  Diamond heat-spreaders for gallium nitride (GaN) devices currently depend
upon a robust wafer bonding process. Bonding-free membrane methods demonstrate
potential, however, chemical vapour deposition (CVD) of diamond directly onto a
III-nitride (III-N) heterostructure membrane induces significant thermal
stresses. In this work, these thermal stresses are investigated using an
analytical approach, a numerical model and experimental validation. The thermal
stresses are caused by the mismatch in the coefficient of thermal expansion
(CTE) between the GaN/III-N stack, silicon (Si) and the diamond from room
temperature to CVD growth temperatures. Simplified analytical wafer bow models
underestimate the membrane bow for small sizes while numerical models replicate
the stresses and bows with increased accuracy using temperature gradients. The
largest tensile stress measured using Raman spectroscopy at room temperature
was approximately 1.0 $\pm0.2$ GPa while surface profilometry shows membrane
bows as large as \SI{58}{\micro\metre}. This large bow is caused by additional
stresses from the Si frame in the initial heating phase which are held in place
by the diamond and highlights challenges for any device fabrication using
contact lithography. However, the bow can be reduced if the membrane is
pre-stressed to become flat at CVD temperatures. In this way, a sufficient
platform to grow diamond on GaN/III-N structures without wafer bonding can be
realised.
