Let's give you some theory and my practical experience.
- ALL diodes behave like are "varicaps" where diode capacitance is reduced from 0V bias to negative bias range in a log scale.
- However the tolerance is huge.
- The special diodes with process controls to tighten tolerances are called Varicaps.
- Diode capacitance increases with power ratings and conductor gap dimensions of the device, while ESR is inversely related to Pd max as size affects all 3 parameters.
- Typically diode Capacitance is measured in pF (not nF)
- Tuning range of 0 to 30V is common, or 0 to 5V with reduced range. ( NOT in mV ! .... you may be thinking of carrier detection)
But to resolve your query, first define your requirements in tuning range and accuracy. ( i.e. a design spec)
A VCXO is much more accurate and VCO chips are also more accurate and stable than a "DIY " VCO using LC parts as temperature stability and tolerances are much bigger.