  The optimization of secondary phase in thermoelectric(TE) materials can
{helps in improvisation of material's efficiency}. Being a potential
{contender} for lower temperature TE application, bismuth
telluride(Bi$_2$Te$_3$) nanoparticles were synthesized via different routes and
profiles to optimize their pure single phase. Systematic characterizations were
performed with the help of X-ray diffraction (XRD), Rietveld refinement and
field effect-scanning electron microscopy(FE-SEM) for structural and
morphological behavior, while TE properties such as Seebeck coefficient,
electrical conductivity and power-factor were measured for the purest sample
chosen. Rietveld refinement in the XRD pattern of the samples revealed that
only a small amount ($\sim$ 1.6\%) of Bi$_2$Te$_3$ was formed in
co-precipitation method, while the hydrothermal technique increases this phase
with increment in synthesis duration. This work focused on the phase evolution
of Bi$_2$Te$_3$ with increasing synthesis duration time at constant temperature
and vice-versa. XRD and Rietveld refinement revealed that the hydrothermal
technique (150 $^\circ$C for 48 hours) can synthesize purest samples (84\%
Bi$_2$Te$_3$ phase in this case). {FE-SEM and Energy Dispersive X-ray analysis
unveiled that the impure phases in the system {were} quantitatively reduced,
and it supported by decline in atomic percentage of oxygen from 37\% to 11\%,
in addition to this, it was also found that particle size was also decreased
with increase in temperature.} The observed electrical conductivity of the
chosen sample is $\sim$20 times greater, while Seebeck coefficient is $\sim$3
times lower than that of pure Bi$_2$Te$_3$ phase. The detailed analysis has
generalized the growth mechanism in Bi$_2$Te$_3$ phase evolution by the
diffusion of Bi into Te nanorods to fabricate hexagonal Bi$_2$Te$_3$.
