Quantum tunneling in transistors

An electron in a system with a potential barrier has a finite probability of reaching a region that is classically forbidden. This phenomenon is known as quantum tunneling, and the probability is known as the transmission coefficient. Quantum tunneling occurs in transistors when the control voltage is lower than the junction voltage of the material. Following the work of Sturge and Bac Toh [1], we measured quantum tunneling occurring in a silicone transistor at different temperatures and for different voltages. This output current is proportional to the transmission coefficient and the Boltzmann factor, which reflects the statistical nature of this phenomenon. We modeled the system as a square potential energy barrier, solved the Schrodinger equation analytically, and calculated the current density as a function of barrier height (which corresponds to the band gap minus the base-emitter voltage).  We found that the experimental data closely follow the expected relationship between base-emitter voltage and tunneling current. We also modeled a simplified system numerically and found a tunneling coefficient that follows the expected behavior, but does not match the amplitude correctly. 

[1] M.D. Sturge and S. Bac Toh, “An experiment to demonstrate the canonical distribution,” American Journal of Physics 67, 1129 (1999).