Capacitance Modeling of Complex Topographical Silicon Quantum Dot Structures

Quantum dot (QD) layouts are becoming more complex as the technology is being applied to more sophisticated multi-QD structures. This increase in complexity requires improved capacitance modeling both for the design and accurate interpretation of QD properties from measurement. A combination of process simulation, electrostatic simulation, and computer-assisted design (CAD) layout packages are used to develop a 3-D classical capacitance model. The agreement of the classical model's capacitances is tested against two different, experimentally measured, topographically complex silicon QD geometries. Agreement with experiment, within 10%-20%, is demonstrated for the two structures when the details of the structure are transferred from the CAD to the model capturing the full 3-D topography. Small uncertainties in device dimensions due to uncontrolled variation in processing, like layer thickness and gate size, are calculated to be sufficient to explain the disagreement. The sensitivity of the capacitances to small variations in the structure also highlights the limits of accuracy of capacitance models for QD analysis. We furthermore observe that a critical density, the metal-insulator transition, can be used as a good approximation of the metallic edge of the QD when electron density in the dot is calculated directly with a semi-classical simulation.