Using Irfz44n with Attiny85

I am building a Buck boost converter which works on 32Khz using Irfz44n.Is it mandatory to use a driver IC to drive the MOSFET ? Can anyone explain it with some calculations.I am using Gate resistor of 100ohm and a pull down resistor (for MOSFET's Gate) of 10k.

Is it mandatory to use a driver IC to drive the MOSFET

With that FET yes it is. Because you need a 10V gate signal to turn it on.

In addition to the voltage Grumpy_Mike referred to there is a gate change and a gate - drain charge both in coulombs. The calculations are not too complex but I think you would be better off looking for a Mosfet switching app note than for me to attempt to describe it here.

These characteristics have to do with how fast you can switch the MosFet. You will likely need to provide between 1 and 2 amps of peak drive to the gate to get a reasonable switching time.

At 32kHz you need to be wary of switching losses and EMI. For the higher switching frequencies GaNFETs
are the way to go, although they are harder to work with (very fine pin pitch surface mount packages,
special driver ICs needed, significant gate leakage current).

No gate resistor is fine, just choose a gate driver with the appropriate output resistance for the current
you need for fast-enough switching. With 32kHz you have 15us on average between switching events,
so the switching should be a tiny fraction of that, like 1%, so 150ns switching time is a starting point.

Calculate the current from the switching time and the total gate charge:

I = gate charge (C) / switching time (s), so 62nC / 1.5e-7 = 400mA