Is the vi characterreistics curve of a pn diode is linear or exponential?

A diode has a fixed voltage drop (c), and if the voltage is less than that, no (or very little) current flows. Once the voltage increases above the voltage drop, the current increases exponentially as the voltage increases. A function that models this is:

I = exp(b*(V-c))

where V is the voltage, I is the current, c is the voltage drop and b is a parameter that determines how fast the current increases; the value of b varies from one diode to another