APPLICATIONS OF FIRST-PRINCIPLES AND EMPIRICAL METHODS

IN DETERMINING ACTIVATED STATES

AT SURFACES AND INTERFACES OF SILICON

There is a wide range of phenomena in semiconductor physics that involve

thermally activated processes. Understanding the microscopic mechanisms

involved in these processes is usually the crucial question. Here we will

discuss two cases that involve activated processes, both related to silicon,

and in which the interpretation in terms of microscopic mechanisms is a

challenge.

The first example involves the dissociation of hydrogen molecules on the

Si(111) 7x7 reconstruction. Experimental observations indicate that H_2

molecules adsorb on this reconstructed surface with a very low sticking

coefficient, which translates to an adsorption barrier of 0.9 eV. The H_2

molecules can be thermally desorbed, and this process involves an activation

energy barrier of 2.5 eV. The most intriguing aspect of experimental results

is that when the molecules are desorbed, they leave the surface in a very

``cold'' state, that is, they carry no internal energy in any of the degrees

of freedom involved (rotational, vibrational or translational). This is

puzzling, since a simplistic interpretation of desorption as the inverse of

the adsorption process would mean that the desorbing molecules should carry

an energy approximately equal to the adsorption barrier.

In order to elucidate what happens in this physical system, we have performed

an extensive study based on first-principles total energy calculations using

density functional theory and the generalized gradient approximation. Our

basic assumption is that the H_2 molecules adsorb onto and desorb from a pair

of surface atoms, an adatom and a rest-atom, which represent the most chemically

active sites on the 7x7 reconstruction. Our total energy calculations give

an adsorption barrier of 0.8 eV and a barrier for thermal desorption of 2.4 eV,

both in excellent agreement with experiment. What is interesting and appealing

about our results, is that a detailed analysis of charge density distributions

reveals that the motion of the Si adatom on the surface makes both

the adsorption and desorption processes possible; this motion also provides

a natural explanation for the puzzling experimental observations mentioned

above. Specifically, the adatom breaks one of its back bonds, pivots closer

to the position of the rest-atom, and this makes it possible for the H_2

molecule to dissociate with each H atom attaching to one of the Si dangling

bonds on the adatom and the rest-atom. The reverse process, the formation of

an H_2 molecule from the two H atoms attached on the Si adatom and rest-atom,

also proceeds through the pivoting action of the adatom, which brings the

two H atoms closer together so they can start forming the H_2 molecule.

Since the cost of breaking of the adatom back-bonds is 0.8 eV, this can

be associated with the adsorption barrier and with part of the desorption

barrier. Once the H_2 molecule has left the surface, the adatom must

pivot back to its equilibrium position, gaining the 0.8 eV of energy when

it reforms the back-bond. This accounting of the energy costs indicates that

the H_2 molecule can leave the surface without carrying any excess energy.

Rather, the excess energy is gained by the surface when the adatom relaxes

to its equilibrium structure. A detailed account of this theory can be found

in: ``Theory of adsorption and desorption of H$_2$ molecules

on the Si(111)-$(7 \times 7)$ surface'', K. Cho, E. Kaxiras and J.D.

Joannopoulos, Phys. Rev. Lett. vol. 79, p. 5078 (1997).

The second problem that we will discuss is the phenomenon referred to as

Solid Phase Epitaxial Growth (SPEG) of silicon. In this phenomenon, a system

consisting of an amorphous film of Si on top of a crystalline Si substrate is

transformed into high-quality crystalline Si when the interface moves into the

amorphous phase. This is a thermally activated process, with an activation

energy of 2.7 eV, which is measured over a very wide range (about 10 orders

of magnitude) of the speed of the interface as a function of temperature.

Moreover, there exist non-hydrostatic pressure experiments indicating that

the activated state is ``short-and-fat'', i.e. the interface speed increases

with stress perpendcular to the interface, and decreases with stress parallel

to the interface. Despite all this detailed information, nothing is known

about the microscopic mechanisms responsible for SPEG.

In order to investigate this problem, we found it necessary to explore first

what is the structure of the crystalline-amorphous interface in Si. To this

end, we created a tight-binding non-orthogonal Hamiltonian, which we fitted

to reproduce a range of structures relevant to low-energy bulk phases, point

defects and atomic motions related to self diffusion in Si. The development

of the model Hamiltonian and its fitting can be found in:

``Non-orthogonal tight-binding Hamiltonians for defects and interfaces in

silicon'', N. Bernstein and E. Kaxiras, Phys. Rev. B, vol. 56, p. 10488 (1997).

Using this Hamiltonian, we were able to produce samples of the amorphous-

crystalline interface, by melting part of the sample while keeping another

part in a cold, crystalline state, and then cooling the molten part slowly.

The resulting interfaces exhibit a number of interesting features which

have been discussed in detail in:

``Amorphous-crystal interface in silicon: a tight-binding simulation'',

N. Bernstein, M.J. Aziz, E. Kaxiras, Phys. Rev. B, vol. 58, p. 4579 (1998).

While the structure of the interface is interesting in itself, the

simulation of SPEG would require a much faster computational method than a

tight-binding approach can handle: it is necessary to let the system evolve for

a large enough number of steps to obtain crystallization of the amorphous

phase. We were able to perform such simulations using the recently developed

Environment Dependent Interatomic Potential (EDIP) for Si. This potential

encompasses a number of important theoretical constraints on its functional

form, and was fitted to reproduce the same structures as the tight-binding

Hamiltonian. Details of the theory for EDIP and its fitting are given in:

``Modeling of covalent bonding in solids by inversion of cohesive energy

curves'', M. Z. Bazant and E. Kaxiras, Phys. Rev. Lett. vol. 77, p. 4370 (1996);

``Environment dependent interatomic potential for bulk silicon'',

M. Z. Bazant, E. Kaxiras and J. F. Justo, Phys. Rev. B, vol. 56, p. 8542 (1997);

``Interatomic potential for silicon defects and disordered phases'',

J. F. Justo, M. Z. Bazant, E. Kaxiras, V. V. Bulatov, and S. Yip,

Phys. Rev. B, vol. 58, p. 2539 (1998).

Using EDIP, we performed simulations at different temperatures, which

clealry indicate the activated nature of SPEG. From these simulations we

extracted an activation energy of 2.0 eV for high temperature and 0.4 eV

for low temperature. We suggest that the low-temperature regime is dominated

by defect motion, whereas the high-temperature regime is dominated by defect

formation (which we expect will have a higher activation energy than motion),

within the amorphous phase. We also find, by monitoring stress during the

simulation, that the activated state has properties compatible with the

experimental measurements mentioned above. Extracting more detailed iformation

from the simulations on the microscopic processes responsible for SPEG is

a very demanding proposition, which will be discussed in this Symposium