# III-Nitride Short Period Superlattices for Deep UV Light Emitters
## 3 Bandgap of AlN/AlGa(In)N SPSLs  
The bandgap structure of III-Ns SPSLs convenient for the deep UV light emitters can be simulated using different software [73; 74; 75]. The BESST (Bandgap Engineering Superlattice Simulation Tool) commercially available package from STR Inc. [76] was used to analyze the results of different teams [77; 78], as well as most of our experimental results. This software is suitable for modelling optoelectronic devices utilizing SPSLs as essential units of their heterostructure designs. The BESST calculates the SPSL electron and hole minibands using a tight-binding approach and numerical solution of the Schrodinger equation with account of complex valence band structure of III-nitride compounds. Coupled solution of the Poisson equation for electric potential, accounting for polarization charges at the heterostructure interfaces, and discrete drift-diffusion transport equations, allows building up the band diagram of a device at an arbitrary bias and calculating the corresponding electron and hole currents, as well as the radiative recombination rate and emission spectrum. Field-dependent mobilities of electrons and holes used in the transport equations are found, self-consistently, with the simulated minibands of SPSLs.  
Fourier-transform infrared optical reflectance (FTIR) [79; 80; 81; 82], photoluminescence (PL) [83; 84; 85], and cathodoluminescence (CL) [41; 42; 86] are widely used to estimate the effective bandgaps of AlN/Ga(Al,In)N SPSLs. At room temperature, these methods are mostly qualitative, although still very useful for express control and adjustment of light-emitter properties during fabrication. The room temperature FTIR and CL were successfully used to facilitate fabrication of the first deep UV LEDs operating at 280 nm using undoped and n- and p-type AlN/Al\({}_{x}\)Ga\({}_{1-x}\)N SPSLs [41; 42].  
As an example, the experimental FTIR and CL effective bandgaps of AlN/Al\({}_{0.08}\)Ga\({}_{0.92}\)N SPSLs and simulations of these structures obtained using two different approaches [46; 76] are shown in Figure 5. One can see that both simulations provide the slope of the optical energy gap dependence on the SPSL period (actually, on the AlN barrier \"effective\" width), similar to that obtained by CL, whereas FTIR data demonstrate a different slope. This may have originated from the fact that FTIR measures the spectral dependence of light absorption, which may involve higher electron minibands and lower hole minibands or levels, whereas luminescence occurs mainly from the ground state minibands, due to their dominant occupation. Simulations by BESST show that SPSLs, regarded here, possess two different electron minibands and up to three heavy- and light-hole minibands, which can be considered as single energy levels at large SPSL periods because of miniband narrowing. Hence, contribution of the extra minibands to the light absorption may explain the difference in the optical energy gap determination by FTIR and CL.  
Of course, the Stokes shift, which is related to the excited state configuration in the well material, is a factor in all radiative recombination processes and, therefore, should also yield to red shift of the CL's estimated bandgap. Note that scatter in the experimental data shown in Figure 5 can be attributed to monolayer level uncertainty in the well and barrier thickness across the wafer, as well to local composition fluctuations in the well alloy [61; 65].  
Figure 4: TEM cross-section of AlN/AlGaN SPSLs (courtesy of Dr. [PERSON]) (**a**) grown directly on bare (0001) sapphire; (**b**) grown on -50 nm thick AlN buffer layer. The white scale bars are 20 nm long. The [0001] direction is shown by black arrows.