Mechanics-Based Approach for Detection and Measurement of Particle Contamination in Proximity Nanofabrication Processes

High-volume manufacturing of devices with nanoscale features has had a significant impact in several applications, including electronics, energy, photonics, and healthcare [1]. As feature dimensions shrink, process tolerances become more strict, and the number of unit processes needed to make the devices increases, especially in the demanding applications of complementary metal–oxide semiconductor (CMOS) fabrication, maintaining high overall process yield along with throughput has become critical for ensuring the viability of nanoscale manufacturing. Despite strict controls in class 10 and better cleanroom environments, one of the main sources of external defects is the presence of contamination particles, which can have a deleterious impact on yield in a nanomanufacturing environment [2]. A nanoscale device goes through several unit processes as it is being fabricated, each of which can be affected by the presence of particles in different ways. With sub-100 nm critical feature dimensions, particles as small as 100 nm can potentially cause catastrophic device failure and loss in process yield. Although contamination control technology, including using highly controlled air flow and filters, has also simultaneously minimized the presence of such particles, still, the likelihood of “killer” particle encounters is nonzero. This necessitates steps to mitigate their impact on yield by first detecting them and then, containing their influence across different process steps [3]. Moreover, the need for efficient particle control and detection is especially true for a class of nanofabrication techniques that rely on mechanical proximity or contact between two or more surfaces to realize the process successfully. While there are several relevant processes that can fall under the gamut of proximity nanofabrication (e.g., mechanical transfer [4] and coating and printing techniques, such as gravure printing and slot-die coating [5]), the most substantial yield challenge lies with the critical nanoscale patterning step. A brief description of some relevant nanoscale patterning techniques has been given next to better understand this problem.

Photolithography has been the process of choice for nanoscale patterning for decades. Given its noncontact nature, it is relatively tolerant of particulate contamination. However, as critical feature sizes have shrunk to the deep subwavelength regions, the use of photolithography for patterning has become increasingly complex and costly. This has spurred the development of high-resolution nano-imprint lithography techniques that pattern substrates through mechanical contact rather than optical means [6].

While there are several different flavors of nano-imprint lithography, one of the more commercially relevant variants is Jet-and-Flash Imprint Lithography (J-FIL™), as shown in Fig. 1 [6]. It has been used in the commercial patterning of CMOS logic and memory devices as well as hard disk media. Together, they have perhaps the strictest requirements in terms of device resolution, process yield, and overall throughput and cost. J-FIL™ is a room-temperature, atmospheric-pressure process that relies on the use of a fused silica master template, which has the desired nanoscale features etched on it, to pattern a substrate such as a silicon wafer using a ultraviolet (UV)-curable resist. The resist is dispensed as a multiplicity of drops of a low-viscosity liquid monomer using a bank of inkjet nozzles. The drops are spread and merged by the action of the overlying template and also fill the nanoscale features in the process without capturing any bubbles or voids. Once a contiguous film is formed, the template–liquid wafer “sandwich” is flood-exposed using UV light. This polymerizes and solidifies the liquid film after which the template is separated, leaving a polymer resist pattern with a residual layer behind. This residual layer thickness is kept intentionally small, typically sub-25 nm, to enable subsequent etch-based transfer of the resist pattern in the substrate.

Despite its high resolution, some critical risks in the J-FIL™ process come from its near-contact nature. They are the susceptibility of the master template to get damaged in the presence of an undesirable particle on the wafer surface, along with device failure and loss of process yield [7]. Permanent template deformation or damage can be catastrophic to the process in terms of cost and process robustness. Not only does the template form one of the more expensive elements in the J-FIL™ infrastructure, any damage to it can lead to repeating defects that can affect several wafers and thus severely dent the process yield [8,9]. Hence, if such particles encounters go undetected, there is potential for not only local damage but also a cascading effect that can impact downstream processing with the same template or wafer.

In general, the detection of submicron particles on substrates has relied on the use of subwavelength optical techniques [10] that rely on the scattered light signal differential because of particles on an otherwise periodic or null background. However, such techniques are usually ex situ, implying that the detection is carried out either before or after the substrate has undergone processing with the particle(s) present. This is not desirable as it adds another handling step and altogether separate tool in the processing line, thus adding to the manufacturing cost. At the same time, due to their low scattering intensity, detection of submicron, particularly sub-100 nm particles, can be especially slow over large areas, resulting in a drop in overall process throughput. This is a significant challenge to high-volume scalability. Hence, the motivation of this work is to investigate an alternative particle detection technique that exploits the inherent mechanics of the process while also not having some of the limitations of subwavelength optical inspection techniques discussed above. A dual benefit of this approach is that upon detection of a particle event, finer template and wafer inspection need not be carried out over the entire area, but can be confined to locations close to the particles themselves. This can lead to significant savings in inspection time and increase the overall process throughput. In addition to this, another important goal of this work is to understand the multiscale challenges in a typical particle event by way of a multiphysics mechanical model. This can be used to augment the inspection and detection capability with the ability to infer potential damage caused to the template and the expected loss in yield because of the particle event.

Inspection of wafers for detection of submicron particles requires a preliminary understanding of the signature of a particle event. An example of a particle event is shown in Fig. 2, where the loss of patterned area due to the presence of a particle can be clearly seen. In the presence of a particle, the template cannot access the imprint monomer on the substrate directly, but has to bend around the same particle thereby leading to local starvation of liquid and forming what is called an exclusion zone. This is because the volume of fluid on the substrate is strictly controlled to maintain a desired uniform mean film thickness. Beyond the exclusion zone, where there is no fluid, there is an additional transition zone, where the film thickness obtained is different from the targeted mean film thickness, again because of particle contact and template bending. An illustration of the geometry is shown in Fig. 3.

To understand this further, 67 particle events that occurred randomly during J-FIL™ processing in a class 10–100 cleanroom environment were analyzed, and their exclusion zone diameters were measured using an optical microscope. The resulting frequency distribution is shown in Fig. 4, which shows that the exclusion zone radius was approximately 100 μm. However, from random measurements of particle counts using a portable particle counter, it was found that such cleanroom environments do not generally allow many particles larger than 10 μm, let alone of the order of 100 μm. Moreover, the transition zone radius is higher than the exclusion zone radius, thereby suggesting that although the particle themselves may be small in size, they leave behind signatures that are much larger. This is the key aspect of the alternative inspection and detection technique—exploiting the inherent mechanics of the process to obtain an amplified signal from the particle and which can be more easily detected using standard optical techniques rather than subwavelength optics. Further validation of this idea has been done with the help of a multiphysics model which captures the key mechanics of the process.

The mechanics of the process is governed by the elasto-visco-capillary interactions at the template–fluid–substrate as well as contact mechanics interactions at the template–particle–substrate interface. There are four coupled physical phenomena at play at these interfaces. They are: (i) flow of a nanoscale thin film across much larger lateral length scales, (ii) bending of the template around the particle, (iii) capillary-driven pressure drop at the liquid meniscus at the exclusion zone edge, and (iv) contact-related deformation of the template. In this section, these phenomena are detailed further with reference to the geometry given in Fig. 3.

In this equation, h is the film thickness profile, p is the pressure profile, and μ is the fluid viscosity.

The Young's modulus, Poisson's ratio, and thickness of the template are given by E, ν, and b, respectively.

where r is a radial coordinate expressing the distance from the point of contact.

The geometry in Fig. 3 can be divided into two regions: dry and wet. The dry region represents the exclusion zone, where there is local starvation of the fluid and which physically also includes the particle. The mechanics of this region is governed by template bending and particle contact. This region then transitions to the wet region through the liquid meniscus at which there is a surface-tension driven pressure drop.

This wet region or the template–fluid–substrate interface extends from the edge of the exclusion zone to the edge of the transition zone, as shown in the geometry in Fig. 3. This is the region where there is a liquid cushion between the template and the substrate, but the film thickness profile is not equal to the desired constant mean film thickness. In this region, the influence of all the phenomena mentioned previously can be seen, as the template deformation is governed by both bending and particle contact. Moreover, there is a thin film of fluid between two surfaces, allowing the use of thin film lubrication, with the pressure drop at the meniscus appearing as a boundary condition. Details of the model setup have been described in the Appendix.

Importantly, the system has been modeled as an axisymmetric geometry in steady-state to make the system analytically tractable. The assumption here is that two particle encounters of the same wafer are sufficiently separated from each other that they can be treated as decoupled events. The model accepts the following inputs: exclusion zone diameter, desired mean film thickness, variation from mean film thickness at transition zone edge, and either the transition zone diameter or the film thickness at the exclusion zone. Based on these inputs, it gives the film thickness variation in the transition zone, contact force at the particle location, and the other of the film thickness at the exclusion zone or the transition zone diameter depending on which of the two was used as an input. It should be pointed out that the transition zone converts to the “bulk” film asymptotically and hence measuring it exactly may not be easy. Typically, the value of the transition zone can be set as the point where the film thickness is within a certain tolerance of the desired mean film thickness. The tolerance can be assumed from post-patterning etching constraints, for example. If the transition zone is indeed measured, doing so accurately is extremely important because its value directly influences the contact force through the Boussinesq solution given in Eq. (4).

If the transition zone radius is left for the model to estimate, the film thickness at the exclusion zone radius needs to be measured. This will require the use of an in situ non-contact optical profilometer system. Hence, the choice of which parameter to measure and which to estimate can be made based upon these constraints.

Because particle events are random in nature, the mechanical model has been first validated by performing controlled particle encounters. For this purpose, a silicon wafer is cleaned thoroughly using Piranha solution, and a matrix of 25 drops across five rows and five columns, of a UV-curable monomer, is dispensed. Each matrix location is a single drop of volume 6 picoliters and is spaced 10 mm apart from the neighboring drop. This matrix is then flood exposed with UV light to cure and polymerize the drops. Because the drops are now solidified, they can be considered as proxies for particles. In this way, a controlled distribution of “particles” with known properties is generated on the wafer and used to experimentally validate the model. This wafer is then imprinted upon immediately, to avoid any further contamination of the surface and introduction of a disruptive noise in the system. As expected, the imprint process on the wafer with particles creates exclusion and transition zones at the same locations where the drops were dispensed. Further metrology was conducted by scanning the particle locations on a Dektak stylus profilometer to obtain the particle geometry, exclusion zone diameter, as well as the film thickness profile in the transition zone. The extent of the transition zone was measured using an optical microscope, as it was beyond the scanning range of the profilometer system.

Of the 25 particles that were initially simulated on the wafer, only four could be used for further analysis. This is because the particle diameter turned out to be very similar to the eventual exclusion zone diameter, leading to a fusion of the particle with the film in 21 events. Unfortunately, due to limitations of the in-house inkjet system, smaller drops cannot be dispensed to test particles of smaller sizes. Nevertheless, the four particles that could be analyzed have been measured individually and the obtained film thickness profile has been compared against model predicted film thickness profile, as shown in Fig. 5. There is good agreement between the model predicted and experimentally obtained film thickness profiles, indicating that the model is a good representation of the system.

The validated model can now be used to estimate the contact force and the extent of yield loss from these four particle events. These have been given in Fig. 6 and reveal that the contact forces are of the order of 1 N and the transition zone diameters are of the order of 1 mm. The magnitude of the contact force provides an estimate of contact stress, which in turn determines whether there has been any in situ permanent yielding of the template. The exact nature of contact stress, given the contact force, can only be obtained if the geometry of the particle is known exactly. This is, unfortunately, not available during a process run. However, if the contact force is deemed higher than a set threshold based on model estimates, the process can be stopped and the particle can be further analyzed to determine whether it has indeed caused permanent damage to the template or not. Typically, inspecting a wafer is easier than inspecting a template, but if this was not the case, the template can be directly inspected for damage. Also, this inspection needs to be carried out in close proximity to the particle location, the area of which can be several orders of magnitude smaller than the area of the entire template, thus drastically reducing inspection time.

As an example, if fused silica was the template material, it is known that its compressive strength is ∼1 GPa, while its tensile strength is ∼40 MPa. Near the point of contact, the stress is primarily compressive, thus, the compressive force can be used to estimate damage. It should also be pointed out that contact leads to a complex stress field with both tensile and compressive components, and the exact nature of the stress field and plastic yield depends on the geometry in the region of contact. Further, the presence of nanoscale features can lead to a difference in the effective yield stress of the material, which should also be factored in when estimating damage because of particle encounters [16].

The obtained transition zone diameters are further evidence that a particle sandwiched between two solid surfaces separated by a fluid cushion can lead to signatures that are substantially amplified than the size of the particle itself. The model can thus be used to estimate the extent of yield loss that can be expected from the given particle event. For example, if the post-lithography etch process allows a latitude of 5 nm in residual layer thickness variation, this value can be entered in the model as the place where the transition zone ends and the film thickness essentially becomes the desired mean film thickness. The model can then estimate the transition zone diameter and provide a real-time value for the expected lost area because of the particle event bringing about higher than desired film thickness variation. If this area is larger than what can be tolerated for the final product wafer, the process can be stopped and the template can be cleaned and replaced.

Apart from in situ detection and metrology, it can be seen that the mechanics of the imprint lithography process itself can be exploited as a technique for particle detection on a wafer. The key here is that the exclusion and transition zones, that determine the spread of the lateral region of influence of the particle, can be two to three orders of magnitude larger than the particle itself, as shown in an exemplar case in Fig. 7. This implies that a single 100 nm tall particle can potentially lead to a nearly 100 μm diameter “perturbation.” This massive signal amplification from a single particle event can then be easily detected using an optical microscope with a camera and allows for more facile detection compared to subwavelength optical techniques. This proposed detection technique might involve running the substrate in the same J-FIL™ tool with a sacrificial template which has no patterns. The liquid cushion can be with a volatile material that can be easily cleaned of without leaving any residue regardless of whether any particles have been detected. Upon detection of particles more than the allowable defectivity budget, the wafer may not be processed further to prevent process yield loss.

Submicron particle contamination is a significant concern in high-volume nanomanufacturing involving proximity or contact of two or more solid surfaces. For the J-FIL™ process, particles can not only disrupt the continuity of the liquid film leading to local starvation and loss of yield area but they can also permanently damage the expensive template. Detection and metrology of particles on wafers typically rely on subwavelength optical techniques that can be limited in throughput for global inspection of surfaces for these particles. However, the inherent mechanics of the J-FIL™ process creates a visible signature from a particle event that can be ∼1000 × larger than the particle itself, which can be seen using a standard optical microscope without the use of subwavelength techniques. Moreover, finer inspection of the template and wafer surfaces for any particle-related damage may be carried out over areas that are several orders of magnitude smaller than the total area of these surfaces, thus increasing process throughput. In this paper, a model has been developed for the mechanics of a particle event which has also been validated with good agreement against controlled particle encounters. This model allows the estimation of the contact force as well as the extent of the lost yield area because of the particle event and can be used in situ during a process run to make more informed decisions on whether the particle can lead to a killer defect. Moreover, this can also inspire an alternative particle inspection technique that relies on the detection of the much larger signature from the particle event rather than the particle itself. Through the mechanical model developed in this paper, this method can be used to not only detect the presence of a particle but also estimate its size and potential for yield loss, while also circumventing some of the constraints seen in subwavelength optical detection techniques.

The authors would like to acknowledge the support of Molecular Imprints, Inc. and Canon Nanotechnologies, Inc. for providing the Jet-and-Flash Imprint Lithography infrastructure.

This work was supported by the National Science Foundation Scalable Nanomanufacturing Program (NSF Contract No. ECCS-1120823) and the National Science Foundation Nanosystems Engineering Research Center on Nanomanufacturing Systems for Mobile Computing and Mobile Energy Technologies (NASCENT) NSF EEC Grant No. 1160494. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

a_i =

coefficients to solve for dry film thickness profile (i = 0, 1, 2, and 3)

b =

template thickness

b_i =

coefficients to solve for wet film thickness profile (i = 0, 1, 2, and 3)

D =

template bending rigidity

E =

template Young's modulus

F =

point force on the surface of semi-infinite elastic medium

h =

film thickness profile

h_c =

contact deformation on a surface of semi-infinite elastic medium

h_d =

film thickness profile in dry region (exclusion zone)

h_w =

film thickness profile in wet region (transition zone beyond exclusion zone)

h₀ =

mean film thickness given by the value in the bulk film beyond the transition zone

h_EZ =

fluid film thickness at exclusion zone edge

h_tol =

maximum allowable difference between the mean film thickness and the asymptotic transition zone film thickness profile

p =

pressure profile

p_d =

pressure profile in dry region

p_w =

pressure profile in wet region

r =

radial coordinate

R₁ =

exclusion zone radius

R₂ =

transition zone radius

t =

time

w =

template deformation profile

γ =

fluid surface tension

θ_s =

fluid contact angle with wafer

θ_t =

fluid contact angle with template

μ =

fluid viscosity

ν =

template Poisson's ratio

At the same time, the Boussinesq solution gives the deformation due to a point load on a semi-infinite elastic medium as Eq. (4). The total deformation in the dry region is given as a sum of the deformation due to bending and contact.

As for the wet region, the thin film lubrication (Eq. (1)) defines the film thickness profile. In its original form, this equation is a nonlinear partial differential equation and represents the transient evolution of the film thickness profile. For the sake of this analysis, it can be simplified by first assuming that the system has reached equilibrium and is in steady-state.

In Eq. (A6), h_tol represents the maximum allowable difference between the mean film thickness and the asymptotic transition zone film thickness profile. It is assumed that this difference is caused entirely because of deformation due to particle contact, since the Boussinesq solution has an asymptotic dependence on 1/r. Hence, there are nine boundary conditions, implying that four more constraints are needed. One of these constraints is the definition of the contact force, which is nothing but the shear force expressed at r = 0. The second constraint is volume conservation, since the volume of fluid dispensed on the system is strictly controlled to maintain a uniform film thickness of h₀. Thus, two variables still need to be measured. They can either be the transition and exclusion zone radii, R₁ and R₂, or film thicknesses at known locations. With this, the system should be fully constrained and provide a unique solution.