### A.3 WKB Formulas for Different Shapes of Energy Barriers

In the classical forbidden region, the shape of the wavefunction is dominated by the
exponential term in equation (A.22).

and stand for the classical turning point at the semiconductor-dielectric
interface and the position of the trap, respectively. Supposing that only a negligible
amount of charges is located in the dielectric, the potential energy can be
expressed as For a trapezoidal barrier (see Fig. A.2), simplifies to If tunneling occurs through a triangular barrier (see Fig. A.2), the classically
forbidden region extends to For negative electric fields (), one obtains while positive electric fields () results in The these two cases are commonly known as the Fowler-Nordheim formulas [186].
For a rectangular barrier with , the integral in equation (A.23)
simplifies to a multiplication.