According to Advanced Organic Chemistry[1],
Neopentyl systems are typically resistant to nucleophilic substitution reactions. They are primary, so do not form stable carbonium ions, and the tert-butyl substituent effectively hinders back-side attack. [...] Under conditions that
favor ionization, rearrangement usually occurs, and the products are derived from tert-amyl cation. Substitution reactions of neopentyl tosylate without skeletal rearrangement can be effected, however, by using good nucleophiles in hexamethylphosphoramide as solvent.
(emphasis mine)
The stereochemistry of the reaction was found as follows,
The use of optically active neopentyl-l-d tosylate allows
the stereochemistry to be established. Complete inversion of configuration was observed, again consistent with a direct displacement of the leaving group
This shows that the reaction takes place via an internal rearrangement which is similar to the mechanism seen in SN2 except that the $\ce{-CH3}$ group acts similar to the nucleophile in this internal rearrangement. After this, the reaction proceeds similar to a normal SN1 reaction. Its energetics diagram looks similar to an SN1 reaction as well.
Why not SN2? It is a primary alcohol after all. This is explained in J. Am. Chem. Soc. 1942, 64 (3), 543–546.
From the fact that 1-bromo-4,4-dimethylpentyne-2 is not hindered in comparison to 1-bromo-heptyne-2 it is concluded that the "neopentyl effect" is not capable of transmission through an unsaturated linkage and is hence not a chemical but a steric effect
This mentioned "neopentyl effect" refers to the lack of SN2 reaction seen even though the halide/alcohol is primary.
References:
- Carey F.A., Sundberg R.J. (1977) Nucleophilic Substitution. In: Advanced Organic Chemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8882-5_5