With semiconductor technology approaching and exceeding 10 nm design rules the quality requirements for photomasks are continuously tightening. One of the crucial parameters is improved control of the critical dimension (CD) across the photomask. As long as linearity and through pitch effects are not involved, the quality measure is typically defined as CD uniformity. This parameter is normally measured on repeating structures of same size and shape, which are not necessarily placed in identical environments. Density dependent process effects, also called loading effects (LE), pose a challenge for the required CD control. There are several possible contributors to this kind of error within the mask manufacturing flow, such as etch driven loading effects, fogging effects during 50kV exposure and develop driven loading effects. All of these operate at different working ranges, starting at millimeters going down to only a few 100 μm scale. It is comparably easy to derive models for large scale phenomena like etch loading or fogging effects, in contrast to that it is not as straight forward to find suitable models for very short-range effects. A large amount of CD measurements taken by CD SEM is needed to identify such signals of low magnitude and short scales, which make the setup very resource intensive. Furthermore, this methodology requires artificial designs and test structures which aim to sample only the effect of interest. In this paper we present a strategy which combines CD SEM measurements from dedicated test masks with the results from regular product masks. The aim is the derivation and validation of the loading effect correction range and strength. In the first step the data from test masks is analyzed to set up the basic correction parameters. Following this, the approach is supplemented by product data where we combine mask CD and design data. The clear field distribution of the design is convoluted with respect to a hierarchy of length scales. This data is the input for a support vector machine analysis. Thus, we employ a flat machine learning algorithm. However, the input data has been set up to reflect multiple layers of convolution. This particular approach has been chosen, as each convolution length scale is associated with mask process properties, thus alleviating the burden of interpretation which typically mars the interpretation of models obtained by machine learning approaches.
The currently increasing demand for photo-masks in the regime of the 14nm technology drives many initiatives towards capacity and throughput increase of existing production line. Such improvements are facilitated by improved control mechanisms of the tools and processes used within a production line. While process control of long range parameters such as the average CD behavior is demanding yet conceptually well understood, other parameters such as the small scales CD properties are quite often elusive to process control. These properties often require a dedicated test mask to be processed in order to be validated. In this paper we introduce a systematic approach towards a product based monitoring of small scale CD behavior which uses a CD characteristic extracted from the defect inspection process. This characteristic represents the influence of CD relevant processes starting from 200m up to 4000 m. Large variations in the scale and magnitude of the CD characteristic are induced by layout specific design variations. However, the shape of these distinct curves is remarkably similar, which enables their use for monitoring as well as controlling the mask processes on the above stated spatial scales. In this paper it is demonstrated, that a meaningful process evaluation can be performed by using the classification capabilities of the support vector machines. The small scales CD characteristics presented in figure 1 originate from two distinct tools. Matching of the two tools can be assessed by training a support vector machine to classify the small scales CD characteristics according to their origin. The classification performance on the resampled training set as well as on the validation set is a robust measure for tool matching. The results of this approach are depicted in figure 2. The left panel shows the AUC statistics of bootstrapping resamples for tool comparison “A”. In this case no noticeable difference between the two tools is found (an average AUC of 0.55 suggest no learnable difference). This is contrasted by the tool comparison “B”, here the classifier has an average AUC of 0.75, indicating a learnable difference in the tool performances. This result is backed by the process understand of both tool types.
The currently increasing demand for photo-masks in the regime of the 14nm technology drives many initiatives towards capacity and throughput increase of existing production lines. Such improvements are facilitated by improved control mechanisms of the tools and processes used within a production line. While process control of long range parameters such as the average CD behavior is demanding yet conceptually well understood, other parameters such as the small scale CD properties are quite often elusive to process control. These properties often require a dedicated test mask to be processed in order to be validated. In this paper we introduce a systematic approach towards a product based monitoring of small scale CD behavior which uses a CD characteristic extracted from the defect inspection process. This characteristic represents the influence of CD relevant processes starting from 200 10-6m up to 4000 10-6m. Large variations in the scale and magnitude of the CD characteristic are induced by layout specific design variations. However, the shape of these distinct curves is remarkably similar, which enables their use for monitoring as well as controlling the mask processes on the above stated spatial scales. In this paper it is demonstrated, that a meaningful monitoring of the CD characteristic can be enabled through the use of machine learning methods. A classical monitoring scheme is typically based on measuring the deviation of each curve from the average behavior. However, the monitoring of a curve and deviations thereof often requires the evaluation of the overall shape of the curve. Thus we propose a monitoring concept which uses a support vector machine in order to learn the shapes of the CD characteristics. It is demonstrated that a statistical model of the CD characteristics can be trained and used in order to monitor single excursions (see Figure 1) as well as overall process changes.
With the substantial surge in the need for high-end masks it becomes increasingly important to raise the capacity of the corresponding production lines. To this end the efficient qualification of matching tools and processes within a production line is of utmost relevance. Matching is typically judged by the processing of dedicated lots on the new tool and process. The amount of qualification lots should on the one hand be very small, as the production of qualification plates is expensive and uses capacity of the production corridor. On the other hand the strict requirements of high-end products induce very tight specification limits on the matching criteria. It is thus often very difficult to assess tool or process matching on the basis of a small amount of lots. In this paper we expound on a machine learning based strategy which assesses the mask characteristics of a qualification plate by learning the typical behavior of these characteristics within the production line variations. We show that by careful selection of reference production plates as well as by setting specification limits based on the production behavior we can manage the qualification tasks efficiently by using a small number of masks. The specification characteristics as well as the specific limits are selected and determined using a Naïve Bayes learner. The resulting performance for prediction of tool and process matching is assessed by considering the resulting receiving operator curve. As a result we obtain an approach towards the assessment of qualification data which enables engineers to assess the tool and process matching using a small amount of matching data under the constraint of substantial measurement uncertainties. As an outlook we discuss how this approach can be used to examine the reverse question of detecting process failures, i.e. the automated ability to raise a flag when the current production characteristics start to deviate from their typical characteristics. Overall, in this paper we show how the rapidly evolving field of machine learning increasingly impacts the semiconductor production process.
As the concepts of machine learning and artificial intelligence continue to grow in importance in the context of internet related applications it is still in its infancy when it comes to process control within the semiconductor industry. Especially the branch of mask manufacturing presents a challenge to the concepts of machine learning since the business process intrinsically induces pronounced product variability on the background of small plate numbers. In this paper we present the architectural set up of a machine learning algorithm which successfully deals with the demands and pitfalls of mask manufacturing. A detailed motivation of this basic set up followed by an analysis of its statistical properties is given. The machine learning set up for mask manufacturing involves two learning steps: an initial step which identifies and classifies the basic global CD patterns of a process. These results form the basis for the extraction of an optimized training set via balanced sampling. A second learning step uses this training set to obtain the local as well as global CD relationships induced by the manufacturing process. Using two production motivated examples we show how this approach is flexible and powerful enough to deal with the exacting demands of mask manufacturing. In one example we show how dedicated covariates can be used in conjunction with increased spatial resolution of the CD map model in order to deal with pathological CD effects at the mask boundary. The other example shows how the model set up enables strategies for dealing tool specific CD signature differences. In this case the balanced sampling enables a process control scheme which allows usage of the full tool park within the specified tight tolerance budget. Overall, this paper shows that the current rapid developments off the machine learning algorithms can be successfully used within the context of semiconductor manufacturing.
In the process of semicondutcor fabrication the translation of the final product requirements into specific targets for each component of the manufacturing process is one of the most demanding tasks. This involves the careful assessment of the error budgets of each component as well as the sensible balancing of the costs implied by the requirements. Photolithographic masks play a pivotal role in the semiconductor fabrication. This attributes a crucial role to mask error budgeting within the overall wafer production process. Masks with borderline performance with respect to the wafer fabrication requirements have a detrimental effect on the wafer process window thus inducing delays and costs. However, prohibitively strict mask specifications will induce large costs and delays in the mask manufacturing process. Thus setting smart control mechanisms for mask quality assessment is highly relevant for an efficient production flow. To this end GLOBALFOUNDRIES and the AMTC have set up a new mask specification check to enable a smart ship to control process for mask manufacturing. Within this process the mask CD distribution is checked as to whether it is commensurable with the advanced dose control capabilities of the stepper in the wafer factory. If this is the case, masks with borderline CD performance will be usable within the manufacturing process as the signatures can be compensated. In this paper we give a detailed explanation of the smart ship control approach with its implications for mask quality.
For the specific requirements of the 14nm and 20nm site applications a new CD map approach was developed at the AMTC. This approach relies on a well established machine learning technique called recursive partitioning. Recursive partitioning is a powerful technique which creates a decision tree by successively testing whether the quantity of interest can be explained by one of the supplied covariates. The test performed is generally a statistical test with a pre-supplied significance level. Once the test indicates significant association between the variable of interest and a covariate a split performed at a threshold value which minimizes the variation within the newly attained groups. This partitioning is recurred until either no significant association can be detected or the resulting sub group size falls below a pre-supplied level.
Traditional control of critical dimensions (CD) on photolithographic masks considers the CD average and a measure for the CD variation such as the CD range or the standard deviation. Also systematic CD deviations from the mean such as CD signatures are subject to the control. These measures are valid for mask quality verification as long as patterns across a mask exhibit only size variations and no shape variation. The issue of shape variations becomes especially important in the context of contact holes on EUV masks. For EUV masks the CD error budget is much smaller than for standard optical masks. This means that small deviations from the contact shape can impact EUV waver prints in the sense that contact shape deformations induce asymmetric bridging phenomena. In this paper we present a detailed study of contact shape variations based on regular product data. Two data sets are analyzed: 1) contacts of varying target size and 2) a regularly spaced field of contacts. Here, the methods of statistical shape analysis are used to analyze CD SEM generated contour data. We demonstrate that contacts on photolithographic masks do not only show size variations but exhibit also pronounced nontrivial shape variations. In our data sets we find pronounced shape variations which can be interpreted as asymmetrical shape squeezing and contact rounding. Thus we demonstrate the limitations of classic CD measures for describing the feature variations on masks. Furthermore we show how the methods of statistical shape analysis can be used for quantifying the contour variations thus paving the way to a new understanding of mask linearity and its specification.
Critical dimension uniformity (CDU) is an important parameter for photomask and wafer manufacturing. In
order to reduce long-range CD variation, compensation techniques for mask writers and scanners have been
developed. Both techniques require mask CD measurements with high spatial sampling. Scanning electron
microscopes (SEMs), which provide CD measurements at very high precision, cannot in practice provide the
required spatial sampling due to their low speed. In contrast mask inspection systems, some of which have the
ability to perform optical CD measurements with very high sampling frequencies, are an interesting alternative.
In this paper we evaluate the CDU measurement results with those of a CD-SEM.
Achieving the required critical dimensions (CD) with the best possible uniformity (CDU) on photo-masks has
always played a pivotal role in enabling chip technology. Current control strategies are based on scanning
electron microscopy (SEM) based measurements implying a sparse spatial resolution on the order of ~ 10-2 m
to 10-1 m. A higher spatial resolution could be reached with an adequate measurement sampling, however the
increase in the number of measurements makes this approach in the context of a productive environment
unfeasible. With the advent of more powerful defect inspection tools a significantly higher spatial resolution
of 10-4 m can be achieved by measuring also CD during the regular defect inspection. This method is not
limited to the measurement of specific measurement features thus paving the way to a CD assessment of all
electrically relevant mask patterns. Enabling such a CD measurement gives way to new realms of CD control.
Deterministic short range CD effects which were previously interpreted as noise can be resolved and
addressed by CD compensation methods. This in can lead to substantial improvements of the CD uniformity.
Thus the defect inspection mediated CD control closes a substantial gap in the mask manufacturing process
by allowing the control of short range CD effects which were up till now beyond the reach of regular CD
SEM based control strategies. This increase in spatial resolution also counters the decrease in measurement
precision due to the usage of an optical system.
In this paper we present detailed results on a) the CD data generated during the inspection process, b) the
analytical tools needed for relating this data to CD SEM measurement and c) how the CD inspection process
enables new dimension of CD compensation within the mask manufacturing process. We find that the
inspection based CD measurement generates typically around 500000 measurements with a homogeneous
covering of the active mask area. In comparing the CD inspection results with CD SEM measurement on a
single measurement point base we find that optical limitations of the inspection tool play a substantial role
within the photon based inspection process. Once these shift are characterized and removed a correlation
coefficient of 0.9 between these two CD measurement techniques is found. This finding agrees well with a
signature based matching approach. Based on these findings we set up a dedicated pooling algorithm which
performs on outlier removal for all CD inspections together with a data clustering according to feature
specific tool induced shifts. This way tool induced shift effects can be removed and CD signature
computation is enabled. A statistical model of the CD signatures which relates the mask design parameters on
the relevant length scales to CD effects thus enabling the computation CD compensation maps. The
compensation maps address the CD effects on various distinct length scales and we show that long and short range contributions to the CD variation are decreased. We find that the CD uniformity is improved by 25%
using this novel CD compensation strategy.
Strict reticle critical dimension (CD) control is needed to supply ≤ 20nm wafer technology nodes. In front end
lithographic processes for example, precise temperature control in resist baking steps is considered paramount to limiting
reticle CD error sources. Additionally, current density during writing and focus are continuously tracked in 50kV e-beam
pattern generators (PG) in order to provide stable CD performance. Despite these strict controls (and many others),
feedback compensation strategies are increasingly utilized in mask manufacturing to reach < 2nm 3σ CD uniformity
(CDU). Such compensations require stable reticle CD signatures which can be problematic when alternate or backup
process tools are employed. The AMTC has applied principle component analysis (PCA) to resist CD measurements of
50kV test reticles fabricated with chemically amplified resists (CAR) in order to quantify the resist CDU capabilities of
front and backup lithographic process tools. PCA results elucidate significant resist CDU differences between similar
lithographic process tools that are considered well matched via CDU 3σ comparisons.
The utility of PCA relies on the statistical analysis of large data sets however, reticle CD sampling is typically sparse, on
the 10-2 m or centimeter (cm) scale using conventional scanning electron microscopes (CD SEM). Higher CD spatial
resolutions can be achieved using advanced inspection tools, which provide CD data on a substantially smaller length
scale (10-4 m), thus yielding a considerably larger CD snapshot for front/backup process tool comparisons. Combining
PCA analysis with high spatial resolution CD data provides novel insights into the opportunities for tool and process CD
Improvement of pattern placement accuracy is essential to solve upcoming challenges in mask making. Placement
errors are driven by multiple effects with electron mediated resist surface charging being a major error source. Modeling
this systematic effect thus allows the determination of the placement errors before plate processing. This opens the door
to an effective charging compensation.
In this paper we study the simulated benefit of two distinct charging compensation models in the context of full-scale
mask production layouts. The potential pattern placement improvements are evaluated using actual placement results
obtained without charging effect corrections. An in depth comparison of the two models is presented, demonstrating the
differences in placement error prediction between using a static or a dynamic charging model. We find that substantial
improvements can be achieved using the dynamic charging model. Productive implementation of this functionality is
the natural next step.
Critical dimensions (CD) measured in resist are key to understanding the CD distribution on photomasks. Vital to this
understanding is the separation of spatially random and systematic contributions to the CD distribution. Random
contributions will not appear in post etch CD measurements (final) whereas systematic contributions will strongly impact
final CDs. Resist CD signatures and their variations drive final CD distributions, thus an understanding of the mechanisms
influencing the resist CD signature and its variation play a pivotal role in CD distribution improvements. Current
technological demands require strict control of reticle critical dimension uniformity (CDU) and the Advanced Mask
Technology Center (AMTC) has found significant reductions in reticle CDU are enabled through the statistical analysis of
large data sets. To this end, we employ Principle Component Analysis (PCA) - a methodology well established at the
AMTC1- to show how different portions of the lithographic process contribute to CD variations. These portions include
photomask blank preparation as well as a correction parameter in the front end process. CD variations were markedly
changed by modulating these two lithographic portions, leading to improved final CDU on test reticles in two different
chemically amplified resist (CAR) processes.
Critical Dimension uniformity (CDU) is one of the most critical parameters for the characterization of
photomasks. Lately it has been shown that advanced CD (critical dimension) SEM tools and mask processes
can distinguish the random short-range CD variation from the global CD signature, which is driven by
process and design characteristics. Current electron beam writers can utilize this global CD signature
information and correct the CDU of photomasks accordingly. Therefore a detailed knowledge of the
signature will benefit strongly photomask CDU.
Electron beam writer based signature compensation relies primarily on CD signatures derived from CD
SEMs. Here higher spatial resolutions of the signature are achieved only by high cycle times at metrology.
The trade off between cycle time and resolution leads to a CD resolution somewhere around one cm. Even
then the photomask will have to stay a substantially percentage of the total cycle time at a non-value added
In this paper we argue that the solution for this dilemma can be found at a completely different process area -
at inspection. We present data showing that the novel CD map feature of the NPI inspection tools enables CD
maps in unparalleled resolution in the mm region. This far exceeds CD SEMs by a factor of 100. Also
utilization of a tuneable spectrum of different features are not limited to selected CD measurement sites. The
CD map is generated in parallel to the traditional defect inspection and works for pre- and post pellicle
inspections equally well.
To evaluate the method we used a single die layout of a current logic design and referenced all data only to
database. Nevertheless, the data presented will demonstrate the excellent repeatability of the CD map
measurement and the good matching to CD SEM measurements.
Reticle critical dimension (CD) errors must be minimized in order for photomask manufacturers to meet tight CD uniformity
(CDU) requirements. Determining the source of reticle CD errors and reducing or eliminating their CDU contributions are
some of the most relevant tasks facing process engineers. The AMTC has applied principal component analysis (PCA) to
reticle resist CD measurements in order to examine variations in the data. PCA provided the major components of resist CD
variation which were rescaled into reticle CD signatures. The dominant component of CD signature variation is very similar
in shape and magnitude between two different chemically amplified resist (CAR) processes, most likely indicating the
variation source is a common process or tool. CD variational signatures from PCA were used as a basis for launching
investigations into potential reticle CD error sources. PCA was further applied to resist CD measurements from alternate
process tools to assist efforts in judging the effectiveness of resist CD signature matching.
KEYWORDS: Signal to noise ratio, Lithography, Principal component analysis, Error analysis, Image registration, Process control, Photomasks, Electron beam melting, Critical dimension metrology, Tolerancing
Current high end chips require an extremely precise fabrication of lithographic masks. Some of the most critical
parameters are the placement of structures on the masks as well as their dimensional tolerances. Improving these two key
parameters has always been one of the central objectives of the Advanced Mask Technology Center (AMTC). To this
end, the AMTC has complemented its process development by a set of enhancement schemes which are used to
compensate residual process signatures. In this paper, improvements achieved in the area of CD uniformity (CDU) and
pattern placement are shown. The correction schemes take first principle considerations as well as empirical findings into
account. Based on this, a set of design and process parameters is used to determine the spatial corrections which will
optimize mask quality parameters. This enables the AMTC to tailor the writing parameters to the needs of each mask
design. Latest results for the 32nm technology show that values as low as 5nm image placement error and 3nm CDU can
be reached at the same time.
Critical Dimension uniformity (CDU) is one of the most critical parameters for the characterization of
photomasks. For years the understanding was that CDU describes a rather random fluctuation of the CD
across the mask. With more advanced CD tools and mask processes the local short-range CD variation (on a
length scale of micrometre) can be distinguished from the global CD signature (typically on a length scale of
centimetre). Recent developments in the pattern generator sector allow correcting for such global CD
signatures. This triggers the current challenge to find stable methods to characterize the global signature of
In our work we present matching results of a technique that calculates the CD signature using exponentially
weighted surrounding points. We investigated different CD SEM tools of different technology generations.
We show that our method allows determination of the CD signature independently of the measurement tool
with low uncertainty and moderate measurement effort. This holds even true when the CDU value is mainly
dominated by the measurement error. Thus our method provides a tool to extend the utilization of older
generation metrology tools as well as the possibility to improve the measurement capability for CD signature
of current tools.
The production process of photo-masks for memory devices is highly demanding since homogeneity of mask parameters
plays a pivotal role for the overall mask quality. Spatially homogeneous mask designs - which are dominant on memory
devices - should in the best case be transferred into a mask exhibiting the same homogeneous behavior. This means that
CD deviations from the mean should ideally bear no systematic signature but at most some random noise. However,
many steps in the mask production process can introduce spatial correlations so that CD deviations are not only
stochastically distributed over the mask but exhibit a pronounced signature. Thus, the determination and quantification of
these deviations is crucial for a) assessing the mask quality and b) driving process improvements to remove CD
The most common data analysis method for separating signatures from noise is to average over a number of samples.
Unfortunately, due to the nature of mask manufacturing often there is only one sample available. In this paper we
propose the technique of Thin Plate Spline Smoothing for the determination and quantification of the CD signature of a
given single mask. This analysis is complemented by two statistical tests which assess the fit quality by analyzing the
residual for normality and correlations.