  A high precision calibration of the nonlinearity in the energy response of
the Daya Bay Reactor Neutrino Experiment's antineutrino detectors is presented
in detail. The energy nonlinearity originates from the particle-dependent light
yield of the scintillator and charge-dependent electronics response. The
nonlinearity model is constrained by $\gamma$ calibration points from deployed
and naturally occurring radioactive sources, the $\beta$ spectrum from $^{12}$B
decays, and a direct measurement of the electronics nonlinearity with a new
flash analog-to-digital converter readout system. Less than 0.5% uncertainty in
the energy nonlinearity calibration is achieved for positrons of kinetic
energies greater than 1 MeV.
