  We revise the Fowler-Dubridge (FB) model for photoelectron emission from
two-dimensional (2D) materials to include the effects of reduced
dimensionality, non-parabolic and anisotropic energy dispersion of 2D
materials. Two different directions of electron emission are studied, namely
vertical emission from the surface and lateral emission from the edge. Our
analytical model reveals a universal temperature scaling of T\b{eta} with
\b{eta} = 1 and \b{eta} = 3/2, respectively, for the surface and edge emission
over a wide class of 2D materials, which are distinct from the traditional
scaling of \b{eta} = 2 originally derived for the traditional bulk materials.
Our comparison shows good agreement to two experiments of photo-electron
emitted from graphene for both surface and edge emission. Our calculations also
show the photoelectron emission is more pronounced than the coexisting
thermionic emission for materials with low temperature and Fermi energy. This
model provides helpful guidance in choosing proper combinations of light
intensity, temperature range and type of 2D materials for the design of
photoemitters, photodetectors and other optoelectronics
