Transport Phenomena in Porous Low-k Dielectrics

To achieve materials with dielectric constants m2.5 while meeting all the properties required for dual-damascene integration at interconnect feature sizes of m 100 nm, it is necessary to introduce controlled porosity into the material. At present, there is controversy involving the nature of the pores generated in the matrix of the materials: Should the pores be closed or open? Does it matter? What pore size is acceptable? Can process gases or water permeate porous materials?

This article will address issues associated with these questions and will make the case for materials requiring pore sizes <5% of the technology feature size. Based on permeation and diffusion analysis associated with micropores (1-3 nm), we determined that transport through porous materials depends more on the diffusion and permeability of the low-k material. The type of pore is of secondary consequence. At this scale, the concept of open and closed pores is substantially blurred and can be reduced to the properties of the matrix material. In this sense, all materials can be considered porous consisting of "open pore networks."

For most dielectric pore generating processes, a material is removed from the matrix, which requires diffusion to facilitate the process. Diffusion is the key property that needs to be considered. Even in pore formation processes where no material is removed and free space is generated via bond modification alone, there is appreciable free volume amenable to high rates of gas transport. We have found that gaseous diffusion through low-k dielectrics occurs rapidly, especially for small gas molecules such as H₂O and CO₂, and especially at elevated temperatures.

Through an understanding of the transport phenomena likely to occur during processing, engineers can devise methods of controlling diffusion between materials. This perspective should help companies planning to employ low-k dielectrics to better manage integration issues in multilevel interconnect structures.

1. Simulation of an amorphous SiO2 matrix shows microscopic voids, which can be considered pores.

The article further discusses the nature of pores and necessary pore size, while examining pore generation methods and relevant material considerations, the important transport considerations in dense and porous materials, and material issues with respect to process integration and differences between open and closed pores.

In the past 20 years, feature sizes have dropped ~100× from 10 µm (10,000 nm) to 100 nm. The industry is already utilizing atomic-scale features in high-performance logic devices with gate dielectric thickness of ~1.4 nm (five rows of atoms). The next three technology generations will drive interconnect features below 100 nm, which will impose a rethinking of how we look at barrier metals and low-k dielectric materials.

For instance, at 100 nm, we should begin to see copper resistivity vs. size effects — since the electron mean free path in copper is ~50 nm. At these dimensions, grain boundaries will cut the line effectively in half because of the copper electroplating process, and provide scattering sites approximately equal to this mean free path. When this occurs, the bulk resistivity of the copper becomes a function of feature size. Similar issues must be considered for porous low-k materials where pores must be tightly controlled and be a small fraction of the minimum feature size.

There is controversy in the industry with respect to acceptable pore size, which can have a range of 5-1000 Å for commercially available low-k materials. Most designers use a ±10% variation in manufacturing rules for allowable feature size variations. Assuming a 100 nm line, the engineer must control feature size to ±10 nm (3σ). A 5% rule arises from the fact that the edge of the interconnect can be increased by the presence of pores on a trench sidewall. The worst-case enlargement of effective linewidth for a pore that is 5% of the feature size is 50 Å.

2. Simulation of a polymethylmethacrylate (PMMA) polymer matrix that shows considerable pore volume is available for material transport.

A number of approaches can be used to generate porous low-k dielectrics. In the future, efforts to continually lower k values will likely result in pore volumes of 25-60%. The need for these levels of porosity is a function of the starting k value of the dielectric. According to the 2001 ITRS,¹ at the 100 nm node it is desirable to use low-k materials with k=2.7, though IC manufacturers are expressing great interest in integrating k=2.2 materials also. If we start with a solid material having a k~4.0, ~60% pore volume is required to attain k=2.2. This may be unacceptable for mechanical strength reasons and jeopardize the integrity and integration of the material. To create harder, engineered materials with dielectric constants of 2.2, required porosity is ~25% with a starting non-porous k value of 2.6, making the material much more attractive from an integration perspective.

Models² describe the relationship between porosity and modulus (that can be related to strength). The Matthiesen model provides a crude approximation of the modulus of a porous material where:

E_mat = (1-x) E_solid (1)

Similar models can predict the effective dielectric constant (k_eff) generated by mixing pores within the solid matrix where:

k_{eff mat} = (1-x) k_solid + x k_air (2)

However, there is a dependence not only on total pore volume but also pore size. As pores become smaller, the strength of the material retaining them increases.^2,3 Because material strength is key to integration and manufacturability, low-k materials need to have very tight pore size distributions at very small pore sizes. Techniques need to be explored that can identify a few outlying pore sizes in a distribution of massive numbers of small pores. For instance, a 200 mm wafer with a 500 nm thick low-k dielectric film and a porosity of 50% contains a staggering number of 2.0 nm pores — on the order of 1.9 × 10¹⁸ /wafer/level (Table 1). Though optical detection of defects or "killer pores" is attractive, it has a low probability of success with killer pores that deviate by only 2-3× from the mean size at densities of 20-40 total per level. The possibility of having a defective pore on the sidewall of a via or trench, which might lead to barrier breakdown within the operating life of the device, indicates a need for three-dimensional defect detection, which is likely to provide greater complexity than is presently appreciated. Killer pores could be ~10-20% of the minimum feature size and still cause a failure.

3. The necessary coefficient of diffusion required to prevent complete transport of gaseous, liquid or solid materials through a material having a specified feature width in a process time of 60 sec.

Pores can be introduced using three basic approaches:

1. By introducing a material into the bulk matrix by chemical attachment, which can be decomposed into a species that is then removed from the material matrix, leaving a small opening or pore.
2. By configuring molecules that form pores by internally rearranging bonds within the material or by generating free space in the matrix, which can be considered a pore.
3. By placing discrete, atomic-sized spheres or other open sub-units into a matrix and then incorporating them into the dielectric during processing.

The third mechanism requires excellent process control because it requires a uniform distribution of discrete objects in a medium. Prior to deposition and setting the film matrix, the pores also must be kept from clustering. Approaches 1 and 2 can be performed in a more statistically well-controlled manner by molecular engineering of the sub-units that will comprise the film. This method allows pore generation of separate pores that are uniformly dispersed in the matrix.

4. Change in diffusion coefficient for gases in polymeric materials as a function of temperature.

5. Typical diffusion coefficient regimes for gases in polymers, gases in metals and metals in metals.

A material's permeability can be used to extract data regarding the quantity of gaseous material transport. Permeability⁵ is the measure of material flux through a cross-sectional area of bulk material of thickness, x, when a pressure differential exists across x. Permeability is related directly to the diffusion coefficient by the solubility of the diffusing species:

P = s * D (3)

where

P = permeability of the material (atoms emitted/cm-sec-Torr)

D = diffusion coefficient (cm²/sec)

s = solubility (atoms absorbed/cm³ of solid-Torr)

Typical activation energies associated with the diffusion coefficient and gas solubility in the low-k dielectric can be obtained for a membrane with unidirectional material flow that has reached steady state using:⁶

t_Lag = x²/6D (4)

where

x = thickness of the membrane

t_Lag = diffusion time (sec) required to achieve steady-state transport

D = diffusion coefficient (cm²/sec)

Based on past permeation experiments on many bulk polymers,⁷ we can estimate D and solubility limit in the material. The lag time to attain steady-state permeation gives the value of D from Equation 4, and permeation rate at steady state, along with the diffusion coefficient, give the solubility of the gas in the material. This data can be used to make reasonable transport time estimates in relevant interconnect structures. Alternatively, this simple formula can provide the necessary coefficient of diffusion, regardless of material, that would not allow transport of materials through a dielectric or metal film of thickness, t.

To provide a perspective of some future issues that will have to be addressed in the interconnect system, let us look at the diffusion in materials in general. Although the solubility of the gas in the matrix is an important parameter, the total amount of transport due to permeation is typically 2-5 orders of magnitude less, since solubilities are on the order of 10^-2 to 10^-5, and will only shift the scale of the analysis that follows.

6. Schematic representation of the interaction between reactive species and interconnect structures during plasma processing.

Table 2 shows representative diffusion coefficients for small gas molecules in polymeric materials. For higher-temperature materials such as polyimides or polysiloxanes, it is evident that many small gas molecules can easily move completely through them for typical process times.

Although it will not be addressed in this article, it is highly probable that gases will flow through a number of very thin barrier metals used in interconnect systems. If temperatures of ~400°C are employed for prolonged periods, the diffusion coefficient may be large enough to allow appreciable material transport. We can use the typical diffusion coefficient regimes for gases in polymers, gases in metals and metals in metals (Fig. 5) to address transport issues in proposed interconnects.

Figure 6 shows a situation routinely experienced by a material system when a gas is exposed to a delineated trench and via in an interconnect structure. The features are so small that gases diffuse rapidly into the matrix. If an atmospheric process is used, the gas incorporation to saturation occurs rapidly. For low-pressure processes, such as etching, with pressures on the order of 10 mTorr, the build-up of absorbed gas in the bulk of the material is mass transport limited. However, at these impingement fluxes, equivalent to about a third of a monolayer per second deposition rate, if all the atoms were incorporated, a 1% incorporation of gas in the dielectric would occur in ~15 sec at room temperature in a 150 nm line.

An added issue associated with etching and CVD (including ALD) processes involves reactive species like fluorine ions and metal-organic precursors. These species can attack the matrix and become trapped. For non-reactive gases, the gas will simply pass through and saturate the material, but the gases can be removed from the material during thermal processing or other means.

Reactive gas processes require a more detailed analysis. The precursor could potentially react within the low-k material and cause metal deposition in the low-k dielectrics, regardless of the k value or density. PVD processes are attractive in the sense that the atoms are confined to the wall surfaces of the interconnect structure and do not possess the vapor pressure characteristics to diffuse into the bulk of the dielectric.

By assuming ≤100 nm feature sizes and performing simple permeation and diffusion analyses for dielectrics, we determined that gases rapidly diffuse through low-k dielectrics. The diffusion coefficients of small gas molecules such as H₂, H₂O, CO₂ and others are so high that, for all practical process times, they can easily pass through device structures on the wafer. This rapid transport effectively renders the closed vs. open pore issue moot, because even solid materials without pores effectively pass many gases through them in the small feature size regime. From an atomic perspective, all materials can appear to be open pore systems.

For all proposed future dielectric material systems, the major question raised by this analysis is not whether appreciable diffusion will occur but rather what the best approaches are to understanding and controlling diffusion through a process selection and integration method.