Field emission from silicon including continuum energy and surface quantization

The quantum well in the surface of silicon arises from band bending which confines electrons to a narrow surface region during field emission. Based on the Wentzel-Kramer-Brillouin (WKB) approximation, a theory is presented for field emission from both the bulk with the continuum energy and the potential well with the quantized energy. The theory shows no exponential rise in emission current as the field increases at higher fields. The estimated emission current is also higher than that predicted by the classical theory.