Supplementary Material (clean, not marked-up)

Supplementary material includes (1) details of the experimental procedure for mapping current density; (2) an example that reassesses the fringe current correction attempt of our prior experimental work where velocity saturation was neglected; (3) closed-form expressions for the drain current and saturation voltage for a patterned-channel transistor; (4) the general formulation of the 2D current flow problem in an unpatterned-channel TFT; (5) a demonstration that the dimensionless parameters in Table 1 uniquely characterize the "shape" of the current distribution in an unpatterned TFT; (6) an exact derivation of the fringe current in an infinitely wide unpatterned TFT; (7) quantitative details of decay of current density away from the contacts.