Mode space approach has been used so far in NEGF to treat phonon scattering
for computational efficiency. Here we perform a more rigorous quantum transport
simulation in real space to consider interband scatterings as well. We show a
seamless transition from ballistic to dissipative transport in graphene
nanoribbon transistors by varying channel length. We find acoustic phonon (AP)
scattering to be the dominant scattering mechanism within the relevant range of
voltage bias. Optical phonon scattering is significant only when a large gate
voltage is applied. In a longer channel device, the contribution of AP
scattering to the dc current becomes more significant