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Truncated cones or cylinders?

Yangrui Hu

April 26, 2017 - Posted in Discussion
​When I did simulations about deep ultraviolet LED, I found that people always use cylinders to simulate nanowires. However, nanowires are not usually cylinders but truncated cones in the experiment, which means the radius of the nanowire becomes larger as growing. So I want to study the case with truncated cones. As the following figure shown, the bottom radius and the height are fixed and theta becomes one of the key parameters to describe the nanowire.
At first, I simulate the simplified model: two perfectly refractive layers in the top and bottom, considering the absorption effect of n-GaN layer, and not filling any material inside the space between nanowires. The simulation result shows that light tends to move towards wider layers. And this result is also obtained with a single nanowire. Why light tends to move towards wider layers? I think it can be explained by Helmholtz equation. Wave equation can be derived from Maxwell equations and Helmholtz equation is a kind of wave equation that can describe the electrical field with a constant frequency.
Compare Helmholtz equation with Schrodinger equation and we can regard the coefficient with refractive index n as optical potential. Then potential will decrease as n increasing and the intensity of electrical field should be larger with higher n. And the effective refractive index in the top layer is larger than the bottom, as the figure shown. So light tends to move upwards.
In the next step, I simulate the complicated model: the silicon substrate, p-GaN on the top with absorption effect, and using parylene to fill the space between nanowires. When theta is small, there are two factors influence light extraction efficiency(LEE): parylene and theta. As theta larger, light move upward which makes LEE lower and the amount of parylene decreases, which makes LEE higher. With these two factors, LEE can get the highest value at a special theta.
When theta is large enough to make nanowires just cover the top plane thoroughly, the effect of theta is not important and the key factor is the radius. Nanowire spacing is fixed and radius is different at different layer with different theta. And LEE can also get the highest value at a special theta. Truncated cones can be applied to make deep UV nanowire LED with wavelength<280nm, because it is very hard to find a proper filling material when wavelength<280nm.

Figure: the structure of a truncated cone
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