JOURNAL OF MATERIALSSCiENCE: MATERIALS IN ELECTRONICS 6 (1995) 3 4 - 4 2 Flow processes in solder paste during stencil printing for SMT assembly S. H. M A N N A N , N. N. EKERE, I. I S M A I L , M. A. CURRIE Department of Aeronautical & Mechanical Engineering, University of Salford, Salford, M5 4WT, UK Solder paste is used for reflow soldering of Surface Mount Devices (SMDs). In this paper we discuss how the various stages of the stencil printing cycle affect the rheological properties of the solder paste. First the heat generated in the paste roll is examined to see what effect it has on solder paste rheology, then we analyse in detail the process of paste withdrawal from a metal mask stencil and discuss those properties of solder paste that lead to a good print in terms of the size and shape of the solder paste particles, and their packing. In order to do this, we review some of the experiments and phenomena that have been shown to occur in dense suspensions, and see what aspects of that work are applicable to solder paste printing. 1. Introduction The use of surface mount technology (SMT) has grown rapidly in recent years, but solder paste, one of the key materials of SMT, is still poorly understood. Solder paste consists of a liquid phase called the vehicle, and a solid phase made of metallic solder spheres. The solder paste is printed onto Printed Circuit Boards (PCBs)through a metal mask stencil, electronic components (SMDs) are then placed over the solder paste deposits, and the whole system is heated so that reflow soldering can occur. In this paper we shall consider only the printing characteristics of solder paste. The printing of solder paste can itself be broken down into various stages [1]. A paste roll is formed by the action of a moving squeegee blade, forcing paste down through apertures in the stencil and onto metal pads on the PCB. Once the squeegee has passed over the apertures, the stencil and PCB are separated mechanically. At this stage printing defects may creep into the process, particularly with fine pitch SMDs where both the apertures, and the gaps between neighbouring pads are small. The narrowness of the apertures may cause skipping, (where the paste is only partially deposited onto the pads, some paste remaining inside the stencil apertures), and the small gap between pads may result in bridging (where neighbouring paste deposits slump together and do not remain as isolated cuboid shapes). Other possible printing defects include peaking of the deposited paste, and scooping, which are usually a result of an incorrect pressure setting of the squeegee blade [2]. At the different stages of printing, different paste properties are important. In the paste roll in front of the squeegee, the bulk rheological properties of the paste are important and can be modelled with the aid of an approximate relationship between shear stress 34 and strain. The temperature of the solder paste affects its rheology and hence the environment is sometimes closely controlled. In Section 2 we will discuss the viscous generation of heat inside the solder paste to see whether this has an effect on printing quality. After the paste has entered the apertures, the next crucial stage is stencil-PCB separation. The factors that influence paste withdrawal from the stencil include paste viscosity, particle size and shape, aperture profile, geometry and finish, pad material, pad surface finish and shape, tensile strength of the paste and volume of solids content in the paste. The speed at which separation takes place is also important [3]. Although different solder pastes give different results at high and low separation speeds, the consensus in the industry is that a lower separation speed leads to less skipping. This is as expected since lower shear rates should result in lower stresses being generated in the paste. In Sections 3, 4 and 5 we look at the issues involved in paste withdrawal from the stencil. Paste slump and bridging at the end of the print cycle depend upon properties such as yield stress of the paste, paste surface tension and gaps between pads. Bridging is thought to occur during th.e squeegee stroke when paste can be forced underneath the stencil, during paste withdrawal and after withdrawal is complete. Bridging due to paste forced under the stencil can be eliminated relatively easily by reducing squeegee pressure and ensuring correct alignment between apertures and pads. However, paste bridging during and after withdrawal is a more complicated phenomenon and depends strongly upon the conditions that the solder paste has previously experienced. Having described the printing process, we return to the subject of solder paste. The liquid vehicle to which solder particles are added consists of solvents, flux (to remove oxides from the surfaces to be soldered), flux 0957-4522 0 1995 Chapman & Hall activators, thickeners, thixotropes and other theological agents. Therefore the vehicle by itself, before the addition of solder particles, is a complicated theological material. At low shear rates it exhibits an apparent yield stress (necessary to stop settling of the particles, and to resist slump), while at higher shear rates it exhibits shear thinning and thixotropic behaviour (which helps the paste pass into the apertures. The thixotropic behaviour is increased upon addition of solder particles because shearing causes breakdown of solder particle formations as well as molecular level formations in the vehicle. Ref. [4] contains an account of the constituents of solder paste. In the case of aperture emptying, the suspension nature of the paste becomes important and forces between solder paste particles determine fluid flow. The first step in modelling the theology of solder paste is to decide which forces need to be taken account of and which can be ignored. Focusing on the case of aperture emptying when the shear stresses and shear rates experienced by the paste are low, we can first calculate the Reynold's number for the paste flow as a whole: R = 9V1 ~ 10- 5 ~t (1) where p is the paste density ( ~ 5 x 103 kg m-3, ~t is the paste viscosity (,,~103pas), 1 is a typical size (e.g. aperture width ( ~ 10 -4 m) and V is a typical velocity (e.g. 20 mm s-1, the speed of the squeegee across the stencil surface). The low value of Reynold's number indicates that turbulent flow will not occur; the flow is laminar and furthermore the Navier-Stokes equations for fluid flow can be simplified to the form used when the Reynold's number is small. The flow of liquid between solder paste particles results in an even smaller value of the Reynolds number as distances between particles are of the order of 10- 6 m. A related number N has been used previously to describe the relative importance of inertial effects in a suspension relative to hydrodynamic forces [5]: ps~-~d2"] / N- ta .~ 1 2. Heat generation in the paste roll Solder paste viscosity depends upon the temperature of the paste. Thus if the environment of the solder paste is kept at a constant temperature, we would expect the solder p a s t e t o print consistently. However, during printing energy is put into the solder paste and is converted through viscous forces into heat. If this heat were to build up in the paste roll, it might have a significant effect, decreasing paste viscosity. To examine the extent of the temperature rise, we inserted a temperature probe into the paste before and after printing one stroke and found no temperature rise (thermocouple resolution: 0.5 K). The experiment was repeated after five printing strokes in quick succession and at a squeegee speed of 20 mm s-1 and a paste of measured viscosity 900 Pa s. Again no temperature rise was found, and after further repetition at higher speeds, it was concluded that no significant rise in paste temperature occurs during printing. In contrast, after stirring a 500 g pot of the same paste for 30 s, a 5 K temperature rise was found. The key to this behaviour lies in where the heat is generated in the solder paste. To calculate this heat rise we will use Riemer's model of a Newtonian fluid roll [7]. This is of course an approximation for our non-Newtonian paste but it is likely to give us reasonable results for the reasons outlined in Ref. [8]. In Riemer's model, the components of paste velocity can be found by using the Navier-Stokes equations of fluid flow at small Reynold's numbers. The resulting expressions for the stress tensor in the fluid are evaluated in the usual way, and the heat generation rate (per unit length of the roll), Q, is given by Q= dr do dd cy~ 2gV : f ( a ) I n (/) (3) where cy~kare the components of the stress tensor, a is the contact angle between squeegee and stencil, I is the contact length of the roll with the stencil, d is the solder particle diameter, 0 and r are polar co-ordinates (with the squeegee tip as origin), V is the squeegee velocity and f(ct) is given by (2) here Ps is the particle density, d is the particle diameter, h is the! gap between particles and ~ is the average paste shear rate. Again the smallness of this number I means that collisions are not important. Similarly, another dimensionless number expresses the relative importance of Brownian motion to hydrodynamic forces at~d again we find it is small, so that Brownian forces can be ignored. Inter~particle (e.g. electrostatic) forces, however, cannot be completely ignored for solder paste because we know that the absolute size of the particles affects the visci)sity. This would not be true if hydrodynamic forces di~minated completely. The smaller the particle size, the more important these colloidal-type forces becomel Ref. [6] discusses the application of computer si~nulations to dense suspensions when colloidal forces b~come important. + f(~) -- sin2 ct + ~2 _ 20tsinacoscx (:x2 _ sin 2 ~)2 x (a - sin a cos(0t - 2a)) (4) where a = t a n - 1 ct - sin ct cos a sin 2 (5) We have introduced the particle diameter d as a lower cutoff in the integration over the volume of the paste roll because the integrand becomes infinite at the origin. However, physically the suspension cannot flow, obeying the Navier-Stokes equations of motion at length scales below d, so the solution becomes invalid at lower length scales. Similarly, the original solution involved an infinite volume of fluid so that there has t o be a correction for the finite paste Volume in eq. (3) which we have not included so that 35 Squeegee / (stationary) J ................. Regionsof maximum J / heatgeneration/~f~/.~\ \ .// .... / ........ ..f _..,~ '.,j .... ' Stencil v sion, particles have been known to form structured layers, but the particles will probably assume a much more random structure in solder paste. In a closely packed arrangement of uniform spheres, the maximum volume packing fraction of spheres is 74% (~/2~). As the volume fraction is reduced, the distance between a sphere and its 12 nearest neighbours is given by [5] ]i h = 37~4 - ~ ........... d Pasteflow streamlines Figure 1 Fluid flow and regions of maximal heat generation in paste viewed in a reference frame where the squeegee is stationary. W 2Q (6) where p is the solder paste density, Cp is the specific heat capacity of the solder paste at constant volume and W is the squeegee stroke length. Substituting typical values for each of the variables, e.g. l = 0 . 0 1 m , W = 0 . 5 m , V = 0 . 0 2 m s -1, g = 103Pas, d = 3 0 x l 0 - 6 m , p=5xl03kgm -3 and C p = 3 5 0 J k g - l K -~, we obtain f i T = 4 . 0 K for = ~/4 and 5 T = 2.2 K for c~ = ~/3 radians. The form of Equation 3, however, is such that the vast majority of the heat is generated near the edge of the roll that is in contact with the stencil surface, as sketched in Fig. 1. In fact over 90% of the heat generation takes place within a 1 mm thick outer layer of the paste roll, and over 50% within a 0.12ram thick layer. This c o n f i r m s t h a t the error involved in using formulae derived for an infinite volume of fluid is small; most of the heat is generated far from the region where finite fluid effects take place. The relaxation time (t) for thermal conduction, which gives an indication of the timescale over which heat is dissipated away, is given by L2pCp t~ - k (7) where k is the thermal conductivity (k,~ 0.65 W m - ~ K - ~ for solder pastes) and L is the length over which the heat is dissipated away. Thus for L = 0.12 mm we have t = 0.04 s and for L = 1.0 mm, t = 2.9 s. Since a typical paste stroke lasts for 25 s, the heat generated in the paste roll has plenty of time to dissipate away into the metal of the stencil or the surrounding air. 3. Geometry of particle packing The way that the particles pack together affects the suspending fluid flow patterns which in turn affects the way the particles pack together. In a colloidal suspen36 (8) where h is the gap between particles, qb is the volume fraction a n d d is the particle diameter. In a randomly packed arrangement of spheres the maximum packing fraction has been variously estimated as 62.5% (experimental [9]) and 63.7% [10]; the average distance between a particle and its closest neighbour (H) is given in one model [10] as Equation 3 is only an approximation to the total heat generated. The temperature rise 6 T in the paste is given by ST-- V pl2~Cp 1 ~/~ H 3~ ~-= 5 +g-1 (9) Since solder pastes are usually specified by fraction of metal content by weight (M), the conversion to volume fraction is q~ = M (10) D. ' ° ( 1 -- M ) + M Pf Here Ps and pf are the sphere and fluid densities, respectively; the ratio of the two densities is aproximately 8.5. Decreasing the fluid density allows a greater metal content fraction at a given volume fraction. Table I shows the values of metal fraction, volume fraction, ratio of gap to particle diameter (h/d) for close packing and ratio of gap to particle diameter (Hid) (closest neighbour). The significance of the results in Table I is that lubrication theory between nearest-neighbour particles is likely to be an excellent approximation, and that particle doublets are extremely likely to form. In lubrication theory, two spheres will never actually touch as the force separating them becomes asymptotically infinite. However, in practice surface roughness effects mean that two or more spheres can make physical contact and form clusters even in the absence of inter-particle forces. These results, however, will change both because solder pastes spheres are not of uniform size and T A B L E I Values of metal fraction by weight, M, volume fraction, ~, ratio of gap to particle diameter (h/d) for close packing, ratio of gap to particle diameter (H/d) (closest neighbour). Values in brackets represent the values of the gaps (in microns) based on d = 28 I~m. Four values of M ranging from 89 92% are shown M (%) qb (%) hid (h) Hid (H) 89 90 91 92 49 51 54 58 1/7 1/7.8 1/9.2 1/I 1.4 (4.2) (3.6) (3.0) (2.5) 1/40 1/51 1/~0 1/112~ (0.70) (0.55) (0.40) (0.25) because the fluid flow will tend to create clusters of particles. A non-uniform size distribution tends to produce better packing and hence a lowering of viscosity. Clustering ha s the effect of increasing the effective solid volume fraction because the fluid trapped inside the cluster contributes to the solid's packing fraction. Therefore clustering increases the viscosity of suspensions. Given a uniform size distribution with no lower size limit, the maximum volume fraction is one. Even with a bimodal distribution, large decreases in relative viscosity can be made provided the ratio of particle diameters is greater than about two (approximately 33% reduction if the volume fraction of smaller particles is 25% for do ~ 55%) [11]. This is because the relative viscosity depends upon the volume fraction generically as [12] - \~/ j (11) where a and b are positive constants of order 1 and dom is the maximum volume fraction allowed before spheres touch and flow is impossible. We see that at high packing fractions the relative viscosity is very sensitive to the value of dora and hence t o the size distribution of particles. One corollary to this fact is that the viscosity of particles of size distribution 20-40 ~tm should be lower than that of particles of 25-45 gm, all other factors being equal. During flow, particle clusters are being formed as the flow brings particles together or pulls them apart. This means that the actual geometric arrangement of the particles is neither close-packed nor random. In particular, the accuracy of the lubrication approximation breaks down if there are large fluid regions in between clusters: the movement of the cluster is then subject to the movement of fluid between clusters. This fluid movement is controlled both by the effect of neighbouring clusters and the fluid flow of the material as a 'whole. To treat both the lubrication forces and far-field effects, a computational model based on Stokesian dynamics has been used [13]. To get an idea of the magnitude of the clustering, let us assume that all the particles are closely packed into spherical clusters. Then, by using Equation 8, we find the ratio of gap between clusters to particle diameter is (in the limit of large cluster sizes the effective volume of clusters increases to do/0.74 due to the fluid trapped between particles, and the ratio of cluster diameter to sphere diameter is (n/0.74)1/3): (iy/~ l J {,=) were hE is the gap between particles and n is the number of particles in the cluster. As can be seen, the clusters overlap at dO= 0.55 and then it makes more sense to talk about the voids between clusters. The gap between clusters is seen to be extremely small; Equation 12 gives a ratio of 0.1 for n = 30, dO = 0.5. In practice, n is likely to be much smaller than 30, as seen from computer simulations [14]. If the clusters are more cubical in shape then the corresponding formula is derived as follows: let the volume of cubes be/3, SO that in the limit of large cubes, the ratio lid becomes 1 1 (n/2~)-& The density of clusters is do/0.74 as before, but this is also equal to (l/(l + h~)) 3, so that finally, substituting for l, (13) and we find for n = 30 and do = 0.5 that the ratio is 0.39. These results mean that lubrication forces are still likely to be dominant almost everywhere in the suspension even in the event of large cluster formation. Since particles in a cluster will not actually be closepacked but more diffuse, we have been looking at a worst case scenario. It has been observed in a computer simulation [14] that a wider particle size distribution actually results in the formation of smaller clusters, which should then provide another reason for wider particle distributions lowering suspension viscosity. A relationship has been found between the particle packing density for dry powders (d?d) arid the maximum volume fraction at which these powders still flow when mixed with a liquid (dof)[9]. The relationship is independent of the density and other liquid properties provided that the fluid is viscous enough to prevent sedimentation of the particles during, the timescale of the experiment. The relationship is illustrated in Fig. 2, and shows that dod = 1.19dof. Fig. 2 also shows how mixing powders of different sizes produces better packing. The utility of this relationship is that it allows dof to be found from a simple experimental procedure: pour a known quantity of dry powder into a beaker and find the volume it occupies. Then divide the resulting dry packing fraction by 1.19 to get dof. The occurrence of the relationship also suggests that the geometrical arrangements of the particles in both the dry and the wet states are related quite simply in a manner that does not depend upon the size distribution. At a solid boundary such as in an aperture, the particles cannot be as densely packed as in the bulk of the fluid because gaps arise which cannot be filled by complete spheres due to the physical boundary. Thus a liquid-rich layer is automatically formed at the walls. "6 = 0.7 o / ~ Limit of d r y 0.6 ~ E 0.5 0 Fraction of 0.5 packing of fluidity 1.0= large particles (bimodal distribution) Figure 2 Schematic representation of a figure from Ref. I-9] showing dry packing and the maximum packing fraction that retains fluidity of the suspension. 37 0.023-- 8 x 10 -5. Thus, in our typical aperture, the probability of such a chain occurring is approximately 0.02, and such chains will not dominate paste flow. Figs 3-8 show the particle size distributions of six commercial solder pastes. Paste D was photographed under a higher magnification than the other pastes (×550 compared to x375) and shows clearly the presence of fines or very small particles that contribute to solder bailing during reflow. The sieving process used to produce particles of a given powder size cannot usually separate out these fines as they are invariably attached to larger particles. Although these particles are numerous, their contribution to metal volume is small: only 0.8% of the total metal volume. During flow these particles are expected to form into clusters (perhaps surrounding larger particles) due to the strong inter-particle forces they must experience. All particle surfaces seem to be smooth rather than very rough for the pastes examined. Particle sizes in pastes E(1) and E(2) are similar and come from the same manufacturer, although E(1) is an RMA flux-based paste and E(2) is a water-soluble paste. Pastes B, C, D, E(1) and E(2) show the skewed distribution characteristic of solder pastes, while paste A has an almost symmetrical distribution. For a given metal content, the greatest reduction in viscosity occurs with a broad, uniform distribution of particles. Table II summarizes the mean diameter of the particles, standard deviation of sizes and percentage of irregularly shaped particles, as well as the sample size of particles measured. There is a degree of subjectivity over which particles should be classed as irregular. Those elongated particles whose ratio of long axis to short axis exceeds 2.0 are classed as irregular as well as any particle with sharp edges. As the orientation of particles can hide the extent of distortion, we would expect the actual percentages of irregular particles to Because particles entering the aperture are deflected by the walls towards the centre of the aperture, we would expect the concentration of particles in the centre of the aperture to be higher than that at the edges but not greater than the average concentration in the paste roll, since particles are restricted at the entry of the apertures while fluid can flow more easily through. Hence both qb and qbm are lower inside a narrow aperture compared to within the bulk of the fluid. 4. Particle s i z e a n d s h a p e The majority of solder paste particles have only small deviations in shape from sphericity and should not change the rheology from that of truly spherical particles. However, a study of photographs of solder powders shows that a small percentage of particles are dumbbell shaped, ellipsoidal or more irregular. Given that the number of particles in an aperture (150 by 150 by 1500 gm) is approximately 1500, we should have a few tens of such particles in each aperture. These particles will tend to cause aggravated cluster formation around themselves, and may contribute excessively to clogging of the apertures. On average we would expect two irregular particles to be separated by about three regular particles if irregular particles form 2% of the whole and by four if irregular particles form 1%o. At 2% the probability of two irregular particles being neighbours is approximately 0.2 assuming 12 nearest neighbours. The probability of three irregular particles being neighbours is 0.02, and the probability of four being clustered together is 0.001. Given an aperture of 1500 particles (and several tens of apertures per component) it is clear that such clusters are quite likely to form. Approximately five particles span the width of an aperture; the probability that three of these are irregular is 5C3 x 0.98 z x Particle size distribution paste A 30 25 20 C == 15 c:r 10 I 33 Figure 3 38 1 35 ,11 I 37 Sizedistribution of particles in paste A. 1 38 I 40 f i I I 41 43 45 46 48 Particle diameter (gm) I I 49 ii , I 51 I 52 I 54 56 Particle size distribution paste B 40 35 30 25 oe¢T 20 15 10 I I I I i I I | I I I I I I 18 19 20 21 22 22 23 24 25 26 27 27 28 29 30 31 32 32 33 34 35 36 36 37 38 39 41 Particle diameter (gm) Figure 4 Size distribution of particles in paste B. Particle size distribution paste C 50 45 40 35 30 25 .= LL 20 15 10 5 0 Panicle diameter (gm) Figure 5 Size distribution of particles in paste C. be slightly higher than is shown in Table 2. The large variation in irregular particles between pastes E(1) and E(2) is unexpected and is in part due to the relatively small sample sizes from which observations for these pastes were made. 5. Wali effects on skipping It is known that non-Newtonian boundary effects play a major role in determining suspension flow patterns. Wall slip is a well-documented phenomenon, and plays art! important role in aperture emptying for sol- der paste. The following phenomena have been observed in dense suspension rheology (see, e.g., Ref. [15]): 1. Wall slip where a lubricating layer forms at the walls. 2. Stick/slip where the stress needed to shear the suspension fluctuates strongly over short timescales. The evidence for the occurrence of (2) in aperture emptying is now outlined. When skipping occurs, much of the.time, only a very thin layer of paste is 39 Particle size distribution paste D 30 25 20 lO 5 o 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Particle diameter (l~m) 33 35 37 Figure 6 Size distribution of particles in paste D. Particle size distribution paste E(1) 20 18 16 14 >, 12 == 10 O" ,= 8 14. 6 4 2 0 , ,I ] 17.8 20.8 1., 23.9 26.9 30 33 Particle diameter (~tm) 36.1 Figure 7 Size distribution of particles in paste E(1). Particle size distribution paste E(2) 30 25 > 20 u c =~ 15 S " 10 . . . . . . . . . . . 17.8 20.8 23.9 26.9 30 33 Particle diameter (~m) II Ii 36.1 Figure 8 Size distribution of particles in paste E(2). observed to adhere to the pad. This is expected because the paste at the bottom layer experiences the greatest stress; it needs to transmit the stress required 40 to overcome the total wall drag, whereas paste in the middle layers of the deposit only needs to transmit enough stress to overcome half of the total wall drag, etc. However, in some cases the stress breaks in the middle of the layers of the deposit. The best explanation of this is that the paste has jammed in the aperture (the stick/slip phenomenon). The larger the ratio of aperture wall area to pad area, the larger is the tensile stress generated in the paste, and the greater the probability of slipping. In passing we note that the use of rubber rheometer walls markedly reduced jamming as the walls could yield slightly [16]. Experiments have been performed in which rheometer walls were roughened to see if wall slip could be reduced [15]. The results confirmed that roughened walls do reduce wall slip; the particles can stick to the walls better and a lubricating layer is not formed so easily at the walls. We would expect rougher wails to produce more stick/slip as well. The phenomenon of wall slip is seen to occur both for dilute suspensions where particles migrate away from the walls (inertial effects; collisions with the walls), and concentrated suspensions such as solder paste. One experimental study of wall slip [17] documents the change in apparent viscosity in a cylinder as the ratio of cylinder diameter (D) to particle diameter (d) is reduced. Fig. 9 sketches the results of the experiment. When Did is greater than about 50 the viscosity is independent of the ratio. As the ratio reduces to about 15, the viscosity also reduces, rising steeply as the ratio reduces to about 7 and then falls again. The explanation given for these results is that first wall slip reduces viscosity, then large amounts of jamming occur (the geometry of the cylinder hinders efficient particle packing), and finally the suspension is not free to deform and slips along the tube as a rigid structure. T A B L E I I Average diameter Of particles, standard deviation of particle diameters, and percentage of irregularly shaped particles, with the total number of particles measured for each paste. Six pastes were analysed; pastes E(1) and E(2) were from the same manufacturer Paste Mean diameter (gm) Standard deviation (gm) Irregular particles (%) Sample size A B C D E(1) E(2) 45.4 29.3 29.2 17.7 28.2 27.4 4.5 3.5 4.2 10.0 3.3 2.8 2.5 2.1 1.1 1.4 6.0 0 569 725 736 218 82 84 cation approximation), is given by [19] •~ O 0~ 3 25 F = ~ r c g U d l n -d 50 (14) where 8 is the distance from the sphere's edge to the wall, U is the stencil/substrate separation velocity and g is the flux viscosity. Dividing by the cross-sectional area of the sphere we find: 30 " 10 7 15 50 Ratio of cylinder diameter to particle diameter Figure 9 Schematic representation of a figure in Ref. [17] which examines how the apparent relative viscosity of a suspension in a cylinder varies as the ratio of cylinder diameter to particle diameter is decreased. In discussing the relevance of these results for solder paste we first note that two ratios are frequently quoted in connection with solder paste. The pad to wall area ratio, which is in favour of the walls for fine pitch, gives a rough indication of the ratio of drag to adhesive forces during withdrawal. Quantitative predictions of force cannot be made because the nature of the forces on the walls and on the pads is different. The other ratio is aperture width to particle size where it is known tlhat reducing the particle diameter eases paste withdrawal. A recent report [18] states that skipping increases appreciably when the ratio of aperture width to particle diameter is 7. Other rules of thumb give 5 or 3 as the minimum possible before skipping is inevitable. What is happening is clear; the particles are hindered from effiicient packing as the wails grow closer and this leads tO jamming as local concentration densities grow in some places and lessen in others. The presence of irregular particles aggravates the situation. It might be aske d why the last decrease in viscosity is not observed in solder paste; the reason is that a stress of a certain magnitude must be maintained to make the whole suspension flow rigidly and perhaps this exceeds the tensile strength of the paste. Of course in a solder paste the inter-particle forces and non-cylindrical geometry imply that the peaks and troughs of Fig. 9 will not apply at the same ratio of Did. During paste withdrawal, the particles nearest the walls should be dragged upwards relative to those in the cen!re because of the following argument. The drag forge on a sphere moving parallel to a wall, in the limit that the sphere almost touches the wall (lubri- U 25 x = 6~-gln-d (15) which can be used as an estimate of the stress on the paste. Substituting U = 2 mm s- 1, d = 30 gm, g = 50 Pa s and 5/d = 1/10 (cf. Table I), we obtain z = 3 × 104 Pa compared to yield stresses of order 5 × l0 z Pa. The corresponding expression for stress generated when paste movement is perpendicular to the wall, when the paste is being pulled downwards by adhesion to the pads can be derived from the lubrication force when a particle moves perpendicular to a plane wall [20] and is given by x = 6t.t5 (16) The ratio between the stresses parallel and perpendicular to the wall is hence 5 25 ~ll _ ~ln ~ T± (17) and for 5/d = 1/10 the ratio is 1/6. This explains why skipping does not automatically occur on all fine pitch pads of dimensions 150 x 150 x 1500 pm (depth × width × length), where the wall area is approximately twice the pad area; the actual force (stress × area) is still in favour of the pads in this case. If we assume (as we have done above) that the average distance between particles is approximately the average distance between particles and the wall, then wall roughness on a scale of 2-3 gm will hinder particle flow, whereas roughness on a scale of 0.2 gm or less will not. Finally we remark on the viscoelastic nature of the paste; if a shear rate is suddenly applied to solder paste that can be modelled as a Maxwellian fluid, the stress developed in the paste can be delayed from reaching its steady-state value for a time of the order of the relaxation time of the paste. The paste is inside the aperture for about 0.03 s so that if the relaxation time of the paste could be designed to be Of this magnitude, 41 skipping could be reduced. The essential point is that if the stress does not exceed the tensile strength of the paste then skipping will not occur. our industrial collaborators for their input and support to this project which is financed by the ACME directorate of SERC. 6. Conclusions References We have seen that the heat generated inside the solder paste roll during printing is conducted away so that no noticeable temperature rise occurs during printing. The results of the particle packing study strongly suggest that lubrication forces between particles and contact forces determine particle flows, and possible values for inter-particle distance were found. We then went on to examine the size distribution of particles in the vehicle, and concluded that to achieve the lowest viscosity, and hence reduce skipping, a wide spread in particle sizes is required. The percentage of irregular particles in commerically available powders was examined, and the probability of occurrence of certain structures examined - the results showing that clusters of irregularly shaped particles will occur in the paste at the percentage levels detected. The ratio of forces pulling paste out of the apertures to those drag forces that can cause skipping were calculated. This ratio was found to be large and hence skipping would not be expected to occur for 150 ~tm wide pads. In practice, however, several studies have shown skipping levels to be appreciable for pad widths of 200 ~tm or less 1-18, 20]. This is because the drag stress on the paste exceeds the paste's tensile strengt h. It was found that the paste will not flow out of the stencil as a rigid body because the wall drag stresses are too high. Instead, relative movement of the particles produces regions of high particle concentration and stresses leading to stick/slip. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Acknowledgements We gratefully acknowledge the help of Professor Williams of Loughborough University (UK) in supplying us with data on solder paste thermal conductivity and specific heat capacity, and we would also like to thank 42 N. N. EKERE, E. K. LO and S. H. M A N N A N , "Process modelling m a p s for solder paste printing'. Paper presented at Nepcon SouthEast '93, Florida, 1993. S . H . M A N N A N , N. N. EKERE, E. K. LO and I. ISMAIL, Soldering and Surface Mount Technol. 15 (1993) 14. N . N . EKERE, I. ISMAIL, E. K. LO and S. H. M A N N A N , J. Electronics Manuf 3(1) (1993) 25. J.S. H W A N G , in "Solder paste in electronics packaging" (Van Nostrand, Reinhold, New York, 1989). R . A . B A G N O L D , Proc. Roy. Soc. Lond. A225 (1954) 49. H . A . BARNES, M. F. E D W A R D S and L. V. W O O D C O C K , Chem. Eng. Sci. 42 (1987) 591. D . E . RIEMER, Solid State Technol. August (1988) 107. S . H . M A N N A N , N. N. EKERE, E. K. LO and I. ISMAIL, J. Electronics Manuf 3 (1993) 113. A . P . S H A P I R O and R. F. P R O B S T E I N , Phys. Rev. Lett. 68 (1992) 1422. L.V. W O O D C O C K , i n "Proc. of a workshop on glass forming liquids", edited by Z. I. P. Bielefeld (Springer Lecture Series in Physics, 277, 1985) p. 113. R . J . FARRIS, Trans. Soc. Rheol. 12(2) (1968) 281. R. M. T U R R I A N , F. L. HSU, K. S. AVRANADIS, D. J. S U N G a n d R. K. A L L E N D O R F E R , AIChE J. 38(7) (1992) 969. J. F. BRADY and G. BOSSIS, Ann. Rev. Fluid Mech., 20 (1988) 111. C. C H A N G and R. L. P O W E L L , J. Fluid Mech. 253 (1993) 1. D . C . H . C H A N G , Powder Technol., 37 (1984) 255. S. B. SAVAGE and S. M c K E O U W N , J. Fluid. Mech. 127 (1983) 453. L . A . M O N D Y , A. L. G R A H A M and M. G O T T L I E B , Xth International Congress on Rheology (Sydney)2 (1988) 137. M. XIAO, K. J. LAWLESS and N. C. LEE, Soldering and Surface Mount Technol. 15 (1993) 5. A. J. G O L D M A N , R. G. COX and H. B R E N N E R , Chem. Eng. Sci. 22 (1967) 637. N. A. F R A N K E L and A. ACRIVOS, Chem. Eng. Sci., 22 (1967) 847. Received 3 April and accepted 12 July 1994