Terahertz detectors are of paramount importance in applications to astronomy and astrophysics. The project aims at modeling inhomogeneous quantum transport of electrons in quantum-well based terahertz detectors by Wigner function equations. These equations are to be solved by a combination of asymptotic reduction to simpler models and numerical methods. Partners expect to produce new methodology and understanding of the governing equations and numerical methods to solve them. The proposed research may have an impact in the design of far infrared detectors. This may be useful to investigate the interstellar medium beyond the frequency range of the instruments currently used by the ESA Herschel observatory. Both partners have collaborated previously, and this project may be the basis for establishing a new collaboration, expertises being complementary and groups having the possibility of involving experimentalist to corroborate the results of their common work. The donor partner has done several advances in the understanding of the complements of laminations in projective spaces, as well, obtained very deep results on embeddings of Riemann surfaces.
Summary of project results
The goal of the Project was to analyze quantum-well based semiconductor detectors (of possible application in astrophysical instrumentation such as used by the ESA Herschel space laboratory) that may work in the 3-5 terahertzfrequency range (beyond the range of current detectors) and their possible limitations due to possible appearance of time and space charge inhomogeneities. Such inhomogeneities are not included in terahertz detector models and quantum models capable to studying them are needed. These models may consist of nonlocal integro-differential equations for the Wigner function or for the nonequilibrium Green function. L.L. Bonilla had previous experience on inhomogeneous Wigner equations and modeling of semiconductor devices and B. Birnir on dynamical effects in quantum wells. The idea of the project was to use the combined expertise for applications to quantum well infrared detectors. During the project and with the help of B. Birnir’s PhD student Jonathan Essen, we developed a numerical code to solve the Wigner equation in simple cases such as ballistic transport for a quantum barrier between two contacts. We tried finite difference and operator splitting methods to solve the problem with different boundary conditions. We are preparing the article on the application of Wigner-Poisson equations to the infrared quantum-well-based TACIT sensor. In 2015, Spanish PhD student, Miguel Ruiz Garcia, supported by a MINECO grant, visited University of Iceland and studied appropriate boundary conditions for quantum well semiconductor devices that we hope to implement for infrared detectors in the future. Miguel has written a numerical code that will be tested first for semiclassical transport and then adapted to the fully quantum case. Once the work on ballistic transport related to the quantum well based TACIT sensor is finished, we will study the influence of more realistic boundary conditions for the Wigner-Poisson system of equations and add scattering by some simple collision models. The results will be applied to designing far infrared sensors. The main beneficiaries of the Project may be device designers and mathematicians and physicists interested in electron transport for quantum well based devices. The main benefit of the project is to describe quantum transport in quantum well-based far infrared sensors, develop appropriate numerical methods and analyze possible charge inhomogeneity in the devices.
Summary of bilateral results
The cooperation between partners is to be continued. On the topic of angiogenesis and the treatment of diseases with inflammatory basis, we are promoting a consortium to apply for a Marie S. Curie ITN network, visited the company deCODE genetics (a successful spinoff by a former Harvard University professor that is a Reykjavik based European leader in analysis of the genomic code), and succeeded in adding both deCODE genetics and the University of Iceland (through B. Birnir) as partners of the consortium. The application will be coordinated by Universidad Carlos III de Madrid and include universities, hospitals and companies of Spain, France and Italy. In addition to the relations and ITN proposal mentioned above, we have discussed with local University authorities the possibility of starting a summer school in the University of Iceland, with Spanish collaboration. We are also promoting Erasmus + agreements between our universities.