Quantum Statistical Singularities in Excitonic Transistors: A Mathematical Framework utilizing Ramanujan Mock Theta Functions

The semiconductor industry faces a fundamental thermodynamic barrier at the 2nm node: the ''Boltzmann Tyranny'' limits the subthreshold swing (SS) of conventional Fermionic transistors to 60 mV/dec at room temperature. This paper explores a conceptual device architecture, the Saha-Bose-Ramanujan (SBR) Framework, which proposes utilizing the collective statistics of excitons in Tungsten Diselenide (WSe$_2$) to theoretically surpass this limit. We present a phenomenological model where Saha Ionization kinetics and Bose-Einstein statistics could enable steep-slope switching near the excitonic resonance, bounded by quasiparticle lifetime broadening. Additionally, we investigate the use of Ramanujan’s Mock Theta functions as a mathematical ansatz for engineering spectral filters with super-exponential decay characteristics. Behavioral modeling suggests that such a mechanism, if physically realized, could offer parametric improvements in leakage and switching speed compared to standard drift-diffusion limits.