Impact of Quantum Confinement Scattering on the Magnitude of Current Fluctuations

Beyond the 45 nm Technology Node Ultra-thin Body (UTB) Double-Gate (DG) MOSFETs (see Fig. 1) are expected to replace their conventional counterparts due to better electrostatic integrity and resistance to short channel effects [1,2,3]. However, as devices are scaled to silicon thicknesses below 5 nm, required for sub-10 nm channel lengths, in addition to parameter fluctuations resulting from discrete dopants in the source and drain regions, trapped charges in the channel and LER [4], variations in the current are introduced as a result of body thickness fluctuations due to atomic scale interface roughness. As the interface roughness patterns are unique to each transistor there will be a variation in drive current from device to device that will hamper their integration into modern chips. The current variations associated with body thickness fluctuations originate from variations in the electrostatic and quantum confinement along the channel [4] and are enhanced due to scattering from the corresponding variations in the quantum potential illustrated in Fig.2. In the case of large self-averaging devices this additional scattering results in a sharp reduction of the mobility for body thicknesses below 5 nm as depicted in Fig. 3. In this paper for the first time we study the magnitude of the current variation in UTB DG MOSFETs considering both electrostatic and confinement variation and the corresponding scattering effects. The study is based on ensemble Monte Carlo simulations employing a ‘frozen field’ approximation. Initially, devices with smooth interfaces were simulated using the Glasgow ‘atomistic’ drift-diffusion simulator [5] at low drain bias of 1 mV to comply with the conditions for using the ‘frozen field’ approximation. The simulations implement quantum corrections by virtue of the density gradient formalism [6]. The electron density obtained from the drift-diffusion simulation was used to initialise the particles in the Monte Carlo module and the quantum potential corresponding to the density gradient formalism was used to calculate the field that acts as a driving force. A close agreement between the result of the driftdiffusion and Monte Carlo simulation illustrated in Fig. 4 validates the use of the ‘frozen field’ approximation. At the next stage we performed statistical simulations of the threshold voltage variations in an ensemble of 200 devices, each with a different randomly generated interface roughness and body thickness pattern. From these devices 3 were chosen, one with a high, one with a low and one with average threshold voltage. Each one was again simulated under the same conditions as their smooth counterpart, but with the surface roughness generated by the drift-diffusion simulator used to alter the boundaries in the Monte Carlo module, thus implementing interface roughness and quantum confinement variation scattering in an ab initio fashion. The variation of the effective quantum potential in the channel for the three selected devices which corresponds to the density gradient formulation is illustrated in Fig. 5 a,b,c. The percentage change in current between rough and smooth transistors was then calculated for the case of drift diffusion and Monte Carlo simulations and presented in Table 1. The results clearly indicate that the variations in calculated current are significantly larger under Monte Carlo simulation than under drift diffusion. This confirms the important role of the scattering from the quantum confinement variation, which is captured only in the Monte Carlo simulations.