Comparison of Electron Direct Transmittance and Tunneling Time of Si (100)/HfO2/Si (100) and Si (110)/HfO2/Si (110) Structures with Ultra-thin Trapezoidal Barrier

An analytical expression of electron direct transmittance and tunneling time through a nanometer-thick trapezoidal potential barrier have been derived by using a phase-time method with Airy wavefunction solution. The expression is applied to Si(100)/HfO2/Si(100) (isotropic) and Si(110)/HfO2/Si(110) (anisotropic) structures calculated under the consideration of barrier width, incident energy, incident angle, and bias voltage. The calculated results are discussed and comparisons between the isotropic and anisotropic heterostructures are discussed.