Efficient Modeling of Charge Trapping at Cryogenic Temperatures-Part I: Theory

• Published in: IEEE transactions on electron devices 2021-12, Vol.68 (12), p.6365-6371
• Main Authors: Michl, Jakob, Grill, Alexander, Waldhoer, Dominic, Goes, Wolfgang, Kaczer, Ben, Linten, Dimitri, Parvais, Bertrand, Govoreanu, Bogdan, Radu, Iuliana, Waltl, Michael, Grasser, Tibor
• Format: Article
• Language: English
• Subjects: Advanced CMOS; Approximation; bias temperature instability (BTI); Computational modeling; Couplings; cryo-CMOS; cryogenic; Cryogenic engineering; Cryogenic temperature; Cryogenics; IP networks; Mathematical analysis; MOS devices; Oscillators; physical modeling; Quantum mechanics; Room temperature; Saddle points; Stationary state; Transistors; Trapping; Wave functions
• ISSN: 0018-9383; 1557-9646
• DOI: 10.1109/TED.2021.3116931

Charge trapping is arguably the most important detrimental mechanism distorting the ideal characteristics of MOS transistors, and nonradiative multiphonon (NMP) models have been demonstrated to provide a very accurate description. For the calculation of the NMP rates at room temperature or above, simple semiclassical approximations have been successfully used to describe this intricate mechanism. However, for the computation of charge transition rates at cryogenic temperatures, it is necessary to use the full quantum mechanical description based on Fermi's golden rule. Since this is computationally expensive and often not feasible, we discuss an efficient method based on the Wentzel-Kramers-Brillouin (WKB) approximation in combination with the saddle point method and benchmark this approximation against the full model. We show that the approximation delivers excellent results and can, hence, be used to model charge trapping behavior at cryogenic temperatures.