76401s

The impact of resist model on mask 3D simulation accuracy beyond

40nm node memory patterns

Kao-Tun Chena, Shin-Shing Yeha, Ya-Hsuan Hsieha, Jun-Cheng Nelson Lai a, Stewart A. Robertsonb, John J. Biafore b, Sanjay Kapasi b , Arthur Lin b

aPowerchip Semiconductor Corp., No. 12 Li-Hsin RD, Hsinchu, Taiwan

bKLA-Tencor Corp., 8834 N. Capitol of Texas Highway, Austin, TX 78759, USA

ABSTRACT Beyond 40nm lithography node, mask topograpy is important in litho process. The rigorous EMF simulation should

be applied but cost huge time. In this work, we compared experiment data with aerial images of thin and thick mask

models to find patterns which are sensitive to mask topological effects and need rigorous EMF simulations. Furthur more,

full physical and simplified lumped (LPM) resist models were calibrated for both 2D and 3D mask models. The accuracy

of CD prediction and run-time are listed to gauge the most efficient simulation. Although a full physical resist model

mimics the behavior of a resist material with rigor, the required iterative calculations can result in an excessive execution

time penalty, even when simulating a simple pattern. Simplified resist models provide a compromise between

computational speed and accuracy.

The most efficient simulation approach (i.e. accurate prediction of wafer results with minimum execution time) will

have an important position in mask 3D simulation.

Keywords: EMF, 3D mask, Mask topography, Lumped parameter resist model, Full physical calibrated resist

model

1. INTRODUCTION

In ArF immersion process where mask pattern pitch (3X and 2X nodes) is many times smaller than exposure

wavelength where strong RET and high NA are required. The light diffraction can not be correctly predicted by the

Kirchhoff approximation mask model (or thin mask model) – as most frequently used in many imaging simulations today.

Precise and accurate forecasting of the wafer pattern requires rigorous electromagnetic field analysis (EMF or 3D mask

mode) which fully considered mask topography effects [1]. Many studies have indicated significant differences in

patterning prediction between Kirchhoff approximations and 3D mask models[2][3][4].

Besides the difference of aerial image, ArF resist kinetics also play an important role which impacts the real image

Optical Microlithography XXIII, edited by Mircea V. Dusa, Will Conley, Proc. of SPIE Vol. 7640, 76401S · © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.846010

Proc. of SPIE Vol. 7640 76401S-1

Downloaded from SPIE Digital Library on 04 Mar 2010 to 192.146.1.254. Terms of Use: http://spiedl.org/terms

obtained on the wafer. However, 3D mask model is well-known for longer execution time and also consumes large

computing resources [4], even for small mask areas of several microns. In product development stage, it’s much

predicted accuracy and time-concerned to cost and market. There is another choice, simplified resist model, which is

generally called LPM model (Lumped-Parameters Model) and may provide a compromise between computational speed

and accuracy.

In this paper, we quantify the CD bias between experiments and aerial image simulations across a range of 40nm

node flash memory patterns. The difference will be used to gauge the importance of using rigorous EMF model. We also

calibrate both the full physical and simplified resist models for 2D and 3D mask simulations. The comparison of CD

accuracy and running time will be used to gauge the importance of using any resist model.

2. 2D & 3D MASK AERIAL IMAGE SIMULATION First, we focus on some well-known typical features of flash product beyond 40nm node to figure out what kind of

feature is sensitive to mask topological effects. For 1D patterns, select-gate features are studied, and for 2D patterns,

landing pad and cut line features are studied (Fig. 1).

SG 1 2 3 4 5 6 7 8 9 10 11 12 SG

WL area

SG 1 2 3 4 5 6 7 8 9 10 11 12 SG

WL area

L 1

L 2

L 3

L 1

L 2

L 3

Figure 1 : Typical features of memory, (a)1D features : Select-gate area, (b)2D features : landing pad area, (c) 2D features : cut line.

In first part, we observe pure optical simulation accuracy of select-gate area design 1. WL1 to WL12 are chosen to

monitor the accuracy because these features are close to SG features which may suffer much proximity effect caused by

strong variation of pattern deployment. △CD is defined with ADI CD difference between simulation and experimental

data.

In fig. 2(a), pure optical aerial image simulation is done with Kirchhoff approximation (2D mask) and EMF mask

(3D mask) compared to experimental data with commercial PR A. It’s obviously that ADI CD bias of EMF mask is much

better than of Kirchhoff approximation, especially WL1 to WL6 CD bias which are closer to SG feature with much

optical proximity effect suffered. The maximum. ADI CD bias is only about 1.2nm of pure optical behavior of EMF

mask.

However, it is quite process related. In fig. 2(b), experimental ADI CDs of two different PR are compared to

simulation results of EMF mask. The maximum. ADI CD bias is increased to 5.6nm with commercial PR B. It implies

that litho process change may induce worse accuracy by different PR parameters. Only aerial image with EMF mask

(a) (b) (c)



simulation is surely enough. Different calibrated PR models of commercial PR A will be discussed in following sections.

TOK commercial PR A

0123456789

10

1 2 3 4 5 6 7 8 9 10 11 12

△C

D (S

im. C

D -

waf

er C

D) (

nm)

Kirchhoff (2D mask)EMF (3D mask)

0123456789

10

1 2 3 4 5 6 7 8 9 10 11 12

△C

D (S

im. C

D -

waf

er C

D) (

nm)

commercial PR Acommercial PR B

Figure 2: △CD of aerial image simulation result benchmark with experimental data of SG features : (a)PR A ADI CD errors with 2D

mask Kirchhoff approximation and with 3D EMF mask, (b) PR A and PR B CD errors with 3D EMF mask.

In Fig. 3, L1, L2, and L3 of landing pad features through different focus with 2D mask Kirchhoff approximation and

with 3D EMF mask are observed. In Fig. 3(a), it’s also obvious that with 3D EMF mask the simulation compensation is

better than with 2D Kirchhoff approximation, and the pure optical model simulation difference of two mask approaches

is shown in Fig. 3(b). The difference range is from 1.4nm to 2.6nm, which is compensated by 3D EMF mask simulation.

Compared to select-gate features, which the simulation difference of 2D and 3D mask is large as 8nm in WL1, the

simulation difference of landing pad seems acceptable due to dense structure. Though it indeed a good way to adopt 3D

EMF mask for landing pad feature to get more accuracy, it also takes a huge time difference to gain.

Landing pad ADI CD with simulation bias

0

1

2

3

4

5

6

2D L1 2D L2 2D L3 3D L1 3D L2 3D L3

△C

D (S

im. C

D -

waf

er C

D) (

nm)

Defocus -0.03umBest FocusDefocus +0.03um

2D mask & 3D mask simulation bias

0.0

0.5

1.0

1.5

2.0

2.5

3.0

L1 L2 L3

Sim

ulat

ion

diffe

renc

e (3

D E

MF

- 2D

Kirc

hhof

f) (n

m)

Defocus -0.06umDefocus -0.03umBest FocusDefocus +0.03umDefocus +0.06um

Figure 3: △CD of aerial image simulation result benchmark with experimental data of landing pad features : (a)PR A ADI CD errors

with 2D mask Kirchhoff approximation and with 3D EMF mask through focus, (b) pure optical model simulation difference of 2D

mask Kirchhoff approximation and 3D EMF mask through focus

(a) (b)

2D Kirchhoff approximation

3D EMF mask

(a) (b)



In Fig. 4, L1, L2, and L3 of cut-line features through different focus with 2D mask Kirchhoff approximation and with 3D

EMF mask are observed. In Fig. 4(a), There is no obvious difference between with 3D EMF mask and 2D Kirchhoff

approximation, and the pure optical model simulation difference of two mask approaches is shown in Fig. 4(b). The

difference range is from 0.4nm to 2.4nm, which is compensated by 3D EMF mask simulation. Compared to select-gate

features, which the simulation difference of 2D and 3D mask is large as 8nm in WL1, the simulation difference of

cut-line feature seems acceptable due to dense structure.

Cut line ADI CD with simulation bias

0123456789

10

2D L1 2D L2 2D L3 3D L1 3D L2 3D L3

△C

D (S

im. C

D -

waf

er C

D) (

nm)


Figure 4: △CD of aerial image simulation result benchmark with experimental data of cut-line features : (a)PR A ADI CD errors with

2D mask Kirchhoff approximation and with 3D EMF mask through focus, (b) pure optical model simulation difference of 2D mask

Kirchhoff approximation and 3D EMF mask through focus

3. DATA COLLECTION AND PR CALIBRATION

3.1 Evaluating goodness of fit with the root mean square error

Model calibration is performed by minimizing the RMS error between simulation and actual data, yielding a set of

kinetic parameters for each modeled resist. The goodness of model fit is estimated by the standard deviation of the error

between the data and predictions [5]:

RMSE is the weighted root mean square of the error associated with the second moment about the mean. The

weighting function wi is calculated from the statistics of repeat trials.

3.2 Feature selection and data collection

The physically-rigorous resist model and LPM model are calibrated using CDSEM S9380 metrology measurements

from wafers processed above. The dataset collected for calibration consisted of 5 focus exposure matrices, including

2D Kirchhoff approximation

3D EMF mask

(a) (b)

Cut-line 2D mask & 3D mask simulation bias

0.0

0.5

1.0

1.5

2.0

2.5

3.0

L1 L2 L3

Sim

ulat

ion

diffe

renc

e (3

D EM

F - 2

DKi

rchh

off)

(nm

)




140nm pitch with line width 70nm and space width 70nm; 180nm pitch with line width 80nm; and 600nm pitch with line

width 100nm and space 100nm. The line sizes on the mask were 67 nm, 70 nm and 73nm. Each F-E matrix was

measured on 4 duplicate wafers, so that an estimation of process variability could be made.

The process conditions for the calibration data:

▪ Wavelength: 193 nm

▪ Topcoat: 30nm OC-301

▪ Resist: 110 nm commercial ArF PR A

▪ Process: 110°/60s PRE, 110°/60s PEB, 72s development

▪ BARC: NISSAN NCA41074

▪ Mask: 6% attenuated PSM

▪ Exposure: 1.30 NA, Annular, 0.9/0.6

3.3 Calibration of rigorous resist model and LPM model

In this work, we calibrated four models by accounting for two different mask characterization – one with 2D mask

(Kirchhoff approximation) and one with 3D EMF mask (FDTD – Finite Difference Time Domain). These models are

calibrated by minimizing the RMS error. After calibration, the quality of the match can be evaluated by inspection of the

RMS error.

Total RMS (nm) Max. RMS (nm) Max. RMS features

Rigorous Resist Model (Kirchhoff ) 2.2 3.8 100nm space / 600nm pitch

LPM Model (Kirchhoff ) 2.2 3.8 100nm space / 600nm pitch

Rigorous Resist Model (EMF mask) 2.6 4.9 80nm line / 180nm pitch

LPM Model (EMF mask) 2.6 5.4 100nm space / 600nm pitch

Table 1: Calibration fitting result : Summary table of total RMS and Max. RMS features.

Table 1 summarizes the comparison amongst four different models and Table 2 summarizes calibration results for

all the features and shows calibration fit results for all the features used for calibration. Fig. 5 shows max. RMS error

matching features of each model with experimental and simulation data. With calibrated PR qualification, cross-section

images of experiment and simulation show good compatible result in fig. 6. Simulated PR profiles of rigorous resist

models show good matching to empirical wafer profiles, especially profiles with 3D EMF mask get compatible top

rounding and PR footing. With LPM model, there is much difference from empirical wafer profiles, which means

insufficient physical parameters to describe the detail reactions and development phenomenon during wafer process. In



this study, we focused on ADI CD matching, which is mainly determined by top view CDSEM image, and the

longitudinal PR profile is not our first concern. LPM model with simplified physical parameters can be accepted.

Table 2 : Calibration fitting result among test features, rigorous resist model with Kirchhoff approximation(a), LPM model with

Kirchhoff approximation(b), rigorous resist model with EMF mask(c), LPM model with EMF mask(d).

(a) (b)

(c) (d)

(a) (b)

(c) (d)



Figure 5 : Max. RMS error matching features of each model with experimental(points) and simulation(lines) data. Rigorous resist

model (Kirchhoff) with 100nm space / 600nm pitch(a), LPM model (Kirchhoff) with 100nm space / 600nm pitch (b), rigorous

resist model (EMF mask) with 80nm space / 180nm pitch (c), LPM model (EMF mask) with 100nm space / 600nm pitch (d).

Figure 6 : Comparison of experimental cross-section image and simulation cross-section image for different test features.

Experimental wafer cross-section profile(a), rigorous resist model with Kirchhoff approximation(b), LPM model with Kirchhoff

approximation(c), rigorous resist model with EMF mask(d), LPM model with EMF mask(e).

4. COMPARISON WITH REAL DEVICE EMPIRICAL RESULT

4.1 2D Kirchhoff approximation mask with PR full physical model and lumped model simulation

We generate full physical model and simplified lumped model to compensate the model accuracy.

Fig. 7 shows 42nm to 100nm proximity features fitting results of LPM model and full physical model. For LPM

model, RMS is 4.61nm, and for FPM model, RMS is 3.42nm. FPM shows better fitting result than LPM does.

(a) (b) (c) (d) (e)

(a) (b)

RMS = 4.61nm with LPM model RMS = 3.42nm with FPM model

70L / 140P

100L / 600P



Figure 7 : Proximity features fitting result by 2D Kirchhoff approximation simulation (a) LPM model (b) Full physical model

In fig. 8, we still choose select-gate design 1&2 WL1 to WL12 to monitor model accuracy. In design 1, the total △CD is well compensated by full physical PR model, which including more details of PR parameters to illustrate litho

behavior. Especially △CDs of WL1 to WL6, which are closer to SG feature with much optical proximity effect suffered,

are also well compensated.

By simplified LPM model, in design1, even the most critical pattern WL1 is well compensated, but △CDs of WL2

to WL9 become worse than full physical model. From Table 1 shown, Kirchhoff LPM model is well generated with total

RMS only 2.2nm, which is same as full physical model dose. But in-sufficient PR descriptions of parameters will cause

wrong result with total ADI CD fitting, even in some critical patterns the fitting result is good. In design 2, full physical

model is also better compensated than simplified LPM model, but the tendency is not so obvious as design 1 showed. It

may be caused by measurement error or more test patterns and parameters need to be considered during PR calibration

progress.

Kirchhoff approximation (2D mask) simulation ADI CD bias

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12

△C

D (S

im. C

D -

waf

er C

D) (

nm)

LPM modelFull physical model

Kirchhoff approximation (2D mask) simulation ADI CD bias

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12

△C

D (S

im. C

D -

waf

er C

D) (

nm)

LPM model

Full physical model

Figure 8 : △CD of Kirchhoff approximation simulation result benchmark with experimental data of SG features (LPM model and full

physical model) : (a) select-gate design 1, (b)select-gate design 2.

4.2 3D EMF mask with PR full physical model and lumped model simulation

In this section, in order to verify 3D EMF mask distribution to simulation accuracy, we also generate full physical

model and simplified lumped model with 3D EMF mask calibration. Select-gate design 2 is applied to verify the

difference between these two models.

Fig. 9 shows 42nm to 100nm proximity features fitting results of LPM model and full physical model. For LPM

model, RMS is 4.92nm, and for FPM model, RMS is 4.17nm. FPM shows better fitting result than LPM does.

(a) select-gate design 1 (b) select-gate design 2



Figure 9 : Proximity features fitting result by 3D EMF mask simulation (a) LPM model (b) Full physical model

In Fig. 10(a), it shows that with full physical model gets better compensation than with simplified LPM model. But

notice that both are time consuming compared to 2D Kirchhoff approximation simulation. In device development early

stage, accuracy is the most important, but also time to market efficiency is needed to be concerned. Depends on user’s

host equipment, Either 3D EMF mask with LPM model or with full physical model is chosen to provide a better

compensation in simulation accuracy and running time.

In Fig. 10(b), full physical models with 2D Kirchhoff approximation and 3D EMF mask are compared. Result shows

better fitting result with 3D EMF mask, but also it’s time-consuming both in calibration and simulation stage.

EMF mask (3D FDTD) simulation ADI CD bias

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12

△C

D (S

im. C

D -

waf

er C

D) (

nm)

LPM model

Full physical model

Full physical model simulation ADI CD bias

0

1

2

3

4

5

6

7

8

1 2 3 4 5 6 7 8 9 10 11 12

△C

D (S

im. C

D -

waf

er C

D) (

nm)

Kirchhoff (2D mask)

EMF (3D mask)

Figure 10 : (a) △CD of 3D EMF mask simulation result benchmark with experimental data of SG features (LPM model and full

physical model), (b) △CD of full physical model simulation result benchmark with experimental data of SG features (2D Kirchhoff

approximation and 3D EMF mask).

4.3 Time consuming benchmark

In Table 3, we compute the running time of single resist simulation of 2D Kirchhoff approximation and 3D EMF

mask on 1D and 2D patterns. Even for a standard line-end pattern, single aerial image (AI) simulation of 3D EMF mask

(a) (b)

RMS = 4.92nm with LPM model RMS = 4.17nm with FPM model



model costs half hour which is tens of run-time of 2D Kirchhoff mask model.

In 2D Kirchhoff approximation model, LPM model saves 80%~90% run-time compared to FPM model; In 3D EMF

mask model, LPM model saves 6%~10% run-time compared to FPM model. Combining with the CD accuracy, LPM can

be a candidate if 3D EMF mask model is needed.

2D_AI 2D_LPM 2D_FPM 3D_AI 3D_LPM 3D_FPM

Dense L/S (1D) 2 s 2 s 2 s 12 s 12 s 12 s Select-gate (1D) 4 s 6 s 16s 92s 96s 106 s

Dense Lineend (2D) 16s 56s 6m46s 38m8s 38m34s 44m56s Landing pad (2D) 30s 1m58s 4m26s >2hours >2hours >2hours

Table 3: Running time summary table of different models with 1D and 2D test patterns

5. CONCLUSION Three typical features of flash memory are examined by 2D Kirchhoff approximation and 3D EMF mask optical

models. Select-gate patterns is the most sensitive to mask topological effects due to it’s various pitch environment.

Four different PR models with LPM and full physical by Kirchhoff approximation and 3D EMF mask calibrated are

observed. All these models are calibrated well by test features and total RMS is from 2.2nm to 2.6nm.

3D EMF mask application significantly improves the simulation accuracy of select-gate pattern beyond 40nm,

especially critical patterns which suffer much optical proximity effect. For LPM model and full physical model

application, definitely full physical model provides more accurate simulation result than LPM model due to more

parameters are involved during calibration progress, but full physical model is time-consuming both in calibration and

simulation stage. More precise parameters in LPM model calibration will provide compatible simulation result to full

physical model, and it would be a compensation solution between simulation accuracy and simulation time.

ACKNOWLEDGEMENT The authors would like to thanks KLA-Tencor lithography teams for their contributions to this paper. PROLITH is

a trademark of KLA-Tencor.

REFERENCES 1. A. Erdmann, ”Mask modeling in the low k1 and ultrahigh NA regime: phase and polarization effects” Proc. of SPIE

Vol. 5835, pp.69-81(2005).

2. M. Saied, F. Foussadier, et. al., “Three-dimensional mask effects and source polarization impact on OPC model



accuracy and process window” Proc. of SPIE Vol. 6520 (2007).

3. K. Sato, M. Itoh, T. Sato, “Mask 3D effect on 45-nm imaging using attenuated PSM” Proc. of SPIE Vol. 6520

(2007).

4. Peter D. Bisschop, T. Muelders, et. al., “Impact of mask three-dimensional effects on resist-model calibration”, JM3

letters Vol. 8(3), Jul.-Sep. 2009.

5. P. Bevington, et. al., “Data Reduction and Error Analysis for the Physical Sciences” McGraw-Hill, 2003.



76401s

Documents