If I remember right it's pretty easy to make a white noise generator from CMOS gates or inverters. But i've never done it.Two Cmos inverters form a square-wave generator, not a white-noise (random frequencies) generator.
One Cmos Schmitt-trigger inverter forms a square-wave generator. It also is not random.
A 3V battery quickly drops to 2V which is too low for an ordinary CD4xxx Cmos IC. Even a 74HCxxx Cmos IC will have an extremely low output current at 2V and 3V.