In order to improve your accuracy what you need is a constant current source.
You can approach a constant current source by increasing the source resistance R1. When you do this you may need to increase the supply voltage. Or use a constant current source circuit.

Also, decreasing your comparator threshold voltage will put you closer to the linear region of the exponential curve. For example, set the comparator reference voltage to 1V instead of 2.5V.

 

In order to improve your accuracy what you need is a constant current source.
You can approach a constant current source by increasing the source resistance R1. When you do this you may need to increase the supply voltage. Or use a constant current source circuit.

Also, decreasing your comparator threshold voltage will put you closer to the linear region of the exponential curve. For example, set the comparator reference voltage to 1V instead of 2.5V.

The original circuit is a current source LM334DT set at 100uA with 100kOhm across it.
I did convert it to voltage source of 10V with 100kOhm in series for calculation.