Page 109 - Sami Franssila Introduction to Microfabrication

88 Introduction to Microfabrication

microdevices, there are always structures of various obtain the profiles shown in Figure 7.18. Hemispherical
shapes and variable spacings, and the film deposition deposition model is an approximization of sputter
over all these spaces needs to be considered. It is far deposition. Trench dimensions have been varied to see
too simple to consider one size only. the effect of the aspect ratio on step coverage. In the
Good step coverage in metallization is essential for 1:1 aspect-ratio trench step, the coverage is ca. 15%,
reliability. Even though the metal film will be continuous but in the 2:1 aspect-ratio trench, the coverage is only
even with, say, 10% step coverage, current density will a meagre 5%. Slightly sloped profile in the 2:1 trench
increase dramatically at the thinnest point, causing a leads to ca. 10% step coverage.
major reliability problem. Note that step coverage over isolated lines is always
the same irrespective of the line aspect ratio: step
coverage depends on the atom arrival angles and, by
7.9 SIMULATION OF DEPOSITION definition, the isolated lines have a large unobstructed
space next to them, and, therefore, will result in identical
Topography simulation (for deposition, etching and step coverage.
polishing) works on fluxes and surface processes: at Monte Carlo (MC) and molecular dynamics (MD)
each grid point, the incoming flux (from the fluid simulations offer more realism, for example, the predic-
phase) and surface-reaction probability are evaluated tion of step coverage based on relaxation (Figure 7.19).
(with a return flux of reaction products in the case Calculations can be speeded up by treating matter as
of etching/polishing, or non-sticking specie in the case 100 ˚ A cluster spheres instead of individual atoms. Clus-
of deposition) to calculate the new surface height. ters, and thus the atoms, come to rest at stable positions,
In principle, the generation of the incoming specie for example when touching three other spheres. The
could be simulated (for instance, ion and radical pro- arrival of new material and the rearrangement of already
duction in plasma) but this is usually not integrated deposited films can be simulated simultaneously. Tem-
into a topography simulator; rather, it is a part of a perature and sticking coefficient are used as parameters
reactor simulator. New surface points are calculated for surface mobility.
and those points are connected to represent the sur- 2D simulation can overestimate the bottom coverage
face. Accuracy is increased by calculating new points by 40%, compared to 3D. This is intuitively easy to
between existing points when they are far apart; and understand because 2D simulation treats the recesses
similarly, by eliminating points that become close to as infinitely long trenches, with very large acceptance
each other. angles along the trenches, whereas 3D simulation takes
Deposition models define atom arrival angles, and into account the real acceptance angle.
various models are available in most simulators: fully
directional, hemispherical, conical, etc. Etch models
include isotropic and anisotropic models, and user 7.9.1 Scales in simulation
definable mixtures of the two. Model selection is
The fundamental simplification of many topography/
very much an empirical question, and the predictive
thin-film simulators is the fact that surface-controlled
power of topography simulation is diminished by this
reactions are assumed. On a microscopic scale this is
semiempirical tailoring of model parameters.
true: material is being added to or removed from a sur-
Input for a typical topography simulation includes
face, but on a macroscale this is a gross simplification.
Etching and deposition processes can be either surface-
• the surface topography already made reaction limited or transport-process limited. The trans-
• the material to be deposited port of reactants from gas flow to surface (as in a CVD
• the deposition model (angular distribution of deposit- reactor) or the removal of reaction products by con-
ing specie) vection (like removal of hydrogen bubbles that result
• thickness/rate and time. from silicon etching) can be more critical to etching
or deposition than the surface processes. Whether it is
Adjustable parameters include surface diffusivity, which the surface reaction or the transport mechanism that
determines how much lateral movement the imping- determines the reaction rate has to be studied for each
ing specie is allowed before it is ‘frozen’ in the process. If the reaction is transport limited, then the sim-
growing film. ulation should be able to model fluid dynamics at the
Topography simulator SAMPLE 2D, developed at reactor scale, in addition to the surface processes at the
University of California, Berkeley, has been used to micrometre scale.