Correction to: Scientific Reports https://doi.org/10.1038/s41598-021-04710-w, published online 28 January 2022

The paragraph following Eq. 34 was incomplete.

“The numerical solution must meet these two boundary conditions.”

“Note that $${x}_{end}$$ refers to the end of the semiconductor model, at the insulator layer $$({x}_{ins})$$. The numerical solution must meet these two boundary conditions.”

Additionally, Eq. 35 was incorrect and contained a duplication of the term $${dx}^{{\prime}}.$$

$$\frac{{\partial }^{2}\phi }{\partial {x}^{2}}=-\frac{\partial E}{\partial x}=-\frac{\rho }{\epsilon }\Rightarrow \phi (x)-\phi (0)=-\underset{0}{\overset{x}{\int }}Edx=-\frac{1}{\epsilon }\underset{0}{\overset{x}{\int }}\underset{0}{\overset{{x}^{{\prime}}}{\int }}\rho d{x}^{{\prime}}d{x}^{{\prime}}$$
(35)

$$\frac{{\partial }^{2}\phi }{\partial {x}^{2}}=-\frac{\partial E}{\partial x}=-\frac{\rho }{\epsilon }\Rightarrow \phi (x)-\phi (0)=-\underset{0}{\overset{x}{\int }}Edx=-\frac{1}{\epsilon }\underset{0}{\overset{x}{\int }}\underset{0}{\overset{{x}^{{\prime}}}{\int }}\rho d{x}^{{{\prime\prime}}}d{x}^{{\prime}}$$
(35)

Lastly, in the Numerical results section, under subheading ‘Identifying optimal parameters’,

“One can see (Fig. 11), that the smaller wavelength the temperature is smaller.”