METODOLOGÍA SUGERIDA PARA DETERMINAR LOS OBJETIVOS ESTRATÉGICOS DE LA RELACIÓN

One of the major advantages of ALD over other deposition techniques is that line-of-sight deposition is not required. This gives the ability to deposit conformal coatings over very

47 complex substrate geometries. To fully and evenly coat high aspect ratio structures, Gordon et al. proposed that several criteria must be met(107):

1. Chemistry 2. Stoichiometry 3. Kinetics

2.2.1.1.1 ALD Surface Chemistry and Precursor Stiochiometry

For chemistry and stoichiometry a difference in surface geometries would have very little effect in governing the success of an ALD coating reaction. In terms of the chemistry requirement, the chemistry of the precursor materials and the surface chemistry of the substrate must be compatible with each other to produce self-limiting monolayer per cycle growth via alternating surface saturation of the precursor species(107). For stoichiometry the number of precursor molecules introduced into the chamber with each step must exceed the number of available surface reaction sites. This includes all exposed surfaces that are at the required temperature within the reactor chamber as deposition will occur on all exposed surfaces(107)_{. For high surface area structures such as powders, trench or pore}

substrates, it is possible for relatively small samples to have a surface area equal to or larger than that of the rest of the reactor. The total combined surface area can in some cases exceed several m2_{, requiring large precursor doses.}

2.2.1.1.2 ALD Kinetics (Planar Surfaces)

For planar surfaces, monolayer coating of the substrate can be achieved with very short exposure times. This can be shown using kinetic gas theory. The flux of molecules on to a surface (number of molecules passing through a plane from one side) can be shown as(107):

48 Where = flux ( ), = partial pressure of precursor near the surface ( ), = molecular mass ( ), = Boltzmann’s constant ( ) and = temperature ( ).

The time required to achieve a saturation dose on a surface is given by:

Where = time ( ) and = saturation dose ( ).

This can be rearranged to give the exposure required to coat a planar surface.

Where = exposure ( ). A more convenient unit of exposure is the non-S.I. unit the Langmuir ( ), which is 10-6 or 7500.6 .

The above equation assumes a unity sticking coefficient of the precursor molecules on the substrate. The sticking coefficient for a particular precursor-substrate combination is determined by several parameters; the geometry of the surface site, the effect of neighbouring adsorbates, the velocity, angle and orientation of the incoming precursor molecule, the surface temperature and the reaction energetics of the contacting atoms. The sticking coefficient can be measured by carrying out a test deposition on the planar surface of a quartz crystal microbalance (QCM) within the ALD reactor, or by measuring the thickness profile of a multi-cycle deposition using a high surface area porous template with pore diameters smaller than the mean free path of the gas molecules at a particular temperature and pressure (108). The exposure equation can be modified to include the effects of a non-unity sticking coefficient:

49 Where = sticking coefficient (no units).

2.2.1.1.3 ALD Kinetics (Non-Planar Surfaces)

For substrates with structural features much larger than the mean free path of the gas phase precursor molecules no modification of the above equation is required. For porous, trench or powder depositions in which the structural features are equal to or smaller than the mean free path, the exposure required for conformal coating is increased. For the porous structures that are the subject of this thesis, the pore diameters can be between 10 to 103 times smaller than the mean free path of the precursor molecules above the sample at typical reactor temperatures and pressures. The result of this is that within the pores, the number of collisions with the sample surface greatly outnumbers collisions between gas molecules. As pressure is simply a reflection of the number of collisions with a unit surface area per unit time, this effectively means that the pressure within the pores is much higher than the pressure within the rest of the chamber. As a consequence, models that assume Knudsen-type flow within the pores can be employed to accurately model the exposure times required for conformal coating (109)_.

Gordon et al. derived an equation for predicting the required minimum precursor exposure(107):

Where = aspect ratio of the pores = . As before, this equation assumes that = 1. Multiplying the right hand side by would allow the equation to be used with different precursor/substrate combinations. For deposition thicknesses that are of a similar scale to the diameter of the pores, for example < 20nm, it is likely that the deposition can noticeably alter the aspect ratio. To account for this, the authors suggested that the

50 minimum exposure should be calculated from the predicted aspect ratio at the end of the deposition cycle.

An alternative set of equations was developed by Elam et al.(109). Monte Carlo simulations were found to agree well with experimental ALD of Al2O3, ZnO and SiO2 onto through-hole

AAO templates with pore diameters of 19, 47 and 65nm, and template thicknesses of 50μm. It should be noted that due to the use of through-hole templates deposition occurred from both sides of the template simultaneously, effectively meaning that the template thickness used in the calculation of minimum exposure times was 25μm.

Where = integrated coverage (1 = full, conformal coating), = time ( )

Where = pore diameter ( ), = pressure ( ), = pore depth ( ), = mass of reactant molecule ( ) and = density of reactive sites ( _{). Setting = 1 and} converting to S.I. units gives:

Elam et al. found that the sticking coefficient between the precursor molecules and the AAO substrate and the aspect ratio of the AAO template determined whether the deposition was diffusion limited or reaction limited(109). For their analysis the diffusion coefficient was quantified by calculating the hopping coefficient based on a random-walk analysis. Via the Monte Carlo simulations it was found that if the sticking coefficient is much larger than the hopping coefficient then the deposition was diffusion limited, with reactive sites filling up in order starting with those at the pore entrance. This type of deposition

51 showed distinct boundaries between coated and uncoated areas within the pores. For this type of deposition regime it was found that was proportional to . Conversely, if the hopping coefficient was much larger than the sticking coefficient then the deposition was found to be reaction limited. For this type of deposition the reactive sites filled up randomly, giving even coverage throughout the length of the pores. For reaction limited deposition it was found that was proportional to .