TO DEVELOP and design integrated circuits which use Silicon-on-Insulator (SOI) technology it is desirable to be able to properly simulate the electrical behavior of the integrated devices using dedicated simulation programs. However, the simulation tools currently available are not capable of predicting reasonable output characteristics when the energy transport model is applied. Instead, by using the conventional energy transport model in simulations of partially depleted SOI MOSFETs an anomalous decrease of the drain current with increasing drain-source voltage has been observed. This work shows that this decrease is a spurious effect, because it is neither present in experiments nor is it predicted by the drift-diffusion transport model. The possibility that the decrease is caused by the details of a particular numerical method has been ruled out by using two different device simulators.
Nevertheless, the applicability of the energy transport model is desirable, because in contrast to the drift-diffusion model it takes nonlocal effects into account, which gain importance in the regime of the ever decreasing minimum feature size of todays devices. The drift-diffusion transport model is not capable of describing such effects.
By making comprehensive simulation experiments the cause of the problem has been identified: When using the energy transport model the electrons in the pinch-off region attain an increased temperature which leads to an enhanced diffusion. The hot electrons of the pinch-off region have enough energy to overcome the energy barrier towards the floating body region and thus enter into the sea of holes. Some of these electrons in the floating body are sucked-off from the drain-body and source-body junctions, the rest recombines with holes of the p-doped substrate. The holes removed by recombination cause the body potential to drop. A steady state is obtained when the body potential reaches a value which biases the junctions sufficiently in reverse direction so that thermal generation of holes in the junctions can compensate this recombination process. Via the body effect the drop of the body potential leads to the decrease in the output characteristics.
For comparison the Monte Carlo method is used which solves BOLTZMANN's transport equation without further simplifying assumptions. In Monte Carlo simulations the spreading of hot carriers away from the interface is much less pronounced than in energy transport simulations. If we assume that BOLTZMANN's equation does not predict the hot carrier spreading, and if the energy transport equations derived from BOLTZMANN's equation do so, the problem must be introduced by the assumptions made in the derivation of the energy transport model. Relevant in this regard is the approximation of tensor quantities by scalars and the closure of the hierarchy of moment equations.
To overcome the problem of spurious negative differential output conductance a modified energy transport model is being proposed. By using a different closure relation and an anisotropic carrier temperature it is possible to sufficiently reduce the artificial vertical diffusion. The modified energy transport model is derived from BOLTZMANN's transport equation. BOLTZMANN's transport equation is multiplied by weight functions of increasing order and integrated over momentum space. The resulting moment equations lead to transport models of different order which are known from literature. During this derivation for the first time also a six-moments transport model has been developed in a consistent way.
The modified energy transport model has been implemented in the general purpose device simulator MINIMOS-NT, and successfully applied to simulate different SOI transistors. Parameter values needed in the modified transport model are taken from Monte Carlo comparison simulations. The suggested modifications turned out to be appropriate to prevent the electrons from reaching the high diffusivities which led to the failure of the standard energy transport simulations.
M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF