PSD (power spectral density) of an exponential

Hello. In my case, I have a function that has this shape :

x(t)=exp(a*t)

where a is a constant.

I know that for a<0 the Fourier transform exists but for a>0 does not but I am not sure about the PSD. I want to calculate the PSD of x(t) for a>0 using pwelch function but I am not sure if the result is valid.

Best,

SIna