, professional knowledge contained declarative and procedural knowledge concerned with the sport sciences and the pedagogy, and were sport specific. Interpersonal knowledge was continuously developed from individual and group interactions. According to Gilbert and Trudel (1999, 2005), intrapersonal knowledge was concerned with understanding of oneself and the ability for retrospection and reflection. Abraham and Collins (1998) also showed that coaches' knowledge referred to rules containing if-then statements.

. These variables were limited to individuals; they did not relate to the practice structures (i.e., training center, federations). To our knowledge, nothing seems to be reported on the constraints represented by these structures and how the coaches manage them.

 showed that to manage constraints, coaches used various operating modes including the use of routines, flexible planning strategies, joint control of training with athletes and reference to past experiences. These two studies showed that the coaches' actions were grounded on different intermixed temporalities that referred to past experiences, current situations and what was expected of the athletes. However, these studies were limited to short time-frames.

. Coaches constantly have to manage with constraints. The studies presented above showed the process used to set out plans (set apart those

Time Management in the Context of Elite Sport Training

Anne-Claire Macquet

Institut National du Sport, de l'Expertise et de la Performance

This article reports on time management in an elite sports context. It aims at characterizing how coaches experience dealing with athletes' time management in a sport and academic institute and their constraints. Ten male coaches participated in this study. Each coach was asked to describe his time management activity during the season. Inductive and deductive analysis revealed two main results. The first showed the coaches dealt with a stringent set of constraints concerned with: (a) season organization, (b) training period and task sequencing, (c) the institute's set times, and (d) the uncertainty linked to the evolution of training. The second emphasized that the coaches used three complex operating modes: (a) the use of organizational routines based on reference to past experience, (b) season shared time management, and (c) time management based on flexible plans. The results are discussed in relation to research that has considered planning and time management.

The primary function of coaches in elite sport contexts consists of organizing athletes' work to achieve results in competitions. Some authors highlighted the importance of this work organization along time (e.g., [START_REF] Côté | The development of coaching knowledge[END_REF][START_REF] Côté | The coaching model: A grounded assessment of expert gymnastic coaches' knowledge[END_REF][START_REF] Gilbert | Validation of the Coaching Model (CM) in a team sport context[END_REF][START_REF] Gould | A survey of U.S. Olympic coaches: Variables perceived to have influenced athlete performances and coach effectiveness[END_REF]. In other words, work organization is related to time organization. [START_REF] Côté | Effective behaviours of expert rowing coaches: A qualitative investigation of Canadian athletes and coaches[END_REF] emphasized that only a few sport psychology studies have considered time organization components. In the literature, time was organized according to a rational model that aims to optimize or rather maximize the time available for work as its goal (e.g., [START_REF] Burton | Sport psychology for coaches[END_REF][START_REF] Burton | The fundamental goal concept: The path to process and performance success[END_REF][START_REF] Gould | A survey of U.S. Olympic coaches: Variables perceived to have influenced athlete performances and coach effectiveness[END_REF][START_REF] Horton | Expert coaches in action[END_REF][START_REF] Weineck | Manuel d'entraînement[END_REF]. Time organization was mainly concerned with planning. Planning consists of the different steps and timeframes that one thinks are required to reach a goal. Each step indicates what has to be done. Everything seems to be predicted to reach the result. [START_REF] Côté | Effective behaviours of expert rowing coaches: A qualitative investigation of Canadian athletes and coaches[END_REF] showed that coaches prepared their athletes for unexpected situations that could have occurred during training sessions or competitions; they plan proactively.

The literature on planning largely focused on the identification of the components used by the coaches to set out plans. Planning was considered indirectly (e.g., [START_REF] Côté | The coaching model: A grounded assessment of expert gymnastic coaches' knowledge[END_REF] or directly (e.g., [START_REF] Abraham | The coaching schematic: Validation through expert coach consensus[END_REF] as a decision making process that was based on the use of knowledge. In their of [START_REF] Saury | Practical knowledge in expert coaches: On-site study of coaching in sailing[END_REF][START_REF] Sève | L'action de l'entraîneur de tennis de table comme action située [Action of table tennis coach as situated action[END_REF] and the constraints the coaches had to manage when they implemented plans. The studies did not account for the adaptive activity of the coaches when they managed constraints over a season. They also did not show how coaches managed different athletes' time, including time for sports training and time for out-of-training activities in a sport structure where athletes are committed to both sports and academic programs within sports institutes and universities (e.g., [START_REF] Bouchetal-Pellegri | Carrière sportive[END_REF]. [START_REF] Côté | Effective behaviours of expert rowing coaches: A qualitative investigation of Canadian athletes and coaches[END_REF] suggested that more research on sports organization was necessary. [START_REF] Gould | A survey of U.S. Olympic coaches: Variables perceived to have influenced athlete performances and coach effectiveness[END_REF] highlighted the need to understand the psychological principles used by experienced coaches and the principles they considered as efficient to help less experienced coaches. They also emphasized the need to take a more multidisciplinary approach to study the performance process.

Performance process within time organization has been studied in sociology, psychology and management sciences within the concept of time management. [START_REF] Grossin | Pour une science des temps: Introduction à l'écologie temporelle[END_REF] and Francis-Smythe and Robertson (1999) showed that managers' time was fragmented, multiple and non linear. Managers had to master fluid and flexible temporal systems and were required to be flexible. [START_REF] Sabelis | Time management: Paradoxes and patterns[END_REF] highlighted the need to investigate the interwoven layers of other temporal traits and aspects. She underlined the interest of reconstructing the process by which time is managed in theory, through training programs and the experience of people 'managing their time'.

In addition to explaining how to manage risky and unavoidable situations and going beyond the simple risk theory, [START_REF] Dupuy | Pour un catastrophisme éclairé[END_REF][START_REF] Dupuy | Dans l'oeil du cyclone[END_REF] has developed a metaphysics of temporality. He presented a model of time management called time of project. This consists of a loop between the past and the future. The future refers to the expectations of events one wants to avoid (e.g., a catastrophe) or to happen (e.g., medals to be won by athletes in major competitions). The future is anticipated and is considered to be already realized. This anticipation becomes the fixed point of the loop. It is from this fixed point that 'the predictor' investigates the 'past' (i.e., a past which is not yet realized). The 'predictor' knows that his/her prediction is going to produce some causal effects in the world (e.g., preparation for competitions). He/she takes them into account to realize or avoid the predicted future. Time of project is looped: future and 'past' are thus codetermined. It appears in the same way as a retrospective causal relation model. In the course of time, the agents adjust themselves to the emerging structural, factual and human constraints to achieve the causal production of the future. Time management refers to this process consisting of anticipating a result at a specific moment, setting timeframes regarding constraints and adjusting them in the course of time to achieve the anticipated result. Time of project model identifies the constant adjustment of flexible plans to achieve a specific result and describes what can be observed when expert coaches manage time in training activities. It provides theoretical and practical insights about time management in sports training activities. It allows for the reduction in tensions linked to the uncertainty of practice, by not trying to predict what is unpredictable but rather by fitting reality into the practice. Previous studies showed the components used to set out plans (e.g., [START_REF] Côté | Effective behaviours of expert rowing coaches: A qualitative investigation of Canadian athletes and coaches[END_REF], the coaches' operating modes during planning [START_REF] Jones | A comparative analysis of expert and novice basketball coaches' practice planning[END_REF] or adaptive activity during training sessions [START_REF] Saury | Practical knowledge in expert coaches: On-site study of coaching in sailing[END_REF]. The time of project model could extend knowledge about coaches' time management activity over a season.

The present article aims at characterizing how coaches manage athletes' time in elite sport settings. More specifically, it aims at characterizing the constraints the coaches have to deal with in managing athletes' time and the coaches' activity when they experience time management in an elite sport and academic training institute.

Participants

Method

Coaches of elite athletes were selected to participate in the study. The criteria employed to select them included: (a) being head coach, (b) coaching in the same institute for sport and academic training, (c) a minimum of 10 years' coaching experience in elite sport, (d) development of several international level athletes, and (e) recognition for outstanding coaching (i.e., considered by their federation as one of the best coaches in France). Ten coaches were selected and agreed to participate in the study. Data saturation was reached after reviewing interviews from the 10 coaches. Coaches ranged in age from 36 to 59 years (M = 47 years, SD = 7 years and 10 months). Nine of them were elite athletes before coaches. They all had French coaching qualifications. They were all male. No female coach fulfilled all these requirements and was available to participate in the interview. This gender exclusivity reflects a gender equity problem in coaching in France; there are very few female coaches of elite athletes in Olympic sports [START_REF] Lamberbourg | Enquête nationale sur les conseillers techniques sportifs féminins [A survey of French female managers and coaches[END_REF]. [START_REF] Dubar | Sociologie des professions[END_REF] explained the gender difference through the concept of the glass ceiling. This ceiling significantly limits female access to positions of power and domination in professional groups. The coaches covered nine Olympic sports: combat, individual and team sports; they referred to different competition calendars. They coached the following sports at the same institute for sport and academic training: fencing, wrestling, judo, cycling, gymnastics, swimming, athletics (n = 2), badminton, and basketball. This institute has agreements with universities, middle and high-schools, companies, and sport federations. It allows athletes at the same time and place to prepare for elite sport competition and to pursue their studies or to work (while some of them work nearby). Most athletes live in the institute. All the coaches were recruited through personal contact by a member of the research team. They were informed of the purposes of the study and assured of anonymity.

Data Collection

An interview was conducted with each coach. It lasted between 75 and 90 min. The coaches were asked to comment on their diary or planning sheets and to describe the concomitant time organization activity. These documents showed evidence of some of their activity. They were used as a starting point. The coach was asked to describe and comment on his time-frames and plans and how he set them [START_REF] Jeannot | Faire du général avec du singulier: Les chefs de service d'une DDE et l'aménagement [Making general from singular: heads of the regional Amenities department and development[END_REF]. The recalling of a specific time or time-frame was followed by comments about the meaning, origin, and carrying through of a particular task. The followsup were concerned with: (a) the international and national sport calendars (e.g., "what events do you take into account first?"), (b) the work orientation for each period (e.g., "what do you do at the beginning of this period?"), (c) the moments for collective or individual work with athletes (e.g., "Is this planning concerned with all the athletes on the team?"), (d) the adjustments in the course of time (e.g., "do you carry out everything that you have envisaged?") and (e) the time-frames imposed by the training center (e.g., "How do you manage time when you take into account different athletes' activities?").

Data Processing

Interviews were transcribed verbatim and given to the participants to confirm the validity of transcription. Data processing was done using the constant comparative method [START_REF] Corbin | Basics of qualitative research: Grounded theory. Procedures and techniques[END_REF]. Interview transcripts were divided into 1230 meaning units considered by the coaches and the related constraints. The properties of these meaning units were compared and classified into 28 categories according to their common features. Each category was labeled and their properties defined. As the data analysis proceeded, two other levels of interpretation emerged from a comparison between properties of categories (see Table 1). Two researchers analyzed the verbal reports separately. The data were constantly compared until saturation was reached, which occurred when no more new categories emerged from the data. The results were given to the participants. They were requested to read them and to indicate whether they felt that the results accurately reflected their time management. They agreed with the results.

Results

The results are presented in two parts in relation to the time of project model. The first deals with the circular process and more specifically the constraints the coaches manage to achieve the anticipated result. The second refers to the cognitive activity the coaches used when they managed these constraints to achieve the anticipated result. These parts are linked together and indicate a holistic view of time management. These results are illustrated by excerpts from the interview transcripts.

Anticipated Result and Constraints of Time Management

To manage time in the current complex, dynamic and constrained world of sports management and organization, the coaches anticipated a specific result in major competitions or a work time span. This anticipation led them to set time-frames according to the constraints and to adjust them to the on-going-events to achieve the anticipated result. For example a coach said:

"My aim for the athletes is to be in shape for the competitions. To do that, I organize the season into important moments, different cycles… In practice, I have to fit everything in between the dates of the major competitions, the mode of selection [. . .] Then, I adapt cycles and training sessions according to the athletes' progress [. . .].

Coaches dealt with a stringent set of constraints to manage time in order to achieve the anticipated result. This set of constraints was related to: (a) season organization depending on the fit between the anticipated result for the athletes and times for "With these top athletes we aim to win medals. To do so, it's up to us to determine a calendar from the international calendar, in order to combine a coherent planning for sport training with academic studies for younger athletes, and sport training with a job for older ones, coherent planning that brings them to the more important competitions in the best possible conditions."

Third Order Categories

In the same way as this coach mentioned, all the coaches anticipated a result (e.g., "winning medals") and then managed constraints linked to the structures, the athletes and the training process. These constraints were concerned with: (a) the dates of competition according to their importance (e.g., "The Continental Championships are in April". The World Championships are at the end of September"), (b) the mode of selection for these competitions (e.g., "the National Championship is selective for the Continental Championship"), (c) the available funding (e.g., "If we don't obtain the funding we've expected, we've to reduce traveling"), (d) the national federation requests for the athletes' involvement in competitions (e.g., "We free up the athletes for the Inter-club Championship"), (e) the organization of training camps (e.g., "When I've some time, I try to organize a training camp to get out of the usual training center"), (f) time for athletes going home (e.g., "Each time, I try to give them time to go home. They need to go home"), (g) their out-of-training activities (e.g., "we have to free them up for their studies or their job"), (h) the supposed opponents' presence and level in competition (e.g., "I try to choose the competitions where I'm sure that there will be many opponents"), and (i) time required to prepare for competitions (e.g., "I need a minimum of four weeks between two important competitions"). In managing these constraints, the coaches organized time spans for competitions, training camps, athletes going home and their out of training activities. The coaches most frequently reported constraints from the dates of competitions impacting upon achievement of the anticipated result (see Figure 1). They did not frequently comment on the national federation requests.

Training Period and Task Sequencing Depending on the Fit Between the

Anticipated Result for the Athletes and Time for Different Sorts of Work. Time organization efficiency was not only a function of a succession of time-frames for a specific work, it also concerned the way the tasks or time-frames were chained together into a temporal sequence. To sequence tasks and periods, coaches anticipated a specific result for their athletes in a time span according to their actual results. For example a coach said:

"We plan a period with each athlete, taking into account his/her results during the last competition or during the last six week period [. . .]. We expected her to reach her optimal form through particular educative drills, at the end of November. We began the period using specific educative drills, using two rotations. We increased the weight of the hammer and the number of repetitions. To avoid the monotony of an annual planning sheet, consisting of doing the same things at the same periods, we change the implement weight, the wire length [. . .] We sequence training days according to the competitive structure. Athletes train on two consecutive days and have one day off, because competitions are organized over two consecutive days: qualifications and the final."

In this excerpt and in the other coaches' data, the sequencing was ruled by different elements: (a) particular moment for a specific piece of work (e.g., "two rotations at the beginning of the period"), (b) progression of the work load over the course of the period (e.g., "increase the weight of the hammer"), (c), the renewing of training to avoid monotony (e.g., "we change the implement weight"), (d) the compliance between training and competitive structure, and (e) specific times for collective or individual work with athletes. Regarding compliance, competitions are organized according to a specific structure, depending on the sport. Preparing for competitions required the coaches to take this organization into account to allow their athletes to become accustomed to performing in such a temporal structure. In relation to specific times for collective and individual work with athletes, a coach reported:

"during March and April, everybody does the same work. In May and June, we're in a competitive period and we take them case by case and day by day."

This organization went from a collective form when they were distant from competition times to an individual form when they were during or just before the competitive period. The coaches most frequently reported elements concerned with a particular moment for a specific work (see Figure 1). They reported elements linked to the renewing of training to avoid monotony less frequently.

The institute's set times.

Coaches worked within an institute that organized schedules for sports and academic training. The coaches adjusted their training times to these schedules and to the availability of facilities For example a coach said:

"Organization depends on academic constraints. I'd prefer they swim at eight, but it isn't possible here, they have to swim after ten."

The coach had to fit in his training schedules around the institute schedules. Coaches also managed the availability of the facilities according to the number of athletes. For example a coach said:

"The first thing that I take into account is the space. We've got a gym for 24 players; we've got two central baskets. We divide the group into two groups of different levels. One group trains in the central area and the second trains on the sidelines. Then we change. We have to adapt the training session to the space; all the players come for training at the same time. Before that, they pursue academic studies …"

This coach organized the athletes' training sessions according to the available space and the schedules of the institute to allow each athlete to train in the best possible conditions.

Uncertainty Linked to the Evolution of Training. This type of constraint was generated by the uncertainty linked to the evolution of training with regard to athletes' activity and changes in the constraints. This uncertainty depended on: (a) events appearing in the course of time such as injuries or a decrease in performance (e.g., "we were involved in a training camp 15 days before the World Championship, this athlete was completely lost, he could not put one foot in front of the other anymore"), (b) changes in the availability of facilities (e.g., "Sometimes the pool is occupied for exams, they only have half a pool to swim in"), (c) coaches' obligations beyond training (e.g., "When I've a meeting, I free them"), and (d) changes in an athlete's involvement in a competition (e.g., "When we were in China, we noticed that she wasn't on the Taiwan table. They forgot to register her."). Uncertainty led the coaches to adjust their plans according to the constraints that appeared in the course of time. The coaches reported more frequently on events appearing in the course of time than changes in an athlete's involvement in a competition (see Figure 1).

Coaches' Cognitive Activity During Time Management

To deal with these constraints, the coaches used complex operating modes. Three modes were identified: (a) use of organizational routines based on reference to past experience, (b) season shared time management and, (c) time management based on flexible plans.

Use of Organizational Routines Based on

Reference to Past Experience. Time management was based on experience over previous years. Coaches based routines linked to the repetition in the competition dates of the international and national calendars and the events experienced with athletes. An excerpt emphasizes the repetitions experienced by coaches:

"We are organized according to the international calendar. I know the important competitions; it always functions in the same way. We get this calendar each year; we choose the competitions to which we want to commit, according to the level of the players and our goals. Then we coordinate it with the national calendar".

This coach organized the season according to the dates of competitions that were broadly known from one year to the next. Another excerpt reveals that time management was based on the use of routines linked to the events experienced with athletes:

"We [the coaches] don't give athletes more than two weeks to go home, three weeks is too much. We know we can release some athletes for three weeks, they will continue to train. For some others that's three weeks to whoop it up, so we prefer to have everybody in the institute. It depends on the period too, we free athletes for Christmas. Many of them go home; we respect this need. It's the same in summer; we give them a little more time because they are saturated".

This coach had learnt he could not organize each period of the year as he would have wanted to. He had to respect athletes' rhythms to keep them involved in the training process. His experience with some athletes led him to compromise between the necessity for athletes to go home and the tendency of some of them to stop training during this period. Some coaches could not release their athletes when they were in competition periods. They tried to but when there was a conflict between times to prepare for competitions and times to go home, they favored competitions instead of home rest. For example a coach said:

"during the Olympic year, the athletes whose families live in the West Indies can't go home, because the season is very dense. They haven't enough time to go home."

Time was managed with regard to the anticipated result; this coach tried to compromise between time to train and time to go home, but he stopped compromising when the compromise could prevent the anticipated result from being achieved.

Season Shared Time Management. Season time management was shared between coaches and athletes. It was based on: (a) discussions and agreements between the coaches about the work to do with athletes, (b) discussions and agreements between the coach and his athletes about the work to do and athletes' requests about their involvement in specific competitions, and (c) a comprehensive coaches' attitude. An excerpt emphasizes that time management was shared between the coaches:

"I plan first with the coaches, we go to one direction of work and we discuss it. Each of us investigates by himself and then we try to discuss it together. In staff meetings, some coaches don't talk very much. Some of them do what they want and it's not good. At a minimum, we have to agree on the direction of the work. If not, we discuss it in order to reach a consensus."

The organization was not always shared by all coaches, some of them preferred working alone and that could be a real problem for the staff. Another excerpt reveals the collaboration between the coach and his athletes: "I set out the time span with him/her, because I've seen that it's very important to obtain the trust of the athlete by involving him/her. Some athletes have difficulty involving themselves during our discussions; they don't want to give their opinion. But I invite them to do so. We look over the content of the training program for each athlete, according to our particular aims. We decide on what sort of drills we're going to do and what sort of teaching aids and procedures we're going to use. We do this in order to obtain the athlete's commitment.

After three or four weeks, we assess the period in order to determine whether to continue or change".

This coach emphasized the importance and sometimes the difficulty of getting his athletes to commit to organizing the training period. Their collaboration concerned the direction, content and duration of the work period. Time management was also based on a comprehensive attitude of the coaches toward the athletes. They wanted the athletes to commit to the training process to achieve the anticipated result. To do so, they tried to organize the training periods taking into account the athletes' individuality. An excerpt emphasizes this attitude:

"I give athletes a general program and then there are adjustments for the athletes who are married and have children. That's completely different from those who are single and live in the institute. I'm aware it's more difficult for them I know I have to organize this. Then, there is a negotiation; it's like an agreement regarding what they want and the goal. This year, an athlete would have liked to prepare for competition for two weeks and then go directly to the European Championships. We tried to negotiate. There was permanent conflict with the athlete and the athlete's club which considered we focused on the athlete too much. We have to be careful, we can discuss it but at a point we must agree on a minimum time frame: two tournaments with one month to prepare for all athletes. She obviously trains before, by herself, in her club and we assess this training."

In this excerpt, time was organized differently for different athletes: a general framework for single athletes and adapted framework for a few married athletes. This coach showed a comprehensive attitude toward the latter. He accepted their will to train near their family, he organized different time-frames for them and at the same time he did not lose sight of the anticipated result. He compromised until the trade off threatened to prevent the athlete achieving the anticipated result. Then, he stopped and imposed a minimum time-frame to prepare for competitions. His comprehensive attitude was counterbalanced by his will to achieve the anticipated result.

Time Management Based on Flexible Plans.

To organize the season or shorter work periods, coaches set plans to give the work a framework. The coaches were prepared to adjust their plans to take into account the uncertainty linked to the evolution of training and the availability of facilities.

Their plans appeared to be flexible. Flexibility depended on the time-span preceding the competition. For example, a coach said:

"In May and June, we're in both a competition cycle and an academic exam period. We have to juggle sport and studies. We have a written time-frame, but we can't have rigid organization. In this period, we listen to athletes, and as soon as the athlete has an unusually painful sprain, we break and delete the session the day after. At this period we have to pay attention to the athletes who listen too much to themselves. In November, we carry out the planned sessions of two weeks. If a problem appears, I say to them: you do the session, you run less fast but you finish it."

The coach adjusted the plan for the athlete's progression differently in this period.

In one case, because of the dynamic and uncertain nature of the setting and the proximity of the competition, the plan was more flexible. In the other case, he generally did what was planned. Coaches kept in mind a framework and adjusted it according to the events which occurred.

Discussion

The results of the current study showed how coaches managed time to allow an anticipated result to be achieved. Coaches dealt with a stringent set of constraints and used complex operating modes. This aim of accommodating constraints led coaches to compromise. The findings will be discussed from three perspectives: time management and planning process, compromises aimed at achievement in the context of constraints and implications for practice.

Time Management and Planning Process

As was found in the planning topic [START_REF] Jones | A comparative analysis of expert and novice basketball coaches' practice planning[END_REF][START_REF] Platonov | L'entraînement sportif. Théorie et méthodologie[END_REF]Weineck, 1996) and goal setting perspective (e.g., [START_REF] Horton | Expert coaches in action[END_REF][START_REF] Burton | Sport psychology for coaches[END_REF][START_REF] Burton | The fundamental goal concept: The path to process and performance success[END_REF], planning was based on a vision of the future (i.e., an anticipated result in a competition or a level reached at the end of a specific time frame). It consisted of the steps and time frames that coaches thought were required to reach the goal. Côté and Sedwigck (2003) showed that planning was proactive. However the present results suggested that planning was also retroactive. Coaches planned regarding an anticipated result that was considered as a fixed point. From this fixed point, they looked at the 'past' (which was not realized yet) and organized the season and its time-frames for: (a) competitions, (b) training camps, (c) athletes' out-of-training activities, and (d) athletes going home. To organize these time-frames, they took into account athletes' and federation requests and available funding. Then they sequenced training periods and tasks, and fitted into the institute's set training times. During the season, they adjusted the training periods according to the uncertainty linked to the evolution of training. This adjustment related to proactive planning which consisted of fitting the anticipated result to the real events to generate an outcome. This proactive planning was followed by the retroactive planning process described earlier to adjust training period sequencing. The use of the retroactive and proactive processes is consistent with [START_REF] Dupuy | Pour un catastrophisme éclairé[END_REF][START_REF] Dupuy | Dans l'oeil du cyclone[END_REF] model. Coaches' actions were based on different mixed temporalities that referred to: (a) past experiences with athletes and the redundancy of the competition calendars, (b) current situations, and (c) the anticipated result. The present results reinforced those shown by [START_REF] Saury | Practical knowledge in expert coaches: On-site study of coaching in sailing[END_REF] and [START_REF] Sève | L'action de l'entraîneur de tennis de table comme action située [Action of table tennis coach as situated action[END_REF] on coaches' activities during short time-frames (i.e., a session), and extended them to longer time-frames (i.e., a season). The present results, therefore provide new insight into how coaches in elite sport settings manage and organize time over the course of a sport season.

As was found in the coaches' knowledge topic [START_REF] Côté | The development of coaching knowledge[END_REF][START_REF] Côté | An integrative definition of coaching effectiveness and expertise[END_REF][START_REF] Abraham | The coaching schematic: Validation through expert coach consensus[END_REF][START_REF] Gilbert | Framing the construction of coaching knowledge in experiential learning theory[END_REF][START_REF] Jeannot | Les métiers flous[END_REF], coaches used professional, interpersonal and intrapersonal knowledge to manage time. Knowledge concerned constraints and was employed in cognitive activity. Professional knowledge involved the constraints imposed upon the coaches when managing time. Some of these constraints were related to the institute in which the sports practice took place; they included the imposed sports training schedules and availability of facilities. These contextual constraints were little reported in previous studies although they are important in countries such as the U.S.A, Germany and France, where the athletes are committed in both sports and academic programs within sports institutes and universities (e.g., [START_REF] Bouchetal-Pellegri | Carrière sportive[END_REF]. As shown by [START_REF] Dubar | Régimes de temporalités et mutation des temps sociaux [time systems and social time change[END_REF] in sociology, coaches appropriated the institute-imposed schedules to construct group and individualized times governed by the achievement of the anticipated result. Interpersonal knowledge was concerned with the uncertainty linked to the evolution of training (except changes in the availability of facilities) and the season shared time management (except the comprehensive attitude). Intrapersonal knowledge referred to: (a) the use of organizational routines based on reference to past experience, (b) the comprehensive attitude, and (c) the time management based on flexible plans.

Time was managed with regard to sports, athletes' out-of-training activities and athletes going home. These results suggested that the role of the coach consisted of sport and personal development of athletes, consistent with the results of previous coaching research that emphasized the need to adopt a holistic view of training [START_REF] Côté | The development of coaching knowledge[END_REF][START_REF] Côté | The coaching model: A grounded assessment of expert gymnastic coaches' knowledge[END_REF]Côté & Sedwigck, 2003;[START_REF] Salmela | Great job coach! Getting the edge from proven winners[END_REF][START_REF] Gilbert | Validation of the Coaching Model (CM) in a team sport context[END_REF][START_REF] Gould | A survey of U.S. Olympic coaches: Variables perceived to have influenced athlete performances and coach effectiveness[END_REF]Wylleman & Lavallee, 2004). Results suggested that times were fragmented and multiple. They were concerned with different athletes' involvement. For example, one coach stressed a specific time fragmentation regarding the locus of training. In training camps, time was organized solely around sports training, while in the institute time was organized around sports training and out-of-training activities. This time fragmentation is consistent with the temporal systems described elsewhere in the literature [START_REF] Audigier | Temps subis, temps construits [Constructive times from inflictive times[END_REF][START_REF] Dubar | Régimes de temporalités et mutation des temps sociaux [time systems and social time change[END_REF]Francis-Smythe & Robertson,1999;[START_REF] Grossin | Pour une science des temps: Introduction à l'écologie temporelle[END_REF][START_REF] Sabelis | Time management: Paradoxes and patterns[END_REF][START_REF] Southerton | Squeezing time'. Alocating practices, coordinating networks and scheduling society[END_REF]. These authors showed that managers' time was divided up by their activities into different time-frames (e.g., meetings, meals). These time-frames succeeded one another, juxtaposed, competed and led managers to adjust them. To avoid or limit conflicts between athletes' times, coaches took into account this time fragmentation. Coaches organized athletes' sports times by giving athlete times for out-of training activities and also time to go home. Sport training theories (e.g., [START_REF] Weineck | Manuel d'entraînement[END_REF] consider that rest is a part of training. However the present results showed that another form of rest was important for athletes: they needed to go home for short periods to avoid burnout. As suggested by [START_REF] Horton | Expert coaches in action[END_REF], this structure aimed to prevent loss of valuable time due to overuse injuries, staleness or burnout.

Compromises Aimed at Achievement in a Context of Constraints

The results showed that coaches compromised on constraints to manage athletes' time to achieve the anticipated result. Compromise activity comprised a continual transformation of the problem with regard to conflicts between constraints [START_REF] Jeannot | Les métiers flous[END_REF]. For example a coach had to deal with time to prepare for competition in the institute and the desire of some married athletes to train near their family. He had to generate a new time organization that was negotiated while keeping the anticipated result in sight. Time management could be considered to be a confrontation between contradictory elements. Compromises resulted from this confrontation. Compromises were made until they prevented the athletes from achieving the anticipated result. The present results reinforced those shown by [START_REF] Jeannot | Les métiers flous[END_REF] in his study on project managers. They also reinforced the role of goal prioritization and coordination explained by [START_REF] Burton | Sport psychology for coaches[END_REF] in sport psychology.

Results showed shared time management between athletes and coaches. Discussions with athletes and coaches through a comprehensive attitude aimed to take into account their focus about the work to be done with athletes. Results suggested that these discussions permitted coaches: (a) to create and maintain a positive training environment, (b) to help athletes to define and adjust their goals, and (c) to build athletes' confidence. The present results reinforced those obtained by [START_REF] Côté | The development of coaching knowledge[END_REF]Gilbert (2003, 2009), [START_REF] Gould | A survey of U.S. Olympic coaches: Variables perceived to have influenced athlete performances and coach effectiveness[END_REF], and [START_REF] Horton | Expert coaches in action[END_REF] on coaches' effective behaviors. They also emphasized the shared work organization that, to our knowledge has only been shown by [START_REF] Saury | Practical knowledge in expert coaches: On-site study of coaching in sailing[END_REF] in time organization.

Compromises consisted of individual inventiveness to achieve the anticipated result and to accommodate constraints. For example, a coach adjusted training to the available space by dividing time with a group and playing in or out of the court. These individual inventions based on compromises are consistent with those presented by [START_REF] Duc | Le travail en chantier[END_REF]. The organization of work requires individual inventiveness to manage uncertain realities of events. The work was not totally prescribed, such as is the definition of work organization. The coaches did not deal with well-structured problems [START_REF] Reitman | Cognition and thought[END_REF] where the data required would be sufficient and available. Rather they dealt with uncertainty and changes; they carried out actions according to the way they interpreted the situation. The present results reinforced those shown by [START_REF] Langa | L'activité des cadres: un objet d'étude [Managers' activity: a study object[END_REF] and [START_REF] Carballeda | Les cadres: des travailleurs en difficulté [Managers: workers in difficulty[END_REF], in their studies about managers' work. Coaches used flexible plans to adjust what was planned to what could be carried out, to achieve the anticipated result. Plans appeared to be more flexible, when the competition was near than when it was distant. Theories of planning consider that coaches have to carry out what is planned (e.g., [START_REF] Platonov | L'entraînement sportif. Théorie et méthodologie[END_REF][START_REF] Weineck | Manuel d'entraînement[END_REF]. However the present results and those of [START_REF] Saury | Practical knowledge in expert coaches: On-site study of coaching in sailing[END_REF] and [START_REF] Sève | L'action de l'entraîneur de tennis de table comme action située [Action of table tennis coach as situated action[END_REF] showed that plans were flexible. They were used as a frame work and proceeded step-by-step, being dependent on-going events. With a stringent set of constraints, coaches did not try to maximize time, as suggested by [START_REF] Horton | Expert coaches in action[END_REF]. Rather, they tried to optimize it in compromising between the requirements and the on-going events.

Implications for Coaching and Coaching Education

These results suggest some implications for less experienced coaches. The coaches could continue to manage time over the season according to professional knowledge [START_REF] Côté | The development of coaching knowledge[END_REF][START_REF] Côté | An integrative definition of coaching effectiveness and expertise[END_REF]. At the same time, they could take into account their athletes' activities beyond sports training, the practice conditions in the training center (which may also be an academic training institute) and the on-going events. A specific framework could be developed containing questions about: (a) the types of constraints linked to time management and with regard to the specificity of each sport (e.g., competition calendar) and training context [START_REF] Côté | An integrative definition of coaching effectiveness and expertise[END_REF] including the institute's set times, and the implications of the constraints for the coaches, (b) the strategies that can be used and the compromises that have to be made which are dependent upon the way coaches interpret situations to manage athletes' time, (c) the outcomes of their retroactive [START_REF] Dupuy | Pour un catastrophisme éclairé[END_REF][START_REF] Dupuy | Dans l'oeil du cyclone[END_REF] and proactive [START_REF] Côté | Effective behaviours of expert rowing coaches: A qualitative investigation of Canadian athletes and coaches[END_REF] planning with regards to the compromises made and the need to use flexible plans, and (d) the existence of intermixed temporalities [START_REF] Saury | Practical knowledge in expert coaches: On-site study of coaching in sailing[END_REF][START_REF] Sève | L'action de l'entraîneur de tennis de table comme action située [Action of table tennis coach as situated action[END_REF]. This framework could be used to learn how to manage time with a stringent set of constraints. It could allow coaches to stand back from their work by leading them to consider: (a) what they can or cannot do to achieve the anticipated result while taking into account the constraints they consider important, (b) where they compromise without preventing the anticipated result from being achieved, and (c) how they can manage new constraints. The framework could allow coaches to be considered as learner and manager at the same time. They could learn from the context, their own experience, and discussions with colleagues about their time management experience (present results). To achieve the anticipated result, they would have to redefine the problem in the light of the constraints which arise [START_REF] Jeannot | Les métiers flous[END_REF] and the constraints' importance for coaches. They would need to develop new time organizations to fit uncertain realities of events [START_REF] Duc | Le travail en chantier[END_REF] and use organizational modes that were efficient in the past [START_REF] Saury | Practical knowledge in expert coaches: On-site study of coaching in sailing[END_REF]. Uncertainty linked to the evolution of training means that coaches manage time by proceeding step-by-step and taking on-going events into account [START_REF] Saury | Practical knowledge in expert coaches: On-site study of coaching in sailing[END_REF].

Conclusion

It seems inappropriate to generalize from a qualitative study of ten coaches. Despite this limitation, this article addresses an issue in relation to the research on coaching and time management by providing a framework that accounts for the process, the knowledge and the strategies used by male coaches of elite athletes when they managed time to prepare athletes for competitions during a season. It emphasizes that coaches: (a) dealt with uncertainty and change, carried out actions according to the way they interpreted the situations, (b) made compromises to achieve the anticipated result in a context of stringent constraints, and (c) used a retroactive and proactive planning activity including flexible plans to adjust what had been planned to what could be carried out, to achieve the anticipated result. This leads to the adoption of a holistic view of training and consideration of time management as a chaotic activity governed by the accomplishment of an anticipated result in a stringent set of dynamic constraints. The challenge remaining will be to discover how time is managed in different sporting contexts and by coaches of varying profiles (e.g., gender, years of experience, expertise).

  -of-training activities (22) Supposed opponent's presence and level in competition (26) Time required to prepare for competition (31) Anticipated result for their athletes in a specific time-span according their actual results (86) Particular moment for a specific piece of work (120) Progression of the work load over the course of a period (60) Renewing of training to avoid monotony (on flexible plans (43) Time management based on flexible plans Note. Numbers in brackets displays how many occurrences contributed to the raw data. competitions, training camps, athletes going home and athletes' out-of-training activities (b) training period and task sequencing depending on the fit between the anticipated result for the athletes and time for different sorts of work, (d) the institute's set times, and (e) uncertainty linked to the evolution of training. Season Organization Depending on the Fit Between the Anticipated Result for the Athletes and Times for Competitions, Training Camps, Athletes Going Home and Athletes' Out-of-Training Activities. Coaches managed time during the season to organize times for competitions, training camps, athletes going home and athletes' out of training activities. They set a season calendar for their athletes fitting in these stringent constraints to achieve the anticipated result. For example a coach said:

Table 1 Results of Qualitative Analysis of Interviews Displaying Hierarchical Categories First Order Categories Second Order Categories

 1

	Anticipated result in major competitions (60)	Season organization

Acknowledgments

This study was supported by a grant from the French Ministry of Health and Sports. The author is grateful to the coaches for their participation to this study, to Nadine Debois for her participation in the data processing and to the reviewers for their helpful comments during the reviewing process.


Yasuo Osone
email: yasuo.osone.td@hitachi.com

THERMAL DESIGN OF POWER SEMICONDUCTOR MODULES FOR MOBILE COMMNICATION SYSYTEMS

We investigated the thermal performance of a power semiconductor module used in mobile communication systems. The module contained hetero-junction bipolar transistor (HBT) fingers, which were fabricated on the top of a semiconductor substrate. We calculated the thermal resistance between the HBT fingers and the bottom surface of a multi-layer printed circuit board (PCB) using a finite element method (FEM) simulation. We used steady state analysis to evaluate the effect of various design factors on the thermal resistance of the module. We found that the thickness of the semiconductor substrate, the thickness of the multi-layer PCB, the thermal conductivity of the bonding material under the semiconductor substrate, and misalignment of thermal vias between each layer of PCB were the most important factors affecting the thermal resistance of the module.

INTRODUCTION

A radio frequency (RF) communication circuit is an electrical component used in mobile communication systems. In a cell phone, about half of the phone's electrical power consumption is accounted for by the heat generate by the power amplifier, which amplifies the transmission signal from a transistor, in the phone's RF circuit.

In the thermal design of power amplifiers, the objective is to develop a package structure of the module where the temperature does not exceed an allowable limit. Since power amplifiers have become progressively smaller, their thermal design has been a key factor in developing cell phones.

Other key factors are the need to decrease turn around times in product development and to find a numerical method to optimize the thermal structure of products, which will be of significant use for thermal design work. Modeling know-how is also important I thermal design because automated modeling is difficult to apply to semiconductor devices.

The objective of this paper is to show the thermal design technique of power amplifier modules in call phones using a finite element method (FEM). We evaluated the effect of various design factors on the thermal resistance of the power amplifier module. The thermal design of cell phones is becoming more important because they are approaching the limits of the allowable amount of heat that can be discharged into the environment. In fact, the heat dissipation densities of smaller power amplifiers have increased to 100 W/cm 2 .

The problem is that, unlike when modeling an automobile, automatic modeling is not easily applied to the numerical modeling of semiconductor modules since their design data -such as mask layout data -are twodimensional.

Further, the modeling has to handle a huge dynamic range. This range extends from the thickness of a 10 nm film to the 10 cm characteristic length of a printed circuit board. By applying FEM, thermal design, which involves optimizing the packaging structure, predicting the device temperature, and reducing the device temperature so that is does not exceed the allowable limit, is feasible.

By applying an FEM technique, we investigated the thermal performance of power amplifier modules with GaAs hetero-junction bipolar transistors (HBTs). The thermal resistance of HBTs had been investigated using various approaches [START_REF] Liu | Theoretical calculations of temperature and current profiles in multifinger heterojunction bipolar transistors[END_REF][2][3][4] [START_REF] Kim | 3-V Operation Power HBTs for Digital Cellular Phones[END_REF] . We believe that numerical methods are most appropriate for developing heatdissipating structures with low thermal resistance. In this study, we considered not only the layout and the shape of the HBT fingers, and the thickness and thermal conductivity of each component in the power amplifier module but also the misalignment of each component.

The results of the simulation showed that that the thickness of GaAs substrate, the thickness of multi-layer PCBs, and the thermal conductivity of bonding material under the GaAs substrate were the dominant factors affecting the thermal resistance of the power amplifier module. The results also showed that the misalignment of GaAs substrate on the heat spreader did not have a major effect on the thermal resistance of the power amplifier module.

Yasuo Osone Thermal Design of Power Semiconductor Modules for Mobile Communication Systems

©TIMA Editions/THERMINIC 2006 -page-ISBN: 2-916187-04-9

THERMAL DESIGN OF CELL PHONES

Figure 1 shows a schematic diagram for a cell phone of the flow path of heat between heat sources and ambient air. Heat dissipated by discrete heat sources assembled on a PCB is first transferred to the PCB, and then conducted through the PCB to the front and rear panels by contact heat transfer. The heat in the front and rear panels is conducted to the skin of the cell phone user. The thermal design of semiconductor modules, such as power amplifiers, baseband large scale integrated (LSI) circuits, application processors, and other devices, usually considers the thermal resistance between the heat source and the PCB. Though the flow path of heat illustrated in fig. 1 and the thermal design model of heat flowing between heat sources and the PCB is not the same, the difference is negligible small because the heat capacity of the panels is much larger than that of the PCB.

Ram et al. stated that the maximum amount of heat dissipated in a handheld computer or cell phone is about 5 W under average conditions [START_REF] Chary | Intel® Low-Power Technologies Can Extend Battery Life and Improve Device Usability[END_REF] . If the total heat dissipation by semiconductors in the cell phone under such average conditions is lower than the maximum amount of heat, the thermal resistance of the front and rear panel is negligible. Since the heat capacity of the panels is much larger than those of other components in the cell phones, the interface between the PCB and the panels can be assumed that the isothermal boundary in the thermal design of the semiconductors in the cell phone.

Figure 2 shows a flow chart of the thermal design process of power semiconductor modules mounted on a PCB when the effect of the case is negligible. The objective of thermal design of a module is to reduce the thermal resistance Rjc between the heat source and the ambient air so that the thermal resistance is lower than the allowable limit. Though both steady state and transient analysis are ideally required for the design, the transient analysis is usually omitted because the transient temperature increase is lower than that of the steady state when the heat dissipation from the heat sources is at a maximum. The steady state analysis will be discussed in the following section.

ANALYTICAL MODEL OF POWER AMPLIFIER MODULE

Figure 3 shows the package structure of the power amplifier module surveyed in this paper. The thickness of the semiconductor substrate in fig. 3 is about 0.1 mm.

Semiconductor devices, such as the HBT fingers, are fabricated on the top surface of the substrate. The package structure of the power amplifier module in this paper has a plated heat sink (PHS) that is plated under the bottom surface of the semiconductor substrate. The heat dissipated from the HBT fingers diffuses through the semiconductor substrate in fig. 3 horizontally to the PHS, the bonding paste-1, and the heat spreader. The temperature distribution in the flow path of heat is not constant even while it goes through the PHS layer. The module package structure is composed of the semiconductor substrate with HBT fingers, a PHS, the bonding paste-1, a heat spreader, bonding paste-2, and a multi-layer PCB. The multi-layer PCB has thermal vias, which are thermally conductive and penetrate the multilayer PCB. Most of the heat dissipated by the HBT fingers goes through the thermal vias to the external boundary of the module because the multi-layer PCB is primarily made of heat-insulating ceramic material.

Figure 4 shows the HBT fingers layout on the semiconductor substrate. To simplify the analysis, we used an orthogonal coordinate system. The shape of each layer was transformed into a rectangular parallelepiped. We assumed that the finger pitch was constant and the center position of the fingers coincided with the center of the semiconductor substrate so that a quarter area model could be used in the FEM analysis to reduce the size of the simulation model. We also assumed that the isothermal temperature at the bottom surface of the model in fig. 3 was 273 K. Other boundary conditions were adiabatic. The thermophysical properties of the materials used in the analysis are shown in Table 1.

We determined the thermal resistance of the HBT fingers at the point where the temperature difference between the bottom surface and the place in which the temperature was higher than any other place in the model. We calculated the thermal resistance of the HBT fingers, the influence of the thickness of each component in the module, thermophysical properties of the heat spreader, and the alignment of the semiconductor substrate on the multi-layer PCB. In the thermal analysis, we used an HBT model that had 96 HBT fingers (16 fingers x 6 columns) and two layers of multi-layer PCB.

We used a massively parallel processing computer (HITACHI SR-8000 Model G1) for the thermal analysis. The theoretical peak performance of the computer was 230.4 GFLOPS, and the total size of the memories of the system was 128 GB. The node size of the model in the analysis was from 1 to 10 M nodes for the thermal design of the power amplifier module.

RESULTS OF THERMAL ANALYSIS

Thermal resistance of the power amplifier module

Figure 5 shows the influence of the thickness of the GaAs substrate and the PHS layer on the thermal resistance of the power amplifier module with HBT fingers. As shown in fig. 5.1, we found that the thermal resistance of the power amplifier module could be reduced by 5.3 % compared to that of the typical model shown in fig. 5.1, if the thickness of the GaAs substrate was reduced to 75 % of the typical thickness of the GaAs substrate.

The thermal resistance of the power amplifier module was positively correlated with the thickness of the GaAs substrate, whereas it was negatively correlated with the thickness of the PHS layer. Figure 5.2 shows that the PHS served as a heat spreader and the in-plane heat diffusion in the PHS layer had a significant effect on the reduction of the thermal resistance of the power amplifier module.

Impact of thickness of ceramic layer and

misalignment on thermal resistance Figure 6 shows the impact of the number of ceramic layers in the multi-layer PCB on the thermal resistance of the power amplifier module. In fig. 6," that the module had no multi-layer PCB and the bottom surface of the heat spreader is isothermal at 273 K. Since the multi-layer PCB shown in fig. 3 has two ceramic layers, "-50 %" means it has one ceramic layer, and "+50 %" means it has three ceramic layers. We found that the number of ceramic layers in the multi-layer PCB had the greatest impact on the thermal resistance of the power amplifier module. The principal flow path of heat in the multi-layer PCB was through the thermal vias. The heat dissipated in the semiconductor substrate diffused one dimensionally through the thermal vias. Therefore, the thermal resistance of the power amplifier module had a linear dependence on the thickness of the multi-layer PCB, i.e., the number of ceramic layers in the multi-layer PCB.

We found that effect of the misalignment of GaAs substrate on the heat spreader on the thermal resistance was not as significant as the other evaluation items. Since the heat spreader diffuses heat through the bonding paste-1 three dimensionally, and the temperature distribution on the top surface of the bonding paste-2 is almost flat even if the location of the GaAs substrate is misaligned, any misalignment of the GaAs substrate seems to have a small effect on the thermal resistance of the power amplifier module.

The flow path of heat in the multi-layer substrate is one-dimensional. Therefore, the misalignment of the thermal vias should have a major effect on the thermal resistance of the power amplifier module. The degree of the impact of the misalignment of the thermal vias on the thermal resistance depends on the base material of the multi-layer PCB, the production method of the circuit board, and the difference of the thermal conductivity of the base material and the thermal vias.

Since most RF module manufacturers procure PCBs for their modules from PCB venders, they are not able to reduce the misalignment of PCB components by themselves. Therefore, improving the robustness of module thermal design will be an important way to reduce the negative effect of misalignment of each component in the module.

Impact of evaluation items on thermal resistance

Figure 8 shows the impact of each evaluation item on the thermal resistance of the semiconductor module. The most important factor among these evaluation items was the number of the ceramic layers in the multi-layer PCB.

The second most important factor was the thermal conductivity of the bonding paste-1. The thermal conductivity of the bonding paste is important because the impact of the thermophysical properties of the bonding paste can include the influence of the interface thermal resistance between the bonding paste and the bonded material. Even if the thermal conductivity of the bonding material is high enough as a thermally conductive material, the substantive thermal conductivity with the effect of the interface should be considered in the thermal design of the power amplifier module.

We also found that the thermal resistance of the module could be increased to 125 % of that of a typical model.

SUMMARY

We used FEM to investigate the thermal performance of a power amplifier module that had HBT fingers on a GaAs substrate. The effect on the thermal performance of not only the layout and the shape of the HBT fingers and thickness, and thermal conductivity of each component in the module, but also the misalignment of each component was determined.

The results of the FEM simulation showed that that the thickness of GaAs substrate, the thickness of multilayer PCB, and the thermal conductivity of bonding material under the GaAs substrate were the dominant factors in affecting the thermal resistance of the power amplifier module. The results also showed that the misalignment of GaAs substrate on the heat spreader did not have a major effect on the thermal resistance of the power amplifier module.

The results also showed that the three dimensional shape of thermal vias are important in the thermal design of power amplifier modules because the flow path of heat of the thermal vias in the multi-layer PCB is onedimensional.

Figure 5 . 2 Figure 5 Figure 6 2 Figure 8

 525628 Figure 5.1 Impact of thickness of GaAs substrate

  -100 %" means

	Yasuo Osone
	Thermal Design of Power Semiconductor Modules for Mobile Communication Systems

©TIMA Editions/THERMINIC 2006

-page-ISBN: 2-916187-04-9


G Mura

G Cassanelli

FAILURE ANALYSIS AND FIELD FAILURES: A REAL SHORTCUT TO REALIABILITY IMPROVEMENTS

Starting from two case histories, where only after thorough Failure Analysis the suddenly appearance of a failure was linked to much earlier events, the possibility of improving the reliability and of adjusting the reliability prediction tools are discussed.

INTRODUCTION

The role of Failure Analysis in the assessment of Reliability is widely acknowledged, and the most celebrated failure mechanisms have been granted along the years by the privilege of the introduction of process steps, in manufacturing microelectronics, that are solely dedicated to their prevention. Electromigration, corrosion, mobile charges, hot electrons, alpha particles, and latchup are taught to microelectronic process engineers to explain the origin of maybe half of the current technological solutions.

Nevertheless, field failures still occur.

Handling field failures is in general a difficult task, that is even worst for those Small-Medium Enterprises (SMEs) that are small customers of the big microelectronic manufacturers: on one side, the overall small or medium volume itself of their production makes even few failures of statistical significance. Conversely, few field failures are not sufficient to adjust reliability figures, as failure rate, MTTF or π factors for any device in the most popular tools for Reliability prediction, whose direct application is of questionable utility just for those SMEs that are less armoured against reliability issues [START_REF] Cassanelli | Reliability Prediction in Electronic Industrial Applications[END_REF].

It remains the hope in miracles, that is in those highly accelerated methods that, often misunderstood, promise to increase the reliability of a system independent on its measurement. The problem is that field returns in general do not correspond to the failures produced during those tests.

The role of Failure Analysis will be here defended, in its deep acceptation, where a complete chain links the root failure mechanism to the observed failure mode (and not only a SEM picture is displayed to show some burnout). Detection of a specific root cause, when achieved, is that answer that is able both to address proper corrective actions in design and/or process and also to indicate more sound values for reliability parameters.

In this paper a couple of case histories in which the final damage of the component is associated to violent thermal phenomena are reported.

The two cases are linked by the common situation of having been mistaken in their diagnosis at the SME's plants, or even at some commercial Reliability Labs. In both cases sudden events have been reported, which was correct for the failure mode, although not necessarily for the failure mechanism. The butler of the situation was then claimed to be some transient Electrical Overstress (EOS) or some unexpected Electro-Static Discharge (ESD), and attention was paid to identify (and to remove) possible transients on currents, voltages, and electromagnetic fields during the operations of the two systems corresponding to the failure appearance.

The answers of the Failure Analysis were so subtly different to not completely destroy the first interpretation, but to back-date the occurrence of the root mechanisms well before the manifestation of the failure mode, and then displacing the focus from one class of operations of the failed system to some completely unsuspected others.

To avoid confusion on the focus of the paper, it is here anticipated that the well known Aluminium-Silicon interdiffusion mechanism will be called into play for both cases, and its main features will also be recalled.

Its role is only to witness the time delay between the first manifestation of the root mechanisms and the final failure modes.

CASE STUDIES

IGBT for racing car electronics

A popular commercial standard-speed IGBT, optimized for minimum saturation voltage and low operating frequencies, mounted in TO-220AB package, and employed in the on-board electronics of a racing car, failed after very few hours of intense operation. More specifically, after one day of repeated tests on the race circuit and regular switching off at night, the system failed because of the short-circuiting of the IGBT as soon as it was switched-on, on the next morning. The electrical measurements confirmed an overall shortcircuit, with some tenths of an Ohm between Emitter (at the top of the chip) and Collector (at the substrate), and some 4 Ohms at each of them vs. Gate.

The first set of hypotheses pointed towards sudden stresses, like EOS or ESD due to some transient event at the switching-on. An accurate Failure Analysis was then started to find the evidence of the real mechanism. The first attempt to remove the plastic package by mixed grinding and chemical etching revealed (fig. 1) an extended thermal damage of the plastic itself all around the thick Emitter wire. Carbonisation of the plastic mould prevented from uniform removal of the package, but a first strong indication for a catastrophic overheating was obtained.

The absence of any electrical connection on the top of the chip to the Collector clearly indicated the short circuit as a bulk failure. On the other hand, the x-ray EDS inspection of the exposed section of the wire revealed a central core nearly completely made of Silicon, surrounded by a region rich in Silicon and Oxygen.

The results were converging towards some strong vertical current flow, closer to some EOS event than to ESD, obviously the latch-up itself can be fired by a not destructive ESD event. Anyway, the dilemma of the sudden or progressive mechanism remains not yet resolved.

The complete removal of the plastic package was then carried out (fig. 2), together with a cross-section of the damaged area (fig. 3). As a result, all the fingerprints 20 µm The key point is that the interdiffusion mechanism is not compatible with a sudden, transient phenomenon that would have resulted in fusion and chaotic recrystallisation of the vertical structure. It should be argued that during the limited life of the device, an overcurrent was allowed to flow, undetected, able to expose the die to excessive temperature.

Al intrusions

Another possibility is some missing control on thermal dissipation, mandatory for such a device. In that case the overdriving of the device could have raised the local temperature well beyond the specifications.

In any case, a strong and sustained current must be indicted for the failure, independent on the sudden, and late, manifestation of the final catastrophic step.

The origin of the overcurrent may be inferred by the statistics for IGBT devices, that indicate the latch-up mechanism as one the most frequent problems. The uncommon situation here is the relatively long survival of the device, up to its ultimate and irreversible short circuit, witnessed by the shown interaction at the wire contact and by the cracking of the die (fig. 4).

CMOS Microcomputer

A single-chip 8-bit CMOS Microcomputer, employed on the control board of a boiler device for domestic application, failed in field operation, after passing the final production tests.

The failure analysis ran parallel to the analysis performed, on specimens with identical history, by the manufacturer, based on the results obtained by an external well-known reliability centre. Their conclusions were: "It is considered that the destruction was caused by electrical overstress… check whether the supplied voltage at pin nn is stable". In the manufacturer's report, the sentence was modified by deleting the focus on some possible voltage instabilities, and adding the specification "such as overcurrent" after the words "electrical overstress".

In both cases, the responsibility of the failure was completely loaded on the customer's shoulders and the corrective actions point only toward some not further specified controls on voltage or current.

A preliminary characterization of a device of the same lot revealed the structure of the multiple metal layer, where a very large upper metal layer (fig. 5) run over the most part of the peripheral circuitry.

At a first glance, the optical inspection of the surface of one of the failed chips only showed minor damages (fig. 6a), ill proportioned to the severity of the measured short-circuit: only a very small area showed some "burning" at the top metal layer in the region of the most strongly failed input pin. No other evidences were found across the whole chip. Some new information came during the chemical delayering of the device (fig. 6b): at the "burning" place, the nitride etch opened a hole into the upper metal layer, and the HF etch was not able to remove some islands of the lower metal layer. In general, this would be not strange at all, because some mix between silicon and aluminium, oxygen, possibly nitrogen and other elements is a normal effect of a thermal excess (fusion). The anomalous thing is that nothing looks melt: the upper metal layer displays a hole with indented boundaries, and the surviving "islands", rich of Silicon as expected, simply preserve, like a cast, the shape of the original aluminium, with its edges and reliefs.

The situation was even more evident on a second chip, where some more extended damage was observed at the surface of the failed pin. It is pointed out by the arrows in fig. 7. The etch of the nitride passivation opened a hole (fig. 7b) where the upper metal layer seemed intact (fig. 7a). The edges of the hole strictly recall a polycrystalline structure, as expected for the aluminium layer. In fig 7b, and even more clearly in the SEM figure 7c, the hole shows an intact lower level metallization or, at least, a layer that preserves the original forms of that layer.

Upon HF cleaning of the surface (fig. 8), the evidence arose for a central, small spot (arrowed) into Silicon from which a "Si-fountain" sprung from the substrate into the metal layers, branching into four different directions. This ultimately allows, with the aid of fig. 7 that compares the same region at different etching levels, to individuate the connection of the different structures of the damage: Silicon (amorphous) was present at the top metal level, which caused its removal under the etch of the passivation, while Aluminium penetrated the Silicon bulk, and was removed during the HF etch.

A 3D reconstruction [START_REF] Pintus | Quantitative 3D Reconstruction From BS Imaging[END_REF] of the SEM images of the exposed Silicon surface (fig. 8b) clearly shows the deep penetration of the damage (the interdiffusion "fountain"), This is the other side of that same Al-Si interdiffusion phenomenon that appeared for the IGBT analysis. In this case, indeed, not the Al penetration into Silicon, but the progressive substitution of Al by Si atoms, coming from some deep contact point, to be found, is displayed. It is the same phenomenon whose seeds have been indicated for the previous IGBT case as "Si extrusions". The phenomenon is quite known, but it is always amazing to see the capability of Si to completely substitute Al, even preserving the shape of the metal layer.

It should be noticed as, once again, the evidence for Al-Si interdiffusion does NOT state that it is the root failure mechanism: the small spot clearly addresses towards ESD. Anyway, it is a secondary consequence, whose occurrence witnesses that the device operated a relevant time after the first failure firing before reaching the short-circuit state that flagged the failure. Now, the interpretation of the failure is unavoidable: an original ESD event caused a local short-circuit, maybe not sufficient to directly bring the circuit to fail, but able to set up a small parasitic current, locally dense enough to fire the Al-Si interdiffusion mechanism.

The progressive evolution of this phenomenon then brought the device to its ultimate state at the observed time.

The relevant point is the casual occurrence of the discharge at some internal point of the circuits, but always under the wide upper metal layer. This suggested the possibility that not an I/O instability could cause the damage, but some capacitive coupling of the large parasitic capacitor, made of the upper metal layer and the substrate, and some huge electromagnetic disturbance near the device. The presence of a power switch very close to the board mounting the failed devices moved to introduce some specific protection (electrical shield and increased spacing between the critical elements), and the result was the complete disappearance of the problem.

DISCUSSION

The reliability prediction methodology proposed in [START_REF] Cassanelli | Reliability Prediction in Electronic Industrial Applications[END_REF] involves different approaches: empirical model prediction techniques, analysis of field return data about similar product, analysis of data about accelerated test and also failure physics of a single component, to asses the reliability of a new product.

The failure analysis of the CMOS microcomputer described in the second case study is used to improve the calculation of the corrective factor K relative to the control board in which the component is mounted. The information are used to decrease the value of λ fs that is the failure rate of the control board obtained through graphical and numerical analysis of the field return data.

The failure of CMOS microcomputer brings to the failure of the control board; but through the performed failure analysis this problem has been solved, so to asses the reliability of a new but similar board the λ fs has to be cleaned by this failure returns.

CONCLUSIONS

The Failure Analysis of devices in particular when failed in the field application, is not a deterministic science and enables us to establish only the most probable cause of the failure.

In both reported cases the sudden occurrence of the failure mode was not related to any sudden firing of the root failure mechanisms, but other hidden causes have been identified, with completely different corrective actions with respect to the first interpretations.

There is a simple and "correct" conclusion to this result: by means of thorough analyses, the first specimen (IGBT) was indicted for some higher sensitivity to latchup, and the second (CMOS) to external-induced ESD events. This could move to correct the corresponding π factors employed for calculating the actual failure λ, drawing a physically sound shortcut to the estimation of the reliability parameters for some critical devices of a given electronic system.

But there is also another conclusion, maybe less polite, that considers the documented case of the CMOS as a standard: when a SME faces a failure problem, the answer from the manufacturer will likely address to customer's responsibilities, possibly documented by some "official" report that displays a couple of pictures and indicts some "butler" as the culprit. Apart from any consideration about the integrity of intents of the parts, the problem exists of enabling the customer of a Failure Analysis to know if the paid job is good or not.

Ten years ago [START_REF] Vanzi | The Rules of the Rue Morgue[END_REF], a paper dealt with the problem of reliability of the Failure Analyses [rue morgue], pointing out as many violations of a simple set of logical rules commonly occur also in authoritative Reports. A decade later, it seems that the situation did not improve, and that a whole class of customers remains undefended against a general lack of culture in reliability. A recall of those rules was worth of consideration in a recent paper [START_REF] Mura | The rules of the Rue Morgue: a decade later[END_REF].

Fig. 1

 1 Fig. 1 Optical micrograph of the top surface after mechanical grinding. The dashed line defines the edges of the underlying chip. The view identifies the three sectioned metal connections (Emitter, Collector and Gate). The curvilinear lines delineate the carbonised plastic area, whose arrowed part belongs to the neighbourhoods of the original wire path.

Fig. 3b SEM

 3b Fig. 3b SEM Detail of the Al intrusions. The polyhedric shape of the Al-filled cavities is a fingerprint of solid-state interdiffusion of Si into the overlaying metallic thin film.

Fig. 2

 2 Fig. 2 DUT surface after the plastic removal. Pointed line indicates the direction of sectioning

Fig. 4

 4 Fig. 4 section of the chip/thermal sinks structure. The creeks roughly crowd along the expected current/heat flux lines from the upper Emitter wire contact to the lower Collector surface.

Fig. 6a

 6a Fig. 6a General view of the surface of the failed input pin of the first chip, upon removal of the plastic package. The arrow points to a small "burnt" area.

Fig. 6b

 6b Fig. 6b Optical micrograph of the damaged area after sequential removal of polyamide (left) and nitride passivation (middle), and finally after HF (right)

Fig. 7

 7 Fig. 7 Optical view of the damaged area after selective polyamide (a) and nitride (b) removal. The SEM image corresponding to b is displayed in (c). The arrows point the interdiffusion region on the top metal layer.

Fig. 8

 8 Fig. 8 (a) Optical view of the damaged area after complete HF etching.

Failure Analysis and Field Failure: a real shortcut to Reliability improvements ©TIMA Editions/THERMINIC 2006 -page-ISBN: 2-916187-04-9

Acknowledgements

The Authors wish to thank prof. F. Fantini and prof. M. Vanzi for the many useful discussions and for their continuous encouragement during the development of the reported study.


Satoshi Kondo

Qiang Yu

Tadahiro Shibutani

Masaki Shiratori

Reliability Evaluation Method for Electronic Device BGA Package Considering the Interaction Between Design Factors

The recent development of electric and electronic devices has been remarkable. The miniaturization of electronic devices and high integration are progressing by advances in mounting technology. As a result, the reliability of fatigue life has been prioritized as an important concern, since the thermal expansion difference between a package and printed circuit board causes thermal fatigue. It is demanded a long-life product which has short development time. However, it is difficult because of interaction between each design factor. The authors have investigated the influence of various design factors on the reliability of soldered joints in BGA model by using response surface method and cluster analysis. By using these techniques, the interaction of all design factors was clarified. Based upon the analytical results, design engineers can rate each factor's effect on reliability and assess the reliability of their basic design plan at the concept design stage.

INTRODUCTION

Recently, in development of electronic devices, shortening of a development period and reduction of cost becomes more important subject. On the other hand, at the same time, a guarantee of quality that user expects should be obtained. From these demands, an efficient design support system for electronics devices is expected Advancing of mounting technology, electronic devices were miniaturized and integrated. Because of this, solder joints of devices were detailed, and heat fatigue destruction of solder joint became a serious problem. This problem was caused by the difference of thermal expansion between a package and printed circuit board. And it is necessary to try to improve this problem at the design stage. However, because of complicated structure of electronic devices, the interaction of each design factor became remarkable and reliability problem has been complicated. So, it is very difficult to give effective changes with design factors for heat fatigue life. Therefore, the design support tool corresponding to the complicated reliability problem is needed. The purpose of this study is to establish the simple and convenience design support technique for electronics devices. As its application, the influence and interaction of each design factor in BGA package on thermal fatigue life was examined. Since BGA package has complicated structure. To investigate the influence of design factors on heat fatigue life, sensitivity analysis was used. But in cases that the package has complicated structure, it is known that sensitivity analysis becomes not much suitable because of the interaction between each design factor. So, in order to clarify this interaction, cluster analysis was used. Furthermore, the technique for clarifying a more detailed interaction of each design factor was also examined. As a result, all interaction was clarified and more collect sensitivity analysis was done. The contents of this study are stated as follows:

1)

Influence analysis by using surface response method 2)

Cluster analysis for clarifying the interaction of each design factor 3)

Cluster analysis, which observe one factor and clarifies more detailed interaction By using these methods, interaction of each design factor is clarified. Moreover, exact sensitivity analysis can be performed by taking interaction into consideration.

NOMENCLATURE

FEM

THE INFLUENCE ANALYSIS ON DESIGN FACTOR TO TOTAL EQUIVALENT INELASTIC STRAIN RANGE

Several methods can be used to evaluate the thermal fatigue life of solder joints [1][2]. In this study, the initial fatigue crack occurring in the solder joints is used for the thermal fatigue life [START_REF] Yu | Fatigue-Strength Prediction of Microelectronics Solder Joints Under Thermal Cyclic Loading[END_REF][START_REF] Yu | Nonlinear Behavior Study on Effect of Hardening Rule of Lead Free Solder Joint[END_REF]. It is known that the total equivalent inelastic strain range per step of thermal load can be used to evaluate the life [START_REF] Verma | A Numerical Study of Fatigue Life of J-Leaded Solder Joints Using the Energy Partitioning Approach[END_REF][START_REF] Pan | Critical Accumulated Strain Energy (CASE) Failure Criterion for Thermal Cycling Fatigue of Solder Joints[END_REF][START_REF] Bhatti | Effect of Global CTE Mismatch on Solder Joint Creep in SMT Devices[END_REF][START_REF] Manson | Interfaces Between Fatigue Creep and Fracture[END_REF].

To clarify the relation between design factors and total equivalent inelastic strain range, sensitivity analysis was used. At first, in the model of fundamental BGA package as shown in Fig. 1, sizes of components, mechanical properties and thermal properties were taken as the design factor shown in Table . 1. Orthogonal table was created by the DOE theory. In this case study, total equivalent inelastic strain range was taken as the characteristic value calculated by using FEM analysis. The detail condition of FEM analysis is stated as follows:

1)

The temperature range is from -40ºC to +125ºC for the thermal load. The time of temperature change take 0.05 hour (3 minutes), and the dwelling time is 0.25 hour (15 minutes) as shown in Fig. 2.

2)

Based upon the symmetry of the package structure, a quarter model was used in this analysis, and the symmetrical boundary conditions are subjected as show in Fig. 3.

3)

The total equivalent inelastic strain range was calculated with the average equivalent strains around 50µm at the corner of the solder bump shown in the circle of Fig. 4.

By performing response surface method, a characteristic value can be expressed on the basis of estimated equation as shown in Table .2. And the influence of the design factor to a total equivalent inelastic strain range was calculated. The table of influence for design factors in Table .3. From this result, it makes clear that the thickness of Encap had affected the most, and in order of influence, CTE and thickness of substrate and Encap's CTE also affect characteristic value. Moreover, the influence figure of a design factor was shown in Fig. 5. We can identify easily how much influence each design factor has on a characteristic value from this figure. This shows that thickness of Encap, CTE of PCB, and CTE of Encap should be made into a level 1 (low value), and thickness of substrate, Young's modulus of substrate, and CTE of substrate must be made into a level 3 (high value) in order to make a characteristic value low. By these studies, the relation between design factors and a heat fatigue life becomes clearer. However, this technique is not taken into consideration about the interaction of each design factors. To clarify the interaction of each design factor, clustering analysis shown below was used.

CLUSTER ANALYSIS

To clarify the interaction of each design factor, cluster analysis was used in this study. Cluster Analysis is the method of calculating the Euclid distance between parameters, and gathering close models one after another, and expressing their relation by a hierarchical structure.

Clustering similar results to the characteristic value acquired in FEM analysis etc., and the interaction of each design factor to a characteristic value makes it clear for comparing each cluster. The values of total equivalent inelastic strain range obtained from FEM analysis based on the orthogonal table were plotted in Fig. 6. A vertical axis shows the total equivalent inelastic strain range that which is a characteristic value, and the horizontal axis shows the data number. Those data were arranged in order of total equivalent inelastic strain range, and the close models have been clustered to four clusters by Euclid distance. In order to investigate the relation of each design factor, each design factor was averaged in a cluster and these values of design factors in each cluster are plotted in Fig. 7. The X-axis shows design factor and the Y-axis shows the design value regularized by design range. No.1 cluster in figure shows the data of a design factor pattern when the value of total equivalent inelastic strain range is smaller, and No.4 cluster shows the data of a design factor pattern when total equivalent inelastic strain range is bigger. The arrow shows the direction where total equivalent inelastic strain range becomes large, and its length indicates the intensity of influence to the characteristic value. From this result, the changing of design factor when total equivalent inelastic strain range was small or big was clarified, and it is possible to grasp all design factor differences at once. Therefore, the whole interaction can be grasped by using this figure. From the result of this cluster, as the thickness and CTE of Encap become smaller, and the thickness and CTE of substrate are made larger, the total equivalent inelastic strain range tend to decrease. In the case of this condition, the trend of Encap's properties shows the opposite to substrate's one. In previous paper, it was reported that whole package would curve upwards [START_REF] Jin | The assessment of influence of design factors on the reliability of BGA solder joints[END_REF]. And the total equivalent inelastic strain range of a solder joint tends to decrease when packages curve upwards as shown in Fig. 8. Furthermore, in the case of thickness of chip factor, when the total equivalent inelastic strain range is high, or low, the value of chip height is both large. This means that the height of a chip is influenced considerably with the other design factor. From this result, it is clear that the influence analysis is not taking interaction of each design factor into consideration and obtained result is a primary. This clustering clarifies the whole interaction of each design factor, but it is still not clear which factors have a interaction concretely. In order to perform a more exact development, it is important to take the detail interaction of design factors into consideration. Then, paying attention to one factor, the method to do clarification with more detailed interaction of each design factor would be examined.

DETAIL ANALYSIS OF INTERACTION BETWEEN DESIGN FACTORS

When there is change added to one certain factor, the method of investigating the influence of other factors was examined. At first, from the result of Fig. 5, cases where the value of thickness of substrate takes maximum or minimum were extracted. And it was arranged in order of the size of total equivalent inelastic strain range as shown in Fig. 9. The X-axis and the Y-axis takes the same as Fig. 5, respectively. The points that are painted show the results of minimum value of thickness of substrate, and the points that are not painted show the result of maximum value of thickness of substrate. By clustering similar results to the characteristic value and comparing the average of each design factor in each cluster, the effect of changing of thickness of substrate was clarified.

The result is shown in Fig. 10. This figure means the influence of changing thickness of substrate value on another design factor. When thickness of substrate is low, thickness of chip should be made low in order to decrease the total equivalent inelastic strain range. But when thickness of substrate is high, it should be higher. It turned out that, when one design factor (in this case, substrate's height) was changed, the influence of another design factor (chip's height) on the characteristic value was reversed. In similar case, when thickness of substrate is low, the factor of CTE of substrate doesn't influence the characteristic value. But when thickness of substrate is high, it influences the characteristic value. Therefore, it became clearer that thickness of chip and CTE of substrate have strong interaction with thickness of substrate. And interaction strength can be calculated from the difference between regularized values (arrows in the figure).

To apply this clustering technique to all design factors, all interaction of each design factor would be clarified.

EXAMPLE OF APPLYING THIS CLUSTERING TECHNIQUE

An example of applying this technique is shown below.

From the previous study, it is known that the reliability assessment could be done easily by calculating the appearance CTE and Young's modulus of whole BGA package [START_REF] Jin | The assessment of influence of design factors on the reliability of BGA solder joints[END_REF]. To estimate the appearance CTE of whole BGA package, the interaction between all design factors was calculated and sensitivity analysis was done. Table .4

shows the interaction strength between all design factors calculated by the clustering method. The strength of the interaction relation between every two factors can be expressed by a sum of the correlation coefficient at the cross points of the two factors. When the sum value is bigger then the average of the all sum values, the two factors have interaction relation, and considering this result, sensitivity analysis was evaluated and estimated equation was calculated. At the same time, sensitivity analysis which considers no interaction was executed, and both estimated equations are compared as shown in Table .5. Two different FEM models of various design conditions were made, and appearance CTE of whole package was calculated from the FEM analysis, estimated equation with considering interaction, and estimated equation without considering interaction. By comparing with the result of FEM analysis, it is clarified that estimated equation with interaction is more accurate than the other one. From this result, effectiveness of this technique was clarified.

CONCLUSION

1)

By using the influence analysis, the influence of each design factor on thermal fatigue life in electronics devices can be evaluated quantitatively. However, because of interaction of each design factor, this method is not much suitable.

2)

Clustering technique can provide the whole interaction of each design factor.

3)

Moreover, by clustering for the observed design factor, detail interaction of each design factor can be extracted.

4)

It was confirmed that exact sensitivity analysis was performed by considering the interaction.

As a result, it was proved that all interaction of each design factor could be clarified and more exact sensitivity analysis could be performed. Therefore, design engineers can rate each factor's effect on reliability and assess the reliability of their basic design plan at the concept design stage.

Fig. 1 Fig. 3 . 3 .Fig. 6 .Fig. 7 .Fig. 8 .ForFig. 9 .Fig. 10 .

 133678910 Fig. 1 Package modelTable 1. Package design factors and value levels

Table . 4

 . All correlation coefficient of BGA package

Table . 5

 . Results from estimated equations

Design factors Min. value Max. value Model 1 Model 2 X1 CTE of encap (10 -6 /℃) 1 2 2 0 1 5 1 6 X2 Young's modulus of encap (GPa) 15 23 18 15.5 X3 Thickness of encap (mm) 0.2 0.6 0.58 0.23 X4 CTE of chip (10 -6 /℃) 2 6 3 6 X5 Young's modulus of chip (GPa) 150

				200	180	175
	X6	Thickeness of chip (mm)	0.1	0.5	0.44	0.29
	X7	CTE of substrate (10 -6 /℃)	1 2	2 0	1 6	1 7
	X8

Young's modulus of substrate (GPa) 15 23

					16	22.5
	X9	Thickness of substrate (mm)	0.1	0.5	0.48	0.47
					CTE	CTE
		Result			(10 -6 /℃)	(10 -6 /℃)
		FEM analysis			4.33	15.8
		Not considering interaction			7.15	13.9
		Considering interaction			4.11	15.6

② ①