MATLAB® for Photomechanics- A Primer
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Numerical modeling is often used to predict the effects of the operating conditions on reliability. In , the thermal modeling of a power transistor is made for two different configurations, with and without heatsink. The simulation allows estimating the temperature of the case. The same subject is discussed by Meyyappan , the main accent being put on the failure mechanisms of wire bonds due to wire flexure.
Several other failure mechanisms were identified, such as wire bond lift-off, cracking, corrosion and electrical leakage. The cracking of wire bond joints, modeled by finite elements , allowed simulating the failure mechanism and the initiation and growth of cracks. Experimentation and testing allow inspection of the physical origins of thermomechanical stress, an essential task for improving the numerical modeling and reducing the risks of failure. It allows a phenomenological analysis and takes into account practical data related to the physical behavior of structures and materials inside a microelectronic device.
Some of the most interesting quantities being measured are the temperature of semiconductor junction and of heatsink, the full deformation and strain fields of the whole device or of some key parts of it - most often wire bonds and die. Simultaneous, synchronous measurement of these quantities may bring essential information for the estimation of device reliability.
The techniques used for testing are based on various principles: electrical, thermal, acoustical, optical — as well pointwise as full-field. There is an impressive number of books, journal papers and scientific conferences covering various subjects related to testing of individual electronic components and of assembled PCB. Some of these techniques will be briefly mentioned here. The main interest of this paper is the full-field measurement coupling a high spatial resolution with a high temporal resolution with temperature and voltage measurements.
The displacement measurement has an extended measurement range and may cope with large and discontinuous displacement fields. The low level of noise allows estimating the curvatures across the object surface. Some other use coherent light. Their sensitivity is higher a fraction of light wavelength. Digital holography and its applications in testing are exposed by Schnars and Jueptner , by Asundi  and by Picart and Li .
Digital holography makes use of great progress in digital computing and is efficient since it may produce a high spatial resolution wrapped phase map across the object surface using just a single specklegram, instead of a group of three or four phase-stepped specklegrams. It may thus be recommended for dynamical applications. Apart from the contributions presented in the literature by some producers of commercial speckle interferometry systems, the number of contributions to this field from the academic world is rather limited.
It was applied to the thermomechanical study of a MOS power transistor. The steady state deformation is measured using full-field ESPI, while the temporally transient regime is obtained pointwise by using a Michelson interferometer. An important contribution was made by Avery and Lorenz , dealing with the in situ measurement of wire-bond strain in electrically active power semiconductors by out-of-plane and in-plane speckle interferometry.
They tried to overcome the problem of displacement discontinuities between emitter wire-bound and die by drawing a contour around the wire-bond, then unwrapping only the region inside this mask. The most important features of the thermomechanical deformation inside a power microdevice addressed by Avery and Lorenz are: unwrapping the full-field displacement maps, thermal modeling and the use of a thermal camera for obtaining the full-field temperature distribution.
The use of a laser as light source is introducing speckle noise in the result of the measurements — the modulo 2pi wrapped phase patterns. Speckle noise and speckle decorrelation are limiting the total number and the spatial density of fringes and create great difficulties in unwrapping the phase maps. Unwrapping difficulties are highly increased by discontinuities in the fringe patterns, as in the case of the heterogeneous inner structure of a power device.
Other limiting factors are the lack of temporal information allowing to follow simultaneously the temporal and the spatial modifications of the deformation map and the lack of synchronized information related to the local temperature in different locations inside the power device. Overcoming these limitations may help in applying the physics-of-failure PoF approach, one of the reliability prediction methodologies . The measurement system In this section is described a measurement system able to acquire data allowing a detailed physical insight on the behavior of microelectronic power devices under thermal stress produced power cycling.
The aim is to dispose of detailed knowledge allowing developing high power components and predicting their reliability.
In particular, the main interest is the full-field measurement of mechanical deformation of the wire bond interconnection between the emitter pad on the die and the external terminal, shown in Fig. The wire bond 1 is connected to the emitter and the wire bond 2 to the base. The wire bond 1 carries the emitter current which has a high value. Its temperature increases by Joule effect. The mechanical consequence of this electro-thermal stress is mechanical bending. The wire bond is the transistor part which is usually the most exposed to fatigue and failure because of large, repetitive bending strain and stress.
The wire bond has two interfaces, the first one between the bond wire and the bond pad on the die and the second one between the bond wire and the emitter terminal.
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The materials used in these parts have very different thermomechanical parameters. The speckle interferometry measurement systems. Full-field out-of-plane displacement measurement.
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In order to acquire detailed physical insight concerning the thermomechanical and thermoelectrical interactions in power microelectronic devices, the data acquisition means of the Photomechanics Laboratory are centered around two speckle interferometry systems able to record series of specklegrams and interferograms, temporally synchronized with the different temperature and voltage pointwise measurements. This measurement system was designed and realized in the Photomechanics Laboratory .
The setup configuration, the processing algorithms and the results obtained in the measurement of dynamic and transient deformations were described in previous papers, such as  and . In the field of thermomechanical stressing of microelectronic devices this high-speed system may record series of full-field, temporally wrapped and unwrapped deformation maps of the inner structure of a high power microwave transistor operating in pulses of about 1 ms, separated by 20 ms.
During this sequence, the different parts of the transistor are successively heating and cooling; the high mechanical deformations resulted are measured by the temporal speckle interferometry system. The size of the measured region is about 2x2 mm. The maximum deformation of each active section of the transistor during its heating is about nm. Figure 2. Die deformation of a high power microwave transistor a at an instant t1 during heating; b at an instant t 2 during cooling The temporal series of full-field displacement maps show that the maximum values of mechanical deformations of different parts of the transistor do not occur simultaneously.
Between two pulses, other hot spots appear in other regions of the die, as shown in Fig. This measurement system is suited for studying small a few mm objects, for which the illumination beams may be less expanded, producing brighter scenes and providing the possibility for the camera to work with small shutter times. The second measurement system is a modified version of an older system, realized in the nineties by Stetson and Brohinski .
It may be used when the temporal sampling rate requirements are compatible with this camera frame rate. The analog camera output signal is split and connected to two different parts of the measurement system. The first part is an ISA-connected pipelined holographic processor  with real-time arithmetic processing, whose output is the wrapped phase pattern displayed in real time on a monitor.
It allows the operator to adjust the object excitation, to check the level of noise and the eventually occurring decorrelations. The wrapped phase displayed represents the phase difference between the current phase and an initial, reference phase. If the deformation is greater than a few micrometers, the fringes become too closed to each other and the spatial unwrapping of the fringe pattern may become difficult.
Some of the wrapped phase maps displayed in real-time are shown in Fig. By adjusting the objective zoom, one is able to display either a larger part of the object or a smaller part. As will be shown in the next section, each of these possibilities has its interest, even without unwrapping whole temporal series of data.
Figure 3. Interferograms showing a , b , c : the wrapped phase maps of die, heatsink and wire bonds; d , e , f : more detailed wrapped phase maps of the interface between the emitter wire bond and the die On Figs. On Fig. Series of several hundred or several thousand specklegrams produced by the camera are also directed towards a second acquisition module, and saved by a PCI frame-grabber driven under Labview . The frame grabber is synchronized, by using the real-time system integration RTSI bus, with a general use data acquisition board.
Several channels of this board are used for acquiring temporal series of data from pointwise measurements: temperature values, either inside the base-emitter junction or of the heatsink, as well as the voltage values. The system is schematically shown in Fig. The results obtained by using this measurement system will be described in Section 3.
Figure 4. Phase calculation from the acquired specklegrams may be done by several algorithms, by using four-bucket, two-bucket or one-bucket phase stepping , , . The series of full-field unwrapped phase maps during the heating of the device may be presented as multimedia files e. The phase calculation and temporal unwrapping, as well as data processing of different temporal histories are achieved with the help of a few programs written in Matlab . Pointwise measurements of base-emitter junction temperature and heatsink temperature.
The associated pointwise measurements synchronized with the full-field deformation measurements are heatsink temperature and base-emitter junction temperature, both being measured inside the power device packaging. As seen in Fig.
Its temperature is measured by a thermocouple, in synchronism with the specklegram acquisition. The mean temperature of the base-emitter junction is obtained directly by measuring the base- emitter voltage and using its dependency with junction temperature. A detailed presentation of this technique may be found in  and . They were found by calibration, by making use, in a least squares procedure, of temperature values programmed for the temperature-controlled oven and base-emitter voltage values acquired by a data acquisition board. For the tested transistor, in case of an emitter current of 0.
Measurement of electrical parameters The power transistor was mounted in common emitter configuration. Since transient high power loading conditions are of great interest  in developing the packaging technology, the tested transistor was thermally stressed by imposing a pulsed voltage cycling.
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The voltage cycling was achieved by using a pulse generator with adjustable duty cycle made with a timer. Along with temperature measurements, the simultaneous measurement of base-emitter voltage V BE and of collector current I C in the common emitter power transistor under test offers the possibility to get a detailed description of the electrical testing parameters. The temporal evolution of the full displacement field of the die surface and of the wire bond allows finding some hot spots on the die.
It also helps making a good thermomechanical modeling and validating numerical models in order to improve device reliability. Real-time observation of the voltage and thermal cycling provide information about the heating and the cooling of the die and wire bonds. The most interesting data are obtained when the transistor was heating during the "ON" pulse. The rest of this paper is concerning only the effects of the heating produced in the first seconds after switching it to conduction by a voltage step applied to its base.
Some of the experimental measurement results will be presented in the rest of section 3. Information acquired during the real-time display of the wrapped phase The large circular fringes seen when displaying in real-time a larger part of the transistor, already shown in Fig. Its transverse deformations are transmitted to the die and to the corresponding extremities of the wire bonds.
For this reason the bending of the wire bond attached to the emitter of the transistor is not symmetrical. The maximum out-of-plane displacement of the wire bond does not occur in the middle. Figure 5 shows the out-of-plane displacements of the two wire bond extremities, already denoted by A and C on Fig. Wire bond shape a initial; b deformed This information is bringing supplementary details to the analysis of wire bond deformation made in . A closer view, like in Fig. These phase distributions were used in two different ways.
First, they allowed computing the wrapped phase difference between the phase at any instant and an arbitrary chosen reference phase. Secondly, the same phase distributions were unwrapped by temporal phase unwrapping, by using a home-made program written in Matlab.
Such an unwrapped displacement map is scaled and presented as a surface in Fig. Figure 6. One of the unwrapped phase maps of the central part of the transistor, including the die and part of the emitter wire bond Another information provided by this displacement map is the anticlastic curvature of the bending wire bond. Such a deformed shape is typical for plate bending.
Figure 7 shows, as gray levels of the unwrapped and scaled interferograms, the deformation map and the out-of-plane displacements of points situated along several arbitrary selected lines. The plot shown in Fig. The plot in Fig. Full-field displacement map of emitter wire bond.
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Maximum curvature. Using the noisy unwrapped displacement maps in estimating the spatial derivatives of the out-of- plane deformation imposes a preliminary masking of the region occupied by the wire bond and the filtering these maps. The results are shown in Fig. Other very effective filtering procedures for interferometric data are Windowed Fourier filtering, described in , Savitzky-Golay filtering  or kriging .modulor.com.ua/includes/chloroquindiphosphat-preis-online-mit-versand.php
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In accordance with the theory of bending of elastic plates  the second derivative of out-of-plane displacement, or curvature, is proportional to mechanical bending stress. Estimating the derivatives is important since it helps in localizing the regions where maximum bending stress and fatigue occur. The region where the curvature is maximal is close to the wire bond interface with the die pad.
The profiles along the x axis of dw dx , the first derivative of the out-of-plane displacement and of the second derivative d 2 w dx 2 are shown in Fig.
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Figure 9. Other plots may represent the temporal variation of collector current and of out-of-plane displacement of any point chosen on the interferometric full-field map, for example the point where the maximum displacement occurs. It is a great option for dogs that need a little extra companionship during the day. Day care is also a great option for your puppy over 12 weeks old.
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Harry Potter. Popular Features. New Releases. Description The term "photomechanics" describes a suite of experimental techniques which use optics photo for studying problems in mechanics. The field has been in existence for some time, but has always lagged behind other experimental and numerical techniques. The main reason for this is that the interpretation of data, which whilst providing whole-field visualization, is not in a form readily amenable to the end-user.
Digital image processing has become common within the photomechanics community. However, one approach does not fit all, and subtle variations in technique and method have been developed by different groups working on specific applications. This primer enables the user to get started with their experimental analysis quickly.