KMS states on Toeplitz algebra

Question

Consider the Toeplitz algebra which is the universal $C^*$ algebra generated by a single isometry $S$ denoted by $C^*(S)$. Define a dynamics on $C^*(S)$ by $\mathbb{R}\to Aut(C^*(S))$ by $t\mapsto \sigma_t$ where $\sigma_t(S)=e^{it}S$. I want to study the KMS states for the dynamical system $(C^*(S),\sigma)$. Can you please suggest a reference for it? It is worked out in the literature. We can show by the fact that the set $span\{S^m(S^*)^n:m,n \in \mathbb{N}\}$ is a dense subalgebra of $C^*(S)$, we can prove that for each $\beta$, a unique KMS state do exist. I mainly want to understand the extremal KMS states and what are its factor types?