Hall voltage dependence on inversion-layer geometry in the quantum Hall-effect regime

A calculation of the Hall voltage is presented within a model of a finite two-dimensional inversion layer. An explicit form for the electric field is obtained and this is found to have a power-law singularity in the corners of the inversion layer. This singularity is most pronounced in the quantum Hall-effect regime where the Hall angle approaches $\frac{\pi }{2}$. The error in measuring the Hall voltage in this regime due to the shorting effect of the source and drain is calculated. This is found to be negligible at the level required for a new determination of the fine-structure constant and development of a new resistance standard using inversion-layer measurements in the quantum Hall-effect regime. Limitations of the model and other possible sources of error are briefly discussed.