Ultra-thin body (UTB) devices are being used in many electronic applications operating over a wide range of temperatures. The electrostatics of these devices depends on the band structure of the channel material, which varies with temperature as well as channel thickness. The semi-empirical tight binding (TB) approach is widely used for calculating channel thickness dependent band structure of any material, at a particular temperature, where TB parameters are defined. For elementary semiconductors like Si, Ge and compound semiconductors like GaAs, these TB parameters are generally defined at only 0 K and 300 K. This limits the ability of the TB approach to simulate the electrostatics of these devices at any other intermediate temperatures. In this work, we analyze the variation of band structure for Si, Ge and GaAs over different channel thicknesses at 0 K and 300 K (for which TB parameters are available), and show that the band curvature at the band minima has minor variation with temperature, whereas the change of band gap significantly affects the channel electrostatics. Based on this finding, we propose an approach to simulate the electrostatics of UTB devices, at any temperature between 0 K and 300 K, using TB parameters defined at 0 K, along with a suitable channel thickness and temperature dependent band gap correction.

In Ultra-thin Body (UTB) devices, besides the Ultra-thin (UT) nature of the channel, which manifests in terms of Quantum Confinement Effects (QCEs), the Band-offsets between the oxide and channel materials at their interface, also tends to strongly impact the channel electrostatics. Despite being very accurate in calculating the band-structure and hence considering QCEs for a given channel material, the Tight-Binding (TB) method tends to be more complicated to use at the channel/oxide interface of MOS devices, while on the other hand the Effective Mass Approximation (EMA) in spite of being less accurate, is a simpler approach to consider the effects of band-offsets at the interface. Given its accuracy, we firstly use the $sp^3d^5s^*$ TB method to calculate the Band-structure and then by considering significant k-points, efficiently incorporate the QCE into the electrostatics of Double-Gate (DG) Silicon-on-Insulator (SOI) MOS devices. Considering these results as a reference, with the assumption of an infinite potential well, we propose a modified Effective Mass Approximation (mEMA) approach, whereby introducing energy correction parameters, along with the effective mass parameters, all of which are shown to be gate bias, channel and oxide thickness dependent, the results obtained from the proposed approach are shown to have good agreement with the results from TB method. In order to analyze the effect of Conduction-Band Offset variations on the channel electrostatics parameters, we consider an $SiO_2$ layer of thickness of $1$ $nm$ and show the effect of different Band-offsets on the integrated charge density and gate capacitance, using the mEMA approach.

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.