Nella Rotundo, Patricio Farrell, Natascha Dropka
Stefan Kayser (WIAS)
01.01.2020 – 31.12.2020
Weierstrass Institute Berlin (WIAS)
It is impossible to measure the temperature distribution within a crystal during growth. Yet, to improve crystal growth this is paramount. Due to temperature fluctuations, microscopic variations appear in the doping concentration. These striations follow the solid-liquid interface and can be measured even in the cooled-down crystal. Traditional techniques to measure striations have a poor spatial resolution, take long time or are inherently destructive. To overcome these limitations, the lateral photovoltage scanning method (LPS) has been proposed. This opto-electrical measurement procedure detects doping inhomogeneities at wafer-scale and room temperature in a non-destructive fashion. The LPS method excites the semiconductor crystal with a laser, creating a voltage difference at the sample edges which is proportional to the local doping variation.
We solve the forward LPS model for a given doping profile via a finite volume discretization and Newton solver embeddings with the open-source ddfermi software tool ddfermi. After solving for the equilibrium solution, we first apply a bias and then turn on the laser. Once we reach the prescribed laser power, we sweep the sample for different laser spot positions. For every laser spot position we need to ensure that potentials at the boundaries satisfy a nonlinear boundary condition derived from modified nodal analysis (MNA). To achieve this, we employ the secant method.
Tauc made three main theoretical predictions: First, the LPS voltage depends on local doping variations. Second, LPS voltage depends logarithmically on moderate laser intensities. And third, eventually LPS voltage saturates for higher laser intensities due to the screening effect. With our computational setup we were able to qualitatively reproduce all three of Tauc’ predictions.
S. Kayser, A. Lüdge, and K. Böttcher, “Computational simulation of the lateral photovoltage scanning method,” In Proceedings of the 8th International Scientific Colloquium, pp. 149–154, 2018.
Please insert any kind of pictures (photos, diagramms, simulations, graphics) related to the project in the above right field (Image with Text), by choosing the green plus image on top of the text editor. (You will be directed to the media library where you can add new files.)
(We need pictures for a lot of purposes in different contexts, like posters, scientific reports, flyers, website,…
Please upload pictures that might be just nice to look at, illustrate, explain or summarize your work.)
As Title in the above form please add a copyright.
And please give a short description of the picture and the context in the above textbox.
Don’t forget to press the “Save changes” button at the bottom of the box.
If you want to add more pictures, please use the “clone”-button at the right top of the above grey box.