Full-band Self-Consistent Monte Carlo Methodology for Strain Induced Effects Study in Nano-MOSFETs

Scaling the conventional MOSFET to a nanoscale regime leads to explore many new materials and novel device structures. Among these approaches, the use of strained-Si as a choice of material for the FET channel is an attractive option to improve the performance of the device and has drawn great attention in recent years [1]. We present a full-band self-consistent Monte Carlo methodology for the analysis of strained Si MOSFET and its impact on the electronic transport properties. In proposed method, the strain distribution in the channel of MOSFET is simulated with TCAD simulations and tuned by experiment measurements. Numerical band structures of strained Si associate with the strain distribution are calculated and tabulated as inputs to a full band self-consistent Monte Carlo device simulator to calculate the performance of the strained Si MOSFET. Biaxial tensile strain is introduced in Si and direction (in-plane) and the lattice constant in the direction is computed using the elasticity theory. The strain-altered band structures of silicon are calculated using the first principle method density functional theory (DFT) with spin-polarized generalized gradient approximation (SGGA) [2]. Figure 1 and 2 shows the calculated band structures and density of states (DOS) of strained Si and unstrained Si. It is observed: (a) four (in-plane) of the six conduction band valleys are shifted upwards in energy and, (b) the heavy hole band moves away from the valence-band edge and hence break the degeneracy between the heavy and light hole bands. The lift-up of conduction bands would result in reduced intervalley or interband scattering. Together with the break-up of degeneracy between heavy and light holes, it could result in having the charge transport properties determined by the small transverse electron mass and the light hole mass mainly, and hence provide a performance boost [3]. The DOS plot shown in Fig. 2 also shows a slight upward shifting in the conduction band at the high-energy tail, which also indicates the reduced interband scattering as implied by the lift-up of conduction bands. A two-dimensional Monte Carlo device simulator with numerical band structures, self-consistently calculated scattering rates, and quantum corrections is developed based on MOCA [4] to get the distribution function from the solution of the Boltzmann transport equation (BTE). Acoustic and optical phonon scattering rates are calculated from the full-band structures. Impact ionization, ionized impurity scattering and surface roughness scattering are also modeled. The full-band calculations also allow for consideration of strain-induced degeneracy breaking and the associated variations in scattering rates. A strained-Si-on-insulator n-MOSFET with 25 nm gate length is built based on the scaled version device in [5] and simulated with the proposed method. Figure 3 shows the drain current-voltage characteristics for strained Si compared to unstrained Si. The drain current is significantly enhanced in strained Si. The effects of various source/drain dopant concentrations are shown in Fig. 4 & 5. It is observed that dopant concentration at 10 cm offers the largest electron velocity due to excess carriers available for injection into the channel. Reduction of the source/drain doping by one order of magnitude leads to a large decrease in drain current is observed. The preliminary calculation results agree with published data and proposed method will be further verified with experiments which are on going.