I wanted to know what are the factors that affect the input impedance of a device, majorly in a MOSFET, how does better isolation between the gate (resulting in less leakage current) result in a higher input impedance?
Wikipedia says about impedance
Impedance extends the concept of resistance to AC circuits [...]
Therefore, it works much like the usual resistance: It denotes the ratio of voltage U to current I over/through a part of an electrical circuit. Like resistance, impedance is the measure for forces "impeding the flow of current"; higher impedance results in less current flow for a given voltage, etc. (But unlike simple resistance, the impedance value may vary over frequency and amplitude.)
Source or output impedance measures the capability (or more correctly: the inability) of a voltage source (or output) to maintain its voltage when current is drawn from the source. This can be imagined like a resistor in series with the source. In actual circuits, lower source impedance is often preferred as it means more power (current) can be delivered by the source which may yield more robust signals among other things.
In the same way, input impedance describes how much current will be drawn by the input from a voltage source to reach/maintain a certain voltage Higher input impedance is often preferred as it means that less power (current) is needed/consumed by the input.
Thus, a high-impedance output will usually not work too well with a low-impedance input; all other combinations should work.
Put in antoher way: The impedance of an output or input can be imagined like a resistor of the same value in series with the signal and thus, it determines the limits of the input or output: An output, for instance, of 5V with an impedance of 1000 Ohm will under no circumstances deliver more than 5V/1000Ohm = 5mA of current, and an attached input should draw significantly less than those 5mA for good signal transfer.
Likewise, an input of 1000 Ohm impedance will never draw more than 5mA when fed with a voltage of 5V, and an attached output should provide significantly more than those 5mA for stable signals.
The major factor of a MOSFET's gate input impedance is the gate's capacity, which needs to be charged or discharged when switching. The higher the gate's capacity the more current is needed to quickly charge/discharge it; this equals a lower input impedance.
The isolation of common MOSFETs can be increased by making the isolating layer thicker. Depending on the materials, this may mean that the capacity of the (imagined) capacitor of gate and substrate decreases which increases the input impedance. - Possibly at the cost of a higher threshold voltage Vth.
In steady state, the leakage current is the major component determining the impedance; as you said: better isolation means higher resistance (and less leakage) and this equals higher input impedance. - Although the leakage current is miniscule and can be neglected, esp. when compared to the current usually used to charge/discharge the gate. (Example: Leakage current may be in the order of 100nA @ 10VGS, which computes to a resistance of 100MOhm - that's mega Ohm.)