A theoretical study on characteristic wavelength of silicon conduction electrons

The characteristic wavelength of conduction electrons is critical to the conduction property of semiconductor nanosheet channels. As semiconductor device technology has advanced, the semiconductor channel has been miniaturized following Moore’s law for several decades. Nowadays, the thickness of a nanosheet semiconductor channel is less than 10 nm, which is widely known as the de Broglie length of silicon conduction electrons. Although the definition of the de Broglie length of conduction electrons is ambiguous, it seems that the quantum confinement effect can occur in semiconductor nanosheets with the thickness being the characteristic wavelength of conduction electrons. If the quantum confinement effect occurs, then the dynamics of a silicon nanosheet become two-dimensional, which is different from the assumptions upon which the drift-diffusion model was developed. If we continue to use the drift-diffusion model in IC design, we should be careful of nanosheet thickness, which is affected by such quantum mechanical effects. It is meaningful to carefully examine the characteristic wavelength of conduction electrons in semiconductor materials. We propose a practical method to determine the characteristic wavelengths of carriers and numerically demonstrate it using silicon conduction electrons.