Weibull Statistics of Silicon Die Fracture

Transcription

1 Weibull Statistics of Silicon Die Fracture C. Boh*, T. Hauck*,. Juritza**, W.H. Müller** *) Freescale Halbleiter Deutschland GbH Schatzbogen 7, München, Gerany **) Technische Universität Berlin, LKM Einsteinufer 5, Berlin Gerany tel , fax bstract In order to guarantee reliability of seiconductor devices for autootive applications an optiized package design is required. Clearly the design ust be based on the best choice of geoetry, aterials and anufacturing processes. It is well known that the various process steps involved during package anufacturing occur at relatively high teperatures. Consequently, due to the isatch of theral expansion coicients of the package aterials, high theral stresses arise at operating teperatures and ay lead to failure of the device. Typical device failure odes include delaination of aterial interfaces or bulk aterial fracture. In this paper we focus on the prediction of silicon fracture in the icrochips of electronic devices. Due to their brittle nature the strength data of silicon dies will scatter and a probabilistic approach to failure is required. For this purpose Weibull theory will be used and cobined with analytical as well as nuerical tools in order to describe the state of stress in the package and in particular within the silicon die. s a result of the analysis the probability of fracture in a icrochip can now be assessed and used for further quality assurance purposes. The paper will start with a brief introduction to Weibull theory and present the 3-Point-Bending (3PB) experients that were used to obtain the Weibull paraeters for characterization of a cobination of surface and edge flaw induced silicon die fracture. Moreover, the ball-on-edge and ball-onring tests will be described and used to separately characterize edge or surface flaws, respectively. Particular ephasis will also be given to the transferability of Weibull probability results fro one specien configuration to another resulting in a change of surface size and stress. In this context it will be described how a stress distribution and, in particular, a ultiaxial state of stress influences the variability in strength. Moreover it will be shown how the corresponding Weibull integrals can be ipleented nuerically and used for postprocessing of finite eleent results. The paper concludes by deonstrating how these procedures can be used for optiizing the design of a real silicon die package. 1. Flaw Population Selective Fracture Tests Depending on the preparation and processing of the silicon die different flaw populations will be induced which essentially lead to different failure odes during use, in particular when the die is ebedded in a olded package and, therefore, subjected to a ultiaxial state of stress acting on the edges as well as on the surfaces. We ay say that surface defects are essentially induced during wafer processing, such as etching and grinding. On the other hand, edge defects will originate fro cutting processes. Figure 1 shows the chipping of a silicon wafer caused by the singulation procedure. During a bending test the different flaw distributions on the chip result in cracks that statistically eanate fro either the surface or the edge (cf., Figure 2). Figure 1: Silicon chipping at sawing street (acceptable and poor quality) Figure 2: Fracture surface of bending test specien Consequently, the question arises as to whether and how the different flaw populations can be distinguished and quantitatively assessed. Due to the statistical nature of brittle fracture, which is also pertinent to silicon, Weibull statistics will preferably be used, which, however, ust first be put in context with experiental setups characteristic of the various flaw populations in question. In particular we shall use the so-called Ball-On-Edge (BOE) test to quantify edge flaws populations, whereas the Ball-On-Ring (BOR) (cf., [1]) test will serve as a tool for surface flaw analysis. It should be noted that the traditionally used 3 and 4 Point- Bending (3PB/4PB) tests always lead to a cobination of surface and edge induced failure. This becoes evident if one realizes that both tests show a axiu tensile stress of equal agnitude along the edges as well as on the surface of the tested specien. In what follows we shall briefly suarize soe essentials on Weibull statistics, coent on results fro 3PB tests, and will then discuss in detail the experiental setup and strength data steing fro BOEtests. 2. Eleents of Weibull Theory During fracture of a batch of speciens ade of brittle aterials soe will fail at very low loads, others are capable of withstanding very high loads, but ost of the show soe interediate strength. Clearly, the strength of a high quality aterial should not show high variability in strength /04/$ IEEE Electronics Packaging Technology Conference

2 Consequently, such products are characterized by a narrow strength distribution, whereas a broad distribution indicates a less advanced aterial, or even a processing fault. By cuulative suation of the probability data, P i, the cuulative distribution of strength in Figure 3 can be constructed. If the ordinate is noralized with respect to the total nuber of speciens in the batch, N, the resulting plot presents a easure for the probability of failure, P i, where i refers to the specien of strength σ : i i Pi =, yi = ln ln, xi = ln σi. N P P i σ i can be fitted reasonably well using a two-paraeter Weibull distribution: Experience shows that for brittle aterials ( ) P σ ( σ) =1 exp σ0 High variability of strength within a particular batch of speciens is characterized by a sall Weibull odulus or - value. σ 0 is known as the scale paraeter. i (1) (2) Based on three principles, viz., (i) statistical hoogeneity and isotropy of the aterial, (ii) statistical independence of subvoluina and subsurfaces, and (iii) the weakest link concept the probability of failure for a body subjected to a spatially varying, but uniaxial, state of stress can, according to Weibull [3], be written for surface doinated flaws: 1 P = 1 - exp = σ ( x, y) σ ax σ ( x, y) σ 0 dx dy, (3) dx dy. (4) and denote the ective and total surface of the specien. σ ( x, y) and σ ax are the arbitrary, uniaxial tensile (positive) stress distribution and the axiu stress at the specien surface, respectively. It is assued that only tensile stresses influence the probability of failure. Soe inforation on how the surface integration is perfored can be found in [2]. 3. Selected Results on 3-PB-Tests 3PB tests were perfored at the Technische Universität in Berlin using a Tytron 250 provided by MTS. The 3PBtest setup is shown in Figure 4. The speciens were loaded until fracture occurred and the loads at fracture were recorded. typical fracture pattern is shown in Figure 5. Figure 4: 3-PB-test setup (top and side view) Figure 3: Distribution of strength for brittle atter In practice these two paraeters are deterined fro experients using a particular specien and loading type. The resulting strength data are either processed using the ethod of least squares or the axiu likelihood procedure (see [2] for details): Figure 3. s entioned above the ean strength of a specien ade of brittle aterials depends on its volue, its surface, its loading conditions and the flaw distribution. Intuitively speaking the ore volue or surface exists the higher the chances for a critical flaw to be present will be. For exaple, a 4PB specien will break ore easily than a 3PB one, because in the case of the latter high tensile stresses are restricted to a uch saller region. Figure 5: 3PB-test specien before and after test Typically strength easureents are presented in a Weibull plot, where the ordinate and abscissa are divided according to ln(ln(1/(1-p))) and ln(σ), respectively. The resulting curve usually atches a straight line that is defined by the Weibull distribution with odulus and scale paraeter σ 0. Figure 6 shows the Weibull plot for 3PB-tests with the Weibull distribution, where the paraeter were deterined using the axiu likelihood ethod Electronics Packaging Technology Conference

3 Fracture Probability [%] PB Measureent Weibull Distribution =5.4 s0= Maxiu Stress [MPa] Figure 6: Weibull plot for 3PB-tests 4. The Ball-on-Edge Test Experiental Setup: The realization of the edge test is shown in Figure 7. The test rig consists of two etal blocks into which spheres have been inserted. The left block (cf., Figure 7) contains three spheres whereas the right block holds only one sphere onto which the force is acting (in horizontal direction). scheatic of the arrangeent is shown in Figure 8. Figure 8: Scheatic of BOE rig The position of the spheres within the blocks defines the stress distribution in the specien. The tensile stress concentration on the lower specien surface directly underneath the single ball triggers brittle failure at this position. The closer the single sphere is oved toward the specien edge the ore the edge will be subjected to tension and the ore the edge flaw population will be assessed. Experiental Results: BOE-tests were perfored at the Technische Universität in Berlin according to the described experiental setup. The speciens were singulated fro wafer by standard sawing procedure at Freescale GbH. Each specien consists of an array of 3x3 silicon chips (cf., Figure 9). batch size of 20 saples was subjected to the testing procedure. The resulting probability of failure vs. the failure load is presented in Figure 10. The graph does significantly deviate fro the typical S-shape of a Weibull distribution (cf., Figure 3). It indicates that two active flaw distributions exist. Consequently, fractographic exaination is required in order to characterize the fracture origin in each specien. Figure 9: Silicon specien array of 3x3 chips 1,0 0,9 Probability of failure, P 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 Figure 7: BOE-test setup top and botto view 0, failure load [N] Figure 10: Probability of failure vs. the failure load Electronics Packaging Technology Conference

4 Indeed, the first three data points below a force of 15 N correlate with a crack initiation at the edge of the specien, whereas the other data points above 15 N correlate with a crack initiation fro the botto surface underneath the ball (cf., Figure 10). The corresponding fragents are shown in Figure 11 and Figure 12. Thus we detect two distinct flaw distributions for edge and surface failure, respectively. Figure 11: Specien fragents indicating edge failure ode shown in the pictures were scaled and in fact reained very sall. The balls were represented with elastic half spheres and discretized with tetrahedral eleents. The elastic specien was discretized with hexahedral eleents. The failure load was applied to the upper ball, whereas the supporting balls were copletely fixed. contact proble was defined between the balls and specien. ll aterials were treated elastically and geoetric nonlinear ects were considered. The analysis of the stress state at different load level revealed a linear relationship between load and stress values (cf., Figure 14). Factors of proportionality where extracted fro the finite eleent analysis for easy calculation of axiu stresses on specien surface and edge at arbitrary loads: σ ax specien edge = k F, k =. (5) specien surface Figure 13: Defored FE esh of BOE rig and specien Figure 12: Specien fragents indicating surface failure ode Stress-nalysis and Weibull Paraeters: The resulting stress distribution at the failure load was calculated by eans of finite eleent analysis. Figure 13 shows the eshes of the specien and the test rig. Note that the deforations Stress σ [MPa] Maxiu tensile stress underneath the ball Maxiu tensile stress at the edge k 2 = k 1 = Force F [N] Figure 14: Maxiu tensile stresses vs. applied force Electronics Packaging Technology Conference

5 The resulting tensile stress distribution in the specien is illustrated in Figure 15. The applied failure load at the upper ball causes a stress concentration on the botto surface underneath the ball (red color). Due to the proxiity of the single sphere to the specien edge, high stress regions appear at the edge of the specien as well (yellow color). Maxiu tensile stresses were taken fro underneath the ball in order to deterine the silicon strength for the surface flaw distribution, whereas axiu stresses were taken fro the edge in order to deterine the silicon strength for the edge flaw distribution. The statistical evaluation of the strength values were perfored separately for each failure ode. The sapled strength data were split into two sets according to the fractographic classification (cf., Figure 11and Figure 12). Each set were treated as an independent discrete strength distribution. The corresponding Weibull paraeters were deterined by eans of the axiu likelihood ethod. Figure 16 shows the Weibull plot with the overall specien failure probability for the BOE-test and the Weibull paraeters for both flaw distributions. 4. Conclusions ball-on-edge (BOE) test procedure was developed with the intention of a local strength easureent in regions of the silicon chip surface and the silicon chip edge. The test rig was designed such, that the fracture origin was triggered at a point close to the die edge in order to capture flaw distributions in this region. The evaluation of the strength data revealed two independent active flaw distributions, one on the chip surface and another one on the chip edge. Weibull paraeters were deterined for both distributions. Further work is required in order to confir the results and to achieve a sufficient statistical confidence. Coparative tests with three-point-bending and ball-onring setup are planned in order to validate the procedure of failure probability prediction for arbitrary specien geoetries. The Weibull paraeter will be used for the prediction of failure probability for a silicon chip situated in a olded package. Figure 15: Tensile stress distribution in specien cknowledgents The authors wish to acknowledge Jörg Feige, Freescale Gbh for specien preparation, Betty Yeung and Vern Hause, Freescale Inc., for silicon strength tests and fractographic analysis. References 1. Jahresbericht 2003, Fraunhofer Institut für Werkstoffechanik IWM, (Freiburg, 2003), pp Boh, C, Hauck, T., Müller, W.H., Juritza,., Probability of Silicon Fracture in Molded Packages, Proc. EuroSiE 2004, Brussels, May 2004, pp Figure 16: Weibull plot of the BOE-test Electronics Packaging Technology Conference