  In this letter we present a calculation of the temperature-pressure phase
diagram of Si in a range of pressures covering from -5 to 20 GPa and
temperatures up to the melting point. The phase boundaries and triple points
between the diamond, liquid, $\beta$-Sn and ${Si}_{34}$ clathrate phases are
reported. We have employed efficient simulation techniques to calculate free
energies and to numerically integrate the Clausius-Clapeyron equation, combined
with a tight binding model capable of an accuracy comparable to that of
first-principles methods. The resulting phase diagram agrees well with the
available experimental data.
