by P. M. Fahey
`S. R. Mader
`S. R. Stiffler
`R. L Mohler
`J. D. Mis
`J. A. Slinkman
`
`Stress-induced
`dislocations
`in silicon
`integrated
`circuits
`
`Many of the processes used in the fabrication
`of siiicon Integrated circuits iead to the
`development of stress In the silicon substrate.
`Given enough stress, the substrate will yield
`by generating dislocations. We examine the
`formation of stress-induced dislocations in
`integrated circuit structures. Examples are
`presented from bipolar and lUIOS-based
`integrated circuit structures that were created
`during developmental studies. The underlying
`causes of oxidation-induced stress and the
`effect on such stress of varying oxidation
`conditions are discussed. The knowledge thus
`gained is used to explain dislocation
`generation during the formation of a shallow-
`trench isolation structure. The importance of
`ion-Implantation processes In nucleating
`dislocations is illustrated using structures
`formed by a deep-trench isolation process and
`a process used to form a trench capacitor in a
`DRAI\/I cell. The effect of device layout
`geometry on dislocation generation is also
`examined. We show how TEM observations
`can be used to provide more information than
`
`solely identifying those process conditions
`under which dislocations are generated. By
`combining TEM observations with stress
`analysis, we show how the sources of stress
`responsible for dislocation movement can be
`Identified.
`
`1. Introduction
`Given enough stress, a silicon substrate will yield by
`generating dislocations. Although it would certainly be
`preferable for this not to occur during the fabrication of
`silicon integrated circuits (ICs), its occurrence appears to
`be an unavoidable by-product of the processes used to
`fabricate such circuits; dislocations often appear at some
`point during the development of a fabrication sequence.
`Once present in the silicon substrate, dislocations can lead
`to charge leakage and electrical shorting between
`elements—effects that can seriously degrade or prevent
`device operation [1, 2].
`There are many sources of stress that arise during IC
`fabrication processes. Some important examples are the
`imbedding of materials with thermal expansion coefficients
`different from that of silicon, deposition of films with
`intrinsic stress, and oxidation of nonplanar surfaces. A
`
`^Copyright 1992 by International Business Machines Corporation. Copying in printed form for private use is permitted without payment of royalty provided that (1) each
`reproduction is done without alteration and (2) the Journal reference and IBM copyright notice are included on the first page. The title and abstract, but no other portions, of
`this paper may be copied or distributed royalty free without further permission 1^ computer-based and other information-service systems. Permission to republish any other
`portion of this paper must be obtained from the Editor.
`
`158
`
`P. M. FAHEY ET AL.
`
`IBM J. RES. DEVELOP. VOL. 36 NO. 2 MARCH 1992
`
`MICRON ET AL. EXHIBIT 1043
`Page 1 of 25
`
`

`
`recent paper by Hu [3] gives an excellent overview of
`these and other stress-related problems. In the present
`paper, we present examples of stress-induced dislocations
`that occur during the fabrication of advanced bipolar and
`MOS-based integrated circuits. This is a timely subject
`because of the growing importance of stress-induced
`defects in evolving IC processes.
`For each succeeding generation of integrated circuits,
`two major trends are evident: The packing density of
`circuits on a chip increases, and device dimensions are
`reduced. Increasing packing density permits a greater level
`of integration per chip; reducing critical device dimensions
`leads to improved device performance for both MOS and
`bipolar structures. Unfortunately, the two trends lead to
`processes in which stress levels increase.
`Higher packing densities are achieved by developing
`devices that occupy smaller areas of the silicon substrate
`and by packing the devices closer together. However, such
`scaling is subject to the constraint that devices must be
`electrically isolated from one another by isolation regions.
`In general, the reduction of the area required for isolation
`has been found to result in larger substrate stresses. In
`addition, as the area occupied by an active device
`continues to shrink, more of the device in each isolated
`cell is in proximity to the edges of its isolation regions, and
`some of the largest stresses develop at these locations.
`Scaling of device dimensions may lead indirectly to
`increased substrate stress. To maintain critical device
`dimensions (e.g., the channel length of a MOSFET or the
`base width of a bipolar transistor), control of dopant
`diffusion is essential. A large degree of such control is
`accomplished by minimizing the temperatures of thermal
`processing. But for oxidation processes, lowering the
`temperature of oxidation leads to higher stress levels in the
`substrate [4-6]. The fundamental reason for this is that an
`oxide growing on a nonplanar silicon surface must
`constantly deform, and oxides become more resistant to
`strain as temperatures are lowered. As an oxide thus
`becomes more rigid, a greater amount of the stress that
`develops during oxidation is accommodated by the
`development of strain in the substrate. Given the pervasive
`use of oxidation steps in IC fabrication, oxidation-induced
`stress is likely to become an increasingly important
`concern in the continuing drive toward lower-temperature
`processing.
`Since stress is responsible for the unwanted appearance
`of dislocations, a question that naturally arises is how
`much stress a silicon wafer can tolerate before dislocations
`are generated. There is no simple answer to this question.
`A variety of studies indicate that stress levels of the order
`of lO' dynes/cm^ or higher should be considered
`significant. In practice, however, the strengths of silicon
`wafers vary depending on a number of factors—in
`particular, the OJQ'gen content and thermal history of the
`
`wafer [7-9]. Also, the generation of stress-induced
`dislocations is a two-step process. Dislocations must first
`be nucleated and must then grow or move into regions
`where they affect devices. The stress necessary to nucleate
`dislocations depends greatly on the particular process of
`nucleation. Nuclei may be found in the as-grown wafer
`[7-9] or may be introduced into the wafer during
`processing. Two common process steps that assist the
`nucleation of dislocations are oxidation and ion
`implantation. Oxidation generates silicon self-interstitials,
`which can coalesce preferentially in strained siliojn [1].
`Vanhellemont et al. [10,11] have discussed in detail the
`homogeneous nucleation of dislocations by condensation of
`self-interstitials. Ion implantation disrupts the crystalline
`structure of the silicon lattice and creates an excess of
`point defects. Although the details of the nucleation
`process following ion implantation are not thoroughly
`understood, it is well established that implantation damage
`can lead to the nucleation of dislocations. The effect of
`implantation on dislocation generation in stressed material
`can be quite dramatic; we demonstrate this with examples
`from bipolar and DRAM technologies (Sections 4 and 5).
`Once nucleated, dislocations can move great distances
`under an applied shear stress, by the process of glide. (The
`level of stress necessary to move dislocations depends, as
`in the case of nucleation, on oxygen content and thermal
`history [12].) Thus, dislocations initially created in a
`locally stressed area can propagate to other parts of a
`device cell (Sections 3 through 5).
`The examples presented in this paper are taken from
`structures used in developing IC processes. During the
`developmental stage, process conditions are often varied to
`extreme cases, yielding important information regarding
`relevant process windows and mformation regarding
`process extendability: for example, extendabiUty by placing
`devices closer together (vs. changing the layout design or
`isolation scheme) or by lowering processing temperatures
`and thereby minimizing dopant diffusion. We have chosen
`examples gathered from process experiments performed as
`part of a few different chip development efforts at several
`IBM laboratories. The examples illustrate the underlying
`causes of stress, how they cause dislocation generation,
`and how solutions to defect generation can be found.
`In Section 2 we examine the underlying causes for the
`development of stress in oxide layers on silicon substrates
`and relate its development to oxidation parameters
`(temperature, pressure, ambience). In Section 3 we present
`an example illustrating the increased susceptibility of a
`process to defect generation as oxidation temperatures are
`lowered. The example explores dislocation generation
`resulting from a shallow-trench isolation process
`compatible with the requirements of a 16Mb DRAM
`technology. In addition to the temperature of oxidation,
`the importance of cell layout geometry is shown to be a
`
`IBM J. RES. DEVELOP. VOL. 36 NO. 2 MARCH 1992
`
`P. M. FAHEY ET AL.
`
`159
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`
`

`
`key factor in determining the onset of defect generation.
`The very important process of defect nucleation by ion
`implantation is discussed in Section 4, where we examine
`the effects of implantation on a deep-trench isolation
`process used in a bipolar technology. Damage created by
`ion implantation can develop into dislocations that glide
`large distances in stressed material. Substrates that
`otherwise show no signs of defects can become heavily
`dislocated after ion implantation. The geometry of cell
`layout again plays a key role in affecting this behavior.
`Finally, in Section 5 we present a detailed stress analysis
`for dislocation generation and propagation in a 4Mb
`DRAM process.
`
`2. Oxidation-induced stress
`Oxidation can introduce stress into siUcon substrates in
`two different ways. The first is associated with the volume
`expansion of SiOj from silicon. A given volume of silicon
`will produce about 2.2 times as large a volume of SiOj. If
`the oxide is not free to expand, it pushes on whatever
`material is constraining its growth. This occurs frequently
`during IC fabrication, for example, during oxidation along
`the sidewalls of polysilicon-fiUed trench structures or at the
`edges of regions masked with Si^N^. A second cause of
`stress is the strain that oxide layers experience when
`oxidation is performed on nonplanar structures. As a
`nonplanar silicon surface is oxidized, the oxide layer is
`constantly forced to stretch or contract as it grows out of
`the silicon surface.
`How much stress is translated from an oxide layer into
`the substrate is determined by how easily the oxide
`deforms as it grows. In the following discussion, we
`consider the deformation of an oxide layer growing on a
`nonplanar substrate. The parameters that determine the
`ability of an oxide layer to deform in response to stress are
`examined, with particular attention focused on the effect of
`oxidation conditions on oxide stress.
`
`• Development of stress in SiO^
`Upon oxidation, the growth of oxide at the Si/SiOj
`interface pushes the oxide above it away from the Si
`surface. On a convex-shaped surface, this causes the oxide
`to experience a tangential tensile stress; on a concave-
`shaped surface, compressive stress results. We are
`primarily interested in how stress develops in the silicon
`substrate during an oxidation step. This requires foremost
`an understanding of how an Si02 film deforms in response
`to the stresses that arise during its growth. Our knowledge
`of such stress-induced deformation processes is not yet
`satisfactory, and the subject remains an active area of
`research. However, in the past few years there has been a
`growing consensus that the best starting point for
`understanding nonplanar oxide growth is to view SiO^ as a
`
`nonlinear viscoelastic material [13, 14]. In recent papers,
`Rafferty, Borucki, and Dutton [13] and Hu [15] have
`provided an excellent illustration of the viscoelastic
`properties of SiOj. They considered the simple case of
`oxidizing a cylinder of silicon. The geometry of this
`problem lends itself to relatively simple analyses of stress
`induced in a growing oxide, yet the oxidizing cylinder
`example brings out most of the essential features of
`oxidation-induced stress on nonplanar surfaces. Hu has
`modeled oxide stress on a cylinder under a variety of
`process conditions. Rafferty et al. have modeled oxide
`stress under a more limited set of conditions than Hu, but
`with a more realistic viscoelastic model for SiO^. In the
`following treatment we use the oxide model of Rafferty
`et al. and reexamine the model predictions of Hu for a
`variety of process conditions. We also use the oxidizing
`cylinder as a vehicle to demonstrate how different model
`assumptions used in process modeling programs manifest
`themselves in predicting oxidation-induced stress.
`Consider a cross section of a silicon cylinder having a
`thin surface oxide layer, the outer surface of the oxide
`located at a radial distance r^. When the cylinder is
`oxidized, the newly formed oxide at the silicon surface will
`push out the original oxide layer. After a given oxidation
`time, the outermost layer of oxide moves from r^ to r,
`stretching out in the process. The stretching process
`requires a tangential strain of e = (r - r^lr^. If the oxide
`grows at a rate X^, it is a simple matter to show that
`/• = (1 - P)X^^, where j8 = 0.44 is the amount of sihcon
`consumed for a given thickness of oxide grown. Therefore,
`the strain rate of the outermost oxide layer on the cylinder
`is given by
`
`( l - ) 3)
`- ^ „.
`
`(1)
`
`The question is how this strain is accomplished. If the
`oxide is highly resistant to deformation, large stresses
`develop in the oxide during the oxidation and,
`consequently, also in the underlying silicon. On the other
`hand, if the oxide can be stretched easily, little stress is
`developed during the oxidation. In general, stress is
`accommodated by a combination of elastic deformation
`and viscous flow. Following the treatment by Hu [15]
`and Rafferty et al. [13], we illustrate the viscoelastic
`deformation process by analogy to a spring and dashpot
`(i.e., damped piston) in series—a combination known as a
`Maxwell element (Figure 1).
`Initially, the system is assumed to be in a state of zero
`stress. Stress is developed by applying a force that moves
`the end of the spring. The total strain in the system is e =
`(A - AJ/A^, where ^^ is the original position of ^. If the
`end of the spring moves at a speed v, the strain rate of the
`system is e = v/A^. The total strain is the sum of elastic
`
`p. M. FAHEY ET AL.
`
`IBM J. RES. DEVELOP. VOL. 36 NO. 2 MARCH 1992
`
`160
`
`MICRON ET AL. EXHIBIT 1043
`Page 3 of 25
`
`

`
`and viscous deformation processes, i.e., e = s^^^^^^ +
`*^viscous- ^^ elastic strain is given by
`(A-B)
`a-
`
`elastic
`
`A
`
`y^
`
`'
`
`(2)
`
`where G is the spring constant, which we identify with the
`elastic modulus of rigidity of the oxide. The stress-strain
`relation for viscous flow is expressed as
`
`B
`'Z •n
`where 77 is the viscosity of the dashpot (i.e., the viscosity
`of the oxide). Equations (2) and (3) lead to the differential
`equation
`
`(3)
`
`- + - = e.
`
`(4)
`
`Equation (4) is a simple but useful expression for
`understanding many of the important factors that
`determine evolution of stress in oxides during growth. By
`using values for G and rj corresponding to SiOj and using
`the expression for e in Equation (1), relative levels of
`stress generated with different oxidation conditions can be
`investigated for the oxidizing cylinder example [13, 15].
`For example, one can calculate the relative stress levels in
`different thicknesses of an oxide film grown at a given
`temperature, or the relative stress levels in an oxide film of
`a given thickness grown at different temperatures.
`In the simplest case, both the growth rate and viscosity
`are assumed constant. In this case. Equation (4) has the
`solution
`
`o- = Tje(l - e"""").
`
`(5)
`This equation states that the oxide starts at zero stress and
`asymptotically approaches a value of 176. Physically, this
`means that the oxide deforms elastically in the initial
`stages of growth; then, as the oxide continues to grow, its
`stress is relieved by viscous flow. In steady state, the
`stress in the oxide is directly proportional to the oxidation
`rate times the viscosity. Obviously, the less viscous the
`oxide, the smaller the saturation value of its stress. Oxide
`viscosity decreases with higher temperatures and
`increasing hydroxyl content (see the papers by Hu [15] and
`StifBer [14] for a summaty of data). Thus, performing
`oxidations at the highest acceptable temperature and in a
`wet rather than a dry oxygen ambience would seem to be
`preferable. However, oxidation rates increase with
`increasing temperature and are higher in a wet oxygen
`ambience than in a dry oxygen ambience. Faster oxide
`growth means that the strain rate is higher and viscous
`flow must increase to avoid stress buildup. Predictions
`regarding such trade-offs in processing conditions can be
`obtained by solving Equation (4). In that regard. Equation
`
`Viscoelastic model of oxide strain. Analogy is made to a spring
`and dashpot (i.e., damped piston) system.
`
`(5) predicts that growing oxides at high temperatures in a
`wet oxygen ambience does indeed minimize stress levels,
`despite growth at relatively high rates. Hu [15] has shown
`that this same quahtative behavior occurs for the more
`general situation of linear-parabolic oxide growth. In
`addition, the analysis of Hu predicts that high-pressure
`steam oxidation should lead to further reductions in oxide
`stress from the levels of atmospheric oxidation—again,
`despite the increased oxidation rates at high pressure.
`The above analysis appUes under the assumption that
`oxide viscosity remains constant during growth. The
`viscosity of SiOj was considered a function of temperature
`and hydroxyl content only. However, it has been shown
`experimentally that the viscosities of glasses decrease
`under high stress [16-18]. Recent treatments [13, 14, 19,
`20] of oxidation-induced stress have attempted to take
`account of this fact. Sutarjda and Oldham [19, 20], Rafferty
`et al. [13], and Stiffler [14] have favored the use of
`EjTing's model [21] to describe viscosity. In Eyring's
`model, the viscosity of the oxide decreases dramatically at
`
`161
`
`IBM J. RES. DEVELOP. VOL. 36 NO. 2 MARCH 1992
`
`P. M. FAHEY ET AL.
`
`MICRON ET AL. EXHIBIT 1043
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`
`

`
`where rj„ is the zero-stress viscosity and V^ is a
`characteristic volume associated with the space cut out by
`a diffusing molecule during ilow. Eyring [21] has analyzed
`the dependence of viscosity on stress from the viewpoint
`of absolute rate theory. However, the quantitative
`predictions of this atomistic approach do not agree well
`with experiment [16]. To obtain agreement with
`experiment, V^ has been viewed as a fitting factor.
`Donnadieu et al. [18] have empirically determined a value
`for V^ of approximately 180 A'.
`As an example of how oxide stress varies as a function
`of process variables, we show in Figure 2 calculations for
`stress in the outermost layer of oxide grown on a silicon
`cylinder 1 /u.m in radius. To produce these plots, we have
`solved Equation (4) using the expression for viscosity rj
`given in Equation (6). We have used a value of G =
`3 X 10" dynes/cm^ [22, 23] and viscosity values for r/j
`from Stiffler [14], and have assumed oxidation rates for
`{100} surfaces using the Deal-Grove formulation [24]
`
`(7)
`
`where k and k^ are the parabolic and linear growth-rate
`constants. For wet oxidations, we have used values for k
`and k^ from Razouk et al. [25]; for dry oxidations, we have
`used values from Hess and Deal [26, 27].
`In Figure 2(a) we show calculated stress values for
`varying thicknesses of oxide grown at different
`temperatures. This plot indicates that stress should
`decrease as the oxidation temperature is increased. This is
`primarily due to the decrease of viscosity with increasing
`temperature. Similar plots by Hu [15], using a stress-
`independent viscosity model, show a stronger temperature
`dependence on stress than that shown in Figure 2(a). A
`secondary effect involves the quicker transition at higher
`temperatures from linear growth rate {X^^ a i) to parabolic
`growth rate ijc^^ « r^"^). In the viscous flow regime,
`stress is expected to decrease as the strain rate decreases
`[Equation (3)]. Therefore, as the oxidation rate decreases
`during parabolic growth, stress should also decrease. The
`effect of parabolic oxide growth is most pronounced for
`the 1100°C case in Figure 2(a), where more of the oxide
`growth takes place in the paraboUc regime compared to the
`lower temperatures of oxidation. Similar plots by Rafferty
`et al. [13], using the same type of viscoelastic oxide model,
`do not show this behavior. For simplicity, Rafferty et al.
`ignored the parabolic growth regime in their treatment and
`assumed oxidation rates to be constant with time.
`Including full linear-parabohc growth-rate behavior for the
`oxide. Figure 2(a) shows that for a given temperature there
`should be a maximum value in the amount of stress in the
`oxide. Once the oxide growth has moved from the elastic
`to viscous regimes, no further increase in stress is
`
`•8
`§
`
`I
`
`.a
`
`100
`
`130
`
`200
`
`300
`
`Oxide thickness (nm)
`
`(a)
`
`10
`
`Oxidation at 900°C
`
`10
`
`-
`-
`
`^^
`
`^
`
`dry
`1 atm
`
`1 atm.
`
`wet
`
`L
`
`5 atm
`
`wet
`
`1
`50
`
`1
`100
`
`1
`150
`
`1
`. . . „ l,
`200
`250
`
`300
`
`Oxide thickness (nm)
`
`(b)
`
`Calculated oxide stress as a function of oxide thickness at different
`conditions, for growth on a silicon cylinder, initially 1 /xm in ra-
`dius: (a) Stress in the outermost oxide layer for different oxidation
`temperatures, (b) Stress developed at 900°C for different ambient
`conditions.
`
`high stresses. The high-stress behavior is described by the
`relation
`
`162
`
`1? =
`
`'7o sinh(o-K/2fcr)'
`
`(6)
`
`p. M. FAHEY ET AL.
`
`mM J. RES. DEVELOP. VOL. 36 NO. 2 MARCH 1992
`
`MICRON ET AL. EXHIBIT 1043
`Page 5 of 25
`
`

`
`expected. As long as the maximum stress level is not
`enough to generate dislocations in the bulk, it should be
`possible to grow any thickness of oxide without defect
`generation. The prediction that the growth of the thicker
`oxide does not necessarily lead to more substrate stress is
`not at all intuitive, and demonstrates the value of the
`viscoelastic analysis. Conversely, the viscoelastic analysis
`indicates that growing relatively thin oxides is no
`guarantee that high levels of stress will not be generated.
`Supportive experimental results for the above predictions
`are presented in Section 3.
`In Figure 2(b) we show the calculated effects of oxidant
`ambience on stress. To take account of changes in
`pressure, we have scaled k,, and k linearly with pressure
`[24, 25]. Reductions in stress going from dry to wet
`oxidations and from atmospheric to high-pressure wet
`oxidations are caused by corresponding decreases in
`viscosities. The predicted stress reduction for high-
`pressure wet oxidation compared to atmospheric
`conditions is dramatic. Note also that in the 5-atm
`oxidation case there is no large elastic contribution to
`stress; i.e., there is no initial increase of stress with oxide
`thickness [Equation (2)] for thin oxides as there is for the
`1-atm dry and wet cases. This is because the oxide
`viscosity at 5 atm is already low enough that oxide iows
`viscously during the entire time of oxidation. While Figure
`2(b) implies a beneficial effect of reducing viscosity, it
`should be kept in mind that the large decreases in oxide
`stress with high-pressure wet oxidation are at present only
`predictions. Hu [15] has made this prediction by using
`available data for the dependence of oxide viscosity on
`hydroxyl concentration at one atmosphere, and
`extrapolating to the case of higher atmospheres. However,
`we have found that such predictions based on
`extrapolation are very sensitive to data fitting of the data
`obtained at one atmosphere. We mention in the following
`discussion some preliminary data indicating that high-
`pressure wet oxidation may not lead to significant
`reductions in oxide stress.
`We have also calculated the effect of reducing the partial
`pressure of oxidant. Consider the effect of reducing the
`partial pressure of ojQ'gen in a dry-oxidation process. The
`viscosity of the oxide is unchanged, but the oxidation rate
`is reduced. Therefore, stress levels should be reduced. For
`the case of dry oxidation at 0.1 atm, the curve for stress as
`a function of oxide thickness practically coincides with the
`1-atm wet-oxidation curve in Figure 2(b); we have not
`plotted the 0.1-atm case because of this close agreement.
`The stress can be reduced simply by diluting oxygen with
`an inert carrier gas. The penalty for this is that it increases
`the time needed to grow the same amount of oxide, and
`the extra time might be ui excess of the allowable thermal
`budget. Reducing the partial pressure of oxidant in a wet-
`oxidation process leads to different results. If we dilute a
`
`wet-oxidation ambience, the growth rate of the oxide fflm
`will go down, but so will the viscosity of the oxide. For
`the case of 0.1-atm wet oxidation, the curve of stress as a
`function of oxide thickness practically coincides with the
`curve of 1-atm dry oxidation in Fipre 2(b); reducing the
`pressure leads to higher stress levels. From these last two
`examples we can immediately see that the worst possible
`situation is a high-pressure dry-oxidation ambience. For
`dry oxidation, increasing the pressure increases the
`oxidation rate without reducing the oxide viscosity,
`resulting in a greater oxide stress with increasing pressure.
`
`• Quantitative modeling of stress in Si
`The preceding discussion summarizes the basic factors that
`determine the buildup of stress in SiOj during oxidation.
`We are primarily interested in modeling stress distributions
`in the silicon substrate for oxidation of arbitrarily shaped
`structures. Modeling this class of problems is considerably
`more involved than simply solving Equation (4). In
`principle, computer simulation using appropriate process
`models can be used to calculate stress distributions for any
`realistic situation. In this paper, we rely primarily on
`simple analytic approximations to evaluate stress; the
`examples of stress generation we have chosen lend
`themselves to such treatments and are easier to understand
`than results from rigorous process simulation. Here, we
`include a brief review of the process-simulation approach.
`Understanding the requirements of associated oxidation
`models gives further insight into the physical processes
`that govern oxidation and the development of stress. We
`also summarize the status of oxidation models and their
`utility in modeling oxidation-induced stress.
`Process-simulation programs differ from one another
`primarily in the numerical methods of solution employed
`and the specifics of the oxidation models; algorithms for
`simulating oxidation are roughly the same. The flow chart
`in F%ure 3 shows the algorithm used in our process
`simulation program FEDSS (Finite Element Diffusion
`Simulation System) [28]. During one time period, oxygen
`diffusion through the SiOj is simulated. This determines
`the flux of oxygen to the silicon surface, which in turn
`determines the local oxidation rate according to the
`Deal-Grove formulation of oxide growth [24]. The strain
`rate is calculated for each element of the oxide using a
`purely viscous flow model (examined further in the
`following discussion). SijN^ is also treated as a viscous
`material—a model supported by the recent work of Griffin
`and Rafferty [29]. The stress and strain at the Si/SiO^
`interface is then treated as a boundary-value problem, and
`the yield in the silicon is determined using elastoplastic
`models. The process is then repeated for the next time
`period.
`One drawback of most process-modeling programs is
`that they do not simulate oxidation in three dimensions.
`
`IBM J. RES. DBVEUJP. VOL. 36 NO. 2 BiJARCH 1992
`
`P. M. FAHEY ET AL.
`
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`
`MICRON ET AL. EXHIBIT 1043
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`

`
`For two- or three-dimensional oxidation simulations,
`correct modeling of stress in the oxide is a critically
`important requirement because of its effects on oxidation
`process. The effects of oxide stress on oxidation rates have
`been observed experimentally in a number of studies. Marcus
`and Sheng [31] first showed oxide growth to be retarded on
`both convex- and concave-shaped surfaces. Even in the
`absence of dislocations, such oxide-thinning effects on
`nonplanar surfaces are known to be reliability concerns
`because of the high electric fields they produce at comers
`[32, 33]. Oxide growth on a variety of shapes (including
`cylinders) was studied by Kao et al. [34-36]. Sheng and
`Marcus [37] have shown oxidation to be retarded in areas
`close to the edges of oxide-isolated regions.
`These observations of retarded oxidation rates are
`beUeved to arise predominantly from stress effects. The
`degree of retarded oxidation rates on convex and concave
`corners for different process conditions is consistent with
`this view. For example, Yamabe and Imai [33] have shown
`that oxidation on the comers of trenches is retarded less
`for growth at high temperatiu'es than at low temperatures,
`less for wet-oxidation conditions than dry-oxidation
`conditions, and less for diluted dry-oxidation conditions
`than atmospheric dry-oxidation conditions. As expected,
`the conditions that lead to highest oxide stress result in the
`greatest amount of oxide thinning at corners. Recent
`results from Imai and Yamabe [38] show oxide-thinning
`effects at comers to be greatly mitigated by the addition of
`small amounts (hundreds of ppm) of l^Fj to dry 0^, even
`though the oxidation rate is increased by the addition of
`NFj. These results strongly imply that the NFj is somehow
`effective in reducing the viscosity of the oxide. This
`contention is supported by the experiments of Kouvatsos
`et al. [39], which show for planar growth under dry-
`oxidation conditions that stress is reduced by the addition
`of NFj. However, there is still some question about the
`relevance of intrinsic stress during planar oxide growth to
`that generated during the oxidation of nonplanar surfaces.
`From current experimental results, it appears that the
`depee of oxide thinning during comer oxidation
`corresponds to the amount of stress developed in the
`oxide. We have recently performed comer oxidation
`experiments to investigate the effect of high-pressure steam
`oxidation on oxide stress. We find that wet oxidation at
`8(K)°C and 10 atm leads to greater retardation of oxidation
`rates around corners than does atmospheric wet
`oxidation—contrary to the predictions of Hu's model [15].
`Our results suggest that whatever reduction in oxide
`viscosity occurs under high-pressure conditions, it is not
`enough to offset the increasing stress that results from
`oxidizing at a faster rate (at least for our specific
`conditions).
`Stress effects have also been suggested as a source of
`field-oxide thinning. Mizuno et al. [^] first observed that
`
`Quasi-Static Oj
`Diffusion in SiOj
`
`C=
`
`Deal-Grove
`boundary conditions
`dC
`-D —9? = /t c
`ox ^fi
`ox ox
`
`Oxide/nitride
`viscous flow
`
`Stress on SiOj/Si
`inter&ce
`
`Elastopiasiic
`defonnationofSi
`
`Stress distribution
`in Si
`
`Increment
`tinie
`
`Flow chart for process-simulation algorithm used in FEDSS [28]
`progiam. D^^ and C^^ are the oxidant difftisivity and concentra-
`tion, respectively, and k^^ is the surface reaction rate defined by
`Deal and Grove [24].
`
`(Umimoto and Odanaka [30] have recently presented
`results of such simulations.) The validity of simulation
`results then depends on the applicability of the plane
`analysis approximation to a given two-dimensional cut. We
`explicitly point out the three-dimensional nature of stress
`problems several times in this paper. Development of
`three-dimensional versions of current process modeling
`programs is a difficult but not unsolvable problem. More
`impetus to develop appropriate propams will undoubtedly
`come from the growing necessity of performing three-
`dimensional analyses on IC structures and the smaller
`computational overhead afforded by increased computer
`power.
`
`164
`