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title: SEM Charging Effect Model for Chromium/Quartz Photolithography Masks authors: Adam Seeger, Alessandro Duci, Horst Haussecker department/institution: Computational Nano-Vision Group, Intel Corporation address for correspondence: Adam Seeger, Intel Corporation, SC12-303, 2200 Mission College Blvd., Santa Clara, CA 95054; email: adam.a.seeger@intel.com key words: SEM, charging, simulation, image analysis, lithography masks PACS Code: 85.40.Hp, 68.37.Hk, 07.05.Tp, 29.85.+c, 42.30.Va

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Summary:

We propose a new model to describe the effect of specimen charging on SEM images. Charging effects cause errors when one attempts to infer the size or shape of a specimen from an image. The goal of this model is to enable image analysis algorithms for measurement, segmentation and 3D reconstruction that would otherwise fail on images containing charging effects. This model is applied to images of chromium/quartz photolithography masks and may also work in the more general case of isolated metal islands on a flat insulating substrate. It does not handle more general topographies, as in [1], [2] or specimens composed entirely of an insulator and it is a severe approximation to the actual physical charging process described in more detail by [3], but can be fit with quantitative accuracy to real SEM images. We only consider changes in intensity and do not model charging-induced distortion of image coordinates. Our approach has the advantage over existing methods of enabling fast prediction of charging effects so it may be more practical for image analysis applications.

Introduction:

Specimen charging is an important issue in electron microscopy because it causes distortion of image coordinates and contrast. The electric field around a specimen exerts a force on electrons and affects where incident electrons hit the specimen (distortion of image coordinates), and the detection of escaping electrons (distortion of intensity signal). Charging will result in errors when one attempts to infer the size or shape of a specimen from an image. Also, when an SEM is used for a controlled exposure in electron-beam lithography, charging can distort the region of exposure creating defects in the final product.

Given a specimen composed of an insulator or electrically isolated conductor, the difference between the number of incident electrons and the number of backscattered electrons (including secondary electrons) results in either a positive or negative charge in the specimen. This fact allows the sign of the charge to be determined from models of secondary and backscattered electron emission (Monte Carlo simulation or empirical formulas). In the case of an insulator, a more complete picture is provided by the dynamic double layer model described in [Melchinger95]. In this model, the numerous secondary electrons which escape very close to the surface of the specimen result in a positively charged layer about 5 nm thick at the surface. Some of the primary electrons become trapped deep in the specimen forming a negatively charged layer at a depth approximately equal to the maximum range of electrons in the material. In between these two layers, there is an electron beam-induced conduction (EBIC) or radiation induced conduction (RIC) layer that allows charge to conduct mainly in a vertical direction. The combination of secondary electrons escaping near the surface and a relaxation current that transports electrons from the lower layer up to the surface helps to explain time dependent charging behavior [Melchinger95]. Because the induced conduction lasts only for a short time after the beam is scanned to a new location, this only allows charge to migrate within a small volume at each beam position.

The total electron yield (ratio between total emitted and incident electrons) is a function of the incident energy. Typically there are two crossover points at energies E1 and E2 where the electron yield is 1. This is illustrated in Figure 1.

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beam energy

1.0

E1 E2

tota

l el

ectr

on

yie

ld

Figure 1: Qualitative graph of total electron yield as a function of energy showing the two crossover points at energy E1 and E2.

The crossover points are significant because when the SEM accelerating voltage is set to the crossover energy where the numbers of incident and emitted electrons are equal, no charging will occur. Because of the dependence on topography and material, for many specimens it is impossible to find a single accelerating voltage that makes the electron yield 1 at all points. It is very difficult to measure the E1 crossover point because it is unstable and Monte Carlo simulations tend to be very inaccurate in this energy regime but there is relatively reliable data for the E2 crossover point. The experimental data for quartz and chrome are shown in Figure 2. This data is for a flat surface and the yield will vary significantly depending on the topography. The plots in Figure 2 show that the E2 crossover point occurs at 2keV for Chromium and 3keV for SiO2.

Chromium

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Figure 2: Experimental data for total electron yield from a flat surface [Joy01]. When the electron emission yield is 1.0 the injected and emitted electrons are equal (around 2 keV for Chromium and 3 keV for SiO2).

In our experiments the specimen is composed of nearly flat chrome islands on top of a nearly flat SiO2 substrate. The main topographic feature is the step edge at the boundary of the chrome regions. Images are acquired with a 1keV accelerating voltage. At this voltage, both the chrome and SiO2 will become charged positively. As the surfaces become more positively charged, the potential difference between the electron gun and specimen will tend to increase and electrons will strike the surface with more energy. Allowing the beam to sit

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on a chrome region, the energy will reach a stable equilibrium at the E2 energy of 2keV and on a SiO2 region, the energy will reach a stable equilibrium of 3keV (see Figure 3).

SiO2

-1kV

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Initial state

(A)

Cr island+ + + + + + + + + + + + +

+ + + + + + + + + + + +

1kV2kV 2kV

SiO2

-1kV

Charged state

(B)

A

B

Figure 3: For an initial accelerating voltage of 1kV, we expect the chrome to become positively charged by a net loss of secondary electrons until its potential is approximately +2kV relative to the electron gun. The quartz should similarly reach a potential that is approximately +3kV relative to the electron gun.

Model Description:

When a chrome region is electrically isolated, there is a limited pool of charge that can be pulled out before the region reaches the equilibrium voltage and we consider the chrome charging in this case as analogous to the charging of a capacitor. Our model describes the charging of the chrome using a resistor-capacitor circuit analogy. We associate with every chrome region a voltage that describes the charging state of the surface. These voltages change with time depending on the position of the beam. When the beam is incident on a chrome region, that region will become more positively charged tending towards an equilibrium positive voltage relative to ground and all other regions will gradually reduce towards the ground voltage as they capture backscattered and secondary electrons. When the beam is on the quartz all the chrome regions will also recapture secondary electrons and their voltages will reduce gradually down to the ground voltage (see Figure 4).

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Vground

Cr island

SiO2

Vchrome

Vgun

Cr island

SiO2

Vchrome

Vgun

charging of chrome discharging of chrome

Figure 4: Secondary electrons emitted from the quartz and scattered by the specimen chamber may help to restore the chrome islands back to a ground potential. Vchrome

E2+Vgun

time

Vground

dischargingcharging

Figure 5: We expect an asymptotic behavior of the chrome voltage as a function of time when the beam hits the chrome (charging) and when it hits the quartz (discharging).

The voltage of the ith chrome region is represented by iV . The ith chrome region charges (discharges) with a time constant i

cµ ( idµ ). The change in voltage when the beam is on the

region ( )R t is described by

( )( )( ) ( )( )( ) ( )

if ,

if ;

i iic c

i id d

V V t R t idVt

dt V V t R t i

µ

µ

� − =�= �− ≠��

where Vc is the maximum possible voltage for the chrome and Vd is the minimum possible voltage for the chrome. We integrate this formula discretely using the pixel dwell time as a time step to compute the voltages for each chrome region as a function of time.

We approximate the observed SEM intensity I(t) for a chrome region i with a linear function of the voltage iV . The intensity for the quartz is instead described by a linear function of the maximum voltage among all iV .

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( ) ( ) ( )( )

( )

1...

if 0,max ( ) if 0;

R tm m

is si N

g V t d R tI t

g V t d R t=

� + >�= � + =��

where , , ,m m s sg d g d are constants such that 0, 0m sg g< < . These functions approximately describe the effect of the chrome voltage on the recapturing of electrons which reduces the observed signal. The function determining intensity on the quartz was inspired by the idea that secondary electrons leaving the quartz would tend to be most influenced by the chrome region that is maximally charged but this choice was somewhat arbitrary and may ignore important effects of geometry.

For the purpose of predicting image contrast, the parameters Vc and Vd are redundant because they introduce a scale and offset that can just as well be determined by the parameters , ,m m sg d g and sd . Therefore, without loss of generality we let Vc =1 and Vd =0.

This model predicts that the image intensity will converge in an approximate sense to an intensity that depends on the fraction of chrome within a scanline of the image. In general, the fraction of chrome will vary depending on the specimen shape but this behavior is shown using synthetic examples where the fraction of chrome is set to different constant values in Figure 6.

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Figure 6: Voltage of the chrome, and the related signal modulation converge to different values depending on the fraction of chrome in a scanline.

Synthetic Examples:

The input to a 2D simulation is a binary image of a specimen where 1 represents chrome and 0 represents quartz and a description of the order in which the beam visits the pixels in the image. We perform a connected components analysis to determine the number of distinct chrome regions. Figure 7 shows an example input image and the resulting simulated intensity

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using arbitrary parameters values ( , , ,m m s sg d g d ) = (-1.6, 5, -1.34, 4) and ( cµ , dµ )=(0.0009, 0.0003) and a raster scan pattern.

a b

Figure 7: The charging simulation shows a characteristic banding pattern related to the amount of

chrome in a scanline.

Figure 8 shows an example with two separate chrome islands. In this case the charging state of the specimen is described by two voltage values. In Figure 9 we show an example of how our simulation predicts a change in the charging effect when a small connection is introduced between two separated chrome regions. This suggests that even a qualitative understanding of the charging effects may be useful in detecting the presence of a conducting path between two parts of a surface.

a b

Figure 8: Multiple chrome islands require modeling a different voltage for each island.

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33.23.43.63.8

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connected

separate

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connected

separate

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Figure 9: The charging model predicts a change in appearance between separated and connected chrome regions. In comparison with actual images, this could be useful in determining electrical connectivity for

a real specimen.

Model Fitting Algorithm:

To fit our model to an experimental SEM image we require a segmentation of the scanned region into quartz and chrome regions. After alignment of this segmentation to the SEM data, we fit the parameters of our model using a gradient descent optimization. A dataflow diagram for the model fitting and simulation along with example images is shown in Figure 10.

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optimization algorithm

, , , , ,c d m m s sg d g dµ µmodelCAD or AFM

SEM

simulation

Figure 10: Given an actual SEM image and the 2D shape of the specimen, we estimate optimal charging parameters. Results:

We tested the model by fitting it to several experimental SEM images. We compared the output of our model to a piecewise constant model and we found that our model was significantly more accurate. Two examples of the fitting results and comparison with a piecewise constant intensity model are shown in Figure 11 and Figure 12.

data simulation

piecewiseconstant fitfor comparison

absolute difference (x2)

Figure 11: Though our simulation contains some residual systematic error, it is significantly more accurate than an optimal piecewise constant fit to the image.

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data simulation

piecewiseconstant fitfor comparison

absolute difference (x2)

Figure 12: Second example comparing residual error in the model with that for a piecewise constant fit.

Acknowledgements: We would like to thank Saghir Munir at Intel Mask Operations for providing us with

combination AFM/SEM data that inspired this approach and allowed us to test it.

References: [1] Davidson, M. and N. T. Sullivan (1997). “An Investigation of the Effects of Charging in SEM based CD Metrology.” SPIE 3050: 226-242.

[2] Ko, Y.-U., S.-W. Kim, et al. (1998). “Monte Carlo Simulation of Charging Effects on Linewidth Metrology.” Scanning 20: 447-455.

[3] Melchinger, A. and S. Hofmann (1995). “Dynamic double layer model: Description of time dependent charging phenomena in insulators under electron beam irradiation.” J. Appl. Phys. 78(10): 6224-6232.