  We report femtosecond time-resolved reflectivity measurements of coherent
phonons in tellurium performed over a wide range of temperatures (3K to 296K)
and pump laser intensities. A totally symmetric A$_{1}$ coherent phonon at 3.6
THz responsible for the oscillations in the reflectivity data is observed to be
strongly positively chirped (i.e, phonon time period decreases at longer
pump-probe delay times) with increasing photoexcited carrier density, more so
at lower temperatures. We show for the first time that the temperature
dependence of the coherent phonon frequency is anomalous (i.e, increasing with
increasing temperature) at high photoexcited carrier density due to
electron-phonon interaction. At the highest photoexcited carrier density of
$\sim$ 1.4 $\times$ 10$^{21}$cm$^{-3}$ and the sample temperature of 3K, the
lattice displacement of the coherent phonon mode is estimated to be as high as
$\sim$ 0.24 \AA. Numerical simulations based on coupled effects of optical
absorption and carrier diffusion reveal that the diffusion of carriers
dominates the non-oscillatory electronic part of the time-resolved
reflectivity. Finally, using the pump-probe experiments at low carrier density
of 6 $\times$ 10$^{18}$ cm$^{-3}$, we separate the phonon anharmonicity to
obtain the electron-phonon coupling contribution to the phonon frequency and
linewidth.
