What is the minimum die area of a chip?
The minimum area of the chip is determined by the most cost effective solution not the smallest physical possible cut. 

The smallest cut defect-free with a kerf is roughly equal to the wafer thickness and the slotted diamond saw roughly equal to 1/2 of the wafer thickness.

Thus the question should be what is the cheapest way to process single diode junctions.  As the biggest demand for single diode junctions appears to be LED's , the question should be what is the maximum number of LED's per wafer? Economy has driven the size of the LED up.  There is no benefit to going smaller.

For any given chip on a die and wafer size, this calculation limits the maximum number of Die Per Wafer.

This is not the limit but is a calculator to determine the mechanical yield of a wafer. 



The trend now is to make small flip chips with bump pads stacked on a system in package (SiP) or system-in-a-package with a number of integrated circuits enclosed in a single chip carrier package.