4.1. Light Extraction Efficiency
a compares the temperature-dependent efficiencies of light extraction from the LED dice to air obtained for green and blue LEDs. As one can see from Figure 6
, the LEE of the green LED is lower than that of the blue one at all the temperatures. This finding disagrees with the increase in RT LEE from the blue to green spectral range observed on SQW-based LEDs [6
]. The LEE increasing with wavelength was attributed in [6
] to temperature-dependent optical properties of the silver-based p
-electrode providing dominant optical losses of the emitted light via its incomplete reflection from the electrode. On the other hand, contribution of internal optical losses in the LED die was also found to be considerable. Nevertheless, in LED structures of similar designs, the optical losses have been shown not to change the general trend of the LEE to rise with the emission wavelength [6
The AR of the green LED differs from those studied in [6
] in two aspects. First, it consists of five InGaN QWs, which makes band-to-band light absorption quite critical for achieving high LEE. Secondly, the AR non-uniformity of the green LEDs results in two different spectral peaks (Section 2
). Regarding that, the sw-emission may be effectively absorbed by the SR producing the lw-emission, which may increase additionally the band-to-band optical losses. As the sw-emission is more pronounced at low temperatures (T
< 100–120 K), this should lead to a greater difference between LEEs of blue and green LEDs in this temperature range, in accordance with the data shown in Figure 6
b. At high temperatures (T
~ 250–300 K), the sw-emission is suppressed and the difference between LEEs of blue and green LEDs in this temperature range (less than ~2%) may be attributed to a difference in the band-to-band light absorption in the MQW active region.
d shows that the RT EQE dependence on the output power plotted in log scale has a nearly dome-like character with asymmetric low-power and high-power wings. In this case, the procedure of the LEE extraction from this dependence based on approximation of the high-power wing with the ABC model [6
] becomes applicable, providing the LEE value of about 66%. The method used in our study, which implies two ARs to co-exist, gives the value of 68% which is quite close to the above cruder estimate.
4.2. Quality Factors and Internal Quantum Efficiency
It has been shown in Section 3.2
that dependence of the EQE of the green LED on output optical power can be interpreted in terms of two co-existing ARs having different quality factors, Qsw
, the temperature dependences of which is given in Figure 6
b. One can see from the figure that Q
-factors of the green LED are much lower than those reported in [5
] for the blue one. This is manifestation of the so-called “green gap” problem, i.e., remarkable decline of the LED efficiency towards longer emission wavelength. Two commonly discussed origins of the “green gap” are: (i) quantum-confined Stark effect leading to spatial separation of electron and hole wave functions inside the InGaN QWs (see, for example, [2
] and references therein) and (ii) degradation of materials quality in InGaN alloys with high indium content [20
]. Recently, implication of composition fluctuations in InGaN to the LED efficiency reduction in the “green gap” has been also demonstrated [22
b shows that the Q
-factor corresponding to sw-emission from the green LED is a few times lower than that corresponding to the lw-emission. Since the Q
-factors determine the maximum IQE values through the relationship
= sw, lw), the lower Qsw
results immediately in a lower IQE value of the sw-emission. The temperature dependencies of maximum IQEs for sw- and lw-emission of the green LED are plotted in Figure 6
c. One can see from the figure that the efficiency of the sw-emission declines with temperature much faster than that of the lw-emission, resulting in suppression of the sw-peak in the emission spectrum at RT. In turn, the IQE corresponding to the lw-emission of the green LED declines faster than the efficiency of the blue LED. This observation is in line with the conclusion made in [23
] that the contribution of Auger recombination to the temperature-dependent IQE reduction is much stronger in green LEDs than in blue ones.
c shows also that absolute maximum of IQE is controlled by the lw-emission irrespective of temperature. The maximum IQE tends to the value of ~92% at zero temperature, i.e., the non-radiative recombination does not vanish completely at cryogenic temperatures. This makes doubtful estimations of the RT IQE based on comparison of the LED emission intensities measured at cryogenic and room temperatures.
4.3. Specific Powers and Recombination Volumes
Output power corresponding to the maximum IQEs of the sw- (
) and lw-emission (
) of green LEDs are plotted in Figure 6
d versus temperature along with the transition power Pt
. The only temperature-dependent output power Pm
of blue LEDs from [5
] is also shown in the figure by the dash-dotted line just for comparison. One can see that
of blue LEDs are rather close to each other in the whole temperature range of study. In contrast,
is about two orders of magnitude lower than
. The reason for this is discussed below in more detail.
The transition power Pt
is situated between
< 200 K and approaches
at RT. The latter corresponds to merging of the sw- and lw-emission peaks at T
= 300 K, as can be seen from Figure 2
In order to get more information from the data obtained, we have plotted in Figure 7
products corresponding to sw- and lw-emission peaks vs. temperature. Since
is the energy of emitted photon, Vr
is the recombination volume, and B
are the radiative and Auger recombination coefficients, respectively (see, for example, [18
product does not include the Shockley–Read–Hall coefficient A
responsible for carrier recombination at point and extended defects. As one can see from Figure 7
products of both sw- and lw-emission peaks are found to be nearly independent of temperature, similar to the case of blue LEDs [5
]. This is evidence for the fact that both radiative and Auger recombination coefficients in the green LED, like in the blue one, have qualitatively similar temperature dependence: either ascending or descending. This result is in qualitative agreement with the recently observed anomalous (ascending) temperature variation of the radiative recombination coefficient [23
], which was attributed to strong hole localization by composition fluctuations in InGaN alloys. Regarding that, the Auger recombination coefficients were found in [23
] to increase with temperature in both blue and green LEDs.
Using the values of the B
- and C
-coefficients at 450 nm and 540 nm reported in [25
] for RT, we have estimated the ratio of the recombination volumes of blue LED (
) and that corresponding to lw-emission of green LED (
). The obtained ratio
indicates that the recombination volumes are comparable with each other. As the active region of the blue LED was specially optimized to provide a uniform carrier injection in all five QWs in the active region, the latter fact enables attributing the lw-emission of the green LED to operation of its active region as a whole.
A similar estimation provides , which demonstrates the recombination volume of the SR responsible for sw-emission to be about two orders of magnitude smaller than that of the SR producing lw-emission. Such a big difference cannot be explained by dominant carrier injection in one of the five QWs. Therefore, a natural interpretation of the result implies that the sw-emission comes from the local lateral areas distributed within the QWs.
4.4. Possible Origins of Active Region Non-Uniformity
Any interpretation of the above results should account for and/or explain four main points: (i) the difference between the wavelengths of sw- and lw-emission; (ii) the sequence of sw- and lw-peaks’ appearance in the emission spectrum with the operating current; (iii) the difference in the recombination volumes associated with sw- and lw-emission; and (iv) the difference in the Q-factors or IQEs of the sw- and lw-emission. We will consider below a number of scenarios for the active region non-uniformity, addressing these points.
The difference in the emission wavelength can be attributed to variation of either composition or width of InGaN QWs in the LED active region. Simulations of InGaN SQW LED structures operating at the current density of 20 A/cm2
carried out with the commercial SiLENSe 5.10 package [26
] have shown that the observed difference between the sw- and lw-emission wavelengths may be associated with either ~2% variation of the indium content in the InGaN alloy or ~0.4 nm (i.e., ~1.5 monolayer) variation of the QW width. Both versions seem to be realistic for green LEDs examined here.
A possible mechanism producing compositional non-uniformity of the active region is partial stress relaxation in the LED structure. Indeed, the critical thickness of the (0001) InGaN/GaN layer is comparable with the QW widths in the green spectral range [27
]. If the total width of all QWs in the LED active region exceeds the critical thickness, stress relaxation becomes possible, resulting, in particular, in an increase of indium content just by a few percent in the top partially relaxed QWs [28
]. The appearance of the sw-emission at low currents and of lw-emission at high currents may be then explained, assuming dominant hole injection into the bottom (unrelaxed) QWs at low currents. This assumption does not agree, however, with the data of experiments carried out on LEDs with color-coded blue/cyan QWs in the active region [29
]. In addition, the above scenario cannot explain a lower IQE of the sw-emission, as compared to lw-emission, and the substantial difference in their recombination volumes.
A similar conclusion can be made about another mechanism, which implies the lw-emission to come from the In-rich clusters more or less uniformly distributed over all the QWs. Here, lw-emission is expected to appear first at low currents and its recombination volume should be smaller than that of the sw-emission, contrary to observations. Two-peak emission spectra may also be explained by contribution of excited states of electrons and holes in InGaN QWs. However, the expected sequence of lw- and sw-peak appearance in the spectra under increase of operating current (lw-peak at low currents and sw-peak at high currents) contradicts our observations as well. Therefore, other mechanisms are necessary in order to interpret the characterization data of our green LEDs.
Here, we suggest the following qualitative model for the active region non-uniformity. First of all, we assume rarely distributed regions with lower indium content responsible for sw-emission to be embedded into the matrix of InGaN with higher indium content, which is responsible for lw-emission. These low-indium regions have a lower height of the potential barriers formed at the InGaN/GaN interfaces for both electrons and holes. This is due to lower band offsets in both conduction and valence bands and lower polarization charges induced at the interfaces. At low LED operating currents, the carrier injection into the InGaN QWs is limited by thermionic emission over the barriers. Therefore, pinching of the current is expected to occur in such a way, as to produce dominant pumping of the low-indium regions and, eventually, the sw-emission of photons. At higher currents, pumping of the high-indium matrix starts to occur, resulting in the lw-emission, which becomes quickly dominant, partly due to a much larger recombination volume.
Such a scenario is consistent with most of observations discussed above but it does not yet explain the difference in the IQEs (Q
-factors) of the sw- and lw-emission regions. The explanation can be given, assuming the low-indium regions to be formed around extended defects like threading dislocations and V-pits. Indeed, less effective indium incorporation is expected next to the dislocation cores because of excess elastic energy related to dislocation-mediated strain. Formation of the InGaN QWs with larger bandgap on the side walls of V-pits has been directly demonstrated in [30
]. Existence of dislocation cores serving as non-radiative recombination centers may explain a lower IQE of the sw-emission regions.
In order to assess whether the small recombination volume
may be attributed to extended defects, we assume the sw-emission to originate from the carriers collected from the area of about
around each of the defects, where Ld
is the carrier diffusion length, Da
is the ambipolar diffusion coefficient, and τd
is the differential carrier life time. Using experimental values Da
~ 0.25 cm2
] and τd
~ 20 ns [23
], typical for green InGaN LEDs operating at low currents, we obtain
~ 5 × 10−9
. In this case, the density of the extended defects necessary to provide the ratio
, which may be tentatively associated with the density of V-pits. Indeed, the carrier injection into semi-polar QWs formed at the side walls of V-pits is not hindered by high potential barriers typically induced at the (0001)-interfaces of polar QWs. Therefore, the current flow through the V-pits may dominate under low-current conditions [32
]. This conclusion is indirectly supported by the experimental correlation between the waving observed in the I–V curves, which is the evidence for carrier leakage through extended defects, and the values of the current corresponding to maxima of the sw-emission efficiency (closed circles in Figure 1
). Of course, the V-pit density of ~106
is just the lower-limit estimate, which does not account for the complex mechanism of current pinching around this type of defect [32
] and dispersion of their dimensions affecting the current flow as well.
It is interesting that the two-peak character of the low-temperature efficiency dependence on current has been reported earlier for both blue and green LEDs [7
]. Moreover, the efficiency maxima were shifted remarkably to lower currents in green LEDs compared to blue ones, in line with our observations. Those data may also be interpreted in terms of competition between the current flow through the V-pits and through the (0001)-interfaces of QWs, assuming the efficiency of the main QWs to be somewhat lower than that of the semi-polar QWs on the side walls of the pits. At RT, the low-current efficiency peaks quenched and the efficiency dependence on current gains a conventional dome-like shape [7
Generally, the above mechanism considering V-pits as the origin of AR non-uniformity is expected to be especially pronounced in green LEDs, as higher indium content in the QWs is known to favor V-pit formation.