Branching programs are usually used as a computation model for non-uniform logarithmic space $\mathsf{L}/\mathrm{poly}$. Is there a reference about Boolean circuits corresponding to $\mathsf{L}/\mathrm{poly}$?
Intuitively, bounded space Turing machines seem to correspond to bounded width Boolean circuits, but I can't find a reference. Is there a reason that branching programs are used for $\mathsf{L}/\mathrm{poly}$ and Boolean circuits are not used?
[Addition after Sam McGuire's answer (in comments)]
Actually, I'm most interested in Boolean circuits corresponding to $\mathsf{L}/\mathrm{quasipoly}$. I guess that it is quasipolynomial-size $O(\log n)$-width Boolean circuits.
I would like to know that, whether it is right or not, whether I should prove it myself or not, whether it is known and there's a reference or not.