Paul Issartel
email: paul.issartel@limsi.fr

Lonni Besançon
email: lonni.besancon@inria.fr

Florimond Guéniat

Tobias Isenberg
email: tobias.isenberg@inria.fr

Mehdi Ammi
email: mehdi.ammi@limsi.fr

Preference Between Allocentric and Egocentric 3D Manipulation in a Locally Coupled Configuration

Keywords: 3D Interaction, Control-Display mappings, Mobile devices

We study user preference between allocentric and egocentric 3D manipulation on mobile devices, in a configuration where the motion of the device is applied to an object displayed on the device itself. We first evaluate this preference for translations and for rotations alone, then for full 6-DOF manipulation. We also investigate the role of contextual cues by performing this experiment in different 3D scenes. Finally, we look at the specific influence of each manipulation axis. Our results provide guidelines to help interface designers select an appropriate default mapping in this locally coupled configuration.

INTRODUCTION

With the rising availability of mobile devices and their increasing processing power, 3D applications are becoming more common on these devices. A fundamental part of interaction with such software is 3D manipulation [START_REF] Bowman | 3D User Interfaces: Theory and Practice[END_REF], i.e. translations and rotations in 3D space. While most mobile devices rely on touch-based control, tactile input requires a 2D to 3D mapping for 3D manipulation. Several projects [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF][START_REF] Neale | RelicPad: A hands-on, mobile approach to collaborative exploration of virtual museum artifacts[END_REF] thus proposed to use the built-in motion sensors found in many mobile devices to provide full 3D input, by detecting the device's own motion and mapping it to virtual objects. Recently, the Tango tablet1 provided a major technological step forward by combining gyroscopes, accelerometers, and visible/infrared cameras to fully track its translations and rotations relative to the surrounding environment. This mode of interaction is thus likely to become more widely used in the future.

A unique aspect of mobile devices is that they integrate input and display capabilities in the same device. This means that users are holding both the input device and the display device in their hands-a "locally coupled" configuration. For this reason, using the motion of a mobile device for 3D input can be interpreted in two ways (see Figure 1):

• the mobile device could be seen as a "handle" to control 3D objects-the allocentric interpretation-or

• the mobile device could be seen as a "window" that moves around 3D objects-the egocentric interpretation.

In the allocentric interpretation, the manipulated 3D objects move in the same direction as the "handle" represented by the mobile device. In the egocentric interpretation, objects move in the opposite direction, as if the viewpoint itself was controlled through a handheld "window".

Device motion Result allocentric egocentric

Figure 1: Illustration of the allocentric and egocentric mappings.

Although either alternative can be obtained by simply reversing the direction of motion in the control-display mapping [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF], the question remains of which mapping should be actually implemented. This is not only relevant if the interface does not offer a way to switch between the two alternatives, but it also affects first-time users. The concept of "compatibility" [START_REF] Chan | Precise effects of control position, indicator type, and scale side on human performance[END_REF], originating from the ergonomics literature, states that a chosen mapping should correspond to the alternative most often expected among the population. Choosing a compatible mapping is thus essential for good usability and minimal fatigue [START_REF] Chan | Precise effects of control position, indicator type, and scale side on human performance[END_REF], and to avoid errors such as accidental inversions [START_REF] Diaz | Accidental inversion during three-dimensional orientational control[END_REF]. Even after extensive training, evidence suggests that a non-compatible mapping still results in reduced user performance [START_REF] Chan | Precise effects of control position, indicator type, and scale side on human performance[END_REF].

In this paper we thus examine which mapping users prefer in various situations, in order to help interface designers choose which mapping to implement in each case.

RELATED WORK

Allocentric and egocentric reference frames

Each interpretation of the locally coupled configuration is a matter of the cognitive relationship between the objects in space, called a reference frame. The literature on spatial cognition generally distinguishes between two fundamental reference frames [START_REF] Klatzky | Allocentric and egocentric spatial representations: Definitions, distinctions, and interconnections[END_REF]: allocentric (also called exocentric) and egocentric. However, most of this literature focuses on the relationship between the user and his or her surrounding objects. In our case, there is both a relation between the user and the mobile device, and a relation between the mobile device and the 3D objects displayed on it. We thus need to examine how we can apply these terms to this specific situation.

Klatzky [START_REF] Klatzky | Allocentric and egocentric spatial representations: Definitions, distinctions, and interconnections[END_REF] defines the two terms in the context of whole-body navigation: egocentric as being related to the "perspective of the perceiver," and allocentric as being related to an external, independent framework. Burgess et al. [START_REF] Burgess | Orientational manoeuvres in the dark: Dissociating allocentric and egocentric influences on spatial memory[END_REF] studied these reference frames in a spatial updating task (judging the relative motion of objects between an initial and a final configuration), which has a certain degree of similarity with our situation. They define the allocentric frame as "the association of object locations to external landmarks" and the egocentric frame as being related to "self-motion." Poupyrev et al. [START_REF] Poupyrev | Egocentric object manipulation in virtual environments: Empirical evaluation of interaction techniques[END_REF] define these reference frames in the context of immersive environments: egocentric interaction techniques are those linked to the avatar's viewpoint, while "exocentric" (i.e. allocentric) techniques are those performed from an external location. In a study by Diaz and Sims [START_REF] Diaz | Accidental inversion during three-dimensional orientational control[END_REF] on accidental inversions, the egocentric condition was viewed from the operators' eyes and the allocentric condition was viewed from outside their body.

Overall, the egocentric term seems to be associated with the idea of the viewing perspective, and the allocentric term with the idea of a fixed, external reference point. In our case, when the manipulated object moves in the same direction as the mobile device, the object appears to be directly controlled by the device's motion and thus to move relative to the surrounding space. We therefore describe such mappings as "allocentric." When the manipulated object moves in the opposite direction, the mobile device appears to directly control the perspective on the object. We therefore call such mappings "egocentric."

Population stereotypes

The relationship between an input device's motion and the motion's result on a display has long been investigated in ergonomics. Although this relationship-or "mapping"-can take many forms, some of them better match the user's mental model. Such mappings are said to be compatible [START_REF] Fitts | SR compatibility: Spatial characteristics of stimulus and response codes[END_REF][START_REF] Chan | Precise effects of control position, indicator type, and scale side on human performance[END_REF]. An important goal for interactive systems design is thus to determine which mapping is most compatible with the target population.

When faced with several functionally equivalent alternatives such as the two mappings we study, the option which is most often expected among the population is called a population stereotype [START_REF] Fitts | Engineering psychology and equipment design[END_REF][START_REF] Wiebe | Application of population stereotypes to computerized tasks[END_REF]. Several population stereotypes have been identified in previous research. Warrick's principle [START_REF] Warrick | Direction of movement in the use of control knobs to position visual indicators[END_REF][START_REF] Wiebe | Application of population stereotypes to computerized tasks[END_REF], for instance, states that the controlled display should move in the same direction as the side of the input device that is closest to it. The clockwise-to-increase principle [START_REF] Wiebe | Application of population stereotypes to computerized tasks[END_REF] states that the controlled display should "increase" or "move up" when the input device is rotated clockwise. These principles, however, were established under the assumption that the input device is separated from the display. In our locally-coupled configuration, in contrast, they are both the same object: the mobile device. Existing population stereotypes thus cannot be applied unless they have been validated under a locally-coupled setting.

Preferred mapping in a locally-coupled configuration

Many interfaces have been proposed that use the motion of a mobile device to control objects on the device's screen. Only few of these works, however, explicitly mention the existence of two alternative mappings (direct/allocentric and inverted/egocentric) and the rationale behind the final choice.

Rekimoto [START_REF] Rekimoto | Tilting operations for small screen interfaces[END_REF] proposed a menu interface controlled by device tilt. Both mappings were discussed, but the chosen alternative (moving the menu behind a fixed cursor, equivalent to our egocentric interpretation) was selected for technical reasons rather than based on an user study. Weberg et al. [START_REF] Weberg | A piece of butter on the PDA display[END_REF] chose the opposite option (moving the cursor in a fixed menu, equivalent to our allocentric interpretation) in their tilt-based menu interface, on the basis that it "felt very intuitive and natural." Bartlett [1] mentioned the existence of two groups of users with different mental models, each expecting the controlled picture to move in an opposite direction when tilting the device. Hinckley and Song [START_REF] Hinckley | Sensor synaesthesia: Touch in motion, and motion in touch[END_REF] also mentioned that slightly more than half of their users had an opposite mental model to others in their tilt-to-zoom technique. Although all this work was conducted in a locally-coupled configuration, it still does not provide sufficient evidence in favor of either the allocentric or the egocentric interpretation. In addition, the studies cited above were conducted on 1D or 2D interfaces, and may thus not be generalizable to 3D manipulation.

Preferred mapping for 3D manipulation

Kaminaka and Egli [START_REF] Kaminaka | Lever controls on specialised farm equipment: Some control/response stereotypes[END_REF] investigated the preferred mapping to translate and rotate a cube through a lever. The lever was alternatively mapped to translations or rotations along each axis. Although this is an actual 3D manipulation task, the 1D input device and non locally-coupled configuration make the results of this study difficult to generalize to our case. Diaz and Sims [START_REF] Diaz | Accidental inversion during three-dimensional orientational control[END_REF] investigated "accidental inversions" of rotations, i.e. what happens when users encounter a mapping opposite to their expectation. Such inversions allow one to identify the actual population stereotypes for 3D rotations. However, the study used a 2D mouse as input device and an external display, which again makes the results difficult to apply to our case.

There appears to be a single study that is fully applicable to our case: Issartel et al. [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF] studied the preferred mapping for 3D manipulation tasks on a locally-coupled mobile device. This work revealed some marked stereotypes in the studied population. However, the study was only preliminary and the number of participants [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF] was relatively low for producing reliable results. Even though both translation and rotation mappings were considered, full 6-DOF mappings were not. Finally, the use of an external tracking marker in the environment could have created a bias toward the egocentric interpretation, a limitation mentioned in the study itself. We thus use Issartel et al.'s [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF] work as a basis but greatly expand the experimental protocol, apparatus, and number of participants to produce broader, deeper, and more reliable results.

MEASURING USER EXPECTATION

It is challenging to determine the "expected" choice of allocentric or egocentric mapping: many experimental biases can affect a study such as prior exposure to the interface, learning effects, or even how the interaction is described to users. We considered several ways to determine this expected mapping.

The first one, inspired by previous work on population stereotypes [START_REF] Wiebe | Application of population stereotypes to computerized tasks[END_REF] and spatial updating [START_REF] Burgess | Orientational manoeuvres in the dark: Dissociating allocentric and egocentric influences on spatial memory[END_REF], would be to show participants a non-interactive description of a manipulation task: for instance, an image representing an object at an initial location, and another image of the same object at a target location. Then, participants would be asked which direction they would move the mobile device to obtain the target result. This protocol has the advantage of only providing the minimum amount of information needed to answer the question, thus avoiding many confounding factors. However, it also has an important drawback: participants never actually use the interaction technique. In our case, it might be difficult for participants to answer questions about this possibly unfamiliar mode of interaction without having experienced it beforehand.

Another way would be to ask participants to perform multiple 3D manipulations in both allocentric and egocentric modes, record Figure 2: The four scenes used in the experiment. In Scene 3, the house model is controlled in the same way as in Scene 2 but the viewpoint is located inside the house. In Scene 4, only the object on the table is controlled by the user while the surrounding environment remains fixed.

the resulting trajectories, and analyze them to detect accidental inversions [START_REF] Diaz | Accidental inversion during three-dimensional orientational control[END_REF]. Such inversions can provide an objective indication that the mapping did not match the user's expectations. This protocol also gets the participants to actually use the interface, although there could be learning effects from prolonged use. It is challenging and error-prone, however, to reliably detect accidental inversions in full 3D trajectories as produced by untrained users. Participants may possibly be taught how to generate "clean" trajectories with extensive training, but this training may also distort their preference between the two mappings compared to the general population.

A third way would be to have participants perform object manipulation tasks in both allocentric and egocentric modes, then rate each mapping. Participants would rate a mapping depending on whether the manipulated object moves and rotates in the direction they expected (which we call the "naturalness" rating). Again, this protocol lets participants actually use the interface, but the actual evaluation now consists of a fully subjective assessment. Compared to the previous approach, this has the benefit of being practically feasible even with novice users, avoiding the biases associated with training. Furthermore, it is also possible that some participants may find both mappings acceptable-or reject both. By letting participants rate both mappings rather than simply choosing the "better" one, this protocol can provide a more detailed understanding of the actual user preference between the two mappings. Therefore, we decided to use this last protocol in our experiment.

CONTEXTUAL CUES

Previous work [START_REF] Burgess | Orientational manoeuvres in the dark: Dissociating allocentric and egocentric influences on spatial memory[END_REF][START_REF] Diaz | Accidental inversion during three-dimensional orientational control[END_REF] has shown that the expected reference frame is not only a matter of personal interpretation, but can also be affected by cues from the environment, i.e. contextual cues. In our configuration, contextual cues would come from the virtual environment because we focus on what happens on the mobile device's screen. Since the virtual environment necessarily varies from one system to another, it is essential to determine whether and how the virtual scene visible on the screen can influence the expected mapping.

First, we can hypothesize that the nature of the manipulated virtual object itself may have an influence. If the object looks like it would be readily manipulable in the real world (e.g., a figurine or a fruit), users may expect to be able to move it directly, i.e. the allocentric interpretation. In contrast, if the object looks like it could be part of the scenery (e.g., a house or a landscape model), users may expect to move around it rather than manipulate it themselves-the egocentric interpretation.

Second, there could be an influence of the geometrical relationship between objects in the virtual scene. If the manipulated object visually moves on the screen whereas other objects in the scene remain fixed (relative to the device), then the surrounding objects may be perceived as an environment relative to which the manipulated object is moving, favoring an allocentric interpretation. If the manipulated object is viewed from inside, then the object is perceived as surrounding the mobile device, which may reinforce the interpretation that the mobile device is moving inside the object (egocentric interpretation) rather than moving the object (allocentric interpretation).

HYPOTHESES AND SETTINGS

Based on these thoughts we had the following hypotheses about which mapping would be expected in different situations:

• H1: When the manipulated object is viewed from inside, users expect an egocentric mapping;

• H2: When the manipulated object is moving within a fixed virtual environment, users expect an allocentric mapping;

• H3: When the manipulated object represents a typically static part of a virtual environment (e.g. a house), users expect an egocentric mapping.

Although Issartel et al. [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF] seemingly disproved hypothesis H2, they suspected a bias caused by the presence of a fixed marker in the real environment, which could have led participants toward an egocentric mental model. We thus wanted to re-test H2 in a markerless tracking setup without this bias.

In order to test the above hypotheses, we designed four different virtual scenes with different contextual cues (Figure 2):

1. a generic object (Stanford rabbit) on a black background, serving as the baseline scene;

2. an object more likely to be perceived as static (a house), on a black background;

3. the house seen from inside;

4. the same object as in Scene 1, surrounded by a fixed house.

Previous studies (e.g., [START_REF] Diaz | Accidental inversion during three-dimensional orientational control[END_REF][START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF][START_REF] Kaminaka | Lever controls on specialised farm equipment: Some control/response stereotypes[END_REF]) often considered translations and rotations separately. The use of device motion as input modality, however, allows full 6-DOF manipulation. It is thus important to also consider both components simultaneously. To investigate the role of each component in 6-DOF manipulation tasks, we stated the following null hypothesis:

• H4: Having a "correct" mapping (which matches user expectations) is equally important for translations and for rotations, i.e. when performing translations and rotations simultaneously, the rating is equally affected by the choice of translation mapping as by the choice of rotation mapping.

Finally, some studies [START_REF] Diaz | Accidental inversion during three-dimensional orientational control[END_REF][START_REF] Kaminaka | Lever controls on specialised farm equipment: Some control/response stereotypes[END_REF] have revealed different user expectations between the axes of manipulation. We therefore hypothesized to find such differences in our configuration:

• H5: Some axes are more important than others in the perceived naturalness of the resulting mapping.

APPARATUS

The experiment was entirely self-contained in a single Tango tablet, providing display, input, and tracking capabilities. The virtual scene was displayed on the tablet's screen together with several tactile buttons to control the experiment. The tablet continuously tracked its own motion in the real world using its built-in sensors. There was thus no external marker in the environment. We captured positions and orientations relative to the fixed initial location where the software was started.

We used this tracking information to implement a relative position control mapping similar to Issartel et al. [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF]. We chose this mapping for its directional compliance so that participants could focus on the sense of motion (allocentric or egocentric) without confusing it with with the axis of motion (which always matches device motion in a directional compliant mapping). We also added a clutching mechanism: the device motion was only applied to the manipulated object while a finger touched the tablet screen. Participants could thus interrupt manipulation to reposition the tablet during complex tasks.

Participants were seated on a chair during the experiment, holding the tablet in landscape mode with both hands. The chair stood in the middle of the room as the presence of nearby fixed objects (e.g., a desk) could have biased participants toward an egocentric interpretation. We used a non-swivel chair to encourage participants to rotate the mobile device itself during rotation tasks rather than rotating themselves on the chair.

PARTICIPANTS

To get more generalizable results than existing exploratory work [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF], we used a larger and broader participant pool. We recruited 30 unpaid participants (12 females) whose age ranged from 20 to 53 (mean=30.3, SD=10.5). Among them, 22 had a university degree while 8 had a high-school degree or less. They all had normal or corrected-to-normal vision.

With this broader user sample it became possible to investigate an additional question: whether the familiarity with 3D software can influence the preference between allocentric and egocentric mappings. However, only 7 participants reported to have sufficient knowledge of 3D modeling software, which was too small to conduct such an analysis. On the other hand, 14 participants-nearly half of them-reported to regularly play 3D video games. We thus chose to focus on gaming experience as an indicator of familiarity with 3D software. Perhaps unsurprisingly, the group of video game players was largely correlated with younger age and male gender. Still, we assumed that the gaming experience itself would have more influence on this experiment than age or gender.

PROCEDURE AND TASK

We first presented participants with the tablet device and told them they would have to "perform translations and rotations in four different virtual environments." In our explanations we took great care to avoid terms such as "translating/rotating the object" or "moving in the virtual scene" since any such mention could have led participants toward an allocentric or egocentric interpretation. There was no prior training phase-we wanted to avoid biases associated with previous usage of the interface. Instead, we demonstrated how to perform translations/rotations by moving and rotating the tablet in front of the participant, and demonstrated the clutching mechanism by pressing and releasing a finger on the screen. The tablet's screen was blanked during this tutorial step.

Participants were then asked to conduct the experiment without further instructions. The experiment itself consisted of a series of conditions, in which two or more mappings were to be evaluated in a given virtual environment. On the bottom of the tablet's screen, several buttons labeled C1, C2, etc. represented the mappings, with the mappings randomly assigned to them. Pressing a button activated the corresponding mapping so participants could switch between mappings to rate them. Except for the third part of the experiment (see below), participants were free to change or go back and forth between mappings at any time during a condition.

To help them assess their own preference, participants were asked to perform 3D manipulation tasks under each mapping. These tasks consisted in translating/rotating a 3D object to a target location, i.e. a docking task. In a typical docking task, the target is normally visually represented in the virtual scene. However, we could not display this target in every condition since having a fixed object in the scene would have resulted in the situation mentioned in hypothesis H2. Moreover, we could not describe this task in terms of "moving an object to a target" as it would have biased participants toward an allocentric interpretation. We thus printed images of the target locations (Figure 2) on a physical sheet of paper, attached to the wall in front of the participants, and which they could consult any time wanted during the study. On each trial, the manipulated object started at a different position and/or orientation. Participants were asked to "try to obtain the same result" as in the images, by any means involving translations or rotations-thus without forcing them into an allocentric or egocentric interpretation. When the target location was reached, the manipulated object changed color to indicate success and was moved to a new location when the finger was released. Participants were encouraged to repeat this task several times to form an accurate opinion before rating a mapping.

When ready to give a rating, participants pressed a button on the tablet's screen and were presented a Likert scale ranging from "not natural" to "natural". We explained the meaning of "natural" to participants as "whether your actions produce translations/rotations in the direction you expected." Again, this definition was carefully worded to avoid any allocentric or egocentric formulation.

Since the Tango tracking system sometimes exhibits a small drift there was a risk that this could lead to unnatural ratings under the above definition. We thus also told participants that "if a slight continuous motion ever occurs without any action on your part, this is a technical limitation that you should ignore in your rating." When all mappings in a condition were rated, the next condition was automatically started.

Part 1: Translation and rotation

In the first part of the experiment, translations and rotations were evaluated separately. Therefore, the conditions consisted of translation-only tasks and rotation-only tasks in the four environments, under two mappings: allocentric and egocentric.

Scene 1-the most generic one-was always presented first to serve as a "baseline" with minimal learning biases. The first two conditions were thus translation tasks in Scene 1 and rotations tasks in Scene 1, presented in an alternate order between participants. The remaining conditions were the 6 combinations of translations and rotations with each of the three other scenes, presented in a random order. Ratings were given on a 4-point Likert scale. This scale was specifically selected to lack a "neutral" point and to encourage participants to decide whether they perceived a mapping as natural or not.

Part 2: Simultaneous translations/rotations

In a second part of the experiment, translations and rotations were performed concurrently (i.e., full 6-DOF manipulation) and each component was alternatively made allocentric of egocentric. There were thus 4 mappings to be evaluated: the four combinations of allocentric or egocentric translations with allocentric or egocentric rotations. These mappings were evaluated within each virtual scene, themselves presented in a random order. We again used a 4-point Likert scale to establish comparisons with the results of the first part.

Part 3: Per-axis inversion

The third part was optional. Since the parts 1-2 already took approximately 30 min, we asked participants to continue voluntarily.

14 participants agreed to continue and with them we examined two conditions, one for translations and one for rotations, presented in random order. Both conditions were set up in Scene 1. In both conditions there were 8 different mappings, in which each manipulation axis (x, y, and z) was alternatively inverted. We then asked participants to rate the techniques on a 3-point Likert scale, thus turning the rating into a choice between "not natural," "neutral," and "natural". We deliberately reduced the rating scale and allowed a neutral point to not overwhelm participants, given the large number of mappings to compare and the small changes between them.

RESULTS AND DISCUSSION

In our analysis we focus on effect sizes-i.e., how much the ratings given to a mapping differ from the ratings given to another mappingto investigate which mapping was preferred in each condition. The ratings obtained from Likert scales are ordinal data, so we used non-parametric statistical tests to quantify the effect sizes. For each condition we performed a Wilcoxon-Pratt signed-rank test on the ratings given to each mapping alternative. We then computed a normalized effect size r from the z statistic produced by this test, as per Fritz et al. [START_REF] Fritz | Effect size estimates: Current use, calculations, and interpretation[END_REF].

Guidelines for the effect size [START_REF] Fritz | Effect size estimates: Current use, calculations, and interpretation[END_REF] are that r>0.5 is a large effect, r>0.3 is a medium effect and r>0.1 is a small effect, but these limits should not be seen as hard thresholds. We also report a bootstrapped standard error σr for each effect size.

Translations

Figure 3 summarizes the ratings given by participants to each mapping in the translation-only tasks.

Scene 1 was always presented first in order to minimize potential biases acquired during manipulation, and was meant as a neutral environment without any of the contextual cues present in the other scenes. Therefore, the ratings obtained from this scene should best approximate the participants' "baseline" mental model. Although the previous experiment by Issartel et al. [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF] showed a strong preference for egocentric translations in such a neutral condition, there was a suspicion that this result could have been biased by the presence of a visible marker in the environment. Because we eliminated this marker in the present setup we had no reason anymore to expect that one mapping would be preferred over the other.

Nevertheless, translation ratings in Scene 1 revealed a small to medium preference in favor of egocentric translations (r=0.27, σr=0.11). While not as definite as in previous results [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF], this preference nevertheless appears to remain true in our markerless setup. The distribution of answers shows that the egocentric mapping was indeed found natural by most participants, whereas the allocentric mapping led to mixed ratings. The egocentric mapping was thus clearly preferred by participants on this first approach to our interface, although the allocentric mapping was not completely rejected either.

Scene 2 showed a similar pattern to Scene 1, with egocentric translations being preferred over allocentric translations. The effect size was actually higher (r=0.41, σr=0.09), though the standard error makes this distinction not completely certain. This second scene was specifically designed to test hypothesis H3 that a typically unmovable 3D object would favor an egocentric mapping. A stronger preference for egocentric translations would thus tend to support hypothesis H3. Yet, even if confirmed this effect appears to be quite small. In addition, since the "baseline" mapping for translations already seem to be egocentric (as demonstrated in Scene 1), an effect that reinforces the egocentric mapping would have little practical implications for the choice of a default translation mapping. In Scene 3, the preference was strongly in favor of the egocentric mapping (r=0.53, σr=0.05), even more than in Scenes 1 and 2. There is thus strong evidence to support hypothesis H1, i.e., that translating an object viewed from inside is preferably accomplished with an egocentric mapping.

Scene 4 also showed an egocentric mapping preference (r=0.30, σr=0.12). This is surprising since we were expecting that manipulating an object within a fixed virtual environment would favor an allocentric mental model (hypothesis H2). When we noticed during the experiment that some participants gave unexpectedly high ratings to the egocentric mapping, we took the opportunity to ask them the reasons behind this choice at the end of the first session. Their comments suggested that they were mainly focused on performing the task and did not pay much attention to the fixed virtual scene. Indeed, since participants went through at least two other conditions before encountering Scene 4, it is believable that the task was beginning to become a "routine" at this point. In addition, since the scene was fixed in screen space it is plausible that some participants merely considered it as a background image and did not adopt the mental model that we expected them to do.

Rotations

Figure 4 summarizes participants' ratings for the rotation-only tasks. The "baseline" condition Scene 1 showed a medium effect (r=0.37, σr=0.10) in favor of allocentric rotations. Most participants rated the allocentric mapping as natural but gave mixed ratings to the egocentric mapping. This confirms the results of previous work [START_REF] Issartel | Analysis of locally coupled 3d manipulation mappings based on mobile device motion[END_REF] which also showed a preference for allocentric rotations in this condition.

The allocentric mapping was also preferred in Scene 2, but apparently less strongly (r=0.24, σr=0.12) than in Scene though the standard error again makes such a distinction uncertain, if confirmed this result would support hypothesis H3 that a typically unmovable object favors an egocentric mental model. As with translations, however, this effect appears to be very small. Unlike translations though, this effect would lead people toward the opposite mapping compared to Scene 1. Yet, because of its small strength it does not seem to be sufficient to change the overall preference for allocentric rotations. In contrast to the other scenes, Scene 3 showed a very marked preference for egocentric rotations (r=0.57, σr=0.04). This is again strong evidence for H1 that manipulating an object viewed from inside is preferably accomplished egocentrically.

Scene 4 showed the same pattern as Scenes 1 and 2, i.e. we saw a preference for allocentric rotations (r=0.28, σr=0.11). Yet, egocentric rotations were still rated as natural by little more than half of the participants. Since the preferred mapping in Scene 1 was already allocentric, we cannot provide any particular support for H2. If anything, the smaller effect size compared to Scene 1 tends to disprove H2 since the egocentric mapping was more readily accepted in this configuration.

Influence of gaming experience

We conducted a second analysis of the translation and rotation results by splitting participants into two groups: those with regular experience with 3D video games (gamers group, 14 participants), and those who reported to seldom or never play such video games (non-gamers group, 16 participants). Although the preference for each mapping in each scene remained the same for both groups, in several cases the effect size was different-i.e. the preference was less marked for one group than for the other (Figure 5).

In Scene 1, non-gamers apparently had a weaker preference for egocentric translations (r=0.14, σr=0.17) compared to gamers (r=0.37, σr=0.16). Since Scene 1 can be considered as "baseline," we can thus observe that-with some reservations due to the standard error-non-gamers may not actually have a strong a priori preference for translations, and that gaming experience may create a bias for the egocentric mapping. Concerning rotations, the preference was nearly identical between gamers (r=0.36, σr=0. 5: Effect sizes and standard error for the preferred mapping in the "gamers" and the "non-gamers" groups. and non-gamers (r=0.38, σr=0.13). It thus appears that gaming experience does not produce any such bias for rotations.

In Scene 2, the gamers' preference for egocentric translations was of a comparable level to Scene 1 (r=0.26, σr=0.18). The non-gamers' preference, however, was much more marked than in Scene 1 (r=0.54, σr=0.07). Gamers thus seem to be less affected by a change of scene contents than non-gamers, possibly because their experience makes them more tolerant to using either mapping in various virtual environments-albeit with a persistent bias toward the egocentric mapping. The difference between the two groups was less clear for rotations, but still hinted at a similar trend (gamers: r=0.18, σr=0.20; non-gamers: r=0.29, σr=0.15). These results may thus support hypothesis H3, but only for non-gamers.

For Scene 3, the preference for egocentric translations was as strongly marked for gamers (r=0.54, σr=0.08) as it was for nongamers (r=0.52, σr=0.08). We can thus infer that the conditions in Scene 3 (viewing the manipulated object from inside) had a strong enough effect to overcome the presumed tolerance of gamers for their non-preferred (allocentric) mapping. Rotations also showed a clear preference for the egocentric mapping among both groups (gamers: r=0.64, σr=0.02; non-gamers: r=0.50, σr=0.09), confirming hypothesis H1.

In Scene 4, like in Scene 2, non-gamers had a strong preference for egocentric translations (r=0.44, σr=0.13), while gamers were more tolerant of either mapping (r=0.13, σr=0.20). We observed the same pattern with rotations: non-gamers had a preference for allocentric rotations (r=0.39, σr=0.14), while gamers were more neutral (r=0.09, σr=0.19). Although these results still contradict H2, they are consistent with our above assumption that gamers may be more tolerant to using different mappings in various virtual environments.

Simultaneous translations/rotations

Figure 6 shows the ratings for each combination of allocentric and egocentric translations and rotations, in tasks involving full 6-DOF manipulation. For conciseness, we use the notation T(tmap)/ R(rmap) in which "tmap" describes the translation mapping and "rmap" describes the rotation mapping. The results for Scenes 1 and 2 both present a similar pattern: pairwise differences in ratings were comparatively larger between T(ego) and T(allo) combinations (medium effect sizes) than between R(ego) and R(allo) combinations -0.12 (0.13) --Figure 6: Ratings in the full 6-DOF manipulation tasks (simultaneous translations/rotations), along with the pairwise effect sizes.

The notation "T(tmap)/R(rmap)" refers to a translation mapping "tmap" and a rotation mapping "rmap".

(small to zero effect sizes). It thus seems that, in these two scenes, the choice of translation mapping is more important than the rotation mapping when performing both simultaneously. This appears to disprove hypothesis H4.

As expected from the translation-only results, T(ego) combinations were rated higher than T(allo) combinations in all scenes except Scene 3. In these scenes, however, the T(ego)/R(ego) mapping was apparently preferred to the T(ego)/R(allo) mapping. This is surprising because our results for the first part of the experiment showed a preference for allocentric rotations in such scenes. Moreover, the T(allo)/R(allo) mapping also seems to be preferred to the T(allo)/R(ego) mapping in Scenes 1 and 4, with a tie in Scene 2. Although these differences are below the standard error, they nevertheless hint at a similar trend in each of these scenes. In addition to the dominance of the translation mapping, there might thus be a preference for having the same mapping for both translations and rotations.

Overall, the four combinations were given comparable ratings in Scenes 1 and 2, the differences between each combination were thus also comparable. These differences were, however, more uniform in Scene 2 than in Scene 1. This could be explained by the lower number of strongly negative ratings for the T(ego)/R(allo) and T(allo)/R(ego) combinations-i.e. two combinations that featured an egocentric mapping. This is consistent with the previously identified small possible effect that would slightly reinforce the preference for the egocentric mapping in Scene 2. It also provides additional (if small) evidence for hypothesis H3.

Scene 3 showed a strong difference between the fully egocentric (T(ego)/R(ego)) combination and the three other combinations. Almost all participants rated the former as natural, whereas the latter (not fully egocentric) three were largely rated as unnatural. Still, among these three lowest-rated combinations, T(allo)/R(ego)the only one to feature egocentric rotations-was rated noticeably higher, despite consisting of two opposite mappings. We can hypothesize that this is due to the larger influence of rotations on visual flow when the manipulated object is viewed from inside. In such a situation, the positive effects of having rotations that match the preferred mapping (egocentric, as per our previous results) appear to noticeably alleviate the negative effects of a non-preferred (allocentric) translation mapping, even though the translation and rotation mappings are different. In any case, these results confirm again the importance of an egocentric mapping when the manipulated object is viewed from inside (hypothesis H1).

Per-axis inversion

Figure 7 shows the ratings given by participants in the third part of the experiment, in which the direction of motion along each manipulation axis was alternatively inverted. The x-axis ran along the left-right direction of the tablet's screen (which was itself held in landscape orientation), the y-axis was aligned with the top-down direction of the screen, and the z-axis was orthogonal to the screen plane. Unlike during the previous parts, we asked for ratings on a 3-point Likert scale.

For translations, one configuration was clearly preferred over the others: the fully egocentric mapping. This is consistent with the results of the previous parts that revealed a preference for egocentric translations in Scene 1. Given the strength of this effect (100% of participants rated this mapping as natural, far above the other configurations) there does not seem to be any advantage to gain from a mixed mapping for translations.

However, one question that still remains is whether some manipulation axes have more influence than others in the perceived naturalness of a mapping (hypothesis H5). One such pattern seems to be visible in the above results: configurations where the y-axis was inverted (i.e. egocentric) were consistently rated higher than the others-with the exception of the fully allocentric configuration. We thus conducted a further analysis by merging the ratings in egocentric and allocentric groups depending on the state (inverted or not) of each manipulation axis. The results indeed revealed a larger effect of the y-axis (r=0.35, σr=0.07), compared to the effects of the x-axis (r=0.18, σr=0.09) and the z-axis (r=0.05, σr=0.10). The reason why the fully allocentric was comparatively rated higher, despite its non-inverted y-axis, could be explained by a preference for a consistent mapping between all axes-similar to the possible preference for a consistent mapping between translations and rotations discussed in the previous section. Nevertheless, the larger influence of the y-axis appears to validate our H5 hypothesis for translations.

For rotations, no configuration was unanimously favored and the differences between each configuration were smaller overall than for translations. Merging the ratings into groups according to each manipulation axis confirmed that the influences of all axes were limited (x: r=0.17, σr=0.09; y: r=0.00, σr=0.09; and z: r=0.11, σr=0.09), which does not confirm H5 for rotations. Yet, one configuration seems to have been strongly disliked compared to all the others: the allo-ego-allo (AEA) mapping. This result is unexpected, and we cannot find any reason that could explain such a sharp drop in ratings. This aspect would thus require further investigation.

CONCLUSION

The "baseline" preference, i.e. which alternative was found most natural with no prior exposure to the interface and minimal contextual cues, was egocentric translations and allocentric rotations among all users. In the gamers group, the baseline for translations was less marked than in the non-gamers group. However, the baseline for rotations was similar.

Regarding contextual cues, H1 was strongly supported by our results: when a manipulated object is viewed from inside, the mapping should be egocentric for both translations and rotations. Surprisingly, H2 was not supported. It appears that manipulating an object within a fixed virtual environment does not induce a preference for an allocentric mapping. There was limited support for H3 that a typically static object should be manipulated with an egocentric mapping. The results hint at a possible weak effect, though not sufficient to overcome other factors (such as the baseline preference).

Gamers seem to be less influenced by the scene contents than non-gamers-except when the manipulated object was viewed from inside. This could mean that gamers are more tolerant to encountering various mappings in 3D applications. Yet, the overall preferred mappings were still the same in both groups. We recommend, therefore, that translations-only mappings should be made egocentric in all cases, and that rotation-only mappings should be made allocentric in all cases except when the manipulated object is viewed from inside-in which case it should be made egocentric.

In full 6-DOF mappings, where users perform both translations and rotations simultaneously, the choice of a "good" translation mapping (egocentric, according to the results of part 1) seems to be more important than the choice of rotation mapping, thus disproving the null hypothesis H4. However, when the manipulated object is viewed from inside, both mappings should be egocentric. In addition, there seems to be a positive effect of having the same mapping for translations and rotations. Therefore, we recommend that a 6-DOF manipulation mapping should be T(ego)/R(ego) (i.e. fully egocentric) in all cases.

We saw no benefit of a "mixed" mapping that selectively inverts some of the manipulation axes, compared to a "fully" egocentric or allocentric mapping. Yet, if such a mixed mapping must be implemented, the y-axis (along the vertical direction of the device's screen) appears to have more influence on the perceived naturalness of translations. This would support hypothesis H5, but only for translations. For reasons we have yet to explain, one mixed mapping for rotations (allo-ego-allo) was found much less natural than all the others.

Figure 3 :

 3 Figure 3: Participants' ratings for each mapping in the translation tasks.

Figure 4 :

 4 Figure 4: Participants's ratings for each mapping in the rotation tasks.

T

  (allo)/R(allo) T(allo)/R(ego) T(ego)/R(allo) T(ego)/R(ego) T(allo)/R(allo) T(allo)/R(ego) T(ego)/R(allo) T(ego)/R(ego) T(allo)/R(allo) T(allo)/R(ego) T(ego)/R(allo) T(ego)/R(ego) T(allo)/R(allo) T(allo)/R(ego) T(ego)/R(allo) T(ego)/R(ego)

Figure 7 :

 7 Figure 7: Ratings and pairwise effect sizes in the per-axis inversion part (labels are in the form "XYZ": A=allocentric, E=egocentric).

  [START_REF] Warrick | Direction of movement in the use of control knobs to position visual indicators[END_REF]

	allo		Translations			ego
	Scene 1
	Scene 2
	Scene 3
	Scene 4
	0.6	0.4	0.2	0	0.2	0.4	0.6
	allo		Rotations			ego
	Scene 1
	Scene 2
	Scene 3
	Scene 4
	0.6	0.4	0.2	0	0.2	0.4	0.6
			gamers	non-gamers
	Figure

http://www.google.com/atap/project-tango/


A L Charley
email: charleyal@chartreuse.cea.fr

P Bandelier

B Mortini

A Lagrange

O Lartigue

P Schiavone

93nm immersion lithography studies with a double grating high NA achromatic interferometer

Introduction

As immersion lithography will be the lithography technique for sub-65nm generation device fabrication, benefits and drawbacks of the introduction of an immersion fluid between the imaging optics and the wafer have to be studied. In this context, it is of high interest to be able to understand the properties of hyper high NA imaging and to do so, to have access to a technique which can mimic an industrial immersion stepper by having the possibility to tune the polarization state and numerical aperture. Interferometric lithography has proven to be a useful method to study projection imaging at high numerical aperture (NA). It has been shown to help addressing several issues of immersion lithography such as polarization state impact on imaging, photoresists material screening as well as preliminary defectivity considerations due to the introduction of water and high index fluid studies [START_REF] Bourov | Proc. SPIE[END_REF][START_REF] Conley | Understanding the photoresist surface-liquid interface[END_REF][START_REF] Dammel | Leaching phenomena and their suppression in 193nm immersion lithography[END_REF]. In the frame of this work, a home-built interferometer with immersion lithography capabilities has been fully designed and mounted in our facilities. Specific designs have been made in order to reach NAs as high as 1.4. All issues preventing the printing of high-contrasted lines over a large area, such as laser beam uniformity and vibrations control have been addressed and 40-nmhalf-pitch resist lines can be currently printed with water immersion lithography. As a result, the interferometer has been used to screen resist and topcoat candidates for immersion lithography before their introduction in a production environment. An overview of our results is presented, focusing on the topcoat/resist compatibility. Besides, in order to prepare hyper NA lithography, We have implemented a simulation model which can be used to predict the light distribution inside a photolithographic stack. This model enables us to predict the resist image created by the interference of two coherent beams in the photo-resist volume. Simulations of polarization effects at oblique angles will be presented as well as the evaluation of image contrast in both TE and TM polarization. The contrast in TM polarization is dropping with increasing NA. Finally, we validate those predictions by experiments on our interferometer.

Experimental setup

The apparatus is based on the interfering beams which are created by illuminating a first diffraction grating followed by a second diffraction grating recombining the diffracted beams on the photo-resist plane (see figure 1). A two grating interferometer of this type had been previously built by MIT researchers for dry lithography [4,5,6] and it has been adapted to immersion interferometric lithography. The setup have been designed and simulations have been performed in order to optimize the grating diffraction efficiency as a function of the etch depth and the fractional linewidth [7]. After calculations, the numerical aperture can be expressed as eq. ( 1) :

Q NA λ = ( 1
)
where λ is the wavelength and Q is an equivalent diffraction grating pitch defined by eq.( 2).

1 2 1 2 1 P P Q - = (2)
The main advantage of this system is to be an achromatic interferometer : thus, temporal coherence is irrelevant and spatial coherence limits only the depth-of-focus within which interference can be obtained. Therefore it is possible to use a basic commercial ArF excimer laser as the exposure source. The other advantage of this interferometer is that the main optical elements, that is the two diffraction gratings, are fabricated using the capabilities of the silicon line available in our laboratory (including e-beam direct writing lithography techniques) ; therefore we are free to shift to various applications such as high index fluids testing and contact holes printing. The source is a 193 nm GAM excimer laser with spatial and temporal coherence lengths of respectively 500 and 930 µm. The laser beam is propagated through a mechanical shutter enabling a precise control of the exposure time, a beam expander x5 to limit the beam divergence and polarizers before reaching the two diffraction gratings setup. Polarization control is made with a polarizer which linearly polarizes the output laser beam followed by a quarter wave plate that can be rotated to tune gradually the polarization between TE and TM mode (fig. 2).

Fig. 2: Schematic of the double diffraction interferometer and its optical environment.

The grating substrate parallelism is controlled with the help of a Fizeau interferometer.

A special system have been designed for water supply and recovery, therefore water is degassed, filtered, temperature controlled and recovered after exposure for analysis.

For the resist/Top Coat interactions studies, results from two Methacrylate based resists will be discussed. Lithographic performances of the resists with or without top coat materials have been checked with the interferometer. Secondly, specie concentration profiles have been monitored by Secondary Ion Mass Spectrometry (SIMS) in order to detect possible resist component leaching phenomenon due to the contact with water during the immersion step [START_REF] Maenhoudt | Opportunities and challenges in immersion lithography[END_REF].

The SIMS tools were a Cameca IMF 6f, using a Cs+ source and a Simslab (VG Instruments), with a Ga+ source.

Experimental results

The three first designs presented in table 1 (respectively 0.32, 0.97 and 1.2 NA) have been mounted in the interferometer and validated. After compaction of the system and the settingup of an anti-vibration table to prevent vibration issues, high contrasted lines have been obtained in all configurations. Figure 3 shows photoresist lines printed with the immersion double diffraction interferometer at NA up to 1.2 using a 193nm immersion photoresist. Though no top coat has been used to act as a barrier layer, no major profile issue can be observed with this resist. 50 nm L/S are well defined and 40nm L/S are achievable. The immersion double diffraction interferometer has been used to print dense contact holes for further studies on contact holes process by double exposure. Figure 4 shows 50 nm contact holes printed in standard immersion resist. It has to be outlined that for this first set of contact hole printing experiments, the resist formulation which were used has been a line and space Shutter λ/2

Laser

Beam expander Polarizer resist formulation, i.e. not fully optimized to achieve such features. However, 50nm contact holes have been printed and further work will now be conducted in order to better optimize resist behavior for such CD targets.

Fig. 4: 50 nm contact holes printed with the immersion double diffraction interferometer Finally significant progresses have been done on diffraction gratings fabrication and we are now able to fabricate diffraction gratings with periods down to 200 nm and diffraction efficiency up to 10 % using our lab facilities. They have been tested and mounted in the interferometer as beam splitter. 55 nm half pitch lines have been demonstrated by this means (see figure 5). Fig. 5: 55-nm-half-pitch photoresist lines printed with the immersion double diffraction interferometer with a home made grating as beam splitter

The validation of this optical element is of high interest since it will help us to switch to various applications such as high index fluids testing and contact holes printing. Indeed this interferometer is well adapted to the test of various fluids, even aggressive ones that can damage the interferometer last optical element since diffraction gratings are easy and relatively cheap to fabricate.

Polarization studies

Since first industrial immersion tools will be unpolarized, it is of high interest to predict the polarization effects at high NA. Such an interferometric setup is well suited for such studies since we are able to tune easily the polarization from TE to TM mode. In this section we evaluate the image contrast in function of polarization by calculation and we confirm the predictions with experiments. Figure 6 represents the two beams interfering in the resist layer. As the image contrast is defined by (I max -I min )/(I max +I min ), contrast in TE remains equal to one whatever the incident angle and contrast in TM drops with increasing incident angle. Fig. 7 shows the image contrast versus NA. In TE polarized light, the electric fields vectors will always fully interfere since they are parallel. In TM polarized light, the electric fields vectors cannot interfere when they are perpendicular (see figure 6). Therefore the contrast drops to zero at NA=1.26. However the contrast loss in resist is less than in air since the resist refractive index is higher, therefore the angle made between the interfering beams is smaller. This will also lead to the fact that at same NA the contrast will not be changed from dry to wet lithography. In our interferometric configurations, NA of 0.32 to 1.2 are available. Polarization studies have been done with the 0.97 NA configuration. In this configuration contrast in TM polarization is expected equal to 0.4 (see figure 7).

Resists and topcoat studies

One of the objectives of our interferometer setting is to propose a first screening of immersion dedicated resist formulations, with or without top-coat, to check their lithographic capabilities, compatibility with top-coat layers and leaching behaviors. Figures 9 to 12 present the lithographic capabilities and fluorine profiles of two 193nm line and space resists, referred as resists A and B. Resist A has been designed for immersion lithography with a top coat barrier layer approach, Resist B is a conventional ''dry'' 193nm resist that has been tested in immersion. SIMS analysis have been then conducted on the same lithographic stacks with or without contact with immersion water for 60s. PAG concentration profile has been monitored following the negative ion containing fluorine. As a result, the variations of fluorine ion concentration as a function of the immersion step can be correlated to the leaching of the resist.

In addition to fluorine ion profiles which are presented here, resist matrix profile can also be controlled with 12 C -and 16 O -species, and even BARC layer can be detected looking at the CN -/ 26 C 2 H 2 -species. Figure 9 represents the fluorine profile, corresponding to the PAG concentration profile in Resist A without top coat. The reference profile (without soaking) shows an over concentration near the surface, that can be related to various causes such as PAG and resist solubility in the casting solvent, PAG / polymer affinities and film formation conditions during the coating step. After 60s of soaking in deionized water, the Fluorine ion profile is modified near the surface. A loss of Fluorine species is observed near the resist surface. This concentration decrease is limited to an average 50nm deep interfacial layer, corresponding to some PAG leaching from the resist to the water in absence of a top coat barrier layer. This characterization result is in good accordance with the lithographic performance of resist A without top-coat, showing some T-topping phenomenon over about 50 nm in depth (Figure 10). On the other hand, the use of a top coat layer avoids T-topping issues. Resist thickness: 190 nm.

On the other hand, figures 11 and 12 represent fluorine profile for Resist B, the conventional ''dry'' formulation tested in immersion. Even without top coat, no PAG loss can be observed at the resist surface after 60s soaking. This result is quite encouraging for the use of such formulation in a non top coat process. However, due to some pattern collapse, we have not been able to obtain 50 nm L/S patterns with Resist B without top-coat. Figure 13 shows the good performance of Resist B with a topcoat approach. Straight profiles have been obtained.

Simulations

We have implemented a simulation model which can be used to predict the light distribution inside a photolithographic stack. This model enables us to predict the resist image created by the interference of two coherent beams in the photo-resist volume. Wavelength, polarization state, NA, refractive index immersion medium and lithographic stack can be chosen. There are no limitations in the number of layers. In particular, it is possible to use double BARC stack. Assuming a development model, the cross section of the printed lines could be predicted.

We have implemented this algorithm in a Matlab environment. The introducing parameters are:

-the numerical aperture NA, which is linked to the incident angle via NA n = × θ sin -the polarization direction -the immersion medium, defined by its optical index at 193nm -the stack, defined by the layers optical index and thickness -the Silicon substrate The lines profiles have been estimated assuming that the resist which is exposed below the dose to clear is remaining and the rest is removed by the developer.

TE polarization

The intensity interfering pattern is calculated inside a photoresist cross section in TE polarization and at 0.97 NA leading to 50-nm half pitch lines (see figure 14). One can notice that the intensity of light inside the resist is not constant in z. In the case above, we have used a BARC thickness at its optimal thickness. Even in this case, we can see depth dose variation which are in the range of 10%.

The corresponding lines profiles can be seen in figure 15. We can notice a slight linewidth variation even at optimum BARC thickness.

Cross section of the lines

TM polarization

The same stack, but with 50 nm resist and in TM polarization shows lower contrast and more variations within the resist thickness (Figure 16). In figure 17, the fringes at the top and at the bottom of stack have been plotted. We can notice a slightly higher contrast at the top of the resist. It is of high interest to have access to lines profiles since we can evaluate the effect of substrate reflectivity leading to standing waves. Some experimental work is now under investigation to confirm those simulations. Further improvements of the simulation tool are on going to evaluate the BARC reflectivity in the resist and a strategy for BARC optimization.

Conclusions

We have completely designed an immersion interferometer to generate resist patterns with period down to 60 nm. The great advantages of this setup compared to others already existing is that it is possible to use a basic commercial ArF excimer laser as the exposure source and that the main optical elements are home-fabricated enabling us to switch to various applications such as high index fluids testing and contact holes printing in a very simple way. Imaging at 0.32, 0.97 and 1.2 NA was demonstrated and polarization effects at oblique incidence angles have been shown. Moreover this interferometer have been used to propose a first screening of immersion dedicated resist formulations, with or without top-coat, to check their lithographic capabilities, compatibility with top-coat layers and leaching behavior.

Finally we have presented a simulation model which can be used to predict the light distribution inside a photolithographic stack. Some simulations have been shown and some work in under investigation for BARC optimization purpose.

Finally we are currently working on the interferometer design to extend it to hyper high NAs, aggressive CDs and to build a monolithic interferometer with home made gratings which will be compatible with high index fluids.

Fig. 1 :

 1 Fig. 1: Schematic of the immersion achromatic interferometric configuration and diagram of diffraction angles, materials refractive index and gratings pitches.

Fig. 3 :

 3 Fig. 3: Photoresist lines at a) NA=0.32 and half-pitch of 150 nm, b) NA=0.97 and half-pitch of 50 nm, c) NA=1.2 and half-pitch of 40 nm.

Fig. 6 :

 6 Fig. 6: Schematic of the interference phenomena occurring in the resist layer in TE and TM mode

Figure 7 :

 7 Figure 7: Resist image contrast versus NA for TE and TM polarization in two beams interferometry.

  Fig 8 shows resist lines of 100 nm pitch in TE and TM polarization. We notice high contrasted lines in TE polarization whereas the )significant in TM polarization. The effect of this low contrast is a noticeable line roughness.

Figure 8 :

 8 Figure 8: 100-nm-pitch photoresist lines in (a) TE and (b) TM polarization

Figure 9 :

 9 Figure 9: SIMS fluorine profiles for Resist A with or w/o a 60s soaking step in water.Resist thickness: 190 nm.

Figure 10 :

 10 Figure 10: 55nm L/S patterns printed by immersion interferometry. Resist A. Left : without top-coat layer, T-top profiles are observed. Right: with a top-coat acting as a barrier layer to PAG leaching. Resist thickness: 190 nm.

Figure 11 :

 11 Figure 11: SIMS fluorine profiles for Resist B with or w/o a 60s soaking step in water.Resist thickness: 100 nm.

Figure 12 :

 12 Figure 12: SIMS fluorine profiles for Resist B with a top coat layer with or w/o a 60s soaking step in water. Resist thickness: 100 nm.

Figure 13 :

 13 Figure 13: 50nm L/S patterns printed by immersion interferometry.Resist B with a top-coat layer.Resist thickness: 100 nm.

Fig. 14 :

 14 Fig.14: Simulated aerial image of two beams interference in TE polarization at 0.97 NA.

Fig. 15 :

 15 Fig.15: Simulated resist line profiles in TE polarization at 0.97 NA. The lines are represented in white, the BARC in light yellow and the air in orange.

Fig. 16 :

 16 Fig.16: Simulated aerial image of two beams interference in TM polarization at 0.97 NA.

Fig. 17 Fig. 18 :

 1718 Fig.17: a) Intensity fringes at the top and bottom of the resist, b) Simulated resist line profiles.The lines are represented in white, the BARC in light yellow and the air in orange.Both simulations are performed in TM polarization at 0.97 NA.