  Hexagonal boron nitride (hBN)-long-known as a thermally stable ceramic-is now
available as atomically smooth, single-crystalline flakes, revolutionizing its
use in optoelectronics. For nanophotonics, these flakes offer strong
nonlinearities, hyperbolic dispersion, and single-photon emission, providing
unique properties for optical and quantum-optical applications. For
nanoelectronics, their pristine surfaces, chemical stability, and wide bandgap
have made them the key substrate, encapsulant, and gate dielectric for
two-dimensional electronic devices. However, while exploring these advantages,
researchers have been restricted to flat flakes or those patterned with basic
slits and holes, severely limiting advanced architectures. If freely varying
flake profiles were possible, the hBN structure would present a powerful design
parameter to further manipulate the flow of photons, electrons, and excitons in
next-generation devices. Here, we demonstrate freeform nanostructuring of hBN
by combining thermal scanning-probe lithography and reactive-ion etching to
shape flakes with surprising fidelity. We leverage sub-nanometer height control
and high spatial resolution to produce previously unattainable flake structures
for a broad range of optoelectronic applications. For photonics, we fabricate
microelements and show the straightforward transfer and integration of such
elements by placing a spherical hBN microlens between two planar mirrors to
obtain a stable, high-quality optical microcavity. We then decrease the
patterning length scale to introduce Fourier surfaces for electrons, creating
sophisticated, high-resolution landscapes in hBN, offering new possibilities
for strain and band-structure engineering. These capabilities can advance the
discovery and exploitation of emerging phenomena in hyperbolic metamaterials,
polaritonics, twistronics, quantum materials, and 2D optoelectronic devices.
