3.1 Theory

Both diffusion and desorption are dependent on the temperature of the system and on an activation energy. The idea is that in order for an atom to move from its present location it must acquire enough energy to over come a barrier to get to the new position. The barrier is defined as $\epsilon + \Delta E$. The concept is illustrated in the Figure 4.

Figure 4: Inter-site Energy Barrier

The beginning and ending energies are not necessarily the same for the atom positions (denoted by $\Delta E$). This also is included in Figure 4 (note the low and high trough regions). The other component of the diffusion rate is the prefactor. This gives the jumping rate of the atom. The diffusion equation is given by:

\begin{eqnarray*}
D= D_0 \exp \left(- \frac{E_A}{k_B T} \right)
\end{eqnarray*}


Desorption of $\mbox{H}_2$from the surface of the silicon is a 1st order kinetic reaction. Though both atoms are required to desorb, it is believed that the position of the dimer rows allows the hydrogen atoms to already be paired and therefore a 1st order reaction happens instead of a 2nd order reaction. The desorption of hydrogen from a terrace is given by

\begin{eqnarray*}
K_d= \nu \exp \left(- \frac{E_d}{k_B T} \right)
\end{eqnarray*}


Chris Siefert and Molly Moore 2002