# A Review of AlGaN-Based Deep-Ultraviolet Light-Emitting Diodes on Sapphire
## 14 IQEs of AlGaN-Based Uneven QWs  
Many of the reported IQEs are determined using the ratio of photoluminescence (PL) intensity at room temperature (RT) to that at a low temperature (LT). The model for this measurement is simplified by considering one type of NRC. This model requires other assumptions. The electron (\(n_{e}\)) and hole (\(n_{h}\)) densities are assumed equal to the representative carrier density (\(n\)) at QWs, and the recombination terms are separated according to the order of the carrier density \(n\): \(An\), \(Bn^{2}\), and \(Cn^{3}\). Here, \(A\) is a nonradiative recombination coefficient related to the Shockley-Read-Hall (SRH) NRCs, which is related to the probability for the carriers to be captured by NRCs. Thus, \(A\) strongly varies with temperature (\(T\)). \(B\) is an emission coefficient linear to the Einstein \(A\) coefficient based on the concept of the possibility of a radiative combination of electron-hole pairs at the QWs. Thus, \(B\) is multiplied by the square of the carrier density in the QWs assuming free carriers. \(C\) implies nonradiative Auger recombination concerning three carriers, and the \(n^{3}\) term is multiplied. In the case of a device with a high carrier density such as LDs, the \(C\)-term is necessary. For LEDs, \(C\) is often approximated to be negligible [77]. At the LT limit, SRH-NRCs are assumed to be occupied and frozen out; thus, all the injected carriers are considered to be converted to EL. When SRH-NRCs are frozen at LT, the quantum yield (\(\varphi\)) can be near 100% by freezing \(A\)(\(T\to 0\)) to zero. The quantum yield (\(\varphi\)) with a function of \(T\) is defined as  
\[\varphi(T)=\frac{Bn}{A(T)+Bn} \tag{1}\]  
Figure 16: (**a**,**b**) Increased EL output in accordance with EL spectral broadening. The sapphire miscut angle was set to 1.0\({}^{\circ}\). The TDD values and the density of macrosteps of the templates are considered to be within a narrow range. The numbers of (**a**) 265 nm and (**b**) 285 nm LED wafers were 11 and 23, respectively. For (**b**) 285 nm LEDs, the dependence of EL output on FWHM of EL spectra is vague to see the relationship between EL output and spectral width when the EL output and spectral width were simply mapped. When the samples wafers were grouped by the wavelength of peak EL, a positive correlation between the EL output and spectral width was seen for all groups of 285 nm LEDs, as indicated by the “+” symbols above the insets. The arrows indicate two overlapping data in graph (**a**). The dotted line in (**b**) shows the weak positive correlation. (Figures are permitted to be reused from Jpn. J. Appl. Phys. [13] © Japan Society Applied Physics). When the number of carriers (\(n\)) injected into QWs is sufficiently large to be \(A\gg Bn\), \(\varphi(T)\) is overestimated at \(T\gg 0\). Therefore, nonsaturated excitation is necessary to obtain appropriate IQE values in this measurement. The junction temperature (\(T_{j}\)) is considered to be increased by a high-energy excitation. The saturated excitation makes it difficult to assume \(T_{j}\) with approximation to the temperature of the sample holder. In the discussion on IQEs, the reported data [24; 25; 41; 61; 132; 133; 134; 135; 136; 137] are collected and shown as solid symbols (\(\blacktriangleright\), \(\blacksquare\), \(\blacksquare\), \(\blacktriangleright\), \(\blacksquare\), \(\blacktriangleright\), \(\blacktriangleright\), \(\blacktriangleright\)) for the measurements under the nonsaturated conditions. Figure 17 shows the IQEs as a function of wavelength. The hollow symbols in Figure 17 indicate the calculated or measured IQEs reported without mentioning nonsaturated excitation. There is another method of enabling the separation of IQE and CIE [129] using I-L characteristics. However, it is based on the given LEE and considered to be a rough estimate.