivity of holes is much slower than electrons, the diffusion lifetime should be dominated by recombination of holes.Here, the diffusion coefficient is obtained by Fick’s law:
h eD
J h ... (5.8) where the diffusion coefficient of hole (Dh)is composed of thermal velocity (vth) and mean-free path (l).
dimensional. Thus, the diffusion coefficient can be written as
ch
Since relaxation time is related to the scattering mechanism, the temperature dependence of diffusion coefficient is varied with different scattering mechanisms. In GaN, there are different types of scattering mechanisms
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dominate the relaxation time: ionized impurity scattering, neutral impurity scattering, deformation potential acoustic phonons scattering, piezoelectric acoustic phonons scattering and dislocation scattering. In a typical nitride based LED, there are no Si doping in InGaN wells. Thus, ionized impurity scattering would not occur and neutral impurity scattering dominate the relaxation time in the low temperature range. The relaxation time of neutral impurity scattering can be estimated as below.
20N a0 radius of acceptor. It is temperature independence and the temperature dependence of diffusion coefficient can be obtained ( DT ) in the low temperature range. As the temperature increases from high temperature range, the lattice scattering becomes to dominate the relaxation time. The relaxation time of deformation potential acoustic phonons scattering is considered shortest in the lattice scattering mechanism. Thus, the deformation potential scattering dominated the relaxation time in the high temperature and can be written as
32 12 deformation potential. Thus, the temperature dependence of diffusion coefficient can be obtained (DT1.5) in the high temperature range. Moreover, the variation of diffusion-limited lifetime with temperature is controlled by the temperature dependence of diffusion coefficient ( tD T1 in the low temperature range and tD T1.5 in the high temperature range).73 diffusion coefficient can be rewritten as
e
Dh h 2KT (2-D) ... (5.14)
e
Dh h 3KT (3-D) ... (5.15) where h is the mobility of holes and the diffusion coefficients are obtained by Einstein relation. Therefore, the temperature dependence of nonradiative lifetime can be estimated from diffusion coefficient obtained by Einstein relation (D~hKTe). In two-dimensional system, the excess carrier mobility is mainly dominated by neutral impurity scattering which is temperature independent [15]. Therefore, the trend of diffusion lifetime with varying temperature can be estimated (DT1). Since the trend of theoretical nonradiative lifetime with varying temperature is (D T1) which is mainly dominated by diffusion control, the experimental result shows well fitted with the trend, as shown in Fig. 5.11. It implies that the nonradiative recombination process is mainly dominated by diffusion control in the range of 20-300K.
To further validate the theoretical results, the radiative lifetime and nonradiative lifetime at 300K were estimated by using the Eq (1) and Eq (3) good agreement with the experimental results. Therefore, both the radiative
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lifetime and nonradiative lifetime can be estimated and fully ascribed by using this method.
5.8 Conclusion
In conclusion, the temperature dependence of PL and TRPL of InGaN/GaN LEDs were investigated and we presented a method to describe the recombination processes. The results exhibited that the decrease of luminescence efficiency with temperature is attributed to the increase of radiative lifetime and decrease of nonraditaive lifetime. In radiative recombination process, the electron-hole pairs recombined in zero-dimensional when temperature was <100K which is attributed to the existence of localized states, and recombined in two-dimensional process when temperature was
>100K which is attributed to a typical quantum-confined effect. In nonradiative recombination process, since dislocations which act as line sinks for minority carriers are locally distributed, and the nonradiative lifetime was found to be correlated with diffusion coefficient with varying temperature, the nonraditaitve recombination process are mainly dominated by diffusion-controlled kinetics.
Therefore, both radiative lifetime and nonradiative lifetime can be estimated by using this method and the theoretical results are in agreement with the experimental results.
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Fig. 5.1 Diffusion-controlled kinetics of recombination process for line-sink defects [9]
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Fig. 5.2. Cross-sectional TEM image of the LED structure. Inset: magnified TEM shows a dislocation thread through the active layers where point A is the location of active layers and point B is the location of a dislocation
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350 400 450 500 550 600 650
20K 40k 60k 100k 120k 140k 180k 200k 240k 260k 300k
Intensity (a.u.)
Wavelength (nm)
Fig. 5.3. Temperature dependence of PL spectra
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0 10 20 30 40 50
Normalized PL Intensity (a.u.)
1000/T (K-1)
Fig. 5.4. The fitted Arrhenius plot of the PL intensity
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40 60 80 100 120
Intensity (a.u.)
Time (ns)
20K 25K 36K 64K 93K 122K 152K 182K 210K 240K 270K 300K
0 50 100 150 200 250 300 0
5 10 15 20
Lifetime (ns)
Temperature (K)
Fig. 5.5. (a) Temperature dependence of TRPL (b)Temperature dependence of the PL lifetimes
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0 10 20 30 40
0.0 0.2 0.4 0.6 0.8 1.0 (a)
Li ght em is s io n e ffi c ie nc y
1000/T (K-1)
0 50 100 150 200 250 300 0
20 40 60 80 100 (b)
L ife tim e (n s)
Temperature (K)
r
nrFig. 5.6. (a) Arrhenius plot of the PL intensity. (b) The temperature dependence of carrier lifetime, radiative lifetime and nonradiative lifetime, respectively
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Eh0
dislocation defects
hv Ee0
valence band conduction
band
A B
dislocation defects
R
Fig. 5.7. Schematic band diagram of the recombination processes with carriers and dislocations
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420 430 440 450 460 470 480 490 500
Intensity(a.u.)
Wavelength(nm)
20K
0 50 100 150 200
102 103 104
470 465 460 455 440 450 445
Intensity (a.u.)
Time(ns)
440 445 450 455 460 465 470
Fig. 5.8. (a) PL spectrum at 20K. (b) PL decay time as function of the emission energy
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Fig. 5.9 The Schematic representation of localized excitonic states and processes in GaAs1-xPx alloys
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2.4 2.5 2.6 2.7 2.8 2.9 3.0 0
5 10 15 20
Intensity (a.u.)
20K
Photonenergy (eV)
PL lifetime (ns)
Fig. 5.10. The PL spectrum at 20K with PL decay time as function of the emission energy
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0 5 10 15 20 25 30 0
20 40 60 80
Non radiative lifetime (ns)
1000/T (K
-1)
Fig. 5.11. Temperature dependence of nonradiative lifeitme. The trend of nonradiative lifetime with varied temperature is controlled by diffusivity
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