A novel Monte Carlo simulation code for linewidth

A novel Monte Carlo simulation code for linewidth measurement in critical dimension scanning electron microscopy Alexander Koschik a, Mauro Ciappa a, Stephan Holzer a, Maurizio Daporb, and Wolfgang Fichtner a a

b

Integrated Systems Laboratory, ETH Zurich, Gloriastrasse 35, CH-8092 Zurich Centro Materiali e Microsistemi, FBK-IRST, I-38123, Povo, Trento, Italy and Università di Trento, Dipartimento di Ingegneria dei Materiali e Tecnologie Industriali, Italy

ABSTRACT Besides the use of the most sophisticated equipment, accurate nanometrology for the most advanced CMOS processes requires that the physics of image formation in scanning electron microscopy (SEM) being modeled to extract critical dimensions. In this paper, a novel Monte Carlo simulation code based on the energy straggling principle is presented, which includes original physical models for electron scattering, the use of a standard Monte Carlo code for tracking and scoring, and the coupling with a numerical device simulator to calculate charging effects. Keywords: critical dimension (CD) metrology, scanning electron microscopy (SEM), CD-SEM, Monte Carlo (MC) modeling, simulation

1.

INTRODUCTION

With the most advanced CMOS technologies, critical dimensions (CD) measurements with sub-nanometer uncertainty must be performed during the manufacturing process to provide a metrics and to avoid yield loss. As an example, this is the case of the linewidth measurement of photoresist lines (e.g. PMMA) that are largely used in optical and electron beam lithography for device integration down to the sub-16nm scale. Besides the use of the most advanced equipment, accurate nanometrology requires that the physics of image formation in scanning electron microscopy (SEM) being modeled to extract the relevant quantitative information. Modern CD-SEM mainly operate at very low primary energies (down to 200 eV). This implies the use of quite complicated physical models defined by a variety of parameters that can become also time-dependent due to unwanted effects as electrostatic charging of the sample. Therefore, up to date Monte Carlo (MC) simulation of the generation and transport of secondary electrons (SE) in materials is still the most straightforward approach to the solution. A novel MC simulation code is proposed that is based on the energy straggling principle. Original physical models have been developed for the interactions. Depending on the sample material, generation and transport of SE are calculated according to consistent models for elastic, electron-electron, plasmon, and phonon scattering, as well as for polaron trapping. Special attention is paid to the dielectrics, whose models have been recently revised and accurately recalibrated for very low primary electron (PE) energies [1]. All models are based on well-defined physical measurables to facilitate the generation of complex 3D multilayered structures. The MC scheme has been mutated from a previous work [2] and takes into account quantum-mechanical barrier scattering at the different material interfaces. Thanks to its recursive structure, the scheme easily keeps track of the hundreds of SE that are generated per PE in a typical shower. In the developed MC code, the interactions of the PE and of the related SE showers are simulated down to electron energies of 0.1 eV. The electron tracking and the physics sections have been completely decoupled. The 3D sample geometry definition, single electron tracking, and quantification of the emitted SE are carried out by the standard MC code PENELOPE [3]. In converse, the scattering physics has been implemented by original, separated library functions for minimum interference of both code parts. Besides the parallelizing capabilities of the code, particular attention has been paid to the implementation of a fully discrete interaction scheme based on the straggling principle, as well as of efficient tracking and ray tracing functions of SE in 3D geometries with arbitrary shape and in the presence of electromagnetic fields. The transport equations of the electron in the materials and in the vacuum are solved under consideration of the local electrostatic field to take into consideration a possible deflection of the primary beam and SE

Scanning Microscopy 2010, edited by Michael T. Postek, Dale E. Newbury, S. Frank Platek, David C. Joy, Proc. of SPIE Vol. 7729, 77290X · © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.853804

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as well as the effects of the induced accumulation/inversion regions in the semiconductor substrate. At present, a static charge distribution in the dielectric has been assumed. The global Poisson equation is solved for the given geometry and boundary conditions (e.g. extraction field) by the external tool SENTAURUS DEVICE [5] that takes into account a rigorous approach for semiconductor materials. The MC code provides the charge distribution to SENTAURUS DEVICE, which returns to MC code the local electric field for the calculation of the electron trajectories. In the case of a calculation under consideration of the electrostatics, the interface/surface potentials as provided by the internal physical models are switched off and replaced by the local potential delivered by the device simulator, in order to obtain a systematic treatment. Section 2 of the paper will introduce the physical models implemented in the developed code with special attention to dielectric materials. Section 3 will focus on the structure of the developed code. Finally, Section 4 will present five applications of the novel code to cases from the literature for comparison purposes.

2.

PHYSICS MODELS

The proposed code includes physical models for the main scattering mechanisms governing the transport of electrons in silicon [2], silicon dioxide, and PMMA in an energy domain ranging from the energy of the primary electron beam down to 0.1 eV. Special attention has been paid to the physical models for dielectric materials (PMMA, SiO2) that are original and refers to the results presented in a recent publication [1]. Scattering models for dielectrics takes into account elastic scattering, electron-electron interactions, scattering with phonons, and trapping by polarons. The proposed code also includes quantum-mechanical modeling of barrier scattering occurring either at the material interfaces, or at the sample surface [2]. This option is disabled, in the case of simulations taking into account the electrostatic field, since in this case, the local potential is directly calculated by an auxiliary device simulator. All these models are used in conjunction with a dedicated Monte Carlo simulation scheme, which is also described in very detail in [1] and that accounts for the entire cascade of secondary electrons.

3.

SIMULATION MODEL

3.1 Objective & Implementation Strategy Typical structures of interest are dielectric lines on silicon substrates with trapezoidal cross section (see Figure 1), while the critical dimensions under investigation are the bottom and/or top line width, as well of the slope of the rising and falling edges.

e

–

PMMA CD

Si

Figure 1. Dielectric material (e.g. PMMA) with trapezoidal cross section on silicon substrate. Linescans are acquired perpendicularly to the structures. A typical linescan consists of 1024 pixels both with and without oversampling.

Linescans are generated by scanning the electron beam with circular cross-section perpendicularly to the dielectric lines. For sake of simplicity, the emitted secondary electrons are detected over a 2π solid angle (see Figure 1) and if not specified, no extraction field is applied. A typical linescan is carried out in a few hundred discrete steps. Each burst includes from 103 up to 104 primary mono-energetic electrons. Although it can be defined arbitrarily, the shape of the beam spot is usually assumed as circular with a typical diameter of 2–3 nm (FWHM). This is also the case of the current density within the beam spot, which is usually assumed as a cylinder-symmetrical Gaussian distribution centered in the beam axis. Due to multiple scattering effects in different material the SE signal does not only depend on the local material properties and topography at the landing spot, but also on the properties in near proximity. In this respect, an important role plays the fact that the surface topology is composed by insulating materials (e.g. SiO2, PMMA). This can

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lead to negatiive or positivee surface chargging dependinng on the SE yield. y The resuulting electric fields can cau use changes inn the SE imagee formation as a result of thee deflection off the primary beam and of the t emitted secondary electrrons. In summary, the proposed code is able too treat accurattely the SE em mission yield depending d on different materials, complex 3D geometries, g annd self-charginng effects. The standardd Monte Carloo code PENE ELOPE [3] has been assum med as a basiss for our ownn developmen nts, among thee choice of pottential other coodes [6–9]. Itt provides bennefits in terms of 3D geomeetry managem ment, ray tracin ng capabilitiess in electromaggnetic fields, tracking and scoring featurres and generral simulation bookkeepingg that is readilly available inn the code. Thee original physics of PENELOPE has been replaced co ompletely by the original pphysics modulle described inn Section 2 witth the scope to t implement an energy sttraggling simu ulation schem me working doown to electro on energies of 0.1 eV. A bloock diagram of the proposedd MC simulatiion tool is sho own in Figure 2.

Figure 2. Left: Block struucture of the prroposed MC codde. The physicss and the MC prrocess are comppletely encapsu ulated in librarry functions (M MCD) and looseely coupled to PENELOPE, P wh hich is mainly used u for trackinng and scoring purposes. p Righht: Program infoormation flow.

3.2 Code Orrganization The main proogram is the PENMAIN P codde of PENELO OPE, which haas been adapteed to allow caalling the subrroutines of ourr physics librarry package innstead of the PENELOPE intrinsic physsics subroutinnes. Care has been taken to o very looselyy couple our phhysics routinees to the main program. In essence, e the tw wo parts onlyy communicatee via subroutiine calls to thee getStepLe ength(curr rentMateri ial) and doS Scatter(cu urrentMate erial) funcctions of our physics libraryy, which completely contain the necessaryy computationn of the mean free path andd the energy annd momentum m changes duee to an interactiion event. Thee latter valuess are returned to t the PENEL LOPE domain for subsequennt tracking op peration. A further suppplement to PENMAIN P is thhe addition off a loop, whicch changes the (scanning) bbeam position n step by stepp. Part of this looop is also wriiting the SE yiield data to thhe output file. It should be noted n that PEN NELOPE already in its origginal version allows a an arbiitrary 3D surfaace setup to be simulated ass well as differrent beam shaapes impinginng the surfacee. Throughoutt this study we w use either ppencil-like beams or beamss with Gaussiaan profile, whhich can addittionally have a cone shapee narrowing toowards the suurface. In thiss first phase a hemisphericaal detector is used. u However, PENELOPE E allows the definition d of active a bodies ssuch that arbittrary detectorss can be easily implemented. Input parameeters like the scanning s beam m parameters as a well as gen neral job param meters are deffined in a textt input file, thee geometry is defined d in a separate s text input i file, botth in PENELO OPE format. Those T files arre generated from f a Pythonn script. This Python P script includes also the t logic to paarallelize the simulation s tassk and run muultiple jobs in parallel p on thee available loadd sharing facillity (Condor). Once the sim mulation enviroonment has been read and set up by the main program m, the electroons undergo seeveral steps inn the main loopp. These are inn principle fouur main compuutational taskss.

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1. 2. 3. 4.

LOCATE the particle in the geometry and retrieve the corresponding material, GETMEANFREEPATH in the current material, STEP by a random fraction of mean free path, INTERACTION process, which can be either elastic, inelastic, phonon excitation, polaron. We use the dedicated low energy physics models as described in Section 2 (Physics models).

An interaction process can lead to the generation of a secondary electron. In this case the particle is put into a LIFO stack. Particles trajectories end, when they either reach the boundary of the simulation model or their energy has reached the lower limit of E= 0.1 eV, whereupon they are supposed to get absorbed and the last-in electron from the stack will be simulated next. Along the trajectory, a boundary in the geometry might be crossed. Depending on whether or not the material changes, barrier scattering does occur, leading to either reflection or transmission of the particle. The barrier scatter algorithm is implemented according to the principles outlined in Section 2. Classical and the quantum mechanical transmission probabilities have been implemented. Particles leaving the simulation model in positive (upwards) direction are counted as backscattered (E > 50 eV) or secondary electrons (E < 50 eV) depending on their energy. For secondary electrons leaving the surface, a simple, yet effective scoring algorithm has been implemented. Once particles emerge from the surface (i.e. particles undergoing a barrier scatter event from any material other than vacuum but towards vacuum) their phase space coordinates are kept in memory. If this very particle stays in vacuum and finally leaves the simulation model, its coordinates at the surface have been recorded. However, if the particle undergoes another barrier scatter event and therefore enters the sample again, its trace is eliminated from the memory. This procedure delivers the detected secondary electron distribution at surface level even for complicated geometries, even in the presence of EM fields leading to bent trajectories. In a first phase, specimen charging has been modeled by assuming steady-state charging conditions. This corresponds to a pre-conditioning phase (e.g. from a flooding electron beam). It is assumed that positive and negative charges are trapped in the dielectrics according to two distinct normal distributions along the z-axis. The related 3D Poisson equation is solved for the given geometry and boundary conditions in the different materials and in the vacuum by the external tool SENTAURUS DEVICE [5]. This approach make possible to take into account accurately all charges induced in the different materials (e.g. semiconductors and metals) and to calculate the related electrostatic potentials. In the final stage, SENTAURUS DEVICE returns to the MC code the local, time-invariant electrostatic field and potential for the calculation of the electron trajectories. In a future configuration of the code, dynamic charge up of the sample can be simulated by an appropriate self-consistent simulation scheme, also including transport and generation/recombination models in the different materials. In order to be computationally efficient in the ray-tracing part of the code (which is part of the PENELOPE main routine), a tensor grid has been used for the electric field mesh. Like this the retrieval of field values for a given position (x,y,z) can be efficiently implemented using indexed look-up. 3.3 Computation Time Considerations The proposed MC simulation scheme works according to a rigorous energy straggling principle, i.e. only discrete events are considered, i.e. no continuous slowing down approximation (CSDA) steps are involved. All particles are followed down to an energy E=0.1 eV, in which case they are absorbed. Energy is lost only in discrete interaction processes (inelastic scattering, polaron, phonon, plasmon). Nodes in the computer cluster used for this study offer CPU clock cycles in the order of 2.5–2.9 GHz. With these machines a typical computation time of 2–7 ms per started primary electron is reached. Per incidence point a set of usually 104 primary electrons is started to get sufficiently smooth linescans, hence computation time for one point is typically in the order of 20 up to 70 s, depending on material, geometry, and energy of the primary electron. Simulating a linescan of 150–200 points on a single CPU accordingly requires in the best case a computation time of just less than an hour. Using massive parallelization with typically 100 CPU nodes simultaneously can reduce the computing time down to less than one minute. In this case, additional time is needed for the more complex post-processing.

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4.

RESULTS & APPLICATION

The used physical models have been validated with experimental data of SE (and BSE) yields from flat surfaces of bulk materials. Additionally, the energy spectrum of the emitted electrons has been compared with available experimental data. Both the SE yield and the energy spectrum have been shown to fit well with experimentally obtained data [1]. Linescans obtained for 3D geometries by the proposed simulation code are compared in the following with results from other SEM image simulation codes available in the literature. In addition, the capabilities of the proposed code are shown based on several realistic examples. 4.1 Step Geometry A step structure has been used to study the SE yield response of the proposed code. Figure 3 depicts the situation for a step in silicon, only. The linescan signal shows the expected quantitative behavior. On the flat surface far away from the step, the SE yield corresponds to that of normal incidence. Approaching the step on the lower side (negative x positions in Figure 3) an increasing shadowing effect is observed. As expected, trajectories of emerging SEs are intercepted by the topography step. The higher the step height and/or the steeper the side wall angle, the more shadowing occurs. At the step itself the SE signal shows a discontinuity. The signal minimum is at the bottom edge position where emerging SEs experience maximum geometric shadowing. The signal maximum is at the position where the generation and escape probability of the secondary electrons reach their maximum. For a pencil beam, this condition is reached close to the top edge. For larger side wall angles, an additional intermediate level within the transition can be recognized. According to the model assumed for the SE yield, its level is a function of angle of incidence of the beam on the side wall surface.

Figure 3. Linescans from a silicon step with different side wall angles (increasing from top left to bottom right, 0.1°, 5°, 10°, 20°) and different energies (increasing from top left to bottom right, 0.3, 0.5, 0.7, 1.0 keV). The shape of the signal is determined by the angle of incidence of the primary electrons, their energy, and the constellation of position of incidence and geometry. The simulations have been performed by a pencil beam.

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The distribution of the emerging electrons can be reconstructed by the scoring algorithm for SE (see Section 3) and is plotted in Figure 4 in conjunction with the local value of the SE yield. At first, it can be noticed that the lateral distribution of emerging SEs has in fact a rather small and limited extent, which is in accordance with the theoretical model [1,2]. For silicon at 0.5 keV the 3σ interval corresponding to a width of less than 10 nm includes almost 99.7% of all emerging SEs. Interesting is also to see that the angular distribution shows a high content of SEs emerging at angles almost perpendicular to the flat surface (note that these are not BSE). When the beam approaches the step, two effects are observed. First, the angular distribution shows a clear asymmetry because of the SEs, which are absorbed at the edge. In fact, this corresponds to the geometric shadowing effect. Additionally, the angular distribution evidences some SEs generated and/or emerging from the side wall region. In the case of a silicon step (low SE yield), this component is still small compared with the geometric shadowing effect. If the beam impinges on the sidewall, the effect of the angle of incidence can be clearly observed. The angular distribution becomes very asymmetric, since the SEs emerge with a distribution centered around the normal to the sidewall surface. The lateral distribution also shows a strong asymmetry, since no SE is emitted in the direction of the increasing slope. Figure 5 shows the calculated distributions in the same sample for a PMMA step on silicon substrate. The most remarkable difference to a pure silicon step occurs at positions where the beam impinges on the silicon surface and emerging SEs can hit the PMMA sidewall. In this case, the SEs can generate additional SEs resulting in a slightly higher yield, due to the higher yield in the insulator material compared to the silicon substrate. This leads to a less pronounced shadowing effect and even to a slight increase of the SE yield of the silicon flat surface in proximity of the step.

Figure 4. Linescans from a 50 nm silicon step with 10° side wall angle scanned with a pencil beam at 0.5 keV. The lateral and angular distributions (in x-direction) of the emerging secondary electrons is shown at different positions.

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Figure 5. Left: Linescans from a 50 nm PMMA step on silicon substrate with 10° side wall angle scanned with a pencil beam at 0.5 keV. Right: The lateral and angular distribution (in x-direction) of the emerging secondary electrons is shown for a x position close to the step. Note the generation of additional SE in the side wall region.

1.6

Novel MC(PENELOPE)

Beam energy = 0.5keV Beam width = 0.0nm Beam angle = 0.0deg

SE signal [a.u.]

1.4 1.2 1.0 0.8 0.6

JMONSEL Novel MC (PENELOPE)

2 1.5 1 0.5

100 0

100nm high 5° step in Silicon -50 -40 -30 -20 -10 0 10 20 30 40 50 Position x [nm]

0

Lp = 110nm Lw = 50nm Lh = 50nm

Beam energy = 0.5keV Beam width = 0.0nm Beam angle = 0.0deg

SiO2 lines on Si substrate -200

(a)

-100

0 100 Position x [nm]

200

Feature height [nm]

JMONSEL Phen. GBS JMONSEL DFT3 GBS

Feature height [nm]

scaled SE yield [a.u.]

JMONSEL Bin. JLN GBS

1.8

50 0

(b)

Figure 6. (a) Linescans of a 0.5keV beam impinging on a 5° Si edge compared with the results obtained by JMONSEL in [10]. (b) Linescan of a 0.5keV beam impinging on three SiO2 lines deposited on Si substrate. Both images have been simulated with a 2π detector. The comparison shows that the proposed code produces a more structured shadowing effect than JMONSEL. The shadowing effect related to the step is reduced, because of a different angular distribution of the emerging electrons due to barrier scattering. Furthermore, the apparent increase of the SE yield from the Si area between the lines in (b) is mainly due to a multiple scattering of the SE emerging from Si with the SiO2 walls that exhibit a much higher SE yield.

The previous step structure has also been used to benchmark the results obtained by the proposed simulation code against published results from the established code JMONSEL [8]. The linescans have been scaled to one for the flat surface level of silicon for quantitative comparison. In Figure 6(a) both codes are directly compared for a silicon step structure. The linescan obtained by the proposed code is in very good agreement with JMONSEL even if the latter uses different physical models [10]. This also demonstrates the proper treatment of 3D geometry and boundary crossing in present approach. The observed discrepancies can be mainly explained by the differences in the physical models used for the secondary electron yield in the different materials [10].

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4.2 Adjacent lines Adjacent lines with trapezoidal cross-section have been also used to assess the performance of the proposed code against data published in the literature. Figure 6(b) shows the comparison with JMONSEL for a structure with three SiO2 lines on a silicon substrate. Again the qualitative agreement is very good. No scaling is applied in this case and absolute signals are shown. Figure 7 shows linescans obtained by simulating three adjacent Si and PMMA lines, respectively, on a silicon substrate. The main difference to the simple step geometry is the fact, that in this case there is an additional geometry shadowing effect due to adjacent structures. This is clearly seen from the outermost edges of the three lines, which give the highest edge peak signal, corresponding to the step geometry case. However the internal edge peak signals are reduced due to additional shadowing effects produced by the neighbouring lines. Note again that the yield levels depend on the individual yield levels of the materials involved in the shadowing process, as described in the previous section. Only pencil beams have been considered so far. Linescans have also been simulated by taking into account the finite size, as well as the beam divergence. A typical spot size in the order of 3-5 nm (FWHM) and a beam divergence of one degree have been assumed. Figure 7 shows the related simulation results in the case of a step geometry. The most important difference to the situation with a pencil beam is the observed edge bloom, the widening of the signal in the sidewall and edge region, as observed in the literature [11].

Figure 7. Linescans from 20 nm high, 16 nm wide Si (left) and PMMA (right) lines on silicon substrate with 5° side wall angle scanned with a pencil-like electron beam and a 5 nm (FWHM) wide beam at 0.5 keV.

Figure 8. Zoom on the edge bloom. SE yield signal from a PMMA step with 0.1° (left) and 5° (right) side wall angle at 0.5 keV using realistic electron beam model. Incident electron beam with Gaussian profile, 5 nm (FWHM) and divergence angle of 1°. Note the shift of the peak away from the actual edge position.

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4.3 Including EM fields due to charge-up Time-invariant electrostatic fields have been assumed in the following, which have been calculated by the commercial tool SENTAURUS DEVICE [5]. Figure 9 shows a composed 3D view of the simulation of a primary beam impinging onto three charged PMMA lines (50 nm in height) on a silicon substrate. The local electrostatic potential is evidenced by the color map in the background. The trajectories of the SE inside the materials and after emerging from the surface are deflected by the local electrostatic field. In this case, positive surface charges (5 1019 cm-3) with a Gaussian depth distribution (σ=7 nm) have been assumed. Due to the fact that a 2π detector has been used in the simulation, no noticeable difference can be observed with the simulation without electrostatic fields.

Figure 9. Simulation of a primary beam (red) impinging onto three charged trapezoidal PMMA lines on silicon substrate (not shown). The surface of the PMMA lines is positively charged and deflects the SE (blue). The calculated electrostatic potential around the PMMA lines is shown by the 2D map in the background. The simulated 2D SEM image associated to this structure is shown in b/w in the bottom.

4.4 Side-wall signals in trench geometries Trenches have been simulated for benchmarking purposes, too. As reported in [12], the signal at the side wall of a trench can vary depending on the aspect ratio. The same geometry as defined in [12] has been assumed for a quantitative comparison. The depth of the silicon trench is 288 nm with a side wall angle of 4 degrees. The bottom width has been assumed to be 80 nm and 300 nm, respectively. A 2.0 nm (FHMW) Gaussian profile has been taken for the primary beam at 0.8 keV. For sake of comparison, the obtained and the literature linescans have been normalized in respect to the outer flat surface. The comparison of Figure 10 shows that both simulation codes deliver results, which are in excellent agreement.

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Figure 10. Linescans at the side wall of a Si trench (right side, only), 288 nm in depth, 4° side-wall angle, bottom trench width is 80 nm (bottom) and 300 nm (top), resp.. Beam conditions have been set to 0.8 keV and 2.0 nm (FWHM) beam width. The results are compared to the linescans from [12].

4.5 Model-based Library Approach According to [13–16], a model-based library approach strategy has been implemented. A linescan library has been compiled for a step structure (Si/SiO2/PMMA on silicon substrate), including pre-computed linescans for a beam width in the 3.0 up to 7.0 nm range (Gaussian, FWHM, in 1.0 nm steps) and for a fixed beam divergence of one degree. Linescans have been also pre-calculated for step angle values ranging from 1° to 10° in steps of 0.5°. The step height has been fixed at 50 nm and it is has been assumed to be known very accurately from independent measurements (therefore not varied). Similarly, the beam energy has been assumed to be known accurately (i.e. within 1%). After de-noising of the experimental linescan using a wavelet filter [17], a simulated annealing (SA) least-squares estimator is used to find the best fitting pre-computed signal from the library that matches the wavelet-filtered signal. The SA method is slower compared to simplex or other methods, but is less prone to converge towards local minima. The step angle, beam width, position offset (x direction), signal offset, and signal scaling factor are the five parameters to be varied during the fitting procedure. The parameters to be extracted (CD) by fitting are the step angle and the position offset. The beam width has also a major influence on the fitting process. Nevertheless, similarly to the linescan offset and scaling factor, it does not represent a relevant parameter for the determination of the CD. The performance of the proposed fitting procedure is shown on a set of 50 random linescans simulated with the same geometry and beam parameters as before. To simulate a realistic signal noise, these linescans have been simulated by a number of PE per step that has been reduced by a factor 100 (150 PE) compared to the signals used for compiling the 4 library (10 PE). Figure 11 shows the fit results. The standard deviation values in the obtained parameters are figures of merit used to define the single-fit uncertainty of the extracted CD. If the simulation step is reduced in such a way that the lateral resolution is increased by a factor of four, the uncertainties in the extracted CD are reduced by a factor of two. It can be shown that an important criterion for an accurate fit is to acquire a sufficiently high number of sample points along the slope region and across the edges.

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Figure 11. 50 linescans from a 50 nm PMMA step on silicon substrate with 2.9° side wall angle scanned with a 4.75 nm (FWHM) electron beam at 0.5 keV are fitted by pre-computed library signals. The indicated parameters are the mean and standard deviation values after the 50 fits. Left: The lateral resolution of the noisy linescans in direction x set to 1 nm. Right: The lateral resolution is reduced down to 0.25 nm. As a consequence of the better lateral resolution at the slope and edge locations, the parameters extracted by the fitting procedure are more accurate.

5.

SUMMARY AND CONCLUSIONS

A novel MC simulator tool for the quantification of CD-SEM images has been proposed. Particular emphasis has been put on scattering models for the low-energy range. The simulator has been compared to other existing codes and its features and capabilities have been assessed in examples. Based on the proposed code an application using a modelbased library strategy has been demonstrated. In conclusion, the proposed simulator has been shown to provide results that are in good agreement with published data.

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