Chapter 4 Excitation power dependent and theoretical model of
4.3 Theoretical model of IQE Calculation
In this study, we quote E. F. Schubert et al. [46] proposed theoretical model to calculate IQE of InGaN/GaN MQW UV LEDs. The three main carrier-recombination mechanisms in a bulk semiconductor are Shockley–Read–Hall nonradiative recombination, expressed as An, bimolecular radiative recombination Bn2, and Auger nonradiative recombination Cn3, where A, B, and C are the respective recombination coefficients and n is the carrier concentration. Auger recombination affects LED efficiency only at very high excitation; thus, in our experiments, the generation rate
and the IQE at steady state can be expressed as
and the integrated PL intensity can be expressed as
Bn
2I
PL =η
(4.3.3)where is a constant determined by the volume of the excited active region and the total collection efficiency of luminescence. By eliminating n in equation 4.3.1 and 4.3.3, we can express the generation rate in terms of integrated PL intensity
5
The connection between theory and experiment is completed by noting that the generation rate can be separately calculated from experimental parameters using
ν
where PLaser is the peak optical power incident on the sample, R (18 %) is the Fresnel reflection at the sample surface, l (15 nm) is the total thickness of the InGaN QWs, Aspot (1.96 × 103μm2) is the area of the laser spot on the sample surface, hυ(3.18 eV) is the energy of a 370 nm photon, and. αm-1) is the absorption coefficient of the In0.1Ga0.9N well at 370 nm.
First, we measured the PL spectrum dependent excitation power, and then the generation rate (G) curves as a function of PL intensity (IPL) can be obtained by using equation 4.3.4. We used equation 4.3.4 to fit the experimental data in Fig. 4.3.1, then we obtained the coefficients P1 =A(Bη)0.5, P2 =1/η, P3 = C/(ηB)1.5. The fitting curves appear to accurately model our experiments, also shown in Fig. 4.2.1. If one assumes a value of B at room temperature of 1 × 10−10 cm3/s, the value of carrier concentration n can also be obtained. By eliminating η from the two coefficients P1
and P2, one can obtain the value of coefficient A finally. The table 4.3.1 shows the nonradiative coefficient A at low and room temperature. The nonradiative coefficient A as a function of dislocation density, including values of 8.66 × 105, 1.64 × 106 at low temperature and 1.28 × 107, 2.45 × 107 s−1 for InGaN/GaN UV LEDs on PSS and conventional sapphire substrate, respectively. Nonradiative coefficient of without PSS UV LED is larger than PSS at low and room temperature. Generally, threading-dislocation density significantly affects the InGaN MQW efficiency, which
supports the argument that threading dislocations behave as nonradiative recombination centers. The results indicated the InGaN/GaN UV LEDs on PSS has better crystal quality and larger quantum efficiency due to the reduction of threading dislocation density.
After that, we know the carrier concentration n and P2, so we can be obtained IQE curves as a function of carrier concentration n in Fig 4.3.2. The calculation of IQE is very similar to our experimental results. Fig. 4.3.3 shows the emission power as a function of current density, different slopes can be attributed to different terms dominating the recombination-rate equation.
We can reproduce the dependence of the internal efficiency on current density, J,
using a simple rate-equation model of the form
2 3
~
An Bn Cn
J
+ + (4.3.8)where n is the QW carrier density and A, B, and C are coefficients for nonradiative, radiative, and (nonradiative) Auger-like recombination, respectively. We thus identify a high-density QW-internal Auger-like process as the culprit for the high-current losses observed, with C = 6.03 × 10−29 and 1.33 × 10−29 cm6/s for InGaN/GaN UV LEDs on PSS and conventional substrate at room temperature. The value of C is higher than the normal Auger coefficient (10-30~10-34 cm6/s). And the calculated order of carrier density (~ 1018 #/cm3) is not in the typical region of Auger recombination (~
1019 #/cm3). The hole mobility decreased at low temperature resulting in hole couldn’t transport to the later QW effectively. The results indicated that the carrier distribution is not uniform in the QW; the carrier density may be attained ~1019 #/cm3 to occur Auger-like recombination insome QW. Therefore, we demonstrated the Auger-like effect affect the efficiency droops at high injection current. The efficiency droop may be dependent on Auger-like effect.
Fig 4.2.1 IQE of InGaN/GaN LEDs as a function of carrier density at 15K and 300 K.
1E12 1E13 1E14 1E15 1E16 1E17 1E18 0.0
0.2 0.4 0.6 0.8
1.0
PL IQEPSS @ 15K NonPSS @ 15K PSS @ 300K NonPSS @ 300K
R el at ive i n ter n al q u an tu m ef fi ci en cy ( % )
Carrier density (#/cm
3)
~ 20 mA
~ 61.0 %
~ 44.2 %
0 1x105 2x105 3x105
Fig. 4.3.1 Generation rate G as a function of integrated PL intensity (IPL)
Fig. 4.3.2 Internal quantum efficiency as a function of carrier concentration n 1E12 1E13 1E14 1E15 1E16 1E17 1E18
0.0
Fig. 4.3.3. Emission power as a function of current density, different slopes can be attributed to different terms dominating the recombination-rate equation
Table 4.2.1 Efficiency parameters on PSS and without PSS InGaN/GaN UV LED
Sample PL IQE (%) Exp. EQE (%) Extraction (%)
PSS NonPSS
~ 61.0%
~ 44.2 %
~43.0%
~28.0%
~70.5%
~63.3%
Table 4.3.1 Nonradiative coefficient A from fitting equation 4.3.4
Sample A (s-1) @ 15K A (s-1) @ 300 K
PSS NonPSS
8.66x105 1.64x106
1.28x107 2.45x107
Table 4.3.2 Experimental IQE and calculation IQE
Sample PL IQE (%) Calculation of IQE (%)
15K 300 K 15K 300 K
PSS ~85.9 % ~61.0% ~82.4 % 60.6%
Non-PSS ~85.9% ~44.2% ~82.4% 41.8%
Table 4.3.3 Auger coefficient calculation and normal C: 10-30~10-34 cm6/s
Sample C (cm6/s) @LT C (cm6/s) @RT
PSS 2.48x10-29 6.03x10-29
NonPSS 3.02x10-29 1.33x10-28
Chapter 5 Analysis of electroluminescence and efficiency droop in InGaN/GaN multiple quantum wells grown on patterned sapphire substrate
5.1 Introduction
Recently some research groups have investigated temperature dependence of the electroluminescence (EL) spectral intensity [47][48][49], which reveals anomalous EL quenching at lower temperatures below 100 K. It is found that the anomalous temperature dependence of the EL efficiency is caused by interplay of the carrier capture and the IQE. One interesting observation of the InGaN/GaN QW diodes so far is that the EL efficiency dramatically decreases when the diode temperature is decreased below 100 K, where the improved EL efficiency is generally expected due to the decreased nonradiative recombination processes. One of the anticipated genuine causes for the low temperature EL quenching may be ascribed to the deep Mg acceptor level of 170 meV in p-GaN [50], which can be deactivated at lower temperatures below 100 K. Therefore, holes are failed to be injected into the QW active region from the p-GaN layer, especially when the electron blocking p-type AlGaN barrier is introduced. For this study, detailed physical mechanisms for the EL enhancement effects under the forward bias conditions have been confirmed. And we have investigated the carrier transport mechanisms particularly by using APSYS simulation.
5.2 Temperature dependent electroluminescence
Temperature dependence of the EL spectra at various injection current levels has been measured between 30 and 300 K. Three-dimensional (3D) plots of the EL results at three injection currents of 0.1, 1, and 20 mA are shown in Figs. 5.2.2 (a)-(c), respectively. First, at the lowest current of 0.1 mA in Fig. 5.2.2(a), the EL intensity shows the highest value at the lowest temperature of 30 K. This result is interpreted as showing the EL efficiency basically determined by the nonradiative recombination centers at low injection current. We can observe the EL intensity decrease slightly from 300 K to 30 K when injection current is 1 mA. When temperature is slightly decreased from 300 K to 100 K at 20 mA, the EL spectral intensity efficiently increases, and reaches the maximum around 100 K. However, with further decrease of temperature down to 15 K, significant reduction of the EL intensity is observed. We will be discussed the detailed physical mechanisms later.
In order to check the EL efficiency, the relative EL efficiency is plotted as a function of temperature in Fig. 5.2.3 and Fig. 5.2.6 at injection currents of 0.1, and 20 mA. Generally, thermal quenching phenomenon was observed in InGaN-based structures. At low injection current, the carrier injected into quantum well, and then the carriers can be confined due to the localized states in the In-rich region. In InGaN-based structures, the emission came from the localized states, which could trap
carriers within this potential minimum. Fig. 5.2.5 shows the schematic drawing of effective localized states and defect states. When the temperature increased, the carrier could receive activation energy to thermalize from radiative or/and localized centers to nonradiative or/and delocalizaed centers resulting in the EL efficiency decreased. When temperature decreased, the forward voltage increased of InGaN/GaN UV LEDs due to the hole concentrations and mobility decreased [51]. But we observed the forward voltage change slightly at low injection current that indicated it didn’t affect the EL efficiency seriously in Fig 5.2.4 (b). Fig. 5.2.7 (b) shows the temperature dependence forward voltage, we found that the EL efficiency decreased while decreased temperature from 100 K to 30 K. There are two possible mechanisms interplay with increasing temperature, and then the EL efficiency is affected by carriers escape from localized states into defect states of low injection current at 0.1 mA. But the temperature dependence EL efficiency at 20 mA decreased when further decreasing temperature, the results can be attributed to the forward voltage increased rapidly due to the hole concentrations and mobility decreased.
A reduction of the EL intensity is clearly seen with decreasing the temperature below 80 K after reaching the maximum EL intensity around 100 K at 20 mA. In Fig 5.2.7 (b), the forward voltage increased about 1 and 1.4 V for InGaN/GaN UV LEDs on PSS and conventional substrate, respectively. Therefore, we conclude that the
variation of Vf plays an important role in temperature dependence EL efficiency, especially, the EL efficiency may be affected when decreasing temperature at high injection current. In high injection current, it appears that the carriers are effectively captured by active centers in the MQW under the application of lower forward voltage at room temperature. But, forward voltage increased while decreasing temperature, they are rather transferred to nonradiative recombination centers as a result of escape from the MQW region, thus reducing the EL efficiency. This is because the carriers can escape out of the well region due to the external field effects in high injection current. We also demonstrated that the higher field existing in the well under the higher forward voltage decreases the radiative recombination rate, which also causes the reduced EL intensity.
5.3 Injection current dependent electroluminescence at 30 K and 300 K
In order to show detailed variations of the EL efficiency as a function of injection current at various temperatures, the integrated EL intensity divided by current, which is proportional to the EL quantum efficiency, is plotted in Fig 5.3.1 and Fig. 5.3.3 as a function of logarithmic current at 30 K and 300 K. The EL quantum efficiency at 30 K increased slightly with increasing injection current due to injected carrier attributed to compensate the nonradiative recombination centers, and reaches the maximum at
about 1mA. We can observe the EL quantum efficiency at 0.1 mA of InGaN/GaN UV LED on PSS is higher than conventional sapphire substrate, and then the EL quantum efficiency reaches the maximum at lower injected current. The results demonstrated the slight variation of EL quantum efficiency due to the reduction of dislocation density of InGaN/GaN UV LED on PSS. While further increasing injection current, the EL efficiency droops rapidly, we observed that the reduction of EL efficiency of InGaN/GaN UV LED on PSS is very similar to conventional sapphire substrate. The results indicated that the reduction of dislocation density didn’t affect the efficiency droop at high injection current. Fig. 5.3.2 shows the schematic drawing of current dependence EL efficiency. While further increasing injection current, the EL quantum efficiency deceased rapidly which the forward voltage drastically increased at 30 K which show in Fig. 5.3.2 (b). We attribute this reduction of EL quantum efficiency at high injection currents to the higher forward voltage which resulting in carriers escape from the quantum well and overflow to p-GaN.
Fig 5.3.3 display the EL quantum efficiency increased obviously with increasing injection current at 300 K, since the nonradiative recombination centers are partially activated at higher temperature. In Fig 5.3.4 (a), we can see the schematic drawing of current dependence EL efficiency at 300 K. Identically, we found that the EL quantum efficiency of InGaN/GaN UV LED on PSS is higher than conventional sapphire
substrate. And the EL efficiency droops more slightly at 300 K with further increasing injection current, which can be ascribed to the reduction of forward voltage at high injection current that show in Fig 5.3.4 (b).
5.4 Analysis of injection carrier density dependence EL efficiency and efficiency droop
Fig 5.4.2 and 5.4.3 show the temperature dependent EL efficiency as a function of injection current of InGaN/GaN UV LED on PSS and conventional sapphire substrate, respectively. We use Shuji Nakamura and Steven P. Denbaars et al. [52]
proposed equivalent circuit model (should add the model and explain what it means for) to explain the temperature dependence EL efficiency as a function of injection current. These four components are put in an equivalent circuit model illustrated in Fig. 5.4.1 (a). This circuit model ensures all injected carriers are traced and are not unintentionally lost. The resistor R1 represents current leakage paths, such as extended crystal defects) and sample surface) For example. This current component is not considered to involve carrier recombination, hence is purely carried by electrons.
There are two diodes. Diode D1 is responsible for current flow due to radiative recombination. This current component results in photon emission and detection upon recombination. Diode D2 is responsible for nonradiative recombination current. Such recombination occurs via nonradiative recombination centers (NRCs) and does not
emit photons within the wavelength range of interest. These two types of recombination are not limited within or near the active region. They are distinguished by whether a photon is emitted and detected within the wavelength range of interest upon a recombination event. Another resistor R2 combined with a switch represents carrier overflow. This component is considered to be the electron unipolar current, i.e., is carried by electrons that do not recombine with holes and exit the system to the p-type contact. Current division between ID1 (through D1) and ID2 (through D2) is defined as:
(5.4.1)
where rR is the radiative recombination rate and rNR is the nonradiative recombination rate. EL efficiency is defined in this current range as
(5.4.2)
where ID = ID1 + ID2 and IT = ID + IR1 have been implemented. Ohms law and the diode equation are taken to identify the fundamental behavior of:
(5.4.3) (5.4.4)
V is the applied voltage, ID0 is the diode saturation current, q is the unit charge, n is the ideality factor, k is the Boltzmann constant, and T is the absolute temperature.
Equations (5.4.3) and (5.4.4) can be related via V to obtain from eq. (5.4.2) as
(5.4.5)
Figure 5.4.1 (b) is going to be compared to experimental results. We can observe the entire curve gradually shifts upwards towards EL efficiency ~ 1 as a result of nonradiative recombination centers deactivation when temperature is reduced. In this model, the EL efficiency increased when increasing injection current, and the EL efficiency curve bending less sharp while temperature is decreasing. The phenomenon indicated that the significant leakage current existed, and the leakage current is reduced when temperature decreased.
Fig. 5.4.3 shows the EL efficiency as a function of injection current at 77 K and 300 K, and the EL efficiency are 60.3 %, and 41.6 % at 20 mA of InGaN/GaN UV LED on PSS and conventional sapphire substrate, respectively. The EL results is similar to the PL efficiency which show in table 5.4.2, therefore, we also can obtained the internal quantum efficiency by temperature dependence EL measurement.
5.5 Comparison of PL and EL efficiency
Fig. 5.5.1 displays the PL efficiency and EL efficiency as a function of carrier density at low and room temperature. We can observe that the PL efficiency is higher than EL efficiency at low carrier density, the results indicated that more leakage current occurred when carrier injected into quantum well due to the injected carriers may be captured by nonradiative recombination centers in n-GaN when using current source. Fig. 5.5.2 (a) demonstrated that some leakage current appeared in n-GaN, but when using 370 nm laser to excited carrier which electron and hole pairs occurred in multiple quantum well without absorption of n-GaN. Further increasing injected carrier density, the PL and EL efficiency decreased due to carrier overflow from quantum well which show in Fig. 5.5.2 (b). And we found that the EL efficiency decreased more rapidly at high injected carrier density, it can be attributed to the forward voltage increased when increasing injected carrier density. The results demonstrated that carriers escape from the quantum well and overflow to p-GaN. Fig.
5.5.3 indicated more carriers injected to p-GaN at high current which resulting in the efficiency droop more quickly.
Fig. 5.4.3 shows the EL efficiency as a function of .injection current at 77 K and 300 K. We discovered that the EL efficiency droops more rapidly at 77 K that it at 300 K. Fig. 5.5.6 and Fig. 5.4.20 display temperature dependence electron concentration
and mobility and temperature dependence hole concentration and mobility [53], respectively. From Fig 5.5.6, we observed the electron concentration and mobility decreased when decreasing temperature, but the electron mobility only a little decayed.
The hole concentration and mobility decreased drastically with decreasing temperature, the hole mobility have one order decayed. This phenomenon caused that hole concentration distribution is not uniformly and is insufficient due to the low hole mobility, therefore, some electrons transport to the later quantum well near p-GaN when electron injected into quantum well. And these injected electrons further reach the p-GaN resulting in the EL efficiency droop more rapidly at 77 K than 300 K. The Schematic drawing of electron and hole concentration distribution at low and high injection current which show in Fig. 5.5.5.
5.6 APSYS simulation of electron and hole concentration distribution and band
diagram at high injection current
We wanted to know the carrier concentrations distribution under high injection current at low and room temperature; therefore, we use APSYS to simulate our sample structure. Fig. 5.6.1 shows the simulation of I-V curve with different hole concentration and mobility. The solid line represents our experimental results and the dash line represents the simulation results, we tried to change the parameters of hole
concentration and mobility to coincide with our experimental results. We can see the simulation of I-V curve is similar to experimental results. Further, Fig. 5.6.2 (a) show the electron concentration distribution in multiple quantum well, the black and red line represents the condition at 300 K and 77 K, respectively. The electron concentration distribution is uniform in the QW, but we can observe the electron concentration in QW near the p-GaN is higher (~five times) than near n-GaN, the results demonstrated that some electrons transport to p-GaN which just like the contention we mentioned above. Fig. 5.6.2 (b) displays the hole concentration distribution in MQW, we found the hole concentration is not uniform in the QW, the hole concentration in QW near p-GaN is higher (~ one order) than near n-GaN. The hole concentration distribution is not uniform which can be attributed to the hole mobility decreased at low temperature resulting in hole couldn’t transport to the later QW effectively. Under this condition where thermal generation of holes is insufficient and injected electrons continuously deplete holes, some of the injected electrons reach the p-GaN and exit the system without being able to recombine. Then, Fig. 5.6.3 shows the radiative recombination rate of each quantum well, we observed that the readiative recombination rate is higher near p-GaN which indicated the hole is insufficient to supply the radiative recombination of QW near n-GaN. Consequently, the results verified the EL efficiency droop more rapidly at lower temperature.
Finally, Fig. 5.6.4 shows the band diagram at high injection current of
InGaN/GaN MQW at low and room temperature. From this picture, high forward voltages for significant currents to flow, so that the conduction band on the n-side of the device is significantly higher than the conduction band on the p-side. This makes it energetically favorable for electrons to escape to the p-side of the device. The band inclined caused that more carriers overflow from quantum well and transport to p-GaN, the results make the EL efficiency droop quickly at lower temperature.
InGaN/GaN MQW at low and room temperature. From this picture, high forward voltages for significant currents to flow, so that the conduction band on the n-side of the device is significantly higher than the conduction band on the p-side. This makes it energetically favorable for electrons to escape to the p-side of the device. The band inclined caused that more carriers overflow from quantum well and transport to p-GaN, the results make the EL efficiency droop quickly at lower temperature.