A quantum mechanical treatment of low frequency noise in scaled NMOS transistors

We present a quantum mechanical treatment of low-frequency noise in scaled NMOS transistors to extend the “unified” noise model [1] and include remote Coulomb scattering and surface roughness - new considerations in the theory. Our experimental work focuses on scaled NMOS device (as shown in Fig. 1) with a composite dielectric consisting of a 0.5 nm oxide covered with a high-K, 1.6nm hafnium oxide with a metal gate, as previously reported in [2]. In the past, Coulomb scattering was assumed to arise from trapping centers located at the Si-SiO₂ interface [3]; however, this cannot give rise to a 1/f noise spectrum. We model remote Coulomb scattering into the dielectric film as traps in these films easily lie within a tunneling distance of the interface. This approach explains the decrease in the Coulomb scattering parameter (α) as a function of gate voltage. In addition, we introduce surface roughness scattering through fluctuations in the normal electric field due to fluctuations in the free carrier density with a surface scattering parameter proportional to the SPICE surface roughness parameter, θ_s.