  We present a background model for dark matter searches using an array of
NaI(Tl) crystals in the COSINE-100 experiment that is located in the Yangyang
underground laboratory. The model includes background contributions from both
internal and external sources, including cosmogenic radionuclides and surface
$^{210}$Pb contamination. To improve the model in the low energy region, with
the threshold lowered to 1 keV, we used a depth profile of $^{210}$Pb
contamination in the surface of the NaI(Tl) crystals determined in a comparison
between measured and simulated spectra. We also considered the effect of the
energy scale errors propagated from the statistical uncertainties and the
nonlinear detector response at low energies. The 1.7 years COSINE-100 data
taken between October 21, 2016 and July 18, 2018 were used for this analysis.
The Geant4 toolkit version 10.4.2 was utilized throughout the Monte Carlo
simulations for the possible internal and external origins. In particular, the
version provides a non-Gaussian peak around 50 keV originating from beta decays
of $^{210}$Pb in a good agreement with the measured background. This improved
model estimates that the activities of $^{210}$Pb and $^{3}$H are the dominant
sources of the backgrounds with an average level of 2.73$\pm$0.14
counts/day/keV/kg in the energy region of 1-6 keV, using COSINE-100 data with a
total exposure of 97.7 kg$\cdot$years.
