6. Summary and Outlook

Modeling of galvanomagnetic effects in semiconductors has been performed using the general purpose device simulator MINIMOS-NT. By implementing a new discretization procedure that takes into account an arbitrary magnetic field, full three-dimensional simulations of a two- and three-drain MAGFETs were carried out. The simulation results obtained with this new discretization agree with experimental data of the two-drain MAGFETs at both 300 K and 77 K.

The new discretization procedure was implemented using a physical model that comprises both magnetic field and the current density. Although the original model includes thermoelectric and thermomagnetic effects, an isothermal approximation of the equation is sufficient for the modeling of magnetic sensors. Because the carrier transport equations are not directly modified by the presence of a magnetic field, in principle any transport equation can be used for the simulation of magnetic effects in semiconductors, in particular also a hydrodynamic transport model.

The main figure of merit from a magnetic sensor is the relative sensitivity. As it has been experimentally shown, the relative sensitivity of a two-drain MAGFET can be improved by cooling the device to 77 K. This improvement comes from the fact that the electron mobility in the inversion layer increases. As a result, the differential current increases and the relative sensitivity is improved. Smaller magnetic fields can be detected with the same magnetic sensor by cooling it to liquid Nitrogen temperature. Simulation results show this improvement. In addition the bias dependence of this relative sensitivity has been investigated at both room temperature and liquid Nitrogen temperature.

Also,    the geometric dependence of the relative sensitivity has been analyzed at both
300 K and 77 K. As theory predicts, longer and wider devices will give better performance. However, if the device is going to be operated at both 300 K and 77 K, simulation results indicate that the maximum is not reached at the same device width.

An improvement of the relative sensitivity can be obtained if a three-drain MAGFET structure is used. Simulation results show such an improvement at room temperature although the performance at 77 K is not spectacularly improved as in the two-drain MAGFET case. However, a particular problem arises using a three-drain MAGFET structure, namely the match of the currents at the drains. Splitting the drain into two parts does not represent an important difficulty, but splitting the drain into three parts is difficult. Chances of getting a mismatch between the side drains are higher.

Although the Hall scattering factor for electrons, used for modeling the magnetic effects in semiconductors, is close to unity according to many sources in the scientific literature, the analysis of the two-drain MAGFET shows that this value is lower from the values found in the literature. This difference can be attributed to the different CMOS technologies. Modern CMOS technologies are used for the measurement of the Hall scattering factor whereas the CMOS process of the two-drain MAGFET is older. The value of the substrate doping is different in both technologies and this affects the scattering mechanisms in the channel.

Another important feature of the new discretization procedure is that it does not affect the matrix properties of the Jacobian (positive diagonal entries), an important feature from the numerical point of view. Those properties of the Jacobian guarantee the existence of a solution and the non-diagonal entries would not compromise the existence of a solution. Fortunately, the non-diagonal entries are a direct function of the grid and the magnetic field, which gives the user the possibility to control the general performance of the equation solver.

The overall performance of any solid-state device under non-zero magnetic field condition must be different from the zero magnetic field case, because the magnetic field deflects the path of the current and either it improves or degrades the performance of the device. By running simulations with arbitrary magnetic fields using the new feature developed in MINIMOS-NT, an analysis for the non-zero magnetic field case can be made. Different examples of solid-state devices that can be analyzed under such condition can be given. Optical sensors can improve their performance by deflecting the path of the generated carriers by incident radiation. Carrying the generated carriers to the depleted region enhances the hole-electron separation by the electric field, increasing the detectivity of the optical sensor. In the case of MOSFETs with nanometric dimensions, the inversion layer can be moved upwards or downwards depending on the direction of the magnetic field and the carrier density. New insight from the quantization of the inversion layer can be obtained if the simulations with magnetic field use the proper models.