Sometimes mathematics can save lives. This is proven by Leila Taghizadeh and her research at the Institute of Analysis and Scientific Computing at TU Wien. Many diseases can be detected in time by going to the doctor regularly or by looking inside the body with sophisticated imaging techniques. But wouldn't it be much more practical to simply attach a sensor to the body that uses electrical measurements to find out in a very short time whether there is a problem?
In order to achieve that, the propagation of electric current and the movement of individual charge carriers must be precisely understood. This requires sophisticated mathematical methods – and this is exactly what mathematician Leila Taghizadeh is working on. In her dissertation, she developed mathematical models for sensor and nanotechnology. On 17 May 2021, she will be awarded the Hannspeter Winter Preis by TU Wien.
Computer models for sensors
"Sensor technologies on a tiny size scale are important for many areas of application, and especially in medical diagnostics, they will play an important role in the future," Leila Taghizadeh is convinced. In order to develop and improve such sensors, however, one must first find a way to precisely describe the transport of charge carriers in these nanodevices.
The laws of physics that determine how charge moves in the nanowires of a chip have been known for a long time. But being able to write down an equation does not mean that we know the solution. "New applications from sensor technology always lead to very challenging mathematical problems," says Leila Taghizadeh. Is there even a solution for a certain system of equations? Can there be several solutions? Is the solution stable – or can it be that a small perturbation completely changes the result?
Semiconductor materials are doped – that means that certain atoms are incorporated into the material. Only through them does the material obtain the desired properties. Are these additional atoms randomly distributed? How can this random distribution be described mathematically? And how does it affect the transport of electrical charge carriers? Leila Taghizadeh got to the bottom of all these questions in her dissertation.
One must also bear in mind that even the largest supercomputers reach the limits of their computing capacity when simulating nanodevices. Therefore, creative solutions have to be found to reduce the computational effort without sacrificing the necessary degree of precision.
Leila Taghizadeh studied mathematics in Iran, where she initially also worked as a university lecturer. In 2012, she moved to Austria to work at the Institute for Analysis and Scientific Computing at TU Wien – first as a software developer, then as a project assistant. In 2019, she completed her dissertation in Prof. Clemens Heitzinger's research group, where she is now continuing her work as a postdoc.
Hannspeter Winter Award for Outstanding Dissertation
Every year the Hannspeter Winter Preis is awarded to a graduate of the doctoral programme among all areas of science at TU Wien. It is endowed with 10,000 euros and is jointly financed by TU Wien and the BA/CA Foundation. The research prize was donated in memory of TU Professor Hannspeter Winter, who was always committed to promoting young female scientists.