Analysis of TPD Spectra on Semiconductor Surfaces by Monte Carlo Simulations
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Rd -k(O)e
k.T
On1
where Rd is the desorption rate, 0 is the fractional surface coverage, k(0) is the coverage dependent pre-exponential factor, Ed(9) is the coverage dependent activation energy, and n is the order of the desorption. A variety of methods have been used to analyze TPD data to obtain activation energy, pre-exponential factor, and order of desorption as a function of adsorbate coverage. 2 These methods primarily use the Arrhenius rate form to analyze the spectra, which limits their use to simple desorption mechanisms. The effects of adsorbate-adsorbate interactions, dynamic surface reconstructions, and two-dimensional islands are examples of important surface processes that are ignored when using the simple Arrhenius form for desorption models. Monte Carlo (MC) simulations can quantitatively examine the individual contributions of these more complicated effects for the TPD spectrum. Using a lattice gas model, where atoms are placed on a discrete lattice, the system is modeled on the molecular length scale, thus leading to the exact microscopic environment known at each step. Models can be used to make transitions based on the local environment, in contrast to the Arrhenius form which essentially 'fits' each step into a functional form. The MC algorithm used in this study makes a direct connection between the number of MC steps taken in the simulation and real time.3 -6 Meng and Weinberg 4 have developed an algorithm to model TPD on metal surfaces, where the assumption is made that the rate of diffusion of adsorbates is much greater than the rate of desorption. This assumption does not hold for semiconductor surfaces for which rates of diffusion and desorption tend to be of the same order of magnitude. In this study, a MC algorithm is developed to model TPD on semiconductor surfaces. Using the MC simulations, hypothetical mechanisms can be input into the model to examine the effects of 109 Mat. Res. Soc. Symp. Proc. Vol. 399 0 1996 Materials Research Society
complex surface processes on TPD spectra. Adsorbate interactions, two-dimensional adsorbate islands, and surface reconstructions are examples of surface processes considered in this work. Methyl desorption from Ga-rich GaAs will be used as a case study to illustrate the methodology. Understanding this process is important for atomic layer epitaxy (ALE) processes, since methyl groups are thought to block adsorption sites from further reactions, thus limiting the layer-by-layer growth mechanism in ALE. MODELING APPROACH 7 To model dynamic processes using MC, the Master Equation must be solved:
dPct dt
.w6 6
)P6 t),(2 )-Y dt
~
-5P(a,
(2)
where P(a,t) is the probability of being in state a at time t, and w(&-a) is the transition probability from state i to state a. To solve the Master Equation, one must choose randomly among the transitions allowable and accept transitions with the probability, w(&-a). The 7 transition probabilities must be consistent with the detailed balance criterion. The detailed balance criterion does not uniquely speci
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