scholarly journals Temperature Dependence of the Electron and Hole Scattering Mechanisms in Silicon Analyzed through a Full-Band, Spherical-Harmonics Solution of the BTE

VLSI Design ◽  
1998 ◽  
Vol 8 (1-4) ◽  
pp. 361-365 ◽  
Author(s):  
Susanna Reggiani ◽  
Maria Cristina Vecchi ◽  
Massimo Rudan
Keyword(s):  
Temperature Dependence ◽  
Spherical Harmonics ◽  
Hole Mobility ◽  
Scattering Mechanisms ◽  
Mobility Data ◽  
Number Of Factors ◽  
Wide Range ◽  
Full Band ◽  
Spherical Harmonics Expansion ◽  
Full Band Structure

By adopting the solution method for the BTE based on the spherical-harmonics expansion (SHE) [1], and using the full-band structure for both the electron and valence band of silicon [2], the temperature dependence of a number of scattering mechanisms has been modeled and implemented into the code HARM performing the SHE solution. Comparisons with the experimental mobility data show agreement over a wide range of temperatures. The analysis points out a number of factors from which the difficulties encountered in earlier investigations seemingly originate, particularly in the case of hole mobility.

scholarly journals Reduced k-points based computationally efficient band structure approach for UTB device simulation

2021 ◽  
Author(s):  
Ravi Solanki ◽  
Nalin Vilochan Mishra ◽  
Aditya S Medury
Keyword(s):  
Band Structure ◽  
Density Functional ◽  
Tight Binding ◽  
Computational Time ◽  
Thin Body ◽  
Computationally Efficient ◽  
Wide Range ◽  
Full Band ◽  
Consistent Solution ◽  
Full Band Structure

The accurate calculation of channel electrostatics parameters, such as charge density and potential, in ultra-thin body (UTB) devices requires self-consistent solution of the Poisson’s equation and the full band structure, which is channel material and thickness dependent. For cubic crystals like silicon, the semi-empirical sp3d5s* tight-binding (TB) model is preferred in device simulations, over the density functional theory, to obtain the full band structure because of being computationally less intensive and equally accurate. However, the computational time of the TB model scales non-linearly with the channel thickness and becomes cumbersome for silicon, beyond 5 nm, primarily because of the increasing size of the TB hamiltonian that needs to be solved over the entire k-space, in the irreducible Brillouin zone. In this work, we precisely identify those k-points corresponding to the energies close to the band minima, where the Fermi-Dirac probability significantly affects electrostatics parameters. This enables us to demonstrate a computationally efficient approach based on solving the hamiltonian only on those reduced number of k-points. The rigorous benchmarking of the channel electrostatics parameters obtained from this approach is performed with results from accurate full band structure simulations showing excellent agreement over a wide range of channel thicknesses, oxide thicknesses, device temperatures and different channel orientations. By showing that the approach presented in this work is computationally efficient, besides being accurate, regardless of the number of atomic layers, we demonstrate its applicability for simulating UTB devices.

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