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Oxygen in Silicon
4
Chapter Four
Oxygen in Silicon Eero Haimi Department of Materials Science and Engineering, Helsinki University of Technology, Espoo, Finland
Single crystal (SC) silicon is one of the chemically purest technical materials used in large quantities. However, in spite of the high purity, there are still trace levels of other elements present in SC silicon. A common additional element, besides doping elements, is oxygen. Oxygen is incorporated to SC silicon during crystal growth. In this respect, there is a fundamental difference between Czochralski (CZ) and float zone (FZ) crystals. Oxygen is accumulating to CZ silicon, because molten silicon dissolves oxygen from silica crucibles used in the growth process. If it is necessary, reduction of inherent oxygen concentration is possible by using magnetic CZ process. FZ silicon appears in lower oxygen concentra tion, since crucibles are not needed in FZ process. In FZ silicon only residual background concentration of oxygen, due to affinity of oxygen for silicon, is observed. Oxygen and oxygen-related phenomena affect the properties of silicon in several ways. From a technologi cal viewpoint, oxygen in silicon can be either beneficial or harmful depending on application. Oxygen can pro vide strengthening of wafer against plastic deformation during processing. Furthermore, oxygen precipitates can act as traps for fast diffusing metallic contaminants. Without this “gettering effect,” degradation of IC fabri cation yield may take place. On the other hand, oxygen precipitates and oxygen-related thermal donors (TDs) may act as defects and may impair processing or device performance when present at unintended locations. In the following, basic aspects of oxygen-related phenomena in silicon, such as oxygen in silicon solid solution, formation of small oxygen aggregates, oxygen precipitation, precipitation induced defects as well as behavior of oxygen in basic heat treatment procedures, have been overviewed.
4.1 Oxygen in Solid Solution
Oxygen in silicon solid solution is placed interstitially in the lattice. Equilibrium oxygen solubility has been studied with various techniques including IR spectroscopy, gas fusion analysis, secondary mass ion spectroscopy, charged particle activation analysis, and x-ray diffrac tion. Generally results scatter to some extent. A fit of experimental results gathered from several groups is given by Mikkelsen [1] in the form of Eq. 4.1: ⎛�1.152eV ⎞⎟ eq Cox � 9�1022 exp ⎜⎜ [ atoms�cm3 ] (4.1)
⎜⎝ kT ⎟⎟⎠
Corresponding partial phase diagram of the Si–O
system, which shows boundary between the solid solu tion of silicon and the two phase region of silicon and silica, as a function temperature and oxygen concentra tion, is presented in Figure 4.1. The equilibrium solubility of oxygen in silicon at room temperature is smaller by several orders of magnitude than near the melting temperature. In practice, this means that as-grown CZ silicon is supersaturated with oxygen after cooling to room temperature due to slowness of out-diffusion in solid state. Typical oxy gen concentration of CZ silicon wafers range from below 5 � 1017 atoms/cm3 (low) to 5–10 � 1017 atoms/cm3 (medium) to above 1018 atoms/cm3 (high) (5 � 1016/cm3 � 1 ppma). Diffusivity of oxygen is dominated by the proc ess of jumping from one interstitial site to another. Experimental oxygen diffusion data in high temperature range (700–1200°C) is well established. Fitted results 59
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n � number of moles k � Boltzmann constant T � absolute temperature
Figure 4.1 ● Partial phase diagram of the Si–O system.
of diffusion constant [1] from several experiments can be expressed as: ⎛ 2.53eV ⎞⎟ 2 Dox � 0.13 exp ⎜⎜− ⎟[cm �s] ⎜⎝ kT ⎠⎟
(4.2)
It has been shown that oxygen diffusivity in high temperature range does not depend much on wafer orientation, annealing ambient, doping concentrations, nor pulling technique of crystal [2]. Low temperature diffusion data are not so well established. The phenom enon of enhanced oxygen diffusivity has been observed frequently and attributed to different causes such as thermal history, presence of metallic contamination and interactions with carbon or hydrogen (for details see Ref. [2]).
4.3 Precipitation of Oxygen
4.2 Formation of Small Oxygen Aggregates Supersaturation of oxygen in silicon solid solution creates a driving force for oxygen aggregation. It can be shown according to standard thermodynamics (for derivation, see for example Ref. [3]) that corresponding chemical driving force, ΔGchem, as a function of oxygen supersaturation can be approximated as: eq �Gchem � nRT In(Cox �Cox ),
where:
Cox � concentration of oxygen
Ceq ox � equilibrium concentration of oxygen
60
Conceptually, the first stage of oxygen aggregation is the formation of O2 dimers from essentially isolated oxygen atoms by diffusion process. The possible role of such constituents as vacancies or carbon in the free energy of dimer formation is under scientific discussion. Aggregation of larger oxygen clusters than dimers is frequently considered to continue also with atom by atom process, although some evidence exists that oxygen dimers may also be mobile. Formation of small oxygen aggregates has gener ally raised interest in two contexts. In its usual inter stitial configuration, oxygen is electrically inactive in silicon lattice. However, annealing of oxygen-rich silicon (1018 atoms/cm3) in the temperature range 350–500°C, several types of electrically active centers called thermal donors are formed. Furthermore, for mation of so-called new donors has been observed at higher temperatures. TDs have been attributed to the growth of small oxygen aggregates as already discussed in Section 3.6. Another area of interest regarding small oxygen aggregates is nucleation of precipitates. There has been discussion about relationship between pre cipitate nuclei and especially new donors. However, much of nucleation studies do not deal with such issues as detailed structure of the small oxygen aggregate or exact mechanism of their formation process. Instead, the emphasis is placed on the later observed precipita tion behavior. In the present text the same approach is followed. Nucleation is discussed further together with precipitation phenomena in the next chapter.
(4.3)
Precipitation of oxygen in silicon is a diffusion control led solid state phase transformation. In the transforma tion silicon oxide is formed. Formation of silicon oxide within silicon lattice requires that oxygen must diffuse together to form a small volume with correct composi tion, and the atoms must rearrange into correct crystal structure; i.e., both kinetic and thermodynamic require ments must be fulfilled. According to the mass balance, the reaction equation of oxygen precipitation in silicon reads: Si + xOi ↔ SiOx
(4.4)
Accurate chemical composition of oxygen precipitates in silicon has been under scientific debate. It is generally
Oxygen in Silicon
agreed that in SiOx the x is less than 2. The specific volume of the oxide is about twice as large as that of silicon. Therefore, the oxide precipitates are originally strongly strained. It has been proposed that stress accu mulation during precipitation is relieved at least par tially by ejection of self-interstitials. Consequently, if conservation of mass and volume in addition to point defect balance is included, the reaction Eq. 4.4 is modi fied to [4]: aSi + bxOi ↔ bSiO x + (a − b)Sii
∑ Ai γi + V Δg el
ΔG
~4πγ r2
r r*
(4.5)
In principle, precipitation of a second phase takes place in three steps: a local fluctuation in chemical potential (embryo), formation of a stable nucleus, and precipitate growth. Proposed theories of nucleation of silicon oxide involve both homogeneous and hetero geneous mechanisms and several propositions for the nuclei structure exist. Regardless of the exact char acteristics of the nucleus, some basic thermodynamic concepts can clarify the nucleation process. The driving force of the phase transformation is supersaturation of oxygen, whereas surface energy and strain energy are setting constraining contributions. Consequently, free energy change of the phase transformation ΔG can be expressed as: ΔG � −V Δg chem +
(4.6)
ΔG
~ –(4/3)π(Δgchem–Δgel)r3
Figure 4.2 ● Free energy changes expressed as a function of nucleus radii.
fact a similar type of equation would be obtained for any nucleus shape as a function of its size. Accordingly, the important concept of critical size of nucleus is introduced; if the precipitate is too small it is not thermodynamically stable. Figure 4.2 illustrates graphically free energy changes expressed in Eq. 4.7 as a function of nucleus radii. Critical radius r* of a thermodynamically stable nucleus is obtained by differentiation of Eq. 4.7, which yields: r* =
where: Δgchem � chemical free energy change per volume
2γ (�g chem − �g el )
(4.8)
By substituting Eq. 4.8 to Eq. 4.7, the activation energy barrier against nucleation ΔG* can be expressed as:
Δgel � elastic free energy change per volume γi � interface surface energy components V � volume of the precipitate
�G* =
Ai � interface surface area components In oxygen precipitation, an aggregate of oxygen atoms constituting a nucleus is formed first. Once formed, the nuclei can either grow further and form oxide precipi tates or dissolve. This can be elaborated on by looking at the terms in Eq. 4.6 separately. Contributions of sur face energy and strain energy oppose the transforma tion. However, the separate contributions have different dependency on the nucleus size. If we ignore the varia tion of γ with interface orientation and assume that the nucleus is spherical with a radius r, Eq. 4.6 becomes 4 �G = − πr 3(�g chem − �g el ) + 4πr 2 γ 3
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(4.7)
This is a function of r that first increases up to an acti vation energy barrier maximum and then decreases. In
16πγ3 3(�g chem − �g el )2
(4.9)
For critical radius of nuclei in the case of strain free nucleation (Δgel � 0), manipulation of Eqs 4.8 and 4.3 8.3 yields: r* =
2γv p eq ) kTIn(Cox / Cox
(4.10)
where: vp � the volume of precipitate per oxygen atom in it. Importantly, Eq. 4.10 shows that the critical size of nucleus increases with increasing temperature (because eq of temperature dependency of Cox ). More comprehensive theoretical treatment of critical radius of nucleus takes into consideration also stressrelieving mechanisms with corresponding crystal defect
61
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interactions. Hence, an equation for r* can be written in the following form [5]:
r* = r*
2γ (1 + δ − ε) ε )3 XkT eq In (Cox / Cox )(C )(CIeq / CI )ni (C (CV / CVeq )nv − 6μ μ m δε vp
(
)
(4.11) where: CI � concentration of self-interstitials CIeq � equilibrium concentration of self-interstitials CV � concentration of vacancies Ceq V � equilibrium concentration of vacancies δ � linear misfit between Si and SiOx lattices (for SiO2 δ0.3) nI � number of self-interstitials emitted nV � number of vacancies absorbed X � ratio of oxygen and silicon in precipitate The compressive strain � in Eq. 4.11 is: ε=
δ 1 + 4μ m /3Kp
where:
μm � shear modulus of silicon
Kp � bulk compressibility of SiOx Interaction of oxygen with the other constituents in association with oxygen aggregation has been observed experimentally. At sufficiently high temperature, crystal line solids contain thermally generated vacancies and self interstitials, which are equilibrium point defects in crystals caused by configuration entropy. In the case of dislocation free SC silicon, the material is usually supersaturated with point defects, because lack of other defects acting as point defect sinks. A fundamental observation regarding intrin sic point defects is that silicon crystals can be grown in either a vacancy or a self-interstitial mode and concentra tion of point defects in grown crystals depend on process ing conditions. In general, excess vacancies favor oxygen precipitation, whereas excess self-interstitials suppress it. It has been found that there is quite a sharp transition around 5 � 1011 cm�3 vacancy concentration between enhanced oxygen clustering and “normal” clustering [6]. In addition to crystal growth, changes in point defect con centration may take place during wafer processing. Wafer surfaces act as source or sink of point defects depending on ambient used. Nitration injects vacancies, whereas oxidation is introducing self-interstitials into silicon 62
[4, 7, 8]. Also oxygen precipitation is introducing self interstitials into silicon. Effect of point defects on oxygen precipitation depends also on possible point defect reac tions. (Interested readers may consult references [6, 9] and references therein for further details.) Graphite is used as heating elements in CZ crystal growth furnaces. In partial vacuum of the growth chamber, there may be sufficient oxygen that reacts with unprotected graphite to form carbon monoxide, which dissolves in the silicon melt. Consequently, carbon can be incorporated in the silicon crystal during the growth process. When present at a concentration above 0.5ppm, carbon strongly enhances oxide precipitate nucleation [10]. In case of heavily boron doped silicon (p � -type), it is found that precipitation is enhanced as a function of increasing boron concentra tion [11–13]. Moreover, in heavily boron doped silicon, maximum nucleation rate of oxide precipitates is shifted toward high temperature regions [14]. According to classical, steady state nucleation theory, the nucleation rate J is given by the Volmer-Weber Becker-Döring nucleation rate equation (for derivation, see for example Ref. [15]) J = ZC * ω
(4.12)
where C* is the concentration of critical-sized nuclei and ω is the frequency of attachment of oxygen atoms to the nucleus. The term Z is the Zeldovich factor, which is a correction factor corresponding to the fraction of atoms, which are included in the precipitate nuclei immediately after nucleation. In practice the Zeldovich factor is a fit ting parameter usually in the order of but smaller than 1. The concentration of critical-sized nuclei C* is given by a Boltzmann type of equation: ⎛ �G* ⎞⎟ ⎟⎟ C* = Cx exp⎜⎜⎜ ⎜⎝ kT ⎟⎠
(4.13)
The term Cx is concentration of nucleation sites. In the homogeneous nucleation models Cx is set equal to the interstitial oxygen concentration or more properly interstitial lattice sites in silicon. Heterogeneous nuclea tion models assume that Cx is equal to the concentra tion of some other constituents such as pre-existing oxygen aggregates, vacancies or carbon. The attachment factor ω is given by ω = 4π(r*)2 Cox
Dox da
(4.14)
where da is the interatomic jumping distance. The total number of precipitates per unit volume is calculated from integrating the nucleation rate with the processing time. Basically, nucleation rate of oxide precipitates in iso thermal heat treatment depends on oxygen concentration
Oxygen in Silicon
in solid solution and processing temperature. Furthermore, heterogeneous factors may have an effect on nucleation rate depending on experimental conditions. Nucleation rate increases with increasing oxygen concentration in solid solution. When experimental nucleation rate is plot ted as a function of temperature, a maximum at a certain temperature is observed. This can be explained as follows. When the temperature is very high, the oxygen super saturation is small or non-existing, leading to small driv ing force and nucleation rate. On the other hand, when temperature is very low, diffusion becomes slow, leading to also vanishing nucleation rates. Nucleation rate is not necessary constant in time. Nucleation rates slow down and number per volume of precipitates reach a saturation value in very long anneals. This has been explained with overlapping of diffusion zones surrounding each nucleus during long anneals. As a different type of time dependency, an incubation time in nucleation rate is observed after processes, where sudden cooling and concomitant sudden supersaturation states are developed. In practice, silicon has already pre-existing nuclei before many processing situations. Due to possibility of nuclei dissolution, number per volume of oxygen pre cipitates after non-isothermal heat-treatment programs may differ from pre-existing nuclei density. As discussed earlier, the size of the nuclei should be larger than the critical size in order to be stable. Furthermore, the criti cal nucleus size increases as a function of rising tem perature. Consequently, at high enough heating rate, the growth rate of a nucleus is slower than the increase of the critical size of nucleus resulting in dissolution of nuclei. In Figure 4.3 selection of nuclei capable of growth using two different two-step heat treatment temperatures has been illustrated [16]. First, there is a pre-existing nucleus size distribution. A subsequent anneal selects nuclei larger than the critical size for further growth. An alternative low temperature anneal would select larger proportion of nuclei than respective high temperature anneal. According to experimental observations, total
Precipitate density
Invisible
As-grown
Visible
Annealing
After annealing
Low temp. High temp. rc 10
rc1
100
N(F>rc) N(r>rc1) 1000
10000
Precipitate size (Å)
Figure 4.3 ● Selection of nuclei capable of growing [16]. Source:
Figure reproduced by permission of the Electrochemical Society.
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dissolution of pre-existing nuclei causes long time lag in subsequent oxygen precipitation [17, 18]. Precipitates are characterized by their size, shape, crystal structure and number per unit volume. In princi ple, the size and the number per unit volume are inter related at their upper boundary values, because there is a finite number of oxygen atoms capable of forming precipitates. In practice, the typical number per volume of oxygen precipitates after device processing is between 103 and 1010 cm�3. Diffusion calculations show that for these densities the diffusion zone of each precipitate does not have much overlap. As a consequence, the size of the oxygen precipitates is nearly independent of the number per unit volume of precipitates (Bergholz, 1994). Shape of a precipitate depends on their formation tem perature as well as oxygen supersaturation and doping level of the silicon. Three temperature ranges have been related to the three typical precipitate shapes, i.e., the needle, the platelet, and the polyhedron in lightly doped silicon. At low temperatures (~400–650°C) precipitates grow as needles. In this temperature range the strainenergy contribution to the precipitate total free energy dominates, since the stress-relieving processes (which become important at higher temperatures) play a minor role. At intermediate temperatures (~650–950°C) platelet-shaped precipitates are typical (although they can be formed also during short high-temperature annealing). These precipitates are square formed plate lets at {100} habit planes, with edges along the �110� directions. At high temperatures (above 950°C) strain is completely released and the precipitates take the shape with minimum surface energy. Due to the anisotropy of interface energy, the preferential shape is octahedron with eight equivalent (111) faces (surface energy of silicon is minimum in the (111) planes) instead of the sphere. In the case of heavily doped silicon, precipitate morphology differs from lightly doped silicon. Plateletshaped precipitates are observed in addition to (100)— also in (110)—and (111)-type habit planes [19] and rod-shape precipitates are not formed [11]. According to Fujimori [20], dependence of precipitate morphol ogy on oxygen supersaturation comes from kinetic con siderations. Growth rate of a precipitate increases with increasing supersaturation of oxygen and kinetics of stress-relaxation processes may become a limiting factor. Consequently, for higher oxygen supersaturation, there is a transition zone in boundary temperature between platelet and polyhedron precipitate formation. The crys tal structures of precipitates formed at higher than about 650°C temperatures are amorphous. This is correlated to precipitate morphology. Only needle-type precipitates are observed to be crystalline. At high enough temperatures precipitates do not nucleate in practice. Only precipitate growth becomes significant. The kinetics of the precipitation of oxygen 63
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in thermal processing can be studied experimentally for instance by following the diminishing infrared absorption at 1107cm�1 band, characteristic of interstitially dissolved oxygen in silicon. Furthermore, transmission electron microscopy can be utilized in determining size of pre cipitates as a function of heat treatment time. It has been confirmed by many observations, that the time depend ence of experimental results are generally in good agree ment with the theory of Ham [21] for diffusion limited precipitation at temperatures above 650°C [22]. Applying the theory of Ham, Sueoka et al. [23] gives the time (t) dependence of the dimensions L (edge) and d (thickness) of platelet precipitates and l (edge size) of octahedral pre cipitates. These types of model are called deterministic growth models: ⎛ C − Cint ⎞⎟0.5 ⎜ ox ⎟ L = Λ(Dox t)0.5 with Λ = 2 2 ⎜⎜ ox ⎟ ⎜⎝ γπCp ⎠⎟⎟ (4.15a)
0.5
d = δ(Dox t)
⎛ γ(C − Cint )⎞⎟0.5 ⎜ ox ox ⎟ ⎜ with δ = 4 ⎜ ⎟⎟ ⎜⎝ πCp ⎠⎟ (4.15b)
⎛ C − Cint ⎞⎟0.5 ⎜ ox ⎟ l = λ(Dox t)0.5 with λ = (8π)1 / 3 ⎜⎜ ox ⎟⎟ ⎜⎝ Cp ⎟⎠ (4.15c) In order to describe the entire precipitation process from nucleation to precipitate growth, a steady-state nucleation model and a deterministic growth model can be combined at the critical size of the nucleus. This allows simultaneous calculation of oxygen loss, number of precipitates per unit volume and the average precipi tate radius during annealings. Furthermore, precipitate size-distribution can also be evaluated using coarsening model together with an iterative numerical calculation scheme [24]. However, for all nucleus radii smaller than the critical size, an equilibrium size-distribution has to be assumed. This assumption is incorrect when rapid temperature ramping takes place. The most realistic simulation strategy describes growth and dissolution of all nuclei and precipitate sizes statistically. This can be done applying Monte Carlo techniques. The drawback of the Monte Carlo approach is excessive computational load. A simulation model using Fokker-Plank equations can overcome much of the computational problems. Similarly to the Monte Carlo method, growth and dis solution of nuclei and precipitates are described statis tically. However, instead of using random numbers for deciding on growth and dissolution, this is described 64
by a set of chemical rate equations. Furthermore, all chemical rate equations are approximated with a single stochastic partial differential equation applying a math ematical transformation. The resulting equation is called a Fokker-Plank equation. For details of Fokker-Planck modeling see, for example, Ref. [25].
4.4 Precipitate-Induced Defects As discussed earlier, oxide precipitates in silicon are originally strongly strained, because the volume expansion connected with oxide precipitate forma tion. Stress relaxation may take place by ejection of self-interstitials. However, ejected self-interstitials are not necessarily arranged originally in minimum energy configuration and stress relaxation is not necessarily complete. Consequently, precipitate-induced defect formation may take place. The ideal case of stress (and strain) fields associated to a precipitate formation without any stress-relaxation process can be calculated using standard theory of elas ticity. General calculations of this type show the effect of precipitate shape on elastic energy: lowest elastic energy is associated to platelet morphology, next low est is associated to needle morphology, and the highest elastic energy is associated to polyhedron morphology. An experimental technique to study actual local lat tice strain around oxygen precipitates is convergent beam electron diffraction (CBED) mode of transmis sion electron microscopy. The local lattice strain can be measured from higher order Laue zone (HOLZ) pat terns. Several of this type of study has been published [26, 27]. As a result of strain analysis from HOLZ pat terns, acquired around a platelet type of precipitate, the strain along the normal direction to the precipitate was found to be compressive. Importantly, however, the strain along the parallel direction to the precipitate was found to be tensile. Based on FEM simulation, the strain formation was considered to take place during cooling of the material [28]. In the case of polyhedron precipitates, contradictory results have been published. Otherwise similar behavior to that in the case of platelettype precipitate, but with lower strain levels, has been reported [28]. On the other hand, results obtained with high-resolution electron microscope indicating that polyhedron precipitates exist practically without strain have been reported [29]. An argument in this dis cussion is that amorphous silica cannot support shear stresses above a glass transition temperature at around 950°C [30]. Apparently, uncertainty concerning stress and strain fields associated to precipitates comes to some extent from the fact that the stress formation is not an equilibrium process, which would depend only on shape and size of a precipitate. Precipitation process
Oxygen in Silicon
involves the inward diffusion of oxygen, the generation of stress at the interface and the outward diffusion of self-interstitials. Consequently, partial stress relaxation takes place already simultaneously with the stress for mation and it is dependent on the process sequence. Self-interstitials formed in the stress-relaxation proc ess associated with oxygen precipitation are likely to be locally supersaturated. The system can further lower its free energy by allowing them to agglomerate. Stacking fault formation is such an agglomeration process. In general stacking faults can be classified as surface stack ing faults and bulk stacking faults. In the case of sur face stacking faults, oxidation induced stacking faults (OISF) are of interest in the present context. They are usually located as a circular band in the wafer originated from vacancy reactions during particular crystal growth processes. Essential factors in formation of OISF are self-interstitials emitted to silicon due to surface oxi dation [31, 32]. Stacking faults in silicon are always associated with precipitates at their centers providing that mechanical damage and heavy metal contamina tion are excluded as cause of the defects. Transmission electron microscopy observations of several workers confirm this [33, 34]. However, only 0.1 to 1% of the precipitates present in wafers nucleate stacking faults. In detailed TEM work of Sadamitsu et al. (1995) it was shown that OISF forms at platelet-type precipitates. Furthermore, it was observed that one of the �110� edges of a platelet precipitate always lies exactly on the (111) OISF plane. As discussed in the previous chap ter, platelet precipitates have expansive strain field in the direction parallel to the precipitate plate. It is well established in other alloy systems that interstitial atoms, having a compressive strain field around them, diffuse toward dilatation-field gradient from the compression volume to the expansion volume. By analogy Sadamitsu et al. propose that silicon self-interstitials injected from Si/SiOx interface are attracted by the expansive strain field around edge of platelet precipitates and subse quently they agglomerate as stacking faults at these locations. According to Marsden et al. [35] the size of a disk precipitate must be greater than a certain critical size in order to act as nucleation center. They defined the minimum size to be 26 nm. Another work by them [36] implies that nucleation mechanisms of surface and bulk stacking faults are similar. Electron microscopy studies reveal that the stacking faults observed in sili con are of extrinsic type and they are bounded by Frank partial dislocation that has (a/3) � 111� type Burgers vector [29]. Infrared laser scattering tomography, scan ning infrared microscopy and x-ray tomography reveal directly the true shape of stacking faults, which have been observed to be predominantly circular [37, 38]. Near the specimen surface the shape may be also oval. A few hexagonal loops observed occasionally are appar
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ently multiple faults [37]. (The size of a stacking fault may extend to tens of micrometers in diameter.) The self-interstitials emission during precipitate growth does not necessarily relax all the stresses leaving residual stresses at precipitates. Furthermore, because the thermal expansion coefficient of silicon is larger than that of silicon oxide, an additive compressive strain develops during cooling after precipitate growth [39]. As an additional means of strain relief, prismatic dislo cation loops can be punched-out into the silicon matrix. Normally, this is associated to sufficiently large pre cipitates. Punched-out dislocations have been observed frequently in TEM studies [29, 33, 40, 41]. They have been determined to be extrinsic types of dislocation loops that lie in the 110-planes orthogonal to the punch ing direction and have 1/2 � 110� type Burgers vector. Prismatic punching can occur only if the strain energy is large enough for loop nucleation to occur. Taylor et al. [39] established a quantitative criterion for such an event using the theory of Ashby and Johnson [42] for prismatic loop nucleation. Occasionally, also other types of precipitation induced defects, such as dislocation dipoles and irregular dislo cation loops, are observed [29]. However, systematic knowledge of their formation is sparse.
4.5 Behavior of Oxygen in Basic Heat Treatment Procedures Heat treatment procedures that silicon wafers expe rience during MEMS device manufacturing consists frequently of several successive anneals in different tem peratures and gas ambient. To some extent the effects of low-temperature steps, high temperature steps, and ramps between the steps can be treated separately. In the following, behavior of oxygen in basic heat treat ments is discussed. The first heat treatment CZ silicon experiences is the in situ annealing after solidification in crystal puller. This is usually called thermal history. Thermal history var ies along the crystal axis and radius. Variation along the crystal axis is a consequence of the fact that the seedend portion of a crystal spends more time in the puller furnace than the end portion. The thermal history of the crystal depends also on the shape of the ingot bot tom, the pulling rate, the puller type, the hot-zone con figuration, and the time that the ingot remains inside the puller in the course of growth process. Variations in thermal history affect oxygen precipitation and the for mation of microdefects. It should be emphasized, that the thermal history effect is always present [2]. Various heat treatment procedures have been developed to erase or homogenize the effects of the thermal history. In fact, 65
Silicon as MEMS Material
it has been emphasized [43] that reproducible results in precipitation treatments cannot be obtained without proper homogenization treatment of the samples. A single heat treatment is an elementary step of more complicated thermal processes in silicon device manufac turing. General precipitation behavior in a single treatment can be characterized as follows. When the temperature of a heat treatment step is decreased, the supersaturation of oxygen and driving force for precipitation rises, but the dif fusion coefficient falls rapidly. Consequently, in the pres ence of adequate numbers of nucleation sites, one predicts a small number of large precipitates from a high-tempera ture anneal, and a large number of small precipitates from a low temperature anneal [44]. A common two step heat treatment combination is so called Lo–Hi treatment, where the low-temperature step (600–800°C) leads to the generation or selection of the nucleation centers and the high-temperature one (�1000°C) to precipitate growth. Generally, precipitate density increases with low-temperature anneal time and precipitate size increases with high-temperature anneal time [44]. Furthermore, ramping speed from the low temperature to the high temperature will select the nuclei capable of growing. Complexity of manufacturing of silicon devices has led to the work for finding standard heat treatments that represent more complicated, multi-step ones, in order to evaluate precipitation behavior of silicon material (Chiou, 1985). An outcome of such a work is the standard ASTM F 1239. Basically, the standard heat treatment is a two step Lo–Hi anneal. As a reference, a single Hi anneal is also performed. The temperatures of Lo and Hi steps are 750 and 1050°C, respectively. Further process details have been explained in the ASTM F 1239 standard. In the standard procedure, precipitation is monitored by measuring the changes in interstitial oxygen concentration with an infrared absorption spectrophotometer. Some general conclusions can be drawn from the observed pre cipitation behavior. Because of the dependency of driving force of precipitation (Eq. 4.3) on oxygen supersaturation, the results of any precipitation test show three character istic regions as a function of initial oxygen concentration of the tested wafers. Namely, zero precipitation, partial precipitation and full precipitation. In Figure 4.4 the gen eral precipitation behavior has been plotted as a function of initial oxygen concentration. Two observations are of significance. The boundary value of initial oxygen concen tration when zero precipitation is observed is higher than the equilibrium value from the phase diagram. This is because driving force is needed for precipitation to occur. Secondly, the slope of the curve is relatively steep in the partial precipitation region. The consequence of this type of behavior is that in the partial precipitation region, the high slope of precipitation function transforms the variation of initial oxygen concentration into variation in 66
Precipitated oxygen (Δ[Oi])
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[oi]c V,C,N,H,B Isi,P,As,Sb Max. ΔΔ[Oi] Zero precipitation
0
Partial
Min. precipitation
100% precipitation
Initial oxygen concentration ([Oi]o)
Figure 4.4 ● Generic curve showing relation between oxygen precipitation as a function of initial oxygen concentration [47].
precipitation. Comparison of the Hi and the Lo–Hi treat ments indicate the contribution of thermal history of the wafers on precipitation, because the single Hi treatment does not obviously involve a nucleation step at all [45]. In arbitrary Lo–Hi treatments, the position of zero precipitation, partial precipitation and full precipitation region in regard to initial oxygen concentration depend primarily on the heat treatment temperature and time. The additional factors include thermal history, doping density and concentration of point defects and impuri ties. Lower pre-anneal temperature and/or longer preanneal time will push the partial precipitation region toward lower oxygen concentrations as will a higher concentration of vacancies, boron, carbon and nitrogen. In Figure 4.5 micrographs of cross-sectional samples of 110 silicon surfaces are shown after ASTM F 1239 heat treatments as examples. Silicon samples were of p-type with two oxygen concentration levels. The concentration levels were 10 ppma and 15 ppma. Samples were taken from similar parts of the crystal to ensure uniform thermal history. After heat treatments, samples were etched with Wright etchant [46] in order to relieve microdefects. Optical micrographs were taken using differential interfer ence contrast (Nomarski contrast). Precipitates are seen as dots and stacking faults as oriented lines in the micro graphs. The micrographs of the samples with 10 ppma oxygen concentration levels are in the upper row and the micrographs of the samples with 15 ppma oxygen concen tration level are in the lower row, respectively. The micro graphs of the samples that have been heat treated only at 1050°C are in the left column. In the right column are the micrographs of the samples that have been heat treated at 750°C and 1050°C. Full precipitation is seen only in the sample with 15 ppma oxygen concentration level that has been heat treated at 750°C and 1050°C. Micrographs show clearly the effects of Lo–Hi heat treatment and oxygen concentration on oxygen precipitation. If first high-temperature heat treatment is long enough, a number
Oxygen in Silicon
100 μm
Cox = 10 ppma, T = 1050 °C
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100 μm
Cox= 10 ppma, T1 = 750 and T2 = 1050 °C
100 μm
Cox = 15 ppma, T=1050 °C
100 μm
Cox = 15 ppma, T1 = 750 and T2 = 1050 °C
Figure 4.5 ● Micrographs of silicon surfaces ASTM F 1239 heat treatments.
Figure 4.6 ● Example of a silicon wafer with stacking faults.
Figure 4.7 ● Example of a silicon wafer with DZ. Source: Figure reproduced with permission of Okmetic Oyj.
of large precipitates grow beyond critical size and initiate stacking faults. An example is presented in Figure 4.6. In device processing, annealing programs are occa sionally carried out to “engineer” oxygen precipitation. Probably the most popular of these treatments is a Hi– Lo–Hi annealing, which is otherwise similar to Lo–Hi annealing, but it comprises oxygen out diffusion annealing at comparatively high temperature (�1100°C) as a first
step. The result of this treatment is a very low precipitate density near the wafer surface, the denuded zone (DZ), and a high defect density in the bulk, as consequence of oxygen depletion at the top 20–100 μm under the wafer surface. In Figure 4.7 a cross-sectional example of such a wafer after Wright etching is presented. DZ formation in this way is a direct consequence of earlier discussed high slope of precipitation function (Figure 4.4). DZ width 67
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Silicon as MEMS Material
(DZW) is influenced by time and temperature of the out diffusion anneal in the case of similar silicon wafers. For constant temperature anneal, experimental results of DZW can be expressed with a following simple equation (for more details see Ref. [2] and references therein): DZW = A + B × t1 / 2
(4.16)
where A and B are experimental constants and t is annealing time. Another way to “engineer” oxygen precipitation properties in silicon is rapid thermal processing (RTP). DZ can be created by installing a proper vacancy con centration profile which rises from the wafer surface into the bulk [6].
References 1. J.C. Mikkelsen, The diffusivity and
solubility of oxygen in silicon, Mat.
Res. Soc. Proc. 59 (1986) 19–30.
2. A. Borghesi, B. Pivac, A. Sassella, A. Stella, Oxygen precipitation in silicon, J. Appl. Phys. 77 (1995) 4169–4244. 3. R.D. Doherty, R.W. Cahn, P. Haasen (Eds.), Physical metallurgy, third ed., Elsevier, Netherlands, 1983, pp. 933–1030. 4. S.M. Hu, Effects of ambients on oxygen precipitation in silicon, Appl. Phys. Lett. 36 (7) (1980) 561–564. 5. J. Vanhellemont, C. Clayes, A theoretical study of the critical radius of precipitates and its application to silicon oxide in silicon, J. Appl. Phys. 62 (9) (1987) 3960–3967. 6. R. Falster, V.V. Voronkov, F. Quast, On the properties of intrinsic point defects in silicon: a perspective from crystal growth and wafer processing, Phys. Stat. Sol. B 222 (2000) 219–244. 7. S.M. Hu, Formation of stacking faults and enhanced diffusion in the oxidation of silicon, J. Appl. Phys. 45 (4) (1974) 1567–1573. 8. W. Bergholz, D. Gilles, Impact of
research on defects in silicon on the
microelectronic industry, Phys. Stat.
Sol. B 222 (2000) 5–23.
9. V.V. Voronkov, R. Falster, Grownin microdefects, residual vacancies and oxygen precipitation bands in Czochralski silicon, J. Cryst. Growth 204 (1999) 462–474. 10. T.Y. Tan, W.J. TaylorF. Shimura (Ed.), Oxygen in silicon, Academic Press, USA, 1994, pp. 353–390. 11. D.A.P. Bulla, W.E. Castro Jr., V. Stojanoff, F.A. Ponce, S. Hahn, W.A. Tiller, Effects of boron concentration upon oxygen precipitation in Cz silicon, J. Cryst. Growth 85 (1987) 91–96. 12. S. Hahn, F.A. Ponce, W.A. Tiller, V. Stojanoff, D.A.P. Bulla, W.E. Castro Jr., Effects of heavy boron doping upon oxygen precipitation in
68
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Czochralski silicon, J. Appl. Phys. 64 (9) (1988) 4454–4465. K. Sueoka, M. Akatsuka, M. Yonemura, T. Ono, E. Asayama, H. Katahama, Effect of heavy boron doping on oxygen precipitation in Czochralski Silicon Substrates of Epitaxial Wafers, J. Electrochem. Soc. 147 (2) (2000) 756–762. W. Wijranakula, Oxygen precipitation and defects in heavily doped Czochralski silicon, J. Appl. Phys. 72 (7) (1992) 2713–2723. J.W. Cristian, The theory of transformations in metals and alloys, first ed., Pergamon Press, 1965 973 p. N. Inoue, J. Osaka, K. Wada, Oxide micro-precipitates in as-grown CZ silicon, J. Electrochem. Soc. 129 (12) (1982) 2780–2788. T.Y. Tan, C.Y. Kung, Oxygen precipitation retardation and recovery phenomena in Czochralski silicon: experimental observation, nuclei dissolution model, and relevancy with nucleation issues, J. Appl. Phys. 59 (3) (1986) 917–931. N. Inoue, K. Watanabe, K. Wada, J. Osaka, Time-lag in nucleation of oxide precipitates in silicon due to high temperature preannealing, J. Cryst. Growth 84 (1987) 21–35. W. Wijranakula, Morphology of oxide precipitates in Czochralski silicon degenerately doped with boron, J. Appl. Phys. 72 (9) (1992) 4026–4030. H. Fujimori, Dependence on morphology of oxygen precipitates upon oxygen supersaturation in Czochralski silicon crystals, J. Electrochem. Soc. 144 (9) (1997) 3180–3184. F.S. Ham, Theory of diffusion limited precipitation, J. Phys. Chem. Solids 6 (1958) 335. J. Vanhellemont, Diffusion limited oxygen precipitation in silicon: precipitate growth kinetics and phase
formation, J. Appl. Phys. 78 (6) (1995) 4297–4299. 23. K. Sueoka, N. Ikeda, T. Yamamoto, S. Kobayashi, Morphology and growth process of thermally induced oxide precipitates in Czochralski silicon, J. Appl. Phys. 74 (9) (1993) 5437–5444. 24. S. Isomae, Computer-aided simulation for oxygen precipitation in silicon, J. Appl. Phys. 70 (8) (1991)
4217–4223.
25. M. Schrems, T. Brabec, M. Budil, H. Pötzl, E. Guerrero, D. Huber, P. Pongratz, Simulation of oxygen precipitation in Czochralski grown silicon, Mat. Sci. Eng. B 4 (1989) 393–399. 26. T. Okuyama, M. Nakayama, S. Sadamitsu, J. Nakashima, Y. Tomokiyo, Analysis of local lattice strains around plate-like oxygen precipitates in Czochralski-silicon wafers by convergent-beam electron diffraction, Jpn. J. Appl. Phys, 36 (6A) (1997) 3359–3365. 27. M. Yonemura, K. Sueoka, K. Kamei, Analysis of local lattice strain around oxygen precipitates in silicon crystals using CBED technique, Appl. Surf. Sci. 130–132 (1998) 208–213. 28. M. Yonemura, K. Sueoka, K. Kamei, Analysis of local lattice strain around oxygen precipitates in Czochralski grown silicon wafers using convergent beam electron diffraction, Jpn. J. Appl. Phys. 38 (6A) (1999) 3440–3447. 29. H. Bender, Investigation of the oxygen-related lattice defects in Czochralski silicon by means of electron microscopy, Phys. Stat. Sol. A 86 (1984) 2245–2261. 30. W.A. Tiller, S. Hahn, F.A. Ponce, Thermodynamic and kinetic considerations on the equilibrium shape for thermally induced microdefects in Czochralski silicon, J. Appl. Phys. 59 (9) (1986) 3255–3266. 31. R.B. Fair, Oxidation, impurity diffusion, and defect growth in
Oxygen in Silicon
32.
33.
34.
35.
36.
silicon—an overview, J. Electrochem. Soc. 128 (6) (1981) 1360–1368. V.V. Voronkov, R. Falster, Vacancy-type microdefect formation in Czochralski silicon, J. Cryst. Growth, 194 (1998) 76–88. D.M. Maher, A. Staudinger, J.R. Patel, Characterization of structural defects in annealed silicon containing oxygen, J. Appl. Phys. 47 (9) (1976) 3813– 3825. C. Clayes, H. Bender, G. Declerck, J. van Landuyt, R. van Overstraeten, S. Amelinckx, Impact of high temperature processing on bulk defects in Czochralski silicon, Physica 116B (1983) 148–161. K. Marsden, T. Kanda, M. Okui, M. Hourai, T. Shigematsu, Determination of the criteria for nucleation of ring-OSF from small as-grown oxygen precipitates in CZ-Si crystals, Mat. Sci. Eng. B 36 (1996) 16–21. K. Marsden, S. Sadamitsu, T. Yamamoto, T. Shigematsu, Generation of oxidation-induced stacking faults in Czochralski-grown silicon crystals
37.
38.
39.
40.
41.
exhibiting a ring-like distributed fault region, Jpn. J. Appl. Phys. 34 (6A) (1995) 2974–2980. J.R. Patel, A. Authier, X-ray topography of defects produced after heat treatment of dislocation-free silicon containing oxygen, J. Appl. Phys. 46 (1) (1975) 118–125. G. Kissinger, J. Vanhellemont, C. Clayes, H. Richter, Observation of stacking faults and prismatic punching systems in silicon by light scattering tomography, J. Cryst. Growth 158 (1996) 191–196. W.J. Taylor, U. Gösele, T.Y. Tan, SiO2 precipitate strain relief in Czochralski Si: self-interstitial emission versus prismatic dislocation loop punching, J. Appl. Phys. 72 (6) (1992) 2192–2196. T.Y. Tan, W.K. Tice, Oxygen precipitation and generation of dislocations in silicon, Phil. Mag. 34 (4) (1976) 615–631. K. Tempelhoff, F. Spiegelberg, R. Gleichmann, D. Wruck, Precipitation of oxygen in dislocation-free silicon,
CHAPTER 4
Phys. Stat. Sol. 56 (1979)
213–223.
42. M.F. Ashby, L. Johnson, On the generation of dislocation at misfitting particle in a ductile matrix, Phil. Mag. 20 (1969) 1009–1022. 43. R. Falster, M. Cornara, D. Gambaro, M. Olmo, M. Pagani, Effect of high temperature pre-anneal on oxygen precipitates nucleation kinetics in Si, Solid State Phen. 57–58 (1997) 123–128. 44. J.G. Wilkes, The precipitation of oxygen in silicon, J. Cryst. Growth 65 (1983) 214–230. 45. H.-D. Chiou, Oxygen precipitation behavior and control in silicon crystals, Solid State Tech. 30 (3) (1987) 77–81. 46. M. Wright-Jenkins, A new preferential etch for defects in silicon crystals, J. Electrochem. Soc. 124 (5) (1977) 757. 47. F. Shimura (Ed.), Oxygen in Silicon, Semiconductors and Semimetals, vol. 42, Academic Press, USA, 1994. 679 p
Further reading A. Borghesi, B. Pivac, A. Sassella, A. Stella, Oxygen precipitation in silicon, J. Appl. Phys. 77 (1995) 4169–4244. S. Sadamitsu, M. Okui, K. Sueoka, K. Marsden, T. Shigematsu, Jpn. J.
Appl. Phys. 34 (SB) (1995) L597–L599. F. Shimura (Ed.), Oxygen in Silicon, Semiconductors and Semimetals, vol. 42, Academic Press, USA, 1994. 679 p
M.D. Chiou, L.W. Shive, in W.M. Bulls, S. Broydo, VLSI Technology, USA, ECS, (1985) pp. 429–435.
69
Chapter Four
Oxygen in Silicon Eero Haimi Department of Materials Science and Engineering, Helsinki University of Technology, Espoo, Finland
Single crystal (SC) silicon is one of the chemically purest technical materials used in large quantities. However, in spite of the high purity, there are still trace levels of other elements present in SC silicon. A common additional element, besides doping elements, is oxygen. Oxygen is incorporated to SC silicon during crystal growth. In this respect, there is a fundamental difference between Czochralski (CZ) and float zone (FZ) crystals. Oxygen is accumulating to CZ silicon, because molten silicon dissolves oxygen from silica crucibles used in the growth process. If it is necessary, reduction of inherent oxygen concentration is possible by using magnetic CZ process. FZ silicon appears in lower oxygen concentra tion, since crucibles are not needed in FZ process. In FZ silicon only residual background concentration of oxygen, due to affinity of oxygen for silicon, is observed. Oxygen and oxygen-related phenomena affect the properties of silicon in several ways. From a technologi cal viewpoint, oxygen in silicon can be either beneficial or harmful depending on application. Oxygen can pro vide strengthening of wafer against plastic deformation during processing. Furthermore, oxygen precipitates can act as traps for fast diffusing metallic contaminants. Without this “gettering effect,” degradation of IC fabri cation yield may take place. On the other hand, oxygen precipitates and oxygen-related thermal donors (TDs) may act as defects and may impair processing or device performance when present at unintended locations. In the following, basic aspects of oxygen-related phenomena in silicon, such as oxygen in silicon solid solution, formation of small oxygen aggregates, oxygen precipitation, precipitation induced defects as well as behavior of oxygen in basic heat treatment procedures, have been overviewed.
4.1 Oxygen in Solid Solution
Oxygen in silicon solid solution is placed interstitially in the lattice. Equilibrium oxygen solubility has been studied with various techniques including IR spectroscopy, gas fusion analysis, secondary mass ion spectroscopy, charged particle activation analysis, and x-ray diffrac tion. Generally results scatter to some extent. A fit of experimental results gathered from several groups is given by Mikkelsen [1] in the form of Eq. 4.1: ⎛�1.152eV ⎞⎟ eq Cox � 9�1022 exp ⎜⎜ [ atoms�cm3 ] (4.1)
⎜⎝ kT ⎟⎟⎠
Corresponding partial phase diagram of the Si–O
system, which shows boundary between the solid solu tion of silicon and the two phase region of silicon and silica, as a function temperature and oxygen concentra tion, is presented in Figure 4.1. The equilibrium solubility of oxygen in silicon at room temperature is smaller by several orders of magnitude than near the melting temperature. In practice, this means that as-grown CZ silicon is supersaturated with oxygen after cooling to room temperature due to slowness of out-diffusion in solid state. Typical oxy gen concentration of CZ silicon wafers range from below 5 � 1017 atoms/cm3 (low) to 5–10 � 1017 atoms/cm3 (medium) to above 1018 atoms/cm3 (high) (5 � 1016/cm3 � 1 ppma). Diffusivity of oxygen is dominated by the proc ess of jumping from one interstitial site to another. Experimental oxygen diffusion data in high temperature range (700–1200°C) is well established. Fitted results 59
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Silicon as MEMS Material
n � number of moles k � Boltzmann constant T � absolute temperature
Figure 4.1 ● Partial phase diagram of the Si–O system.
of diffusion constant [1] from several experiments can be expressed as: ⎛ 2.53eV ⎞⎟ 2 Dox � 0.13 exp ⎜⎜− ⎟[cm �s] ⎜⎝ kT ⎠⎟
(4.2)
It has been shown that oxygen diffusivity in high temperature range does not depend much on wafer orientation, annealing ambient, doping concentrations, nor pulling technique of crystal [2]. Low temperature diffusion data are not so well established. The phenom enon of enhanced oxygen diffusivity has been observed frequently and attributed to different causes such as thermal history, presence of metallic contamination and interactions with carbon or hydrogen (for details see Ref. [2]).
4.3 Precipitation of Oxygen
4.2 Formation of Small Oxygen Aggregates Supersaturation of oxygen in silicon solid solution creates a driving force for oxygen aggregation. It can be shown according to standard thermodynamics (for derivation, see for example Ref. [3]) that corresponding chemical driving force, ΔGchem, as a function of oxygen supersaturation can be approximated as: eq �Gchem � nRT In(Cox �Cox ),
where:
Cox � concentration of oxygen
Ceq ox � equilibrium concentration of oxygen
60
Conceptually, the first stage of oxygen aggregation is the formation of O2 dimers from essentially isolated oxygen atoms by diffusion process. The possible role of such constituents as vacancies or carbon in the free energy of dimer formation is under scientific discussion. Aggregation of larger oxygen clusters than dimers is frequently considered to continue also with atom by atom process, although some evidence exists that oxygen dimers may also be mobile. Formation of small oxygen aggregates has gener ally raised interest in two contexts. In its usual inter stitial configuration, oxygen is electrically inactive in silicon lattice. However, annealing of oxygen-rich silicon (1018 atoms/cm3) in the temperature range 350–500°C, several types of electrically active centers called thermal donors are formed. Furthermore, for mation of so-called new donors has been observed at higher temperatures. TDs have been attributed to the growth of small oxygen aggregates as already discussed in Section 3.6. Another area of interest regarding small oxygen aggregates is nucleation of precipitates. There has been discussion about relationship between pre cipitate nuclei and especially new donors. However, much of nucleation studies do not deal with such issues as detailed structure of the small oxygen aggregate or exact mechanism of their formation process. Instead, the emphasis is placed on the later observed precipita tion behavior. In the present text the same approach is followed. Nucleation is discussed further together with precipitation phenomena in the next chapter.
(4.3)
Precipitation of oxygen in silicon is a diffusion control led solid state phase transformation. In the transforma tion silicon oxide is formed. Formation of silicon oxide within silicon lattice requires that oxygen must diffuse together to form a small volume with correct composi tion, and the atoms must rearrange into correct crystal structure; i.e., both kinetic and thermodynamic require ments must be fulfilled. According to the mass balance, the reaction equation of oxygen precipitation in silicon reads: Si + xOi ↔ SiOx
(4.4)
Accurate chemical composition of oxygen precipitates in silicon has been under scientific debate. It is generally
Oxygen in Silicon
agreed that in SiOx the x is less than 2. The specific volume of the oxide is about twice as large as that of silicon. Therefore, the oxide precipitates are originally strongly strained. It has been proposed that stress accu mulation during precipitation is relieved at least par tially by ejection of self-interstitials. Consequently, if conservation of mass and volume in addition to point defect balance is included, the reaction Eq. 4.4 is modi fied to [4]: aSi + bxOi ↔ bSiO x + (a − b)Sii
∑ Ai γi + V Δg el
ΔG
~4πγ r2
r r*
(4.5)
In principle, precipitation of a second phase takes place in three steps: a local fluctuation in chemical potential (embryo), formation of a stable nucleus, and precipitate growth. Proposed theories of nucleation of silicon oxide involve both homogeneous and hetero geneous mechanisms and several propositions for the nuclei structure exist. Regardless of the exact char acteristics of the nucleus, some basic thermodynamic concepts can clarify the nucleation process. The driving force of the phase transformation is supersaturation of oxygen, whereas surface energy and strain energy are setting constraining contributions. Consequently, free energy change of the phase transformation ΔG can be expressed as: ΔG � −V Δg chem +
(4.6)
ΔG
~ –(4/3)π(Δgchem–Δgel)r3
Figure 4.2 ● Free energy changes expressed as a function of nucleus radii.
fact a similar type of equation would be obtained for any nucleus shape as a function of its size. Accordingly, the important concept of critical size of nucleus is introduced; if the precipitate is too small it is not thermodynamically stable. Figure 4.2 illustrates graphically free energy changes expressed in Eq. 4.7 as a function of nucleus radii. Critical radius r* of a thermodynamically stable nucleus is obtained by differentiation of Eq. 4.7, which yields: r* =
where: Δgchem � chemical free energy change per volume
2γ (�g chem − �g el )
(4.8)
By substituting Eq. 4.8 to Eq. 4.7, the activation energy barrier against nucleation ΔG* can be expressed as:
Δgel � elastic free energy change per volume γi � interface surface energy components V � volume of the precipitate
�G* =
Ai � interface surface area components In oxygen precipitation, an aggregate of oxygen atoms constituting a nucleus is formed first. Once formed, the nuclei can either grow further and form oxide precipi tates or dissolve. This can be elaborated on by looking at the terms in Eq. 4.6 separately. Contributions of sur face energy and strain energy oppose the transforma tion. However, the separate contributions have different dependency on the nucleus size. If we ignore the varia tion of γ with interface orientation and assume that the nucleus is spherical with a radius r, Eq. 4.6 becomes 4 �G = − πr 3(�g chem − �g el ) + 4πr 2 γ 3
CHAPTER 4
(4.7)
This is a function of r that first increases up to an acti vation energy barrier maximum and then decreases. In
16πγ3 3(�g chem − �g el )2
(4.9)
For critical radius of nuclei in the case of strain free nucleation (Δgel � 0), manipulation of Eqs 4.8 and 4.3 8.3 yields: r* =
2γv p eq ) kTIn(Cox / Cox
(4.10)
where: vp � the volume of precipitate per oxygen atom in it. Importantly, Eq. 4.10 shows that the critical size of nucleus increases with increasing temperature (because eq of temperature dependency of Cox ). More comprehensive theoretical treatment of critical radius of nucleus takes into consideration also stressrelieving mechanisms with corresponding crystal defect
61
Silicon as MEMS Material
PA R T I
interactions. Hence, an equation for r* can be written in the following form [5]:
r* = r*
2γ (1 + δ − ε) ε )3 XkT eq In (Cox / Cox )(C )(CIeq / CI )ni (C (CV / CVeq )nv − 6μ μ m δε vp
(
)
(4.11) where: CI � concentration of self-interstitials CIeq � equilibrium concentration of self-interstitials CV � concentration of vacancies Ceq V � equilibrium concentration of vacancies δ � linear misfit between Si and SiOx lattices (for SiO2 δ0.3) nI � number of self-interstitials emitted nV � number of vacancies absorbed X � ratio of oxygen and silicon in precipitate The compressive strain � in Eq. 4.11 is: ε=
δ 1 + 4μ m /3Kp
where:
μm � shear modulus of silicon
Kp � bulk compressibility of SiOx Interaction of oxygen with the other constituents in association with oxygen aggregation has been observed experimentally. At sufficiently high temperature, crystal line solids contain thermally generated vacancies and self interstitials, which are equilibrium point defects in crystals caused by configuration entropy. In the case of dislocation free SC silicon, the material is usually supersaturated with point defects, because lack of other defects acting as point defect sinks. A fundamental observation regarding intrin sic point defects is that silicon crystals can be grown in either a vacancy or a self-interstitial mode and concentra tion of point defects in grown crystals depend on process ing conditions. In general, excess vacancies favor oxygen precipitation, whereas excess self-interstitials suppress it. It has been found that there is quite a sharp transition around 5 � 1011 cm�3 vacancy concentration between enhanced oxygen clustering and “normal” clustering [6]. In addition to crystal growth, changes in point defect con centration may take place during wafer processing. Wafer surfaces act as source or sink of point defects depending on ambient used. Nitration injects vacancies, whereas oxidation is introducing self-interstitials into silicon 62
[4, 7, 8]. Also oxygen precipitation is introducing self interstitials into silicon. Effect of point defects on oxygen precipitation depends also on possible point defect reac tions. (Interested readers may consult references [6, 9] and references therein for further details.) Graphite is used as heating elements in CZ crystal growth furnaces. In partial vacuum of the growth chamber, there may be sufficient oxygen that reacts with unprotected graphite to form carbon monoxide, which dissolves in the silicon melt. Consequently, carbon can be incorporated in the silicon crystal during the growth process. When present at a concentration above 0.5ppm, carbon strongly enhances oxide precipitate nucleation [10]. In case of heavily boron doped silicon (p � -type), it is found that precipitation is enhanced as a function of increasing boron concentra tion [11–13]. Moreover, in heavily boron doped silicon, maximum nucleation rate of oxide precipitates is shifted toward high temperature regions [14]. According to classical, steady state nucleation theory, the nucleation rate J is given by the Volmer-Weber Becker-Döring nucleation rate equation (for derivation, see for example Ref. [15]) J = ZC * ω
(4.12)
where C* is the concentration of critical-sized nuclei and ω is the frequency of attachment of oxygen atoms to the nucleus. The term Z is the Zeldovich factor, which is a correction factor corresponding to the fraction of atoms, which are included in the precipitate nuclei immediately after nucleation. In practice the Zeldovich factor is a fit ting parameter usually in the order of but smaller than 1. The concentration of critical-sized nuclei C* is given by a Boltzmann type of equation: ⎛ �G* ⎞⎟ ⎟⎟ C* = Cx exp⎜⎜⎜ ⎜⎝ kT ⎟⎠
(4.13)
The term Cx is concentration of nucleation sites. In the homogeneous nucleation models Cx is set equal to the interstitial oxygen concentration or more properly interstitial lattice sites in silicon. Heterogeneous nuclea tion models assume that Cx is equal to the concentra tion of some other constituents such as pre-existing oxygen aggregates, vacancies or carbon. The attachment factor ω is given by ω = 4π(r*)2 Cox
Dox da
(4.14)
where da is the interatomic jumping distance. The total number of precipitates per unit volume is calculated from integrating the nucleation rate with the processing time. Basically, nucleation rate of oxide precipitates in iso thermal heat treatment depends on oxygen concentration
Oxygen in Silicon
in solid solution and processing temperature. Furthermore, heterogeneous factors may have an effect on nucleation rate depending on experimental conditions. Nucleation rate increases with increasing oxygen concentration in solid solution. When experimental nucleation rate is plot ted as a function of temperature, a maximum at a certain temperature is observed. This can be explained as follows. When the temperature is very high, the oxygen super saturation is small or non-existing, leading to small driv ing force and nucleation rate. On the other hand, when temperature is very low, diffusion becomes slow, leading to also vanishing nucleation rates. Nucleation rate is not necessary constant in time. Nucleation rates slow down and number per volume of precipitates reach a saturation value in very long anneals. This has been explained with overlapping of diffusion zones surrounding each nucleus during long anneals. As a different type of time dependency, an incubation time in nucleation rate is observed after processes, where sudden cooling and concomitant sudden supersaturation states are developed. In practice, silicon has already pre-existing nuclei before many processing situations. Due to possibility of nuclei dissolution, number per volume of oxygen pre cipitates after non-isothermal heat-treatment programs may differ from pre-existing nuclei density. As discussed earlier, the size of the nuclei should be larger than the critical size in order to be stable. Furthermore, the criti cal nucleus size increases as a function of rising tem perature. Consequently, at high enough heating rate, the growth rate of a nucleus is slower than the increase of the critical size of nucleus resulting in dissolution of nuclei. In Figure 4.3 selection of nuclei capable of growth using two different two-step heat treatment temperatures has been illustrated [16]. First, there is a pre-existing nucleus size distribution. A subsequent anneal selects nuclei larger than the critical size for further growth. An alternative low temperature anneal would select larger proportion of nuclei than respective high temperature anneal. According to experimental observations, total
Precipitate density
Invisible
As-grown
Visible
Annealing
After annealing
Low temp. High temp. rc 10
rc1
100
N(F>rc) N(r>rc1) 1000
10000
Precipitate size (Å)
Figure 4.3 ● Selection of nuclei capable of growing [16]. Source:
Figure reproduced by permission of the Electrochemical Society.
CHAPTER 4
dissolution of pre-existing nuclei causes long time lag in subsequent oxygen precipitation [17, 18]. Precipitates are characterized by their size, shape, crystal structure and number per unit volume. In princi ple, the size and the number per unit volume are inter related at their upper boundary values, because there is a finite number of oxygen atoms capable of forming precipitates. In practice, the typical number per volume of oxygen precipitates after device processing is between 103 and 1010 cm�3. Diffusion calculations show that for these densities the diffusion zone of each precipitate does not have much overlap. As a consequence, the size of the oxygen precipitates is nearly independent of the number per unit volume of precipitates (Bergholz, 1994). Shape of a precipitate depends on their formation tem perature as well as oxygen supersaturation and doping level of the silicon. Three temperature ranges have been related to the three typical precipitate shapes, i.e., the needle, the platelet, and the polyhedron in lightly doped silicon. At low temperatures (~400–650°C) precipitates grow as needles. In this temperature range the strainenergy contribution to the precipitate total free energy dominates, since the stress-relieving processes (which become important at higher temperatures) play a minor role. At intermediate temperatures (~650–950°C) platelet-shaped precipitates are typical (although they can be formed also during short high-temperature annealing). These precipitates are square formed plate lets at {100} habit planes, with edges along the �110� directions. At high temperatures (above 950°C) strain is completely released and the precipitates take the shape with minimum surface energy. Due to the anisotropy of interface energy, the preferential shape is octahedron with eight equivalent (111) faces (surface energy of silicon is minimum in the (111) planes) instead of the sphere. In the case of heavily doped silicon, precipitate morphology differs from lightly doped silicon. Plateletshaped precipitates are observed in addition to (100)— also in (110)—and (111)-type habit planes [19] and rod-shape precipitates are not formed [11]. According to Fujimori [20], dependence of precipitate morphol ogy on oxygen supersaturation comes from kinetic con siderations. Growth rate of a precipitate increases with increasing supersaturation of oxygen and kinetics of stress-relaxation processes may become a limiting factor. Consequently, for higher oxygen supersaturation, there is a transition zone in boundary temperature between platelet and polyhedron precipitate formation. The crys tal structures of precipitates formed at higher than about 650°C temperatures are amorphous. This is correlated to precipitate morphology. Only needle-type precipitates are observed to be crystalline. At high enough temperatures precipitates do not nucleate in practice. Only precipitate growth becomes significant. The kinetics of the precipitation of oxygen 63
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Silicon as MEMS Material
in thermal processing can be studied experimentally for instance by following the diminishing infrared absorption at 1107cm�1 band, characteristic of interstitially dissolved oxygen in silicon. Furthermore, transmission electron microscopy can be utilized in determining size of pre cipitates as a function of heat treatment time. It has been confirmed by many observations, that the time depend ence of experimental results are generally in good agree ment with the theory of Ham [21] for diffusion limited precipitation at temperatures above 650°C [22]. Applying the theory of Ham, Sueoka et al. [23] gives the time (t) dependence of the dimensions L (edge) and d (thickness) of platelet precipitates and l (edge size) of octahedral pre cipitates. These types of model are called deterministic growth models: ⎛ C − Cint ⎞⎟0.5 ⎜ ox ⎟ L = Λ(Dox t)0.5 with Λ = 2 2 ⎜⎜ ox ⎟ ⎜⎝ γπCp ⎠⎟⎟ (4.15a)
0.5
d = δ(Dox t)
⎛ γ(C − Cint )⎞⎟0.5 ⎜ ox ox ⎟ ⎜ with δ = 4 ⎜ ⎟⎟ ⎜⎝ πCp ⎠⎟ (4.15b)
⎛ C − Cint ⎞⎟0.5 ⎜ ox ⎟ l = λ(Dox t)0.5 with λ = (8π)1 / 3 ⎜⎜ ox ⎟⎟ ⎜⎝ Cp ⎟⎠ (4.15c) In order to describe the entire precipitation process from nucleation to precipitate growth, a steady-state nucleation model and a deterministic growth model can be combined at the critical size of the nucleus. This allows simultaneous calculation of oxygen loss, number of precipitates per unit volume and the average precipi tate radius during annealings. Furthermore, precipitate size-distribution can also be evaluated using coarsening model together with an iterative numerical calculation scheme [24]. However, for all nucleus radii smaller than the critical size, an equilibrium size-distribution has to be assumed. This assumption is incorrect when rapid temperature ramping takes place. The most realistic simulation strategy describes growth and dissolution of all nuclei and precipitate sizes statistically. This can be done applying Monte Carlo techniques. The drawback of the Monte Carlo approach is excessive computational load. A simulation model using Fokker-Plank equations can overcome much of the computational problems. Similarly to the Monte Carlo method, growth and dis solution of nuclei and precipitates are described statis tically. However, instead of using random numbers for deciding on growth and dissolution, this is described 64
by a set of chemical rate equations. Furthermore, all chemical rate equations are approximated with a single stochastic partial differential equation applying a math ematical transformation. The resulting equation is called a Fokker-Plank equation. For details of Fokker-Planck modeling see, for example, Ref. [25].
4.4 Precipitate-Induced Defects As discussed earlier, oxide precipitates in silicon are originally strongly strained, because the volume expansion connected with oxide precipitate forma tion. Stress relaxation may take place by ejection of self-interstitials. However, ejected self-interstitials are not necessarily arranged originally in minimum energy configuration and stress relaxation is not necessarily complete. Consequently, precipitate-induced defect formation may take place. The ideal case of stress (and strain) fields associated to a precipitate formation without any stress-relaxation process can be calculated using standard theory of elas ticity. General calculations of this type show the effect of precipitate shape on elastic energy: lowest elastic energy is associated to platelet morphology, next low est is associated to needle morphology, and the highest elastic energy is associated to polyhedron morphology. An experimental technique to study actual local lat tice strain around oxygen precipitates is convergent beam electron diffraction (CBED) mode of transmis sion electron microscopy. The local lattice strain can be measured from higher order Laue zone (HOLZ) pat terns. Several of this type of study has been published [26, 27]. As a result of strain analysis from HOLZ pat terns, acquired around a platelet type of precipitate, the strain along the normal direction to the precipitate was found to be compressive. Importantly, however, the strain along the parallel direction to the precipitate was found to be tensile. Based on FEM simulation, the strain formation was considered to take place during cooling of the material [28]. In the case of polyhedron precipitates, contradictory results have been published. Otherwise similar behavior to that in the case of platelettype precipitate, but with lower strain levels, has been reported [28]. On the other hand, results obtained with high-resolution electron microscope indicating that polyhedron precipitates exist practically without strain have been reported [29]. An argument in this dis cussion is that amorphous silica cannot support shear stresses above a glass transition temperature at around 950°C [30]. Apparently, uncertainty concerning stress and strain fields associated to precipitates comes to some extent from the fact that the stress formation is not an equilibrium process, which would depend only on shape and size of a precipitate. Precipitation process
Oxygen in Silicon
involves the inward diffusion of oxygen, the generation of stress at the interface and the outward diffusion of self-interstitials. Consequently, partial stress relaxation takes place already simultaneously with the stress for mation and it is dependent on the process sequence. Self-interstitials formed in the stress-relaxation proc ess associated with oxygen precipitation are likely to be locally supersaturated. The system can further lower its free energy by allowing them to agglomerate. Stacking fault formation is such an agglomeration process. In general stacking faults can be classified as surface stack ing faults and bulk stacking faults. In the case of sur face stacking faults, oxidation induced stacking faults (OISF) are of interest in the present context. They are usually located as a circular band in the wafer originated from vacancy reactions during particular crystal growth processes. Essential factors in formation of OISF are self-interstitials emitted to silicon due to surface oxi dation [31, 32]. Stacking faults in silicon are always associated with precipitates at their centers providing that mechanical damage and heavy metal contamina tion are excluded as cause of the defects. Transmission electron microscopy observations of several workers confirm this [33, 34]. However, only 0.1 to 1% of the precipitates present in wafers nucleate stacking faults. In detailed TEM work of Sadamitsu et al. (1995) it was shown that OISF forms at platelet-type precipitates. Furthermore, it was observed that one of the �110� edges of a platelet precipitate always lies exactly on the (111) OISF plane. As discussed in the previous chap ter, platelet precipitates have expansive strain field in the direction parallel to the precipitate plate. It is well established in other alloy systems that interstitial atoms, having a compressive strain field around them, diffuse toward dilatation-field gradient from the compression volume to the expansion volume. By analogy Sadamitsu et al. propose that silicon self-interstitials injected from Si/SiOx interface are attracted by the expansive strain field around edge of platelet precipitates and subse quently they agglomerate as stacking faults at these locations. According to Marsden et al. [35] the size of a disk precipitate must be greater than a certain critical size in order to act as nucleation center. They defined the minimum size to be 26 nm. Another work by them [36] implies that nucleation mechanisms of surface and bulk stacking faults are similar. Electron microscopy studies reveal that the stacking faults observed in sili con are of extrinsic type and they are bounded by Frank partial dislocation that has (a/3) � 111� type Burgers vector [29]. Infrared laser scattering tomography, scan ning infrared microscopy and x-ray tomography reveal directly the true shape of stacking faults, which have been observed to be predominantly circular [37, 38]. Near the specimen surface the shape may be also oval. A few hexagonal loops observed occasionally are appar
CHAPTER 4
ently multiple faults [37]. (The size of a stacking fault may extend to tens of micrometers in diameter.) The self-interstitials emission during precipitate growth does not necessarily relax all the stresses leaving residual stresses at precipitates. Furthermore, because the thermal expansion coefficient of silicon is larger than that of silicon oxide, an additive compressive strain develops during cooling after precipitate growth [39]. As an additional means of strain relief, prismatic dislo cation loops can be punched-out into the silicon matrix. Normally, this is associated to sufficiently large pre cipitates. Punched-out dislocations have been observed frequently in TEM studies [29, 33, 40, 41]. They have been determined to be extrinsic types of dislocation loops that lie in the 110-planes orthogonal to the punch ing direction and have 1/2 � 110� type Burgers vector. Prismatic punching can occur only if the strain energy is large enough for loop nucleation to occur. Taylor et al. [39] established a quantitative criterion for such an event using the theory of Ashby and Johnson [42] for prismatic loop nucleation. Occasionally, also other types of precipitation induced defects, such as dislocation dipoles and irregular dislo cation loops, are observed [29]. However, systematic knowledge of their formation is sparse.
4.5 Behavior of Oxygen in Basic Heat Treatment Procedures Heat treatment procedures that silicon wafers expe rience during MEMS device manufacturing consists frequently of several successive anneals in different tem peratures and gas ambient. To some extent the effects of low-temperature steps, high temperature steps, and ramps between the steps can be treated separately. In the following, behavior of oxygen in basic heat treat ments is discussed. The first heat treatment CZ silicon experiences is the in situ annealing after solidification in crystal puller. This is usually called thermal history. Thermal history var ies along the crystal axis and radius. Variation along the crystal axis is a consequence of the fact that the seedend portion of a crystal spends more time in the puller furnace than the end portion. The thermal history of the crystal depends also on the shape of the ingot bot tom, the pulling rate, the puller type, the hot-zone con figuration, and the time that the ingot remains inside the puller in the course of growth process. Variations in thermal history affect oxygen precipitation and the for mation of microdefects. It should be emphasized, that the thermal history effect is always present [2]. Various heat treatment procedures have been developed to erase or homogenize the effects of the thermal history. In fact, 65
Silicon as MEMS Material
it has been emphasized [43] that reproducible results in precipitation treatments cannot be obtained without proper homogenization treatment of the samples. A single heat treatment is an elementary step of more complicated thermal processes in silicon device manufac turing. General precipitation behavior in a single treatment can be characterized as follows. When the temperature of a heat treatment step is decreased, the supersaturation of oxygen and driving force for precipitation rises, but the dif fusion coefficient falls rapidly. Consequently, in the pres ence of adequate numbers of nucleation sites, one predicts a small number of large precipitates from a high-tempera ture anneal, and a large number of small precipitates from a low temperature anneal [44]. A common two step heat treatment combination is so called Lo–Hi treatment, where the low-temperature step (600–800°C) leads to the generation or selection of the nucleation centers and the high-temperature one (�1000°C) to precipitate growth. Generally, precipitate density increases with low-temperature anneal time and precipitate size increases with high-temperature anneal time [44]. Furthermore, ramping speed from the low temperature to the high temperature will select the nuclei capable of growing. Complexity of manufacturing of silicon devices has led to the work for finding standard heat treatments that represent more complicated, multi-step ones, in order to evaluate precipitation behavior of silicon material (Chiou, 1985). An outcome of such a work is the standard ASTM F 1239. Basically, the standard heat treatment is a two step Lo–Hi anneal. As a reference, a single Hi anneal is also performed. The temperatures of Lo and Hi steps are 750 and 1050°C, respectively. Further process details have been explained in the ASTM F 1239 standard. In the standard procedure, precipitation is monitored by measuring the changes in interstitial oxygen concentration with an infrared absorption spectrophotometer. Some general conclusions can be drawn from the observed pre cipitation behavior. Because of the dependency of driving force of precipitation (Eq. 4.3) on oxygen supersaturation, the results of any precipitation test show three character istic regions as a function of initial oxygen concentration of the tested wafers. Namely, zero precipitation, partial precipitation and full precipitation. In Figure 4.4 the gen eral precipitation behavior has been plotted as a function of initial oxygen concentration. Two observations are of significance. The boundary value of initial oxygen concen tration when zero precipitation is observed is higher than the equilibrium value from the phase diagram. This is because driving force is needed for precipitation to occur. Secondly, the slope of the curve is relatively steep in the partial precipitation region. The consequence of this type of behavior is that in the partial precipitation region, the high slope of precipitation function transforms the variation of initial oxygen concentration into variation in 66
Precipitated oxygen (Δ[Oi])
PA R T I
[oi]c V,C,N,H,B Isi,P,As,Sb Max. ΔΔ[Oi] Zero precipitation
0
Partial
Min. precipitation
100% precipitation
Initial oxygen concentration ([Oi]o)
Figure 4.4 ● Generic curve showing relation between oxygen precipitation as a function of initial oxygen concentration [47].
precipitation. Comparison of the Hi and the Lo–Hi treat ments indicate the contribution of thermal history of the wafers on precipitation, because the single Hi treatment does not obviously involve a nucleation step at all [45]. In arbitrary Lo–Hi treatments, the position of zero precipitation, partial precipitation and full precipitation region in regard to initial oxygen concentration depend primarily on the heat treatment temperature and time. The additional factors include thermal history, doping density and concentration of point defects and impuri ties. Lower pre-anneal temperature and/or longer preanneal time will push the partial precipitation region toward lower oxygen concentrations as will a higher concentration of vacancies, boron, carbon and nitrogen. In Figure 4.5 micrographs of cross-sectional samples of 110 silicon surfaces are shown after ASTM F 1239 heat treatments as examples. Silicon samples were of p-type with two oxygen concentration levels. The concentration levels were 10 ppma and 15 ppma. Samples were taken from similar parts of the crystal to ensure uniform thermal history. After heat treatments, samples were etched with Wright etchant [46] in order to relieve microdefects. Optical micrographs were taken using differential interfer ence contrast (Nomarski contrast). Precipitates are seen as dots and stacking faults as oriented lines in the micro graphs. The micrographs of the samples with 10 ppma oxygen concentration levels are in the upper row and the micrographs of the samples with 15 ppma oxygen concen tration level are in the lower row, respectively. The micro graphs of the samples that have been heat treated only at 1050°C are in the left column. In the right column are the micrographs of the samples that have been heat treated at 750°C and 1050°C. Full precipitation is seen only in the sample with 15 ppma oxygen concentration level that has been heat treated at 750°C and 1050°C. Micrographs show clearly the effects of Lo–Hi heat treatment and oxygen concentration on oxygen precipitation. If first high-temperature heat treatment is long enough, a number
Oxygen in Silicon
100 μm
Cox = 10 ppma, T = 1050 °C
CHAPTER 4
100 μm
Cox= 10 ppma, T1 = 750 and T2 = 1050 °C
100 μm
Cox = 15 ppma, T=1050 °C
100 μm
Cox = 15 ppma, T1 = 750 and T2 = 1050 °C
Figure 4.5 ● Micrographs of silicon surfaces ASTM F 1239 heat treatments.
Figure 4.6 ● Example of a silicon wafer with stacking faults.
Figure 4.7 ● Example of a silicon wafer with DZ. Source: Figure reproduced with permission of Okmetic Oyj.
of large precipitates grow beyond critical size and initiate stacking faults. An example is presented in Figure 4.6. In device processing, annealing programs are occa sionally carried out to “engineer” oxygen precipitation. Probably the most popular of these treatments is a Hi– Lo–Hi annealing, which is otherwise similar to Lo–Hi annealing, but it comprises oxygen out diffusion annealing at comparatively high temperature (�1100°C) as a first
step. The result of this treatment is a very low precipitate density near the wafer surface, the denuded zone (DZ), and a high defect density in the bulk, as consequence of oxygen depletion at the top 20–100 μm under the wafer surface. In Figure 4.7 a cross-sectional example of such a wafer after Wright etching is presented. DZ formation in this way is a direct consequence of earlier discussed high slope of precipitation function (Figure 4.4). DZ width 67
PA R T I
Silicon as MEMS Material
(DZW) is influenced by time and temperature of the out diffusion anneal in the case of similar silicon wafers. For constant temperature anneal, experimental results of DZW can be expressed with a following simple equation (for more details see Ref. [2] and references therein): DZW = A + B × t1 / 2
(4.16)
where A and B are experimental constants and t is annealing time. Another way to “engineer” oxygen precipitation properties in silicon is rapid thermal processing (RTP). DZ can be created by installing a proper vacancy con centration profile which rises from the wafer surface into the bulk [6].
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Further reading A. Borghesi, B. Pivac, A. Sassella, A. Stella, Oxygen precipitation in silicon, J. Appl. Phys. 77 (1995) 4169–4244. S. Sadamitsu, M. Okui, K. Sueoka, K. Marsden, T. Shigematsu, Jpn. J.
Appl. Phys. 34 (SB) (1995) L597–L599. F. Shimura (Ed.), Oxygen in Silicon, Semiconductors and Semimetals, vol. 42, Academic Press, USA, 1994. 679 p
M.D. Chiou, L.W. Shive, in W.M. Bulls, S. Broydo, VLSI Technology, USA, ECS, (1985) pp. 429–435.
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