3D lumped parameter model for lithographic simulations

Byers, Jeff M.; Smith, Mark D.; Mack, Chris A.

doi:10.1117/12.474490

Cited by 13 publications

(10 citation statements)

References 4 publications

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“…For example, one technique is to first calculate the acid distribution generated by the photo acid generator (PAG) according to the aerial image inside the photo resist, then to derive the CD from the diffused acid distribution image 3,4 . We report a technique to improve simulation accuracy by extending the simulation method.…”

Section: Methodsmentioning

confidence: 99%

Improvement of simulation accuracy using a non Gaussian kernel

et al. 2009

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We compared a simulator's predictions with the critical dimension (CD) value measured on the wafer. We used sub resolution assist features (SRAF) in the experiment to keep the focus margin, the minimum size of the mask was small and comparable with the absorber's thickness. Therefore, it seems that we need a rigorous model and a variety of parameters for high prediction accuracy.We investigated the prediction error and found its behavior was not complicated. The dependence of the prediction errors was related to the space until the next feature, but the relationship was not linear; rather, it went up and down periodically like a Bessel function. This fact gave us the idea that it might be possible to improve the simulation accuracy by using a special convolution kernel but not a Gaussian function.We used a complementary kernel and tried to find a suitable shape to match the prediction error.The convolution kernel consisted of a complex number in order to represent phase change and amplitude loss. The kernel was applied to the simulator's mask plain. The results showed a significant improvement in simulation accuracy and a reduction in the route mean square (RMS) of the CD fitting error for all features with or without SRAFs. We used this model for optical proximity correction (OPC) and verified its accuracy with a printed wafer image. The range of the final CD variation of 40 nm line on the wafer was 1.9 nm, and the model also showed good agreement with the experimental two-dimensional feature shape.

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Section: Methodsmentioning

confidence: 99%

Improvement of simulation accuracy using a non Gaussian kernel

et al. 2009

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“…The LPM has been extended to work for 3D structures [13]. A similar model was also published by another group [14].…”

Section: Introductionmentioning

confidence: 93%

Lumped parameter model for chemically amplified resists

2004

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Recently the Lumped Parameter Model (LPM) has been extended to three dimensions enabling fast calculations of full resist profiles. This resist model incorporates most of the lithographically significant physical phenomenon of resist systems. This model works well to match isolated and semi-isolated line resist systems. However, it is not very successful at matching contact hole or isolated trench resist systems. The reason for this mismatch can be traced to the influence of base quencher present in chemically amplified (CA) resists yet absent from the original LPM. The quencher effectively splits the aerial image into two complementary images. These two images (acid and base) simultaneously diffuse and react with each other. A single aerial image diffusion model cannot approximate the resulting coupled quenching-diffusion system.An improved LPM that incorporates quencher and its diffusion is presented. Successful implementation of this model requires solving the coupled quenching-diffusion system in a fast and accurate manner. Several solution methods are discussed. The agreement between the Lumped Parameter Model and a full CA resist model is greatly improved. This improvement will enable fast and more accurate calculations of resist affects on threedimensional imaging bias.

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“…The only parameter in equation (18) that is not found in Table 1 is P threshold . We choose this parameter as the value of P that gives a develop rate for equation (12) so that the entire resist thickness will clear during the develop time. We will use a resist thickness of 350nm, which leads to P threshold = 0.328.…”

Section: Relationships Between the Simplified And Full Resist Modelsmentioning

confidence: 99%

“…The bulk development rate is described by the enhanced Mack model [13,14], (12) where k enh is the rate constant for the develop rate enhancement mechanism, n is the enhancement reaction order, k inh is the rate constant for the develop rate inhibition mechanism, l is the enhancement reaction order, and R resin is the development rate of the polymer resin. It is also necessary to specify the duration of the develop process, or develop time, t dev .…”

Section: Governing Equations For Simplified and Full Resist Modelsmentioning

confidence: 99%

“…The "Simplified" group of models predicts the response of the photoresist directly from the aerial image. These models include the aerial image threshold resist model, the variable threshold resist model [8], and the Lumped Parameter Model [9][10][11][12]. The basic philosophy behind the Simplified models is that the model should describe the resist with a minimal number of parameters, and calculations with the model should be very fast.…”

Section: Introductionmentioning

confidence: 99%

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Comparison between the process windows calculated with full and simplified resist models

2002

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While numerical simulation is generally regarded as indispensable for wavefront engineering tasks such as OPC decoration and phase-shift mask design, full resist models are rarely used for this purpose. By "full resist models", we mean models derived from a physical, mechanistic description of the chemical response of the photoresist to exposure and the subsequent PEB and develop processes. More often, simplified models such as an aerial image threshold model or the Lumped Parameter Model (LPM) are used because these models are much faster and make optimization of optical extension technology more tractable. Simplified resist models represent a compromise between computational speed and simulation accuracy. The purpose of this study is to quantify the differences between the process windows calculated with simplified and full resist models.Our approach is first to fit the parameters in the simplified models to match results obtained with a full resist model, and then to compare the predictions of the simplified resist models with those obtained with the full model. We take two approaches to model tuning: mathematical derivation of relationships between the models, and least-squares fitting of FE matrix data for isolated and dense lines.

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3D lumped parameter model for lithographic simulations

Cited by 13 publications

References 4 publications

Improvement of simulation accuracy using a non Gaussian kernel

Improvement of simulation accuracy using a non Gaussian kernel

Lumped parameter model for chemically amplified resists

Comparison between the process windows calculated with full and simplified resist models

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