The design of the UVC LEDs featuring a single quantum well is executed using the ATLAS TCAD simulator. The respective structures are illustrated in Figs. 1a and 1b.
The conventional blue LED labeled as LED1, depicted in Fig. 1a, follows the p-GaN/p-AlGaN/AlGaN/n-GaN/GaN structure. It is grown on a Silicon Carbide substrate. The growth process entails a 500 nm thickness of GaN buffer layer, succeeded by a 200 nm thickness of n-GaN having a doping level of 1 × 1018 cm− 3. The active layer consist of an Al0.22Ga0.78N single quantum well, measuring 3 nm in thickness. This is succeeded by a 100-nm- Al0.2Ga0.8N EBL (electron-blocking-layer) with p-type doping concentration of 1 × 1017 cm− 3, and a 150-nm-thickness of p-GaN cap with a p-doping concentration of 1 × 1017 cm− 3. The LED's geometric arrangement adopts a rectangular shape measuring 2 × 2 µm, with nickel (Ni) electrodes, 10 nm in thickness, serving as the p-type contact material and Ti (Titanium) as n-type contact material.
In Fig. 1b, the alternate LED configuration denoted as LED2 exhibits a closely resembling layer arrangement. However, a distinction lies in the active layer where the AlGaN is substituted with BAlGaN. The determination of energy band gaps for AlxGa1−xN and ByAlxGa1−x−yN (evaluated at 300K) is conducted through Equations (1) and (2).
EgAlGaN = xEg(AlN) − x(1 − x)b + (1 − x)Eg(GaN) ----------------------------------------------------(1)
Here "x" represents the proportion of Aluminum, the energy gap values are established as Eg(AlN) = 6.2 eV [19] and Eg(GaN) = 3.4 eV [20], with the bowing parameter denoted as "b" being 1.43 [21] [22].
Eg(ByAlxGa1−x−yN) =\(\frac{xy.Eg\left(BAlN\right).u=y\left(1-y-x\right). Eg\left(AlGaN\right).v+\left(1-y-x\right).x.Eg\left(BGaN\right).w}{x\left(1-x-y\right)+y\left(1-x-y\right)+xy}\) --------------(2)
Equations (3) and (4) are employed to calculate the energy band gaps of ByGa1−yN and ByAl1−yN
Eg(ByGa1−yN)= (1-y)Eg(GaN) + yEg(BN)– c(1-y)y ---------------------------------------------------(3)
Eg(ByAl1−yN)= (1-y)Eg(AlN) – d(1-y)y + yEg(BN) ----------------------------------------------------(4)
Here, "y" signifies the boron amount, and the energy gap value for BN is given as Eg(BN) = 5.5 eV [23],[24]. Additionally, the bowing parameter "c" is established as 9 [17], and the bowing parameter ‘d’ is determined as 14 [25],[26].
u=(1‒y‒x)/2; v=(2‒2y‒x)/2; w=(2‒y‒2x)/2.
Subsequently, the energy band_gap of B0.01Ga0.99N is determined to be 3.32 eV, while that of B0.01Al0.99N is calculated as 2.29 eV. Moving on, the band-gap energy of Al0.22Ga0.78N equates to 2.3 eV, and for B0.01Al0.22Ga0.77N, the value stands at 1.81 eV.
The simulation is conducted using the TCAD tool. Employing the finite element approach, the software establishes a mesh that spans the entirety of the design structure under scrutiny. It subsequently solves the fundamental semiconductor equations through iterative processes at each point within this mesh. These simulations are performed at 300 K (room temperature). The interfacial polarization is the summation of both piezoelectric and spontaneous polarizations, as indicated by Eq. (5):
Table 1
BN, AlN and GaN materials physical parameters
Parameters | GaN [28] | AlN [37, 38, 39, 40] | BN [29] |
Lattice constant a0 (Å) | 3.189 | 3.113 | 2.536 |
Piezo electric constant e13 (C m2) | -0.49 | 1.27 | 0.27 |
Piezo electric constant e33 (C m2) | 0.73 | 1.46 | -0.85 |
Elastic constants (C13 Mbar) | 1.03 | 108 | 7.4 |
Elastic constants (C33 Mbar) | 4.05 | 373 | 107.7 |
Ptotal = Psp + PPZ ----------------------------------------------------------- (5)
The piezoelectric polarization is expressed by Eq. (6):
PPZ = 2 [(e31 – (C13/C33))*e33] *[(a-a0)/a0] ------------------------------ (6)
Using the piezoelectric constants e33 and e13 (C m²), along with elastic constants C33 and C13 (Mbar), and the lattice constants a and a0 in the equilibrium plane structure, the inherent properties are established. In the case of binary materials such as BN, GaN and AlN, the pertinent property are sourced from the ATLAS TCAD user manual and corroborated references [25, 26, 27]. These calculated values are utilized within ATLAS, as tabulated in Table 1.
The "calc.strain" model adeptly considers the lattice mismatch existing between the distinct materials, while the polarization model computes the polarizations characteristic to each material. Addressing this phenomenon, the simulations integrate a polarization value that is proportionally scaled by a coefficient, defined through the "polar.scale" command. This coefficient varies within the range of 20% [30] to 80% [31]. Within LED simulations that are GaN-based, a common value is 50% [32]. For the simulations showcased in this research, this coefficient retains the value of 50%. The lattice constant of in-plane for BAlGaN is approximated, while for GaN, it approximates around 2.44%. The lattice mismatch existing between B0.01Al0.22Ga0.77N and GaN is roughly 2.25%.