  Heterostructures formed by stacking layered materials require atomically
clean interfaces. However, contaminants are usually trapped between the layers,
aggregating into blisters. We report a process to remove such blisters,
resulting in clean interfaces. We fabricate blister-free regions of graphene
encapsulated in hexagonal boron nitride of$\sim$5000$\mu $m$^{2}$, limited only
by the size of the exfoliated flakes. These have mobilities up
to$\sim$180000cm$^2$V$^{-1}$s$^{-1}$ at room temperature,
and$\sim$1.8$\times$10$^6$cm$^2$V$^{-1}$s$^{-1}$ at 9K. We further demonstrate
the effectiveness of our approach by cleaning heterostructures assembled using
graphene intentionally exposed to polymers and solvents. After cleaning, these
samples reach similar high mobilities. We also showcase the general
applicability of our approach to layered materials by cleaning blisters in
other heterostructures based on MoS$_{2}$. This demonstrates that exposure of
graphene to processing-related contaminants is compatible with the realization
of high mobility samples, paving the way to the development of fab-based
processes for the integration of layered materials in (opto)-electronic
devices.

Mesoscale and Nanoscale Physics