Alexander C. Wei

Microfluidic simulations for immersion lithography

The premise behind immersion lithography is to improve resolution by increasing the index of refraction in the space between the final projection lens of an exposure system and the device wafer by inserting a high-index liquid in place of the low-index air that currently fills the gap. We present a preliminary analysis of the fluid flow characteristics of a liquid between the lens and the wafer. The objectives of this feasibility study are to identify liquid candidates that meet the fluid mechanical requirements and to verify modeling tools for immersion lithography. The filling process was analyzed to simplify the problem and identify important fluid properties and system parameters. Two-dimensional computational fluid dynamics (CFD) models of the fluid between the lens and the wafer are developed and used to investigate a passive technique for filling this gap, in which a liquid is dispensed onto the wafer as a puddle, and then the wafer and liquid move under the lens. Numerical simulations include a parametric study of the key dimensionless groups influencing the filling process, and an investigation of the effects of the fluid/wafer and fluid/lens contact angles and wafer direction. The model results are compared with experimental measurements.

Modeling and experimental investigation of bubble entrapment for flow over topography during immersion lithography

In immersion lithography, the air gap that currently exists between the last lens element of the exposure system and the wafer is filled with a liquid that more closely matches the refractive index of the lens. There is a possibility that air bubbles, which represent a refractive index discontinuity, may be present in the liquid within the active exposure region and cause errors in imaging. One potential source of bubble generation is related to the flow of liquid over previously patterned features, or topography, during scanning or filling. This microscale entrainment mechanism is investigated experimentally and analyzed using computational fluid dynamics (CFD) modeling. The contact angle is a critical parameter that governs the behavior of the contact line and therefore the entrainment of air due to topography; the same topography on a hydrophobic surface is more likely to trap air than on a hydrophilic one. The contact angle can be a strong function of the flow velocity; a hydrophilic surface can exhibit hydrophobic behavior when the velocity of the free surface becomes large. Therefore, the contact angle was experimentally measured under static and dynamic conditions for a number of different surfaces, including resist-coated wafers. Finally, the flow of liquid across 500-nm-deep, straight-sidewall spaces of varying width was examined using both experimental visualization and CFD modeling. No air entrainment was observed or predicted over the velocity and contact angle conditions that are relevant to immersion lithography. The sharp-edged features studied here represent an extreme topography relative to the smoother features that are expected on a planarized wafer; therefore, it is not likely that the microscale entrainment of bubbles due to flow over wafer-level topography will be a serious problem in immersion lithography systems.

Preliminary microfluidic simulations for immersion lithography

The premise behind immersion lithography is to improve the resolution for optical lithography technology by increasing the index of refraction in the space between the final projection lens of an exposure system and the device wafer. This is accomplished through the insertion of a high index liquid in place of the low index air that currently fills the gap. The fluid management system must reliably fill the lens-wafer gap with liquid, maintain the fill under the lens throughout the entire wafer exposure process, and ensure that no bubbles are entrained during filling or scanning. This paper presents a preliminary analysis of the fluid flow characteristics of a liquid between the lens and the wafer in immersion lithography. The objective of this feasibility study was to identify liquid candidates that meet both optical and specific fluid mechanical requirements. The mechanics of the filling process was analyzed to simplify the problem and identify those fluid properties and system parameters that affect the process. Two-dimensional computational fluid dynamics (CFD) models of the fluid between the lens and the wafer were developed for simulating the process. The CFD simulations were used to investigate two methods of liquid deposition. In the first, a liquid is dispensed onto the wafer as a “puddle” and then the wafer and liquid move under the lens. This is referred to as passive filling. The second method involves the use of liquid jets in close proximity to the edge of the lens and is referred to as active filling. Numerical simulations of passive filling included a parametric study of the key dimensionless group influencing the filling process and an investigation of the effects of the fluid/wafer and fluid/lens contact angles and wafer direction. The model results are compared with experimental measurements. For active filling, preliminary simulation results characterized the influence of the jets on fluid flow.

Simulation of the coupled thermal optical effects for liquid immersion micro-/nano-lithography

Immersion lithography has been proposed as a method for improving optical microlithography resolution to 45 nm and below via the insertion of a high refractive index liquid between the final lens surface and the wafer. Because the liquid will act as a lens component during the imaging process, it must maintain a high, uniform optical quality. One potential source of optical degradation involves changes in the liquid’s index of refraction caused by changing temperatures during the exposure process. Two-dimensional computational fluid dynamics models from previous studies have investigated the thermal and fluid effects of the exposure process on the liquid temperature associated with a single die exposure. Here, the global heating of the wafer from multiple die exposures has been included to better represent the “worst case” liquid heating that will occur as an entire wafer is processed. The temperature distributions predicted by these simulations were used as the basis for rigorous optical models to predict effects on imaging. This paper presents the results for the fluid flow, thermal distribution, and imaging simulations. Both aligned and opposing flow directions were investigated for a range of inlet pressures that are consistent with either passive systems or active systems using filling jets.

Predicting microfluidic response during immersion lithography scanning

Immersion lithography has been proposed as a method of improving optical lithography resolution to 50 nm and below. The premise behind the concept is to increase the index of refraction in the space between the lens and wafer through the insertion of a high refractive index liquid in place of the low refractive index air that currently fills the gap. This paper presents three studies related to potential problem areas for immersion lithography. The first study investigates the entrainment of air as liquid flows over features in the wafer topology. Bubbles are undesirable because they introduce changes in the index of refraction in the optical path that can lead to imaging errors. The second investigation examines liquid heating due to the absorption of the incident energy by the fluid as well as heat transferred from the exposed wafer and viscous heating. This temperature elevation can lead to changes in the liquids index of refraction which may lead to optical degradation of the fluid. The final investigation examines the potentially significant normal and shear stresses induced on both the lens and wafer surface due to the increased viscosity and density of the liquid as compared with air. These mechanical loads may cause the lens to distort or shift in its mounting. This paper presents the results of the numerical thermal, flow, and structural simulations used to analyze these various critical issues.

Gas flow modeling for focused ion beam (FIB) repair processes

Focused Ion Beam (FIB) systems can be used to repair photomasks by accurately depositing and/or removing absorber material at the nanometer-scale. These repairs are enabled or enhanced by process gases delivered to the area of ion beam impact on the sample. To optimize gas delivery, three-dimensional computational fluid dynamics (CFD) models of selected gas delivery systems for FIB tools have been developed. The models were verified through an experiment in which water vapor was dispensed onto a cryogenically-cooled substrate. Water vapor hitting the sample surface immediately freezes. The height of the deposited ice on the sample surface is proportional to the product of the local gas flux and the exposure time. The gas flux predicted by the CFD model was found to be in good agreement with the experimental measurement. The CFD models were used to predict the mass flux of process gas and the pressure distribution at the sample surface for various gas delivery system designs. The mass flux and pressure relate directly to the amount of reactants that are available for the FIB repair processes. Parametric studies of key gas dispense system geometric parameters are presented and used to optimize the gas dispense system geometry.

Modeling and experimental investigation of bubble entrainment for flow over topography during immersion lithography

In immersion lithography, the air gap that currently exists between the last lens element of the exposure system and the wafer is filled with a liquid that more closely matches the refractive index of the lens. There is a possibility that air bubbles, which represent a refractive index discontinuity, may be present in the liquid within the active exposure region and cause errors in imaging. One potential source of bubble generation is related to the flow of liquid over previously patterned features, or topography, during scanning or filling. This microscale entrainment mechanism is investigated experimentally and analyzed using computational fluid dynamics (CFD) modeling. The contact angle is a critical parameter that governs the behavior of the contact line and therefore the entrainment of air due to topography; the same topography on a hydrophobic surface is more likely to trap air than on a hydrophilic one. The contact angle can be a strong function of the flow velocity; a hydrophilic surface can exhibit hydrophobic behavior when the velocity of the free surface becomes large. Therefore, the contact angle was experimentally measured under static and dynamic conditions for a number of different surfaces, including resist-coated wafers. Finally, the flow of liquid across 500-nm deep, straight-sidewall spaces of varying width was examined using both experimental visualization and CFD modeling. No air entrainment was observed or predicted over the velocity and contact angle conditions that are relevant to immersion lithography. The sharp-edged features studies here represent an extreme topography relative to the smoother features that are expected on a planarized wafer; therefore, it is not likely that the microscale entrainment of bubbles due to flow over wafer-level topography will be a serious problem in immersion lithography systems.

Thermomechanical modeling of the pin-chucked EUV reticle during exposure

Extreme ultraviolet (EUV) lithography has emerged as the forerunner in the selection process to become the industrys choice as the technology for next-generation lithography (NGL). An advantageous characteristic of the EUV reticle is that it is reflective, so it can be chucked across the entirety of its backside. This chucking will aid in meeting flatness requirements as well enhancing the heat removal ability of the chuck when compared to the mounts used for optical reticles. The EUV exposure process occurs in a vacuum environment, which precludes the use of vacuum chucks; therefore, electrostatic chucks are the favored choice. One concern is that particles may become lodged between the chuck and reticle, causing distortions to occur once the reticle is chucked flat. To counter this effect, electrostatic pin chucks have been proposed. However, because of the lower heat transfer ability of the pin chuck due to the interstitial gap, thermal issues may arise. A predominant pin-chuck configuration has yet to emerge, and there is no set of standards to facilitate new designs. The intent of this paper is to provide general guidelines to assist in preliminary designs. Parameters that were seen as potentially important factors in pin chuck performance were chosen and the results are presented.

Preliminary analysis of laser-pulse-induced pressure variation for immersion lithography

We describe an assessment of the pressure rise that may be induced by the short-duration but high-power pulses associated with the immersion lithography exposure process. A conservative model provides an upper bound on the pressure rise related to the expansion of the fluid near the wafer due to rapid heating. This rapid heating process is simulated as a constant heat flux from the substrate. The resulting temperature rise causes a change in pressure that propagates into the fluid at the speed of sound. The net change in the mass of the fluid contained within the pressure wavefront must be zero. This continuity requirement allows an estimate of the pressure rise and its penetration depth into the gap. For the nominal conditions associated with 193-nm immersion lithography, the model predicts that the pressure near the wafer surface may rise by as much as 7.3 kPa during the laser pulse. At the end of the laser pulse, this pressure rise will extend nominally 75 µm into the gap. Following the laser pulse, this pressure rise will rapidly decay as the pressure wavefront continues to propagate across the gap and eventually out of the under-lens region.

Localized resist heating due to electron-beam patterning during photomask fabrication

Localized resist heating effects that occur during electron beam (e-beam) patterning of optical masks can lead to critical dimension (CD) errors. These errors are due to unexpected resist development or underdevelopment, which is related to the temperature history of the resist. Eliminating this source of error requires a knowledge of the localized temperature history and how resist properties are impacted by elevated temperatures. Computer simulations of electron beam patterning of an optical mask can address the temperature history of the localized heating not possible through experimentation. Presented are the results of a study to determine the feasibility of using finite element (FE) analysis to predict these thermal effects. Two models were created to demonstrate its capabilities. The first shows that FE modeling is capable of high spatial resolution temperature profiles. The second demonstrates that FE models can be programmed to run complete patterning simulations.