  We propose a model for the spectral formation of Gamma Ray Burst (GRB) prompt
emission, where the phenomenological Band's function is usually applied to
describe the GRB prompt emission. We suggest that the GRB prompt emission is
mainly a result of two upscattering processes. The first process is the
Comptonization of relatively cold soft photons of the star off electrons of a
hot shell of plasma of temperature T_e of the order of 10^{9} K (or kT_e~100
keV) that moves sub-relativistically with the bulk velocity V_b substantially
less than the speed of light c. In this phase, the Comptonization parameter Y
is high and the interaction between a blackbody-like soft seed photon
population and hot electrons leads to formation of a saturated Comptonization
spectrum modified by the sub-relativistic bulk outflow. The second process is
an upscattering of the previously Comptonized spectrum by the plasma outflow
once it becomes relativistic. This process gives rise to the high-energy
power-law component above the peak in the EF(E)-diagram where F(E) is the
energy flux. The latter process can be described by a convolution of the
Comptonized spectrum with a broken-power-law Green function. Possible physical
scenarios for this second upscattering process are discussed. In the framework
of our model, we give an interpretation of the Amati relation between the
intrinsic spectral peak photon energy and radiated energy or luminosity, and we
propose a possible explanation of the GRB temporal variability.
