Nonpolar { ̅ } Plane
In order to confirm the efficiency, the PL internal quantum efficiency (IQE) measurement was performed. We performed the temperature dependent PL measurement at low temperature and room temperature and define it by observing the tendency of the curves [15]. This could be expressed as the following :
η𝑖𝑛𝑡 =number of photons emitted from active region per second
number of electrons injected into LED per second = 𝐶𝐼𝐼𝑃𝐿⁄𝐸𝑃𝐿
𝐸𝑋⁄𝐸𝐸𝑋 (5.22)
Where IPL and IEX are PL intensity and excitation intensity, respectively. EPL and EEX
are PL photo energy and excitation photon energy, respectively. C is a constant affected by mostly carrier injection efficiency by laser, light extraction and correction efficiency of PL, and does not depend on either excitation power density or measurement temperature.
From the theoretical of carrier dynamics, we can assume that the IQE is 100% at low temperature (LT) (about 15K in our experiment). In order to cancel the constant C, we divide the IQE at every temperature by the IQE at LT, consequently, the IQE of the LED at every temperature (T) can be rewrite as:
η𝑖𝑛𝑡(𝑇) = (𝐶
The Table 5.4 showed the measurement of the IQE and the activation energy, and binding energy of HT- and LT-sample. For the HT-sample, the IQE of core-shell semipolar { ̅ } Green and nonpolar { ̅ } Blue InGaN/GaN MQWS structure were about 23.92% and 18.86%, respectively. It was found that there is a great enhancement for the suppressing the QCSE and reducing localize state in 3-D core-shell structure. In addition, the IQE of core-shell semipolar { ̅ } Yellow and nonpolar { ̅ } Green InGaN/GaN MQWS structure were 11.12% and 19.86% for LT-sample, respectively. The lower IQE in LT-sample resulted from the lower growth temperature, indicating the poor crystalline quality of InGaN well layer.
And the temperature dependent IQE curve could be fitted by the following 15K was used in our experiment), A and B are constants, k is the Boltzmann constant, T is the temperature, Ea is the activation energy for PL quenching, and Eb is generally associated to the free exciton binding energy [16]. 錯誤! 找不到參照來源。9 shows
the Arrhenius plot for (a) HT-sample and (b) LT-sample, and the fitting curves of activation energy were included. In Table 5.4, the activation energy of core-shell semipolar (10-11) Green and nonpolar { ̅ } Blue InGaN/GaN MQWS structure were 65 meV and 50 meV for HT-sample. In general, the quenching of the luminescence with temperature can be explained by thermal emission of the carriers out of a confining potential with an activation energy correlated with the depth of the confining potential [17]. One could understand it through the schematic of activation energy in 錯誤! 找不到參照來源。8. It is suggested that the localization of carriers operates as excellent radiative recombination centers. In other words, high localization energies of excitions can provide deep potential wells that suppress the diffusion of electrical carriers toward versus non-radiative defects. The carrier localization in the active layer also has a significant effect on the performance of LEDs, resulting in an increase in radiative recombination efficiencies [18]. And the activation energy of core-shell semipolar { ̅ } Yellow and nonpolar { ̅ } Green InGaN/GaN MQWS structure were 45 meV and 68 meV for LT-sample, respectively. The lower activation energy in semipolar { ̅ } facet was attributed to more non-radiative center in higher In layer, resulting in poor confinement in this MQW structure.
In order to further check the degree of carrier localization effect in all samples, we analyzed the peak shift of the InGaN MQWs emission over the investigation temperature range. The TDPL was measured
at P = 10 mW (carrier density about 1E16 cm-3). In general, the wavelength redshifts until a temperature of ~100 K corresponding to a maximum of the localization energy, then, it blueshifts up to
the full-delocalization temperature of ~200 K, where it starts red shifting again. The anomalous temperature behavior of the peak energy is S-shaped (decrease-increase-decrease) [17, 19-22]. In
5-10, the anomalous temperature behaviors of two different growth facets, semipolar { ̅ } pyramid and nonpolar { ̅ } sidewall, were clearly observed.
For both of the semipolar { ̅ } and nonpolar { ̅ } MQWs, the peak energy monotonically decreases with increasing temperature. It is different from the general red-blue-red shift (S-curve) behavior in the c-plane MQWs, which is caused by the localized tail states as well as the fluctuations in In distribution in InGaN MQWs [17, 23]. The absence of S-curve indicates the significant reduction of localized potentials in the 3-D core-shell MQWs. This could be due to the better strain relaxation provided by the nanostructure and/or the growth property of the pyramidal semipolar facets and vertical nonpolar sidewall [24, 25].
Therefore, the band-tail model should be suitable for discussion of this exciton localization effect. Based on the band-tail model, if Gaussian-like distribution of the density of states for the conduction and valence band is assumed, the temperature-dependent emission energy could be described by the following
expression:
𝐸(𝑇) = 𝐸( ) −𝛽+𝑇𝛼𝑇2 −𝑘𝑇𝜎2 (5.25)
where E(T) is the emission energy at T, E( ) the energy gap at K, and α and β are Varshni’s fitting parameters. The third term comes from the localization effect, in which σ indicates the degree of localization effect, i.e., the large value of σ means a strong localization effect, and k is the Boltzmann constant. The fitting is made based on Equation 5.25 in each case, and the fitting experimental data in
the temperature range of 120-240 K. The fitting curve are included in the
5-10, and fitting parameter σ is 1 meV of semipolar (10-11) green MQWs and 1 meV for the nonpolar { ̅ } MQWs. It is revealed that almost zero localization in 3-D core-shell MQWS structure.
On the other hand, once the wave-function overlap between electron and hole is enhanced, the transition probability of carriers in quantum well, which is associated
with radiative recombination lifetime, is expected to be increased. In this section, the radiative recombination lifetime is qualitatively determined by time-resolved photoluminescence (TRPL). TRPL is indispensable technique to study the dynamical process of photoexcited carriers such as relaxation, radiative, nonradiative, and localization processes.The transient luminescence intensity obtained by the data of TRPL is generally fitted by a combined exponential and stretched exponential line shape [26-28]:
𝐼(𝑡) = 𝐼1𝑒−𝜏1𝑡 + 𝐼2𝑒−(𝜏2𝑡)
𝛽
(5.26)
where I(t) is the PL intensity a time t, 𝛽 is the dimensionality of the localized centers [29-31], and 𝜏1 and 𝜏2 represent the initial lifetimes of the carriers. Normally, the fast decay term 𝜏1 is used represent 𝜏𝑃𝐿 since the PL intensity is limited by the fast decay component [27].
Moreover, the effective carrier lifetime can be expressed as following equation:
1 reocombination lifetime, and transfer time toward lower-lying energy levels. If radiative recombination occurs at the bottom of energy levels, the term of the transfer time can be neglected so that the equation is simplified as shown below and as
The relative probability of radiative recombination is given by the radiative probability over the total probability of recombination. Therefore, the internal quantum efficiency (IQE) can be expressed in terms of the radiative and nonradiative lifetimes [21, 22]:
𝜂𝑖𝑛𝑡(𝑇) =𝜏𝜏𝑟−1
𝑃𝐿−1 =𝜏 𝜏𝑟−1
𝑟−1+𝜏𝑛𝑟−1 (5.29)
The IQE gives the ratio of the number of light quanta emitted inside the semiconductor to the number of charge quanta undergoing recombination. Note that not all photons emitted internally may escape from the semiconductor due to critical angle and reabsorption mechanisms. By using the above equation, the internal quantum efficiency is determined by the competition between radiative and nonradiative recombination processes. In this material system, the radiative recombination rate is affected by the QCSE and exciton localization effects.
At low temperature (regard as absolute 0K, and it is 15K in our experiment), the carriers have no kinetic energy that the nonradiative probability is equal zero. The Equation 5.28 can be rewrite as:
𝜏𝑃𝐿 = 𝜏𝑟 (5.30)
However, as the temperature increases to higher temperature, both of radiative and nonradiative process have to be taken into account. To separate the 𝜏𝑃𝐿 into 𝜏𝑟 and 𝜏𝑛𝑟, using Equation 5.23 and Equation 5.24, we can get the equation like this:
𝜏𝑟(𝑇) =𝐼𝐼𝑃𝐿(𝐿𝑇)
𝑃𝐿(𝑇) 𝜏𝑃𝐿(𝑇) (5.31)
And the 𝜏𝑛𝑟(𝑇) can be calculate from Equation 5.24.
錯誤! 找不到參照來源。5-12 shows the TRPL measurement of the nonpolar { ̅ } blue emission at (a) 15 K, (b) 300K and the semipolar { ̅ } green emission at (c) 15 K, (d) 300K. The faster recombination lifetime of blue emission nonpolar { ̅ } on lifetime is due to the suppressing internal electric field. Two possible mechanisms may respond for the faster recombination rate in nonpolar { ̅ } surface, including the lower In content and no spontaneous polarization filed.
shows the calculated value of PL lifetime (𝜏𝑃𝐿), radiative lifetime (𝜏𝑟) and non-radiative lifetime (𝜏𝑛𝑟) of each temperature by using the Equation 5.31. Furthermore,
4 revealed that radiative lifetime (𝜏𝑟) of both nonpolar { ̅ } blue emission and semipolar { ̅ } green emission, and the fitting curve were included. In the
experiment, the excition radiative lifetime is dependent on the temperature.
The rremains constant at low temperature below ~50 K as shown in Equation 5.32. This is explained that the radiative lifetime is nearly constant for a localized exciton below 50 K. On the other hand, the r increases linearly above 180 K. This is related to 2D confined exciton [32]. It indicates that, at low temperature, the excitons are trapped in localized potentials due to inhomogeneous In composition in MQWs. As temperature increases, excitons are excited out of the traps and become free excitons in the 2D MQWs, resulting in approximately linearly increasing radiative lifetime. The measured radiative lifetime at room temperature for nonpolar { ̅ } Blue MQWs and semipolar { ̅ } green MQWs are 1.47 ns and 1.79 ns, respectively. These rvalues are about two orders of magnitude smaller than the typical r on c-plane (0001) MQWs [33]. The faster radiative recombination is the strong evidence to the suppression of polarization field in InGaN/GaN MQWs.
However, it is worth noting that the faster r is not directly related to the enhancement of IQE. It is known that nr also plays an equally important role in the IQE. The measured nr is also significantly shortened as well in the experiment. It is attributed to samller potential localization for MQWs grown on the semipolar facets.
The localized potential has been considered as one of the important factors in preventing the capture of excitons by the threading dislocation defects [34, 35]. The
suppression of localized potentials will result in the increase of the probability of the capture of excitons by the defects and therefore shorten nr. As a result, even though
r is shortened by two orders of magnitude, the IQE is not enhanced in a similar magnitude.