Properties of Silicon Crystals

Chapter 3

Properties of Silicon Crystals Jari Paloheimo Okmetic Oyj, Vantaa, Finland

Many properties of Czochralski (CZ) silicon wafers originate partially or totally from the crystal growth used to produce the single-crystalline silicon. For example, the diameter and orientation of the as-grown crystal are already close to those of the final wafers. Furthermore, the conductivity type (p or n), selection of the dopant element and its concentration (which induces certain electrical resistivity), oxygen concentration and amount of carbon, and the homogeneity of these concentrations in the microscopic and macroscopic scales all originate from the growth process. Also, other important qualities (e.g., the amount of harmful transition-metal impurities and many of the typical defects encountered in silicon processing) are contributed by the initial crystal material. In the optimal case, the most important quality factors of the crystal, considering the planned use of the wafers, are properly identified beforehand; the allowed range of properties is specified; the quality is controlled by the crystalgrowing process; and the resulting quality becomes ascertained from the crystal and/or wafers. Such procedures, if handled properly, give a good starting point for the subsequent device processing on the wafers. Furthermore, feedback about the yield and quality problems encountered in wafer and device processing gives useful information for further improvements in the crystal quality. In the worst case, the crystal may contain too many impurities or defects, or have a tendency toward later defect formation because of insufficient initial information or knowledge, compromises in the crystal quality or cost, inherent limitations of the growth process, or some other more accidental reason. The insufficient quality could lead to rejection of the crystal material or wafers or, if unfit wafers are delivered to customers, to negative influence on the yield or quality of their product, which can be an integrated circuit, discrete device, sensor structure, solar cell, or some other type of application. In this chapter, the typical properties of CZ silicon crystals are reviewed, covering impurities and defects, 56

their effects, control, and incidence. We concentrate on the properties of as-grown crystal, while the contributions by wafer processing are only mentioned briefly. Specifically, the quality factors that have proven to be of the greatest practical importance in the crystal-growing industry for 4
8 in. nominal crystal diameters, which is also the range used in microelectromechanical systems (MEMS), are covered. The connections of impurities and defects to the success or failure of later device fabrication on the wafers are indicated where possible; although, due to the extent of the subject, only major items can be covered. More detailed information can be found in the references of this chapter and in the other chapters of this book.

3.1 DOPANTS AND IMPURITIES The CZ silicon crystals contain small amounts of impurities of which some are essential, in controlled amounts, for the quality of the crystal and wafers, while other impurities are harmful if their concentration is too high and, thus, the latter elements must be avoided. The acceptor or donor impurities and oxygen, in suitable amounts, are among the former, useful elements. The acceptor and donor dopants are usually elements from groups III and V of the periodic table of elements, the most used ones being boron (acceptor, for p-type crystals) and phosphorus, antimony, and arsenic (donors, for n-type crystals) (Table 3.1). These typical dopants are substitutional impurities (i.e., they replace silicon atoms in the lattice) and donate one hole or electron per each acceptor or donor atom to the valence or conduction band of silicon, respectively [1,2]. The acceptors and donors are used to control the charge carrier concentration (and resulting resistivity) and type of charge carriers of the crystal. These parameters are essential considering the operation of the semiconductor devices processed on the wafers [1]. Instead of boron, some other elements from group III could also be

Handbook of Silicon Based MEMS Materials and Technologies. DOI: http://dx.doi.org/10.1016/B978-0-323-29965-7.00003-8 © 2015 Elsevier Inc. All rights reserved.

Properties of Silicon Crystals Chapter | 3

TABLE 3.1 Table of Elements Indicating Substitutional Dopant Impurities of Silicon Period

Group III

IV

V

Si

P(D)

(A)

2

B

3

Al

4

Ga

As(D)

5

In

Sb(D)

The elements most used, in practice, as acceptors and donors in CZ crystals are indicated by (A) and (D), respectively.

used as acceptors in CZ crystals but have certain limitations and are not common in practice. For example, gallium doping has been suggested for solar cell applications in order to avoid the initial degradation of the efficiency observed in solar cells made of boron-doped CZ silicon [3]. The three donors—phosphorus, antimony, and arsenic—are not replaceable by each other, at least selfevidently, because they have different properties. For example, the different dopant elements have different limits for the lowest resistivity achievable and the amount of axial variation of resistivity within crystal depends on the dopant. Furthermore, the diffusion and redistribution behavior of the dopants in the wafer during device processing also varies [1]. For high doping levels of phosphorus and arsenic certain safety issues exist in crystal growing and later processing and may require precautions. In practice, the users of the wafers already specify, for each wafer product, the dopant element to be used in the crystal. Boron and phosphorus are typical in lightly doped crystals while all four elements (i.e., boron, phosphorus, arsenic, and antimony) are used in the highly doped case. Oxygen originating from the silica crucible is one of the most characteristic impurities in CZ silicon in contrast to float-zone (FZ) silicon, which contains practically no oxygen. A suitable oxygen concentration is considered to be among the main quality factors to be controlled in the crystal-growing process. Oxygen in interstitials gives the wafers mechanical strength against thermal, gravitational, or mechanical stress during heat treatments, decreasing the risk of slip dislocation formation and wafer warping [4,5]. Furthermore, oxygen forms precipitates [6
8], which are often used for impurity gettering in device processing where gettering is a method to remove harmful metal impurities from the device region of the wafer [9]. Also, too high an oxygen concentration can be harmful if it induces too strong precipitation of oxygen and formation of defects. Nitrogen can be intentionally added to crystals in concentrations around 1015 cm23 to control the microdefect formation [10], mainly to enhance oxygen precipitation or to reduce the size of vacancy-originated defects, and/or to

57

strengthen the crystal [11]. Nitrogen has the potential for commercial applications in large-diameter wafers but is not used in standard smaller-diameter CZ silicon wafers and is also not expected to offer benefits in typical MEMS. Germanium co-doping of the crystal (i.e., use of Ge in addition to donor or acceptor impurity) is possible, to control defect formation [12], but is only rarely used in practise. Germanium, similarly to silicon, belongs to the fourth group of the periodic table of elements, and it has no effect on the charge carrier concentration. Ge doping can be used for lattice constant engineering and, in principle, optimized Ge co-doping in highly boron- or phosphorus-doped p1 or n1 crystals would compensate the effect of boron or phosphorus on the lattice constant [13
16]. Ge co-doping has not been used in crystals for MEMS applications so far. Only one acceptor or donor dopant element is used in one growth, the other acceptor or donor dopants being avoided because their coexistence could cause a shift of resistivity or other, possibly unpredictable, effects. However, unintentional dopants have several potential sources and cannot be totally avoided, although their concentration can be kept at an acceptably low level. For example, small amounts of aluminum and boron dopants originate to the melt and crystal from standard silica crucibles made of natural quartz containing these impurities. Aluminum is an acceptor and, if present at high concentrations on the wafer surface, has been found to influence the growth and quality of oxide layers grown on wafers [17]. Fortunately, the concentrations originating from crystal growing, typically about 1013 Al atoms/cm3, do not yet cause surface-quality problems, although aluminum may have some effect on the resistivity of the wafers if these have very high resistivities. Dopants from earlier runs may also reside inside the furnace chamber and in the hot zone, or even in the seed crystal, and could end up in the next crystals if this risk is not properly taken into account in the crystal-growing procedures. Also polysilicon contains minor amounts of dopants such as boron and phosphorus. All these contributions can become harmful if the resistivity target is very high. The harmful impurities in CZ silicon crystals include carbon, transition-metal impurities (e.g., Fe, Cu, and Ni) [18
21], and alkali and alkali earth metals (e.g., Na). These impurities, as well as accidental dopants, may originate from the starting materials (polysilicon, recycled silicon, if used, and dopants), silica crucible, and materials and contamination of the furnace and the hot zone (see Chapter 2 and, e.g., Ref. [22]). Contamination may also be caused by procedures or mistakes by the operators or malfunction of the crystal-growing furnace. Carbon is electrically inactive in silicon, while transition-metal impurities may form deep impurity levels within the band

58

PART | I Silicon as Mems Material

gap between the conduction and valence bands, behave as recombination centers or as unwanted acceptors and/or donors, or form complexes with dopants under certain conditions. Transition metals are also relatively fast diffusers in silicon at temperatures above room temperature; copper, especially, remains quite mobile even at room temperature. The transition metals, or their precipitates, may decrease the recombination or generation lifetimes and the minority carrier diffusion lengths, and cause leakage currents in the junctions of the devices, lower efficiency of solar cells, quality problems with gate oxides in metal-oxide-semiconductor structures, or even a shift of the resistivity [18,19,21,23]. The exact effect of the metal impurities depends considerably on the metal, its concentration and state, defects formed, and the type and resistivity of the silicon wafer. For example, iron can be very effective in decreasing the recombination lifetime, especially in p-type silicon, while copper is considered to have a greater impact on the lifetime of n-type wafers than on p-type wafers [21].

3.2 TYPICAL IMPURITY CONCENTRATIONS The typical concentrations of a few characteristic impurities in CZ crystals are listed in Table 3.2. The concentration of the specified dopant (or, actually, the resistivity value), as well as the oxygen, carbon, and iron concentrations, are routinely measured. The values indicated are valid for semiconductor-grade crystals, where contamination levels are typically low, and are applicable, especially, for nominal crystal diameters of 4, 5, 6, and 8 in., covering the diameters used in present and near-future MEMS. In most cases, these carbon and metal concentrations of the as-grown crystal are not the limiting factors, considering the success of device processing, and can be tolerated. However, considerably higher contamination concentrations of the crystal are possible in some cases (e.g., in solar-grade crystals) if lower-quality production materials are used for cost reduction, especially if the residual silicon remaining in the crucible after previous growth (so-called “pot scrap”) is recycled into the next charge to replace pristine polysilicon. The solubilities of various elements in silicon crystal at high temperatures can be found in Ref. [26] and references therein, and are among the limitations and mechanisms to be taken into account in crystal growth. The actual concentration of the dopant and other impurities in CZ growth are typically much below their solubility at the melting point of silicon, Tm  1412 C. The solubility in the melt and crystal in the vicinity of Tm may be approached only in the following anomalous cases: (i) The melt, by mistake or by furnace malfunctions,

TABLE 3.2 Typical Range of Concentration of Impurities in Semiconductor-Grade CZ Silicon Crystals, Grown with or without a Magnetic Field Impurity

Typical Concentrations in Crystals

Specified acceptor or donor dopant*

0.02 ppba
2000 ppma

1 3 1012
1 3 1020 cm23

Other acceptors or donors

,1 ppba

,5 3 1013 cm23

Oxygen*

5
18 ppma

2.5 3 1017
9 3 1017 cm23

Carbon

,0.5 ppma

,2.5 3 1016 cm23

Iron

,1 ppta

,5 3 1010 cm23

The concentrations of the impurities denoted by the asterisk (*) are controlled to their optimized and/or specified values, while other impurities are considered to be contamination. Notice that 1.0 ppma corresponds to 5.0 3 1016 atoms/cm3. The interstitial oxygen concentrations are given in “new ASTM units” (ASTM F 121-83 [24]) and carbon concentrations are given in ASTM F 123-86 units [25].

becomes highly contaminated by carbon or some other impurity. (ii) Very large amounts of acceptor or donor dopants are added to the melt to reach resistivities below standard levels. If the solubility limit is reached, particles start to form in the melt, especially at the solid
melt interface, probably causing dislocations in the crystal and making the growing of single crystals impossible [27]. For example, according to our experiments on carboncontaminated crystals, dislocations start to appear in the CZ crystal and its single crystalline structure is lost if the carbon concentration of the crystal reaches approximately 11
13 ppma (concentration is expressed in units of ASTM F 123-86 [25]), in reasonable agreement with the values for the solubility of carbon reported in the literature, suggesting that silicon carbide particles are responsible for the effect. Still, the standard carbon concentrations in commercial crystals are considerably below the solubility limit. Even if the concentrations of impurities in the crystal are below the solubility at Tm, the solubilities start to decrease with decreasing temperature, often leading to supersaturation of impurities in the crystal and wafers at lower temperatures. In fact, this supersaturation becomes the driving force for the later formation and growth of impurity precipitates of oxygen and transition metals, for example, if these precipitates are first able to nucleate. The interstitial oxygen concentration of the crystal Oi can be varied over a relatively wide range by changing the process parameters (e.g., the rotation rate of the crucible, the argon gas mass flow, the pressure inside the furnace, the shape and intensity of the magnetic field, the hot zone structure, and/or the melt height position) as has been discussed in greater detail in Chapter 2 and

Properties of Silicon Crystals Chapter | 3

in Refs. [27
29], and references therein. Oxygen and carbon concentrations are typically measured by using infrared absorption techniques (for more details, see Chapters 4 and 19). The calibration factors used to calculate the concentration from the measured absorption coefficient are not unique. Several different factors have been defined and used, and, thus, the measured or specified values of interstitial oxygen and substitutional carbon should preferably include a reference to one of the standards to make the values exactly defined. In this chapter, we have systematically used the “new ASTM units” (also called ASTM F 121-83 [24], or DIN) for oxygen and ASTM F 123-86 [25] for carbon. The infrared absorption measurement of oxygen or carbon is accurate and practical in lightly doped p- and n-type crystals, and the Oi of these crystals is routinely measured from samples sliced from every crystal; however, the infrared measurement becomes inaccurate or even impossible in highly doped p1 and n1 crystals because of their strong free-carrier absorption. Therefore, other methods, such as gas fusion analysis (GFA) or secondary ion mass spectroscopy, have to be used in such cases (e.g., Ref. [30]). Typical carbon concentrations is about 0.0 ppma in the beginning of the body and few tenths of parts per million atoms in the end of body. Carbon concentration rarely exceeds 0.5 ppma. The carbon in crystals largely originates from polysilicon charge and from the carbon of the graphite parts of the hot zone (for more details on the contamination mechanisms, see Chapter 2). Fortunately, such amounts of carbon have only a relatively minor impact on crystal and wafer quality and can be tolerated, while much higher concentrations could enhance oxygen precipitation in later heat treatments and be harmful [2,8,31
33]. In some cases, even the concentration of 0.5 ppma could enhance the oxygen precipitation [33], while for considerably higher concentrations of greater than 2 ppma, the effect becomes quite clear [31,32]; however, the latter values are not common in semiconductorgrade CZ crystals. Metal impurities are tolerated in even much lower concentrations than carbon in the crystal and may be detrimental in the ppta levels in some cases. For example, the carrier lifetimes that are important parameters in a variety of device structures [1] can be very sensitive to the iron concentration [23]. In lightly boron-doped, p-type silicon, assuming that iron is in iron-boron pairs, the recombination lifetime of the minority carriers (electrons) is limited to the value 23

τðμsÞ  1:5 3 10 =NFeB ðcm Þ 13

(3.1)

where NFeB is the concentration of the FeB pairs (see Ref. [20] and references therein). Also, other impurities, defects, and/or high dopant concentrations (low resistivity)

59

[34] may decrease the lifetime. For example, the lifetime values of p-type (boron-doped) silicon, measured by using microwave photoconductance decay (μ-PCD) method, can exceed 1000 μs only if the resistivity is high enough, at least around 10 Ω-cm, assuming that the metal impurity concentrations are low at the same time. This effect is among factors why high lower limits of lifetime in the specification are not always realistic. For more information about the detection and identification of various metals by using minority carrier recombination lifetime measurements, we refer to Refs. [21,23,35], and, for other metal detection methods, we refer to Ref. [19] and references therein. The target for the iron concentration appears quite challenging at first glance. Fortunately, the crystal strongly rejects typical harmful metal impurities during growing, as discussed in Section 3.3, leading to much purer crystal when compared with the melt, allowing the crystal to reach the low impurity concentrations needed. For example, a typical iron concentration in the order of 1010 cm23 in crystal (see Table 3.2), according to Eq. (3.1), would allow the recombination lifetime to have a sufficiently high value of about 1000 μs in p-type silicon. However, it is important to note that the values indicated above are for the as-grown crystal, while the connection between the initial metal concentration of the crystal and the lifetime in the final device structure is not simple to analyze because of the additional metal contamination and diffusion, precipitation, and/or gettering of metals during wafer and device processing. In fact, the exposure of wafer surfaces to metals in later processing after crystal growing in most cases dominates the metal contamination and should be controlled to tolerable levels, possibly by applying gettering methods [9] to remove the metals from the active surface region.

3.3 CONCENTRATION OF DOPANTS AND IMPURITIES IN AXIAL DIRECTION The concentration of the dopant, carbon, and metal impurities increases along the crystal body. Thus, wafers fabricated using silicon material from different parts of the crystal may behave differently. Much about the axial concentration profile can already be gleaned by closely looking at the normal freezing equation, which expresses the impurity concentration variation as a function of the solidified mass fraction of the melt (g): cs ðgÞ 5 k0 c0 ð12gÞk0 21

(3.2)

Here, c0 is the initial concentration in the melt and k0 is the equilibrium distribution (segregation) coefficient, which has a characteristic value for each impurity in silicon [36] (see Note 1 [37]). In a relatively typical case, the

60

PART | I Silicon as Mems Material

value of g is quite small—a few percent at most—in the beginning of the body, while g  0.9 in the end of the body of the crystal, although the exact values depend on the process details. Table 3.3 gives the distribution coefficients, k0, of some of the most important impurities in silicon. Oxygen has the highest value of k0 of all elements, k0  1 [38], while the dopants and especially the transition metals have lower values of k0 and are rejected by the growing crystal. In practice, to reach exact agreement between the theoretical segregation behavior and experiments, an effective value keff of the distribution

TABLE 3.3 Equilibrium Distribution Coefficient k0 of Typical Impurities in Silicon (see Refs. [26] and [36] and references therein, and Ref. [38] for Oxygen) Element

k0

O

1

B

0.8

P

0.35

Ge

 0.33

As

0.3

C

0.07

Sb

0.023

Ga

8 3 1023

Al

2 3 1023

Na

1.7 3 1023

N

7 3 1024

Cu

4 3 1024

Ni

 1 3 1025
1 3 1024

Fe

8 3 1026

coefficient, slightly different from k0, should be used instead of k0 in Eq. 3.2 (see Note 2 [39]). According to Eq. 3.2, the concentration cs increases (decreases) with increasing g for k0 ,1 (k0 . 1), while cs 5 c0 if k0 5 1. Theoretical concentration curves for a few typical impurities are shown in Figure 3.1. For impurities that have k0 {1 (e.g., transition metals), the shapes of the curve become almost independent of k0 (i.e., cs(g)  k0c0(1
g)21, where k0 is a prefactor only), further indicating that the ratio cs/c0 of the body (g  0.0
0.9) varies in the range of  k0. . .10 3 k0. Thus, in principle, CZ growing is an effective method to purify silicon of impurities with k0 {1. Equation 3.2 predicts the axial concentration profiles correctly only if the impurity does not evaporate from the melt surface and additional impurity is not supplied into the melt during pulling. Considering various dopant elements, boron in p and p 1 crystals and phosphorus in lightly doped, n-type crystals obey Eq. (3.2) with reasonable accuracy. On the other hand, the normal freezing equation is not useful with oxygen which evaporates from the melt surface and is supplied to the melt from the dissolving silica crucible during pulling [28,40]. The equation should also be used with care with carbon and metal impurities, which are, to some extent, supplied to the melt during pulling, or with highly doped n 1 crystals with large concentrations of phosphorus, antimony, or arsenic, which noticeably evaporate from the melt. The oxygen concentration of a crystal preferably should be axially uniform, the values within the given specification, and suitable for the planned use of the wafers. Knowledge about the suitable oxygen concentration range is included in the wafer specification. In lightly doped products, intermediate Oi targets are in the range of 13
15 ppma; however, significantly different targets are also common. The concentration is controlled during crystal pulling (see, e.g., Refs. [27
29,40], and FIGURE 3.1 Concentration of impurities in the crystal versus solidified fraction of the melt, g, calculated from the normal freezing equation. The concentration has been scaled by the initial melt concentration, c0.

1.E+01 1.E+00

cs(g)/c0

1.E−01 1.E−02 k0 = 1 k0 = 0.8 (boron) k0 = 0.35 (phosphorus) k0 = 0.07 (carbon) k0 = 0.0017 (sodium) k0 = 8E-6 (iron)

1.E−03 1.E−04 1.E−05 1.E−06 0

0.1

0.2

0.3

0.4

0.5

0.6

Solidified fraction of melt, g

0.7

0.8

0.9

1

Properties of Silicon Crystals Chapter | 3

61

16 Oi (ppma) (new ASTM)

15 14 13 12 11 10 9 8

Crystal 1 (high Oi) Crystal 2 (low Oi)

7 6 0

0.2

0.4

0.6

0.8

Solidified fraction of melt, g FIGURE 3.2 Experimental oxygen concentrations versus the solidified fraction of the melt, g, in two lightly doped crystals that have different targets for Oi.

Chapter 2) by using proper values for the process parameters for each oxygen target and measurements of the actual result after growth. Examples of the measured oxygen concentration curves of two crystals with significantly different oxygen targets are shown in Figure 3.2. Relatively uniform oxygen concentrations can be achieved in lightly boron-doped p-type and in lightly phosphorus-doped n-type crystals, the typical variation of axial Oi (measured at radius r 5 0) being within 61 ppma from the target value. The dopant has no effect on crystal’s oxygen concentration in lightly boron- or phosphorus-doped p- or n-type crystals; however, according to the literature, in highly boron-doped p 1 crystals, the oxygen concentration may be increased by 20% for similar process parameters [28,40,41], but this shift depends on the process conditions and boron concentration and may also be practically negligible. Moreover, the oxygen concentration is not as easy to accurately measure in p1 or n1 crystals, which also complicates their exact oxygen control. Thus, oxygen control in p1 crystals is less accurate than in lightly doped cases. The precise control of oxygen is even much more difficult in highly doped n1 crystals as the dopant evaporates, which has as a consequence that the evaporation of dopants and the evaporation of oxygen are interrelated and cannot be optimized independently by the process parameters. Furthermore, the oxygen evaporation from n1 melt is enhanced, the evaporating oxygencarrying species typically being oxides of the dopant instead of SiO [42]. Because of these reasons, the oxygen concentrations in n1 crystals are often relatively low and have relatively large axial variation [43]. The carbon concentration in the beginning of the crystals is typically low, about 0.0 ppma, according to the infrared absorption measurements. The carbon

FIGURE 3.3 Striations (dopant density variations) in phosphorusdoped n1 ,100. crystal. Vertical direction is parallel to the growth axis. The area is 800 μm 3 600 μm. The striation period is about 25 μm in this sample.

concentration increases with length at a faster rate than the normal freezing equation (Eq. (3.2)) predicts because of the accumulation of carbon contamination from the atmosphere into the melt during crystal pulling. This additional carbon contamination can be kept at reasonable levels by using suitable hot zone design and growth parameters and procedures, typically leading to low carbon values of less than 0.5 ppma in the end of the body, typically located at g  0.9. In principle, the precipitation of oxygen in the crystal could be enhanced by intentionally adding small, controlled amounts of carbon into the initial charge, but such attempts would lead to relatively unpredictable or uneven results as the wafers from different parts of the crystal would inevitably have very different carbon concentrations. In practice, low carbon concentrations are preferred in the final use of the wafers and, thus, the maximum allowed carbon concentration is quite often given in the wafer specification. In actual crystals, the axial variation of oxygen and dopants is not smooth but includes microscale variation. These striations are caused by fluctuations in the melt flow and/or melt temperature and growth rate of the crystal, and can be revealed by using various methods (see Chapter 2 and Refs [44] and [45]). Figure 3.3 shows an example of dopant density striations in phosphorus-doped n1 ,100. crystal. The dopant density (and corresponding resistivity) striations often show dominating periodicity within about 10. . .150 μm in the growth direction, for example  25 μm in Figure 3.3. Too strong striations can be harmful (e.g., [46]) but proper crystal growth process keeps their amplitudes relatively small, and the striations are not an issue for most applications, including typical MEMS devices.

62

PART | I Silicon as Mems Material

1.E+04 p-type / boron

1.E+03

n-type / phosphorus

Resistivity (Ω-cm)

1.E+02

FIGURE 3.4 Resistivity versus dopant density at 23 C, calculated according to SEMI MF723-0307. The two separate curves correspond to borondoped (p-type) (upper, solid curve) and phosphorus-doped (n-type) silicon (lower, dashed curve).

1.E+01 1.E+00 1.E+12

1.E+13

1.E+14

1.E+15

1.E+16

1.E+17

1.E+18

1.E+19

1.E+20

1.E−01 1.E−02 1.E−03 1.E−04 Dopant density (cm–3)

3.4 RESISTIVITY The resistivity, ρ, and conductivity type (p-type vs. ntype) of crystals are controlled by adding precise amounts of the specified acceptor or donor impurities into the charge before or after melting. It is actually the resistivity that is defined in the wafer specification instead of dopant or charge carrier concentration because the resistivity can be measured relatively easily and accurately. The resistivity and carrier concentrations are connected by the following equations [1]: ρ 5 ðqμp pÞ21

for p-type silicon; and

ρ 5 ðqμn nÞ21

for n-type silicon

(3.3a) (3.3b) 219

where q is the elementary charge 1.602 3 10 C, μp (μn) is the mobility of holes (electrons), and p (n) is the density of holes in the valence band (electrons in the conduction band). The mobility values of Eqs 3.3a and 3.3b are not constants, but instead are dependent on the dopant densities, mainly at high concentrations of much greater than 1015 cm23. The carrier concentration induced by the doping is approximately equal to the dopant density for the typical dopant elements and densities. In the lightly doped region, at concentrations of less than 1016 cm23, the resistivities at 23 C are approximately (based on SEMI MF723-0307 [47]) ρ ðΩ-cmÞ  1:3 3 1016 =NA ðcm23 Þ for boron-doped; p-type silicon; and

(3.4a)

ρðΩ-cmÞ  4:5 3 1015 =ND ðcm23 Þ for phosphorus-doped; n-type silicon

(3.4b)

Here, NA (ND) is the boron (phosphorus) concentration. The simple Eqs. 3.4a and 3.4b are only for the lightly

doped case; they have relatively limited accuracy at higher concentrations. A more general and accurate correlation between the resistivity and dopant concentration, valid in lightly and highly doped p-type and n-type silicon, can be presented by using parameterized functions, which can be found in SEMI MF723-0307 [47], together with the references to the experimental data on which the fit is based. The resulting accurate curves are shown in Figure 3.4 and are basically for boron and phosphorus, although the latter curve is also a relatively good approximation for antimony and arsenic. The correlation is very practical as it allows the calculation of the axial resistivity profile if the axial concentration profile is known (e.g., from the normal freezing equation) or, correspondingly, the axial concentration profile if the axial resistivity variation is known (e.g., from resistivity measurements). Figure 3.5 shows typical examples of experimental resistivity curves of lightly boron- and phosphorus-doped, p- and n-type crystals, indicating a larger resistivity variation along the crystal for the dopant with a smaller value of k0 (i.e., phosphorus in this case) (see Table 3.3). The actual curve shapes can be explained and analyzed by using the relationship of SEMI MF723-0307 [47] and the normal freezing equation (see Eq. (3.2)). The resulting fitted values of the distribution coefficients, denoted by k in the figure, are quite close to the values of k0 in Table 3.3. As a rule of thumb, the concentration of boron in p- or p 1 -type (phosphorus in n-type) crystals will vary by a factor of about 1.6 (  4.5) within the typical body length of g  0.0 to g  0.9 in CZ growth because of normal freezing behavior. According to Eqs. (3.4a) and (3.4b), the resistivity will vary along the body by approximately the same factors as given above for the dopant concentrations. The resistivity in lightly boron- or

Properties of Silicon Crystals Chapter | 3

10

100 Fraction of body within specification (%)

9 Resistivity (Ω-cm)

63

8 7 6 5

Resistivity p-type (boron) Resistivity n-type (phosphorus) Theory for boron (with k = 0.77) Theory for phosphorus (with k = 0.34)

4 3 2 0

0.2

0.4

80

p-type / boron n-type / phosphorus

60 40 20 0 1

0.6

0.8

1.5

2

2.5

3

3.5

4

4.5

5

Resistivity ratio of specification

Solidified fraction of melt, g FIGURE 3.5 Experimental axial resistivity variation in typical p-type (boron-doped) and n-type (phosphorus-doped) crystals presented as a function of g in the body. The solid and dashed curves are obtained by fitting the normal freezing equation to the resistivity curve shape. The fitted values of the distribution coefficients are given in the figure.

phosphorus-doped crystals approximately obeys the following equation: ρðgÞ  ρðg 5 0Þ 3 ð12gÞ12k0

(3.5)

Depending on the dopant element and the resistivity specification, which defines the upper (ρmax) and lower (ρmin) limits of the resistivity allowed for the wafers, either the whole crystal or only part of it is within the resistivity specification, the latter case giving a lower commercial crystal yield and higher cost per wafer. Figure 3.6 shows the fraction of the body within the resistivity specification as a function of the ratio ρmax/ρmin of the limits of the resistivity specification. The curves of Figure 3.6 are approximations calculated by using Eq. 3.5, assuming that the resistivity in the beginning of the body at g  0.0 is accurately adjusted to be equal to ρmax and the body ends at g  0.9. Although the model in Figure 3.6 is an approximation, it already describes the main trend. The optimal case, with 100% of the body in the specification, is only reached for a specification that is wide enough (see Note 3 [48]). For example, for a resistivity specification 8.0
14.0 Ω-cm (i.e., for ρmax/ρmin 5 14.0/8.0 5 1.75), Figure 3.6 suggests that the whole body of a boron-doped p-type crystal can be adjusted to be within the specification, while only about 60% of the body of a phosphorusdoped n-type crystal is within the requested range for a similar specification, while the rest of the crystal would be unfit. The different shapes of the curves give a natural explanation for the fact that relatively wide resistivity specifications are preferred for phosphorus-doped wafers, while considerably narrower specifications are possible for boron-doped wafers. Dopants with k0{1 (e.g., gallium, which is only rarely used), would result in an even larger

FIGURE 3.6 Fraction of body within resistivity specification in boronor phosphorus-doped crystals. Here, the resistivity ratio is defined as the ratio ρmax/ρmin between the upper (ρmax) and lower (ρmin) resistivity limits allowed by the wafer specification.

resistivity variation compared with that of boron or phosphorus [3]. In highly doped n1 crystals—doped with antimony, arsenic, or phosphorus—the resistivity curves cannot be predicted by using Eq. 3.2. This is because the resistivity curves of n1 crystals are contributed by dopant evaporation from the melt, which depends on the dopant element and the process parameters, such as argon gas mass flow, the pressure of the chamber during pulling, the hot zone design, and the dopant concentration in the melt. Therefore, the enrichment of dopants in n1 crystals is slower and the axial resistivity variations smaller than the normal freezing equation would suggest [27,49], which results in a narrower distribution of resistivities within a crystal (see Figure 3.7), which is largely beneficial considering the quality of the wafers. In extreme cases, the resistivity may even increase with the body length position in n1 crystals if evaporation is very strong [27], but this process region is typically not used. The resistivity curve shape and the parameters effecting dopant evaporation in n1 crystals are often optimized experimentally, although simple parametrized evaporation models can also be used, for predicting the resulting resistivity curves in some accuracy, prior to actually testing a process change. Most of the lightly doped CZ crystals have resistivity targets somewhere between 1 and a few tens of ohm-centimeter in the beginning of the body. The highest and lowest resistivities achievable in CZ crystals are far beyond this range in both directions, and depend on the dopant and process conditions. A variety of resistivities have been used in MEMS, from low-resistivity p1 and n1 wafers to very high-resistivity p2 and n2 wafers. If the resistivity target is too low compared with the capability of the growth process, it becomes impossible to grow the crystal without dislocations.

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PART | I Silicon as Mems Material

1.25 Beginning of crystal

1

End of crystal

0.8 0.6

1.15 1.10 1.05

0.4

1.00

As (n+) (no evaporation) As (n+) (with evaporation) Sb (n+) (no evaporation) Sb (n+) (with evaporation)

0.2

6 in. p<100> 6 in. n<111>

1.20 Scaled resistivity

Resistivity/Resistivity at g = 0

1.2

–75 –60

–45 –30

0.95 –15 0

15

30

45

60

75

Radius (mm)

0 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Solidified fraction of melt, g FIGURE 3.7 The figure indicates the theoretical result of the normal freezing equation for antimony- and arsenic-doped crystals and, schematically, the behavior with evaporation. Note that the latter curves, which include evaporation, are not unique, but will vary if any process parameters or conditions affecting evaporation are changed.

Constitutional supercooling is among the mechanisms limiting the lowest resistivity [50,51], and its occurrence is theoretically relatively well understood. Typically, the lowest resistivity specifications for highly doped 6 in. crystals are below 3 mΩ-cm for boron and arsenic, below 1.5 mΩ-cm for phosphorus, and below 17 mΩ-cm for antimony. These lowest resistivities are, as a general rule, used in the fabrication of power devices, for example, power MOSFET’s, while they are not very common in MEMS. Even resistivities below 1 mΩ-cm are available in the market for boron and phosphorus but only in limited amounts. The highest resistivities achievable in CZ crystals are above a few kilo-ohm-centimeters and are only reached by carefully controlling the purity in order to avoid unintentional dopants. Nowadays, the high-resistivity CZ wafers compete with FZ wafers in applications where high-resistivity substrates are essential.

3.5 RADIAL VARIATION OF IMPURITIES AND RESISTIVITY The measured or specified value of the resistivity or oxygen concentration typically refer to the value at the radius r 5 0 unless otherwise defined, and describes accurately only a fraction of the wafer area, missing the periphery area. The dopant and oxygen concentrations typically decrease, and resistivity increases, toward the wafer edge, the resistivity in most cases showing U- or W-shaped curves along the diameter as shown in Figure 3.8. This radial dependence of the dopant concentration adds to the

FIGURE 3.8 Resistivity profiles of lightly boron-doped 6 in. p ,100. and lightly phosphorus-doped 6 in. n ,111. crystals, scaled by the resistivity at r 5 0. The differences between the two curves are due to different dopants and orientations.

2 Oxygen gradient (%)

0

–100

0 −2 −4 8 in. p<100>, Process A 8 in. p<100>, Process B

−6

–75

–50

–25

−8

0

25

50

75

100

Radial position (mm) FIGURE 3.9 Measured radial variation of oxygen in lightly borondoped 8 in. p ,100. crystals grown by using different process parameters. Here, the oxygen gradient, defined later in Eq. (3.6b), is expressed as a function of the radius of the measurement point.

variations of properties of the devices if these are sensitive to the charge carrier density and resistivity of the substrate. Large radial variations in oxygen may result in large variations in oxygen precipitation behavior and gettering efficiency or a greater risk of slip formation during thermal cycles. The amount of radial variation of dopants and oxygen also shows dependence on the body length position in the crystal due to the corresponding changes in the process parameters, the amount of the remaining melt, and the melt flow characteristics. The radial profiles also vary to some extent from one wafer to the next because the profiles are contributed by varying concentration striations [44,45]. Examples of the experimental curves for resistivity and oxygen are shown in Figures 3.8 and 3.9, respectively.

Properties of Silicon Crystals Chapter | 3

65

1.3 Crystal a Scaled resistivity

1.2

a

b

b

1.1 Melt Isotherm Facet

1.0 6 in. n+ (100) (As)

0.9

–75 –60 –45

0.8 –30 –15 0

6 in. n+ (111) (As) 6 in. n+ (111) rescaled by 0.87

15

30

45

60

75

Radius (mm) FIGURE 3.10 Resistivity profiles of As-doped 6 in. n 1 ,100. and ,111. crystals, scaled by resistivity at r 5 0. The difference between the orientations is due to the {111} facet in ,111. orientation, more clearly seen after the curve for ,111. is rescaled by a factor of 0.87.

Relatively high crystal rotation rates and suitable values for other parameters affecting the mixing of the melt and its concentration variations are essential for reaching tolerable radial variation in the crystal, although a certain amount of radial inhomogeneity still remains. The radial resistivity variation is affected by the dopant and orientation, and relatively different radial profiles are obtained for different products. For example, the variation is greater in phosphorus-doped (n-type) versus boron-doped (p-type) crystal of the same orientation. In fact, the variation is often greater for the dopants that have lower k0 values, because a small k0 allows and gives rise to greater variations in the effective value keff in the radial direction, while the impurities with k0  1 (such as boron with k0  0.8 or oxygen with k0  1) could lead to better radial uniformity. In fact, in borondoped p ,100. crystals, the radial variation of the resistivity is only a few percent (see Figure 3.8). On the other hand, as shown in Figure 3.9, the oxygen concentration typically decreases with r due to evaporation of oxygen-containing species from the melt, which leads to lower concentrations at the melt surface and in the melt close to the crystal edge than in the melt below the crystal at r  0, where the melt is more protected by the crystal from oxygen evaporation. Evaporation may also contribute to some extent to the radial resistivity variations for the dopants antimony, arsenic, or phosphorus in n1 crystals. In n 1 crystals, the concentration of antimony, arsenic, or phosphorus will decrease and resistivity will increase significantly with increasing r (see Figure 3.10). Furthermore, ,111. -oriented crystals often have greater radial variation in the resistivity than corresponding ,100. -oriented crystals (see Figure 3.10). This

FIGURE 3.11 Formation of a {111} facet in the center of the meltcrystal interface in a ,111. -oriented crystal. The facet is only formed if the isotherm of the melting point (T 5 Tm) is convex in the center region and the crystal orientation is ,111. (see the figure on the left). The facet results in a lower-resistivity region (b) in the core of the crystal and wafers compared with the surrounding “normal” area (a) as shown in the figure on the right.

difference is due to the formation of a planar {111} facet in the center of the growth interface of the ,111. crystal during growing [27,52,53], as schematically presented in Figure 3.11. The {111} facet region has a larger effective distribution coefficient than the surrounding interface (for impurities with k0 , 1) because of the fast lateral growth of atomic layers in the {111} facet. This increase in the intake of the dopant leads to a lower-resistivity region in the center of the crystal and wafers. However, we should point out that the facet is formed in the center of a ,111. crystal only if the isotherm of the melting point is convex toward the melt in the center of the growth interface. The facet, in such cases, is due to the difficult nucleation of the close-packed {111} plane, which needs a considerable amount of undercooling to form [52,53]. In other cases, such as ,111. crystals with a concave interface, or ,100. or ,110. crystals with either a convex or a concave interface, no facet is formed in the center and the radial resistivity profiles remain practically independent of the orientation. Figure 3.10 shows experimental data on a 6 in. n 1 ,111. crystal in which a {111} facet has decreased the resistivity in the crystal core due to an increase in the value of keff for arsenic by a factor of more than 1.1 in the facet. This effect can lead to considerable radial variation in the resistivity of n 1 ,111. crystals. Also, the resistivity profile of the lightly doped 6 in. n ,111. crystal in Figure 3.8 has a contribution from a facet, which, in this case, has a radius of close to 20 mm. Contrary to the case of dopants and resistivity, a ,111. facet has practically no effect on oxygen concentration. Thus, in lightly doped crystals, the radial oxygen variation is almost independent of the crystal orientation, whether it is ,100., ,111., or ,110., and also independent of the dopant. The radial oxygen or resistivity variations in silicon wafers are often described or specified by “gradient” values, which are defined as the relative change in

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PART | I Silicon as Mems Material

resistivity or Oi from the center (r 5 0) to a certain radius value (r) closer to the edge, that is (3.6a)

Oxygen gradientð%Þ 5 100 3 ½Oi ðrÞ 2 Oi ðcenterÞ=Oi ðcenterÞ

(3.6b)

For example, for oxygen gradient, the measurement point r defined in wafer specifications is typically 10 mm inward from the wafer edge. Thus, r 5 65 or 90 mm in the measurements for a wafer diameter of 150 or 200 mm, respectively (see SEMI MF951-0305 [54]). The typical absolute value of the measured oxygen gradient in lightly doped ,100., ,111., or ,110. crystals is about 5% or less for the standard measurement position. (In n 1 crystals, the oxygen gradient values are often much higher but are not routinely measured.) In wafer specifications, the absolute values of the gradients in Eqs. (3.6a) and (3.6b) are typically limited to a certain range. Further variations in resistivity and oxygen take place even up to the crystal surface, as shown for oxygen in Figure 3.12, where the relative shift in Oi (i.e., the oxygen gradient) is indicated as a function of r in Eq. (3.6b). In this particular case, the gradient for r 5 65 mm was  4%, but it increased considerably if measured closer to the crystal edge. Oi at r  75 mm was about 14% (or  2 ppma) below Oi at r 5 0. The region very close to the edge has the largest gradient values but is also more difficult to measure accurately and is not routinely studied. Also note that the excess diameter of the crystal relative to the diameter specified for the wafer (i.e., some of the material with the highest gradient) is removed by grinding, which slightly improves the quality. The radial variations in the resistivity and oxygen are the ones most accurately controlled and specified among the impurities. However, also other impurity concentrations have radial dependence. For example, the iron concentration may increase and, correspondingly, the recombination lifetime in p-type crystal (Eq. (3.1)) decreases in the vicinity of the crystal surface, while the core maintains a higher purity. The drop of lifetime can be seen in standard lifetime maps. This increased contamination has been found to originate, to large extent, from the diffusion of iron from the furnace atmosphere directly into the hot crystal surface during growth [55]. The surface region influenced most has a depth in the order of 10 mm in these cases. Figure 3.13 shows an example of radial variation of measured recombination lifetime and Fe concentration close to the edge of a 6 in. p ,100. crystal. Very close to the edge lifetime is around 100 μs and Fe concentration 1 3 1011 cm23. The clear correlation between the measured lifetime and Fe concentration indicates that Fe is the main reason for the drop of lifetime near the edge, see Eq. 3.1.

–2 Oxygen gradient (%)

Resistivity gradientð%Þ 5 100 3 ½ρðrÞ 2 ρðcenterÞ=ρðcenterÞ

0

–4 –6 –8 –10 –12 –14 –16 –18 65

70

75

Radial position (mm) FIGURE 3.12 Relative shift in Oi in the vicinity of the crystal edge compared with Oi at r 5 0. The results are for a 6 in. p ,100. crystal with a diameter of 157 mm (radius 5 78.5 mm) and Oi(r 5 0)  13.6 ppma. Note that during further processing of the crystal into wafers, the radius in excess of 75 mm is removed. The actual results are indicated by symbols, while the dashed line is only a guide for the eye.

3.6 THERMAL DONORS Thermal donors (oxygen donors) are a class of several species of electrically active oxygen complexes, consisting of small aggregates of a few oxygen atoms [56,57]. Thermal donors are important defects as they are quite common in CZ silicon and may have a harmful and unpredictable/unstable effect on the resistivity and even the conductivity type of lightly doped crystals and wafers if the thermal donors are not properly taken into account. The carrier concentration will be decreased (increased) by the amount of electrons added by the thermal donors (ΔnTD) in p-type (n-type) crystals, leading to a corresponding increase (decrease) in the resistivity. In extreme cases, if ΔnTD exceeds the initial hole concentration of a p-type material, a change in the conductivity type from p to n takes place, and the resistivity becomes defined by the remaining electrons. The most important thermal donors to be considered in crystal growth are the species formed at relatively low temperatures, at 300
500 C, especially around 450 C, while the species formed at higher temperatures are less important, and are not discussed further here. The concentration of thermal donors depends on the interstitial oxygen concentration Oi and the time spent at the critical temperatures during cooling of the crystal or during subsequent heat treatment of wafers [56,57]. The generation rate of thermal donors is highest at  450 C, while already considerably lower at 400 C or 500 C, and is proportional to Oni where n  4 at 450 C (i.e., the generation is relatively strongly depending on the oxygen concentration). In FZ silicon, practically no thermal donors are

Properties of Silicon Crystals Chapter | 3

67

900 800 700

Lifetime (µs)

600 500 400 300 200 100 0 0

10

20

30

40

50

60

70

80

70

80

Distance from crystal edge (mm) 1.8E+11

Fe concentration (cm–3)

1.6E+11 1.4E+11 1.2E+11 1E+11 8E+10 6E+10 4E+10 2E+10 0 0

10

20

30

40

50

60

Distance from crystal edge (mm) FIGURE 3.13 Recombination lifetime of minority carriers (a) and Fe concentration (b) of a 6 in. p ,100. crystal as a function of the distance from the crystal edge. Special samples sliced perpendicular to the crystal radius were used to increase the accuracy of measurements near the crystal edge. Measurements were performed by using the μ-PCD method. Fe concentration was estimated by using the method presented in Refs. [23,35].

PART | I Silicon as Mems Material

1200

Crystal temperature (°C)

formed as Oi  0 ppma, while in CZ silicon, the Oi level has an important effect on their formation rate. The donor concentration increases approximately linearly with the time spent at the formation temperature, although it may finally saturate and even start to decrease after prolonged treatment [57]. According to Ref. [58], the formation of thermal donors is enhanced (suppressed) in heavily doped, p-type (n-type) silicon with a dopant concentration greater than 1016 cm23. However, the intentional dopant concentration in highly doped crystals typically exceeds the thermal donor concentration considerably and, thus, thermal donors have no detectable effect on the resistivity of p 1 or n 1 crystals. The crystal will always experience the 450 C region during the growth process as the crystal cools from the melting point of 1412 C toward room temperature. The temperature versus time behavior during growth (i.e., the thermal history) is a property of each particular CZ growth process. Figure 3.14 shows an example of thermal history curves [7] where, as usual, the beginning of the body has experienced a longer thermal history than the end part. According to a simple model, the thermal donor concentration in the asgrown crystal is approximately inversely proportional to the cooling rate at around 450 C. The critical temperatures of 400
500 C are also encountered during later processing of the wafer and/or devices. In practice, the concentration of thermal donors in the crystal after growing is often large enough to have a detectable or even major effect on the resistivity of lightly doped p- or n-type wafers. The added electron concentration ΔnTD may exceed 1015 cm23 after crystal growth at relatively high Oi’s, although ΔnTD is much smaller for low Oi’s. The highest ΔnTD and the greatest effect on the resistivity are typically found in the beginning of the body, which has a longer thermal history than the end part, although any axial variation in Oi also contributes [7,27]. Figure 3.15 shows an example of the resistivity behavior of a p-type crystal in which the boron acceptors are partially compensated by thermal donors after crystal growth, after letting the crystal cool down to room temperature. The beginning of the body of the as-grown crystal, especially, is almost fully compensated and has a high resistivity. An analysis of the resistivity shift shown in Figure 3.15 leads to the following values of the added electrons: ΔnTD  2 3 1015 cm23 in the beginning of the body and ΔnTD  5 3 1014 cm23 in the end of the body. The results suggest that for this crystal, the body region before 600 mm has experienced a much longer thermal history at the critical formation temperatures compared with the region after 1200 mm, in agreement with the expected as well as simulated differences in the thermal history of the various crystal parts. A comparison of the value ΔnTD  1015 cm23 and Oi  15 ppma 5 7.5 3 1017 cm23

1000

Seed section

800

600 Tail section 400 0

2

4

6

8

10

Time after solidification (h) FIGURE 3.14 Measured thermal history of a 6 in. ,100. crystal. Time of 0 corresponds to the moment of solidification at the melting point. The curves are from [7], reproduced by permission of ECS
The Electrochemical Society.

1.E+03 Before donor killing After donor killing

Resistivity (Ω-cm)

68

1.E+02

1.E+01

1.E+00 0

200 400 600 800 1000 1200 1400 1600 1800 Length position (mm)

FIGURE 3.15 Resistivity versus length position in the body of a boron-doped p-type crystal. The resistivity has been measured before (upper curve) and after (lower curve) thermal treatment (“donor killing”) of the samples at 650 C, eliminating the thermal donors. The effect of thermal donors is greatest in the beginning of the body. The interstitial oxygen concentration of the crystal is about 15 ppma in new ASTM units. (The lines connecting the points are only guides for the eye.)

indicates that only a minor fraction of oxygen has formed thermal donors, as expected. To prevent the effects of thermal donors, it has been a common practice to heat-treat lightly doped p- and n-type wafers at about 650 C for at least some tens of minutes during wafer fabrication [59]. The treatment at above

600 C will effectively eliminate the thermal donors [58] as indicated by the resistivity curves in Figure 3.15. Cooling the wafers relatively quickly from 650 C through the 450 C region to room temperature after the “donorkilling” treatment leaves the thermal donors no time to reform, and the subsequent resistivity values and conductivity type will be defined by the “stable,” intentional dopant element boron or phosphorus only. In principle, thermal donors may also be formed or eliminated, even multiple times, during any subsequent wafer or device processing step at around 450 C or above 600 C, respectively. The relative shift of the resistivity (Δρ/ρ), caused by the thermal donors, becomes increasingly probable if the wafer has a very high resistivity, for example, above 100 Ω cm or even much higher. For this reason, in highresistivity wafers Oi is typically kept low and annealings near 450 C in the last steps of device fabrication are avoided. In extreme cases, the thermal donors existing after finishing the processing may cause quality problems or failure of the devices if the remaining resistivity shift is large enough to harm the device properties. For example, the threshold voltage of metal-oxide-semiconductor fieldeffect transistors, processed on lightly doped substrates, can shift due to thermal donors [60]. If the type of a boron-doped substrate permanently changes from p to n due to thermal donors, this will ruin the electrical properties of intended p-n junctions to the substrate [1], if such junctions exist in the design and are essential for the operation of the device. Note also that Oi in the wafer may decrease from its initial, crystal-originated value during device processing as a result of oxygen out-diffusion (typically due to denuded zone (DZ) formation) or precipitation [59,61], or Oi may possibly even increase because of oxygen in-diffusion [62]. These changes in Oi have an effect on subsequent thermal donor formation in the regions of the wafer where Oi has shifted (i.e., close to the surface for out-diffusion and in the bulk for precipitation) [59,61]. There are also other type of mechanisms, connected with oxide interfaces, shifting the carrier concentration in high-resistivity substrates [63].

3.7 DEFECTS IN SILICON CRYSTALS A large variety of grown-in and process-induced defects have been identified in CZ silicon crystals and wafers (see, e.g., Refs. [2,8,27,64]). Some of the defects are directly connected to the success or failure of the crystal growth process or defined by the growth parameters, while other defects are contributed or dominated by the following process steps from crystals into wafers and, finally, into devices. Also the ease of detection of the defects varies from simple visual inspection of crystals to more difficult or indirect methods. Crystal defects can

Temperature (°C)

Properties of Silicon Crystals Chapter | 3

1400 1300 1200 1100 1000 900 800 700 600 500 400 300

69

Vacancies, self-interstitials, OISF ring radius (1412°C)

Voids (vacancy clusters) (1000–1150°C) Dislocation loops (self-interstitial clusters) (1000°C)

Nuclei for oxygen precipitation (500–800°C) Thermal (oxygen) donors (450°C)

0

1

2

3

4

5

6

7

8

9 10 11 12 13

Time from solidification (h) FIGURE 3.16 Thermal history of a crystal (the timescale starting from the moment of crystallization) and the formation temperatures of various defects during crystal growth. The formation temperatures indicated are approximate consensus values collected from the literature. (The thermal history curve is only schematic.)

also be classified according to their dimensionality into point defects, line defects, area defects, and volume defects (see Chapter 1). We will concentrate on those defects that can have a direct connection to the crystal growth and its process parameters, defects that are important considering the intended use of the wafers, and are, in many cases, also measured regularly. Such defects include (slip) dislocations, twins, bubble inclusions, vacancies and their aggregates (octahedral microscopic voids that can be detected, for example, as crystal-originated particles (COPs), on the wafer surface), self-interstitials and their aggregates (large dislocation loops), stacking faults (SFs) formed near the wafer surface by oxidation treatments (i.e., oxidationinduced stacking faults (OISFs, or OSFs)), oxygen precipitates, bulk SFs, and dislocation loops. Among these defects, SFs and dislocation loops are often caused by oxygen precipitates (see Section 3.9 and Chapter 19). Some of the typical defects found in crystals and wafers have a strong correlation to the thermal history of the crystal during its growth (see Figure 3.16 where the dominating formation temperatures of defects [8,33,57,64
68] are approximately indicated). The effect of the defects on the properties and yield of devices processed on the wafers are characteristic to each particular process and application, although certain general trends and risks can be indicated. The defects may lead to failure or to decrease of the quality of devices or, more specifically, to a decrease of carrier lifetimes (e.g., metal or oxygen precipitates), an increase of leakage currents in devices (e.g., metal precipitates, dislocations, or SFs), or quality problems with gate oxides (e.g., voids or other defects such as metal precipitates near the wafer

70

PART | I Silicon as Mems Material

surface) [2,19,20,23,69]. Decoration of dislocations or SFs by metal impurities may further increase the detrimental influence of these defects on the junctions of the devices. Considering MEMS fabrication, defects such as oxygen precipitates and SFs may increase the surface roughness and decrease the anisotropy in anisotropic wet etching [70,71]. Therefore, in MEMS wafers, the highest oxygen concentrations are avoided to suppress the formation of oxygen precipitates and associated defects, especially if wet etching is used to form the structures for the sensors. Furthermore, considering optimized crystal properties and the control of defects, special wafers (e.g., silicon-on-insulator wafers (see Chapter 7)) often have slightly different requirements and quality risks compared with the more ordinary wafers. Short descriptions of the typical defects in CZ silicon are given from the point of view of crystal growth in the list below, while we refer to the literature for more detailed information. Dislocations and slips: The dislocations are line defects, which in silicon lie on the {111} slip planes. The word “slip” is used to denote the formation and propagation mechanism of dislocations, as well as the visually detectable lines formed on crystal or wafer surfaces by a large number of dislocations. The CZ single crystals are grown as dislocation-free, although, sometimes, due to a disturbance at the melt-crystal interface and/or high thermal stress in the crystal, dislocations may appear, multiply, and propagate in the crystal during growth. The crystal after this point soon becomes multicrystalline [27,72]. Dislocations are also spread backwards to the already-formed crystal within a characteristic distance of the same order of magnitude as the crystal diameter, while the even earlier region still remains dislocation-free [73]. (In some rare, exceptional cases of highly borondoped p 1 crystals, dislocations have been found to propagate along the body without causing polycrystallization [16], contrary to the general behavior.) Dislocations in wafers could have a negative impact on the device yield, and wafers with dislocations already in the beginning also suffer from further dislocation generation more easily than dislocation-free wafers. Therefore, the dislocated, as well as the even worse, multicrystalline parts of the crystal are rejected from further processing into wafers, which correspondingly decreases the crystal yield. Fortunately, most of the crystals are dislocation-free through the whole body. Furthermore, it is relatively easy to detect the position where the dislocations first appeared during growth as the crystal shape changes, especially as its characteristic growth lines are cut and disappear starting from the position where the dislocations appeared [72]. The reason for this external shape change is that the dislocations decrease orientation-dependent differences in the growth at the growth interface [52]. More specifically, small

{111} side facets at the edge of the interface, responsible for growth-line formation, shrink and, finally, disappear due to dislocations, which also ends the growth lines. Visual inspection of the crystal, especially the continuity of the growth lines and the existence of slip lines on the surface, is among the basic quality control methods used for material quality verification. A crystal experiences high thermal stresses during growth [73] but the crystal reaches a low-stress state after it has cooled to room temperature if there are no dislocations (i.e., no plastic deformation). Only some marginal stresses remain in the as-grown, dislocation-free crystal, and are caused by nonuniform distribution of dopants or oxygen, or by defects. Later processing of the wafers may cause formation of a variety of defects and, correspondingly, increase of the stresses [74]. Although only dislocation-free material is processed into wafers, which are, thus, initially dislocation-free, the strength of the wafers against the slip formation and plastic deformation in later high-temperature processing is increased by interstitial oxygen, while formation of large oxygen precipitates exposes the wafers to slip generation [8,75]. The risk of such plastic deformation can be reduced by selecting the target of Oi properly (although other requirements for oxygen also have to be taken into account) and by keeping the axial and radial variations of Oi within reasonably tight limits. In addition to oxygen, dopants at high concentrations have an impact on dislocation generation. According to Ref. [5], concentration of boron, phosphorus, or arsenic in excess of 1019 cm23 (resistivity in the sub 10-mΩ-cm region) increases the critical stress for dislocation generation. Twins: A twin in silicon crystal corresponds to a defect where the lattice is changed to its mirror image on the other side of a {111} plane, called a “twinning plane” [76]. In ,100. and ,111. crystals, the vector perpendicular to the twinning plane is inclined with the growth axis by an angle of about 54.7 or 70.5 , respectively, while in ,110. crystal, the angle is either 35.3 or 90.0 , the latter case corresponding to a twinning plane parallel to the crystal axis. Twins may be found after the CZ silicon crystal has lost its single-crystalline structure and is becoming multicrystalline. They are also sometimes seen even without the loss of structure, although quite rarely. The twins are not allowed in wafers because the twin boundary and the shift of the crystal orientation would probably lead to failure of devices. Thus, the unfit region, where the twinning plane penetrates the crystal, is rejected as well as any misoriented material. Bubble inclusions: Relatively large, approximately spherical pits, with sizes up to several millimeters, are occasionally seen on wafer surfaces. These pits originate from small volumes of gas (e.g., argon) remaining as bubbles in the melt after melting [2]. Also, gases in silica

Properties of Silicon Crystals Chapter | 3

FIGURE 3.17 Photograph of a 6 in. wafer rejected after slicing due to a large bubble inclusion.

crucibles [77] or gases originating from post-melting doping or silicon feeding procedures [78] can sometimes contribute to the pocket formation. Some of the bubbles may remain in the melt, possibly at the melt-crucible interface, for quite a long time and finally become transported with the melt flow to the melt-crystal interface where the silicon solidifies around the bubble, causing a void. During this overgrowth process, the bubble causes a minor, local disturbance in the temperature and growth rate near the bubble, but the crystal remains dislocation-free. Notice that contrary to bubbles, solid particles (e.g., of SiO2, SiO, graphite or SiC) very easily generate dislocations and lead to loss of single-crystalline structure, if particles in the melt do not have enough time to dissolve, and are able to reach the growth interface and become trapped as inclusions into the growing crystal [2,27,79]. The reason for the dislocation formation is that the surface of the particles interacts but is not compatible with the silicon lattice, and the overgrowth cannot produce perfect silicon crystal. Wafer slicing, lapping, grinding, etching, or polishing may reveal the in-grown bubbles as air pockets on the wafer surface or as holes through the wafer, the latter case being shown in Figure 3.17. Fortunately, the incidence of bubbles in wafers can be kept at a very low level by using suitable crystal-growing and wafer-inspection procedures, and bubble inclusions are typically not a major quality issue. The rare wafers with large open pockets of sizes of the order of 1 mm are relatively easily detected and identified by the eye and are rejected in

71

wafer fabrication, while much smaller pockets may contribute to the defect count in the final surface inspection [80]. However, hidden voids in the bulk of the wafers pass the tests and may sometimes cause local yield losses in device processing, especially if the bubble becomes open after removal of material from the wafer surface. Vacancies and self-interstitials and their clusters: The vacancy- and self-interstitial-related defects have a strong connection to the process conditions used during crystal growth [64,66,67,69,81] and will be discussed in more detail in Section 3.8 below. OISFs: The OISFs are generated by silicon selfinterstitials injected into the wafer during oxidation of the wafer surface. An OISF test, either a standard one (e.g., SEMI MF1727-0304 [82], SEMI MF1810-0304 [83]) or a test representative of the oxidation cycles in a particular fabrication process, is used to determine a well-defined value for the OISF concentration of the sample wafers. The result has correlation with the tendency of the wafers to form OISFs during oxidation steps during actual device processing. Figure 3.18(a) shows an example of OISFs revealed on the surface of a phosphorus-doped n ,100. wafer. The OISFs are formed as the injected selfinterstitials agglomerate into SFs of an extrinsic type between two adjacent {111} planes, the defects being bound by Frank partial dislocation loops [2,27]. The defects in Figure 3.18 can be seen in positions where SFs intersect the wafer surface. The lines of the defects on the surface of ,100. wafers have two possible directions, which have an angle of 90 between each other, while OISFs in other wafer orientations have their characteristic angles. The OISFs preferably nucleate at defects such as metal precipitates, mechanical defects or damage, or oxygen precipitates if these exist in the wafer [2], and the OISF density may reflect the quality of the crystal, as well as the effects of further processing steps prior to the OISF test. It is quite common for the users of the wafers to specify the upper limit for the OISF density of the wafers (e.g., 100 OISFs/cm2). The actual concentration of OISFs in boron-doped p ,100. wafers is typically on the order of 1 cm22 after a standard OISF test, while slightly higher values are often found in phosphorus-doped n ,100. wafers, especially in those taken from the region close to the tail of the crystal. On the other hand, the OISF concentrations in n1 crystals doped with antimony, arsenic, or phosphorus are low. The reason for the higher OISF density in lightly phosphorus-doped, n-type material is still unclear to a certain degree, but the increment seems to be contributed, for example, by the thermal history of the end part of the crystal. Furthermore, impurities may play a role here and the addition of copper into the melt has been found to increase, and aluminum possibly to decrease, the OISF density in phosphorus-doped, n-type crystals [84].

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The OISFs can either be distributed relatively evenly over the wafer surface or the distribution may, for example, reflect the location of mechanical defects or contamination if such exist. Furthermore, in some cases, a dense “ring” of OISFs is formed, resulting from a certain distribution of self-interstitials and vacancies, and is controlled by the crystal-growing process conditions [64,67,69]. The circular shape and the narrow width of only a few millimeters of the OISF ring allow the distinguishing of the OISF ring from OISFs of other origins. Figure 3.18b shows a microscope picture taken from the ring region of an OISF ring. The origin of the ring will be discussed in more detail in Section 3.8. Oxygen precipitates: The formation and properties of oxygen precipitates and their useful and harmful influences [6,8,9,19,75] are central items, which will be discussed in more detail in Section 3.9.

3.8 CONTROL OF VACANCIES, INTERSTITIALS, AND THE OISF RING

FIGURE 3.18 (a) OISF on the surface of a lightly phosphorus-doped n ,100. wafer. The defects were relatively uniformly distributed over the surface. (b) Example of OISFs in an OISF ring of a highly borondoped p 1 ,100. wafer. Here, OISFs were concentrated in the narrow ring, while the rest of the area was practically free of OISFs. The figure is taken from the ring region.

High OISF concentrations are sometimes seen in highly boron-doped p1 ,100. wafers, resulting from the enhanced oxygen precipitation in the bulk due to high boron concentration. The strong precipitation induces and favors SF formation over the whole thickness of the p 1 wafer [8,85], although the result is expected to be sensitive to the resistivity, oxygen concentration, length position in the crystal, and the corresponding thermal history. Additional heat treatments of the wafers prior to their oxidation may also increase the risk of high OISF density if the wafers have a tendency to form OISFs. In ,111. -oriented wafers of any type and resistivity level, the OISF concentrations are typically low and lower than in ,100. wafers with the same doping level and dopant. Possible explanations for the orientation dependence of OISFs have been suggested [2].

The growth parameters and conditions of the crystal, especially the growth rate, and doping influence the amount of vacancies, self-interstitials, and related defects in the resulting crystal [69,81,86
88]. A CZ crystal grown at a high growth rate is known to contain defects called voids, originating from vacancy clustering, revealed as COPs, D defects, or flow-pattern defects, while at low growth rate, silicon self-interstitials form clusters revealed as (large) dislocation loops or A defects [69,87]. An intermediate growth rate would result in a ring-like OISF region and voids only inside the ring, while the outside region is practically void-free, but may contain dislocation loops. The effect of the voids, dislocation loops, and/or OISF ring on the quality and yield of devices depends on the detailed case (exact device structure and its process) and the properties of the defects (e.g., the size distribution and density of the voids or dislocation loops). Voids are known to deteriorate the quality of gate oxides [69,89], while dislocation loops are a potential risk for the yield of certain devices (e.g., Ref. [90]). The theoretical models of the incorporation of vacancies and silicon interstitials into crystals and the formation of the corresponding defects have been discussed in more detail in review articles such as Refs. [64] and [67], so we will not go into the details of the theory or modeling of the defects. Our presentation below is based on the literature, as well as our own experience, and will focus on the results that have the greatest importance in practice for understanding the main connections between the crystalgrowing process and crystal quality in order to guarantee the high quality of the crystal and wafers. The focus is on the CZ crystals, especially on lightly boron-doped

Properties of Silicon Crystals Chapter | 3

0.0025

A

0.0020 v/G (cm2/ K min)

p ,100. crystals because these are the standard product most frequently discussed in the literature, although relatively similar defects have also been detected in other dopant-orientation combinations [91], as well as in the FZ crystals (see Ref. [69] and references therein). One of the main conclusions of the models and experiments is that the growth rates (v) of the CZ crystal and the vertical temperature gradient (G) of the crystal in the vicinity of the solid-melt interface, or, more specifically, the ratio v/G, already very accurately predicts whether the resulting crystal at the corresponding length position becomes vacancy-rich (for v/G . Ccrit) or self-interstitial-rich (for v/G , Ccrit) [64,81]). The critical v/G ratio, Ccrit, has been suggested to have a value of about 0.0012
0.0013 cm2/K-min in lightly doped crystals [67,88]. While either vacancies or selfinterstitials dominate depending on the value of v/G, the concentration of the other minority species becomes negligible due to mutual annihilation of vacancies and self-interstitials. The simple criteria based on the v/G ratio is, according to the literature, due to the larger equilibrium concentration of vacancies at the solid
melt interface at the melting point (compared with that of self-interstitials), favoring vacancies because of the convection by crystal movement during pulling, while, on the other hand, self-interstitials have a higher diffusivity, favoring a flux of self-interstitials from the interface into the crystal. The growth rate (which to reasonable approximation equals the pulling rate of the crystal during the particular length position in the body) and G influence these transport processes and the remaining concentration of the point defects. Also, the dopants and impurities influence the balance between vacancies and self-interstitials [86,88,92
95]. For example, in highly boron-doped p 1 crystals, the critical value Ccrit of the v/G criteria will increase considerably with increasing boron concentration [88]. The point defect species dominating after the annihilation process becomes increasingly supersaturated as the crystal temperature decreases, which finally leads to the formation of larger aggregates—voids in vacancy-rich and dislocation loops in self-interstitial-rich crystals, respectively. Most of the dominating point defects are consumed by the aggregation. The vacancy-rich (voidrich, COP-rich) crystals are more common of these two crystal types among commercial products [64]. The voids typically have a small size of around 0.1 μm and their concentration in standard vacancy-rich material is in the order of 1 3 106 cm23 (e.g., Ref. [96]) and typically about 100
200 COPs (small pits detected as particles), with sizes above the detection limit of 0.10 μm are detected on the polished 6 in. wafer front surface. In interstitial-rich wafers, however, only few particles, which are possibly COPs, are detected on the 6 in. wafer surface. The voids

73

B OISF ring

0.0015

C

Critical v/G for OISF ring

0.0010

D

Critical v/G for v-i boundary v-i boundary

0.0005 0.0000 0

10

20

30

40

50

60

70

80

Radius (mm) FIGURE 3.19 Simulated v/G versus r profiles for 6 in. crystals with various thermal environments and pulling rates (cases denoted by solid lines A through D). The approximate critical v/G values, denoted by dashed lines, are from Refs. [67] and [88], and can be used to estimate the radial position of the interface between the vacancy-rich and selfinterstitial-rich regions (v
i boundary) (lower dashed line) and the OISF ring location (upper dashed line), respectively. The arrows indicate the radial positions of the v
i boundary and OISF ring for the growth process of curve B.

are formed during crystal growing at around 1150
1000 C where aggregation of supersaturated vacancies takes place and void-size distribution is formed [65,66] (see Figure 3.16). The v/G ratio at the growth interface and the cooling rate at the aggregation temperature have effects on the resulting void size distribution. The dislocation loops in self-interstitial-rich material are much larger, within 1
100 μm, compared with voids; have a lower concentration, around 104 cm23; and are formed near 1000 C [65,86,87,97]. In the actual crystal-growing processes, the value of the axial temperature gradient G is not constant, but typically increases (and v/G decreases) with r (see Figure 3.19). Estimations of G(r) are obtained by using crystal growth simulations. In practice, v is controlled by the pulling rate of the crystal, while G(r) is largely defined by the hot-zone design, although it is also affected by various growth parameters, including the pulling rate. Curve A in Figure 3.19 corresponds to vacancy-rich and D to interstitial-rich cases, respectively, while curve C is approximately in the boundary and could basically, if the process could be controlled and maintained precisely, lead to only relatively few vacancy- or self-interstitial-related microdefects [65,81,90,98]. If v/G reaches the critical value at certain r, vacancy-rich and selfinterstitial-rich regions are formed at different radial regions (see curve B in Figure 3.19). However, in the case of such “mixed-quality” crystals, their oxidized wafers will typically suffer from an OISF ring which is formed close to the radius corresponding to the vacancy-interstitial boundary, although slightly toward the vacancy-rich side, at r, where v/G is

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FIGURE 3.20 Map of the recombination lifetime of an 8 in. p ,100. wafer, measured by using the μ-PCD method. The wafer has a lower lifetime region at a radius of 40 mm, which corresponds to the radius where an OISF ring would be formed in an OISF test.

slightly above Ccrit. The combination of experiments and modeling of G has indicated a critical value of Ccrit,OISF  0.00134 cm2/K-min for this v/G ratio where the OISF ring appears in lightly doped crystals [88]. The OISF ring shows a highly increased tendency to form OISFs in densities of the order of 1000 cm22 in the ring in ,100. wafers, for standard OISF test, while few OISFs are found elsewhere. The OISF ring is typically quite narrow, a few millimeters at most. For example, the v/G profile denoted by B in Figure 3.19 is expected to result in wafers with an OISF ring having a radius of 66 mm. The ring originates from nuclei for oxygen precipitates in the ring region, formed already during crystal growing. Due to these defects, the OISF ring region already shows a reduced recombination lifetime in samples taken directly from the as-grown crystal, without any oxidation treatments [99]. An example of lifetime deterioration at the OISF ring position of an as-grown crystal is shown in Figure 3.20, although this measurement technique exaggerates the width of the ring. Furthermore, the OISFs of the OISF ring can have similar negative effects on the devices as SFs of other origin. The OISF ring, voids, and dislocation loops may cause yield losses of the devices processed on the wafers.

It is possible to totally avoid the formation of the OISF ring, if necessary or practical, by using suitable process parameters in crystal growing [69,87] to fulfill the quality requirements defined in the specification and necessary for the intended use of wafers. The commercial lightly doped CZ crystals have typically been grown in the vacancy-rich region without an OISF ring, while there has been more variation in the quality of commercial highly boron-doped p1 crystals [100]. In p 1 ,100. crystals the critical v/G value, Ccrit, increases with boron concentration [88]. Therefore, the p 1 crystals tend to become self-interstitial-rich with decrease of resistivity. The shift of Ccrit upwards is already so large at resistivity below about 10 mΩ-cm that commercial 6 in. and 8 in. p 1 ,100. wafers in this resistivity region are almost inevitably grown in the self-interstitial-rich region (i.e., v/G , Ccrit) and are practically COP-free [88,100]. Formation and properties of thermally induced defects in p 1 wafers with or without an OISF ring has been studied in more detail in Refs. [85] and [92]. Antimony, arsenic and phosphorus also have effect on vacancies and selfinterstitials and related defects in n 1 crystals and wafers [94,95]. For example, the COP density of arsenic-doped wafers has a strong dependence on the resistivity, and has been reported to have a maximum at 4
5 mΩ-cm [94,95]. Our corresponding results for As-doped case is

Properties of Silicon Crystals Chapter | 3

FIGURE 3.21 Dependence of the number of COPs of sizes greater than or equal to 0.10 μm per wafer (front surface), for 6 in. As-doped n 1 wafers, versus resistivity. The line is only to guide the eye. For comparison, the corresponding value for standard lightlydoped, vacancy-rich 6 in. p ,100. wafers is around 100
200 COPs/wafer.

1.E+04 6 in. As-doped <100>

Number of COPs ≥ 0.10 µm per wafer

75

6 in. As-doped <111> 1.E+03

1.E+02

1.E+01

1.E+00 0

1

2

3

4

5

6

Resistivity (mOhm-cm)

shown in Figure 3.21. The results show that the COP density of highly As-doped 6 in. ,100. and ,111. wafers is very high at 5 mΩ-cm (even much higher vs that of lightly doped wafers), but COP density decreases again with decrease of resistivity from 5 mΩ-cm, and the wafers become practically COP-free at resistivity below 3 mΩ-cm. In small-diameter wafers or in MEMS applications, the voids of standard vacancy-rich, lightly doped wafers (with no OISF ring) have so far not caused significant quality problems in the majority of cases. On the other hand, large-diameter wafers used, for example, for dynamic random access memory fabrication, can have tighter requirements with regard to voids [89,98] and, therefore, in these cases, controlling the void distribution by using an optimized crystal-growing process and/or additional wafer treatments becomes quite important. Furthermore, in actual crystal production, other quality aspects, discussed earlier in this review, as well as crystal yield and the total production cost of crystal and wafers, have to be taken into account in addition to vacancies, self-interstitials, and the OISF ring when optimizing the process conditions. For example, very low pulling rates lead to lower productivity of crystal growing and may also increase the risk of losing the single-crystalline structure, which are factors that increase the production cost of lightly doped, interstitial-rich material compared with that of vacancy-rich silicon.

3.9 OXYGEN PRECIPITATION During CZ crystal growth the oxygen in the melt, originating from the silica crucible, becomes incorporated into

the crystal with a distribution (segregation) coefficient of k0  1 [38] as the melt solidifies. The oxygen concentration is controlled to an optimized value for each application, if possible. A magnetic field can be used to reach the lowest or highest oxygen targets more easily. Typical oxygen levels in the crystal are in the range of 5
18 ppma (in new ASTM units). All of the oxygen is initially, that is, immediately after crystallization, in solid solution, and the oxygen atoms are in interstitial positions. As crystal cools during growth, the solubility of oxygen decreases and finally becomes lower than the actual Oi [6]. For typical Oi levels, this happens at temperatures below about 1200
1150 C. The supersaturated oxygen has a tendency to precipitate, to decrease the level of supersaturation. Precipitation may start as small nuclei formation during crystal growth, and nucleation and precipitation may further proceed during thermal cycles of wafer and device fabrication. In this section we will shortly review the main phenomena related to oxygen precipitation but maintain a practical approach and will not go into theoretical models. More detailed information about oxygen precipitation can be found in the literature, including comprehensive review articles [2,6,8,101,102].

3.9.1 Oxygen Precipitation and Its Quality Effects In most cases, almost all of the oxygen still remains in interstitials even after the crystal has cooled to room temperature. The oxygen concentration of lightly doped crystals is measured from samples taken from the crystal by using infrared absorption technique which, although only

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PART | I Silicon as Mems Material

sensitive to Oi, does not miss much of the total oxygen at this point, and this Oi value is considered the oxygen level of the crystal, and is used for comparison with the oxygen specification. The interstitial oxygen is electrically inactive and does not have effect on charge carrier concentration, resistivity or recombination lifetime of minority carriers. Although the loss of Oi to oxygen precipitate nuclei (and thermal donors) during crystal cooling is only a minor fraction of total oxygen, typically much less than 1 ppma (i.e., {5 3 1016 cm23), the nuclei can have quite large effect on later precipitation properties. The oxygen is known to have useful but also harmful effects in device fabrication, and a suitable initial oxygen concentration and optimized process parameters for device fabrication are necessary to benefit from oxygen, to obtain the best result for the device properties, yield and cost. The positive influences of oxygen are: (i) Possibility to use oxygen precipitates and related defects to collect harmful metal impurities, present during device processing, away from the device region into oxygen precipitates. This method is called internal gettering (IG) and is one of the various gettering methods [8,9]. (ii) Interstitial oxygen increases the mechanical strength of the wafers against plastic deformation (slip formation) during heat treatments [4,5]. The slips are harmful for the devices and also cause wafer warpage. The negative effects of oxygen may include: (i) Oxygen precipitates and related defects [2] are harmful to devices if located in the active region. Oxygen precipitates are typical sources and nucleation sites of SFs and dislocation loops in the bulk and, sometimes, also in the surface region of the wafers. (ii) Anisotropic chemical etching, used, for example, to form sensor structures, results in worse quality of the etched surfaces if defects caused by oxygen precipitates exist [70,71]. (iii) Thermal donor formation at or near 450 C is fast, especially at high Oi, and may become especially problematic in high-resistivity wafers, for example, at resistivity above 100 Ω-cm, as thermal donors easily shift the resistivity [103]. At lower resistivities the thermal donors can be treated properly and are not an issue. (More information about thermal donors can be found in Section 3.6 and references therein.) (iv) Oxygen contributes to the initial degradation of the efficiency of solar cells fabricated using boron-doped wafers [3]. As indicated by the list above, control of oxygen precipitation is a quite important in device fabrication. The supersaturation is the driving force for the oxygen to form small nuclei or, if nuclei already exist, to grow these nuclei into actual larger oxygen precipitates. The oxygen precipitates are particles of amorphous or crystalline SiOx (x  2) in the bulk of the wafers, and can have sizes ranging from about 10 nm to a few hundred nanometers [6,8], while the oxygen precipitate nuclei are

much smaller oxygen clusters, around 1 nm, and are more difficult to detect and their direct quality effects are minor compared with large precipitates. Large enough supersaturation and large enough diffusivity of oxygen are both necessary for precipitation to take place, limiting the “active” temperature range of nucleation and precipitation to about 500
1200 C. Below 500 C nucleation becomes slow because of already quite low diffusivity of oxygen, but some activity of oxygen still exists down to about 300 C as thermal donors are formed at 300
500 C, especially near 450 C [56,57]. Formation of oxygen precipitate may cause injection of silicon self-interstitials to the surrounding lattice, often resulting in formation of stacking faults and/or dislocation loops next to a precipitate, contributing to the properties and quality of the wafer. Already during the cooling of the crystal, nuclei for oxygen precipitates may form at temperatures about 800
500 C (see Figure 3.16), while nucleation is negligible at above 900 C [7,33,65,104]. These nuclei of the asgrown crystal will have an effect on later precipitation in wafers during their heat treatments. Only after large enough nuclei have first been formed at below 850 C, during crystal growth and/or during possible annealing of the wafer, can they be efficiently grown into actual precipitates at higher temperatures, around 950
1200 C, in later annealing of the wafer. The thermal history (cooling rate) of the crystal at 800
500 C depends on the growth process and crystal length position, see Figure 3.14. Wafers from the beginning of the body have had longer thermal history at 800
500 C during crystal growth, that is, stronger nucleation, compared with wafers from the end of body [7]. Typical cooling rates of 6 in. or 8 in. crystals are around 1 C/min at 650 C for the beginning of the body, and the corresponding time spent at the temperature range of 800
500 C is at least a few hours, while cooling is much faster in the end of the body where cooling rates around 4
10 C/min at 650 C are relatively typical. The cooling rate of the end of body could be decreased by keeping the crystal hot longer after finishing the body but such procedure would increase the total cycle time of crystal growth and is not commonly used. Any variation of Oi in crystal versus length position, or radial variation of Oi, also causes variation in the nucleation and precipitation. Target of crystal growth is to keep Oi relatively constant in the axial and radial directions but some variation still exists in practise, see Sections 3.3 and 3.5. In most cases, Oi(r) is lower in the periphery versus the center, which dependence has a corresponding effect on the precipitation during wafer annealings: Oxygen precipitation is often stronger in the center versus the periphery. Carbon impurities may strengthen oxygen precipitation [2,8,31
33] but, in practise, the actual carbon concentrations in semiconductor-grade crystals are too low to have major effect.

Properties of Silicon Crystals Chapter | 3

FIGURE 3.22 Amount of precipitated oxygen (ΔOi) versus initial oxygen concentration, at r 5 0 and 65 mm, for high-oxygen 6 in. p ,100. wafers, for a one-step treatment at 950 C for 20 h. The line is only a guide for the eye.

18 ΔOi at r = 0

Precipitated oxygen Δ Oi (ppma)

16

77

ΔOi at r = 65mm

14 12 10 8 6 4 2 0 12

13

14

15

16

17

18

19

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InitialOi (ppma) at measurement radius

3.9.2 Dependence of Precipitation on Oxygen Level and Annealing Process Annealing of the wafers may already take place during wafer fabrication (e.g., during donor killing of wafers or during growth of additional layers of oxide, polysilicon or epitaxial silicon on the wafer surfaces) and can, as a sideeffect, influence the subsequent precipitation. However, the major annealings are performed during device fabrication where various thermal cycles, of total time up to a few tens of hours, are used, for example oxidations, chemical vapor depositions, diffusion of dopants, or other type of annealings [2]. These heat treatments may form new nuclei, increase the size of the nuclei, grow preexisting nuclei into actual precipitates, or further increase the size or density of precipitates. The heat treatments may also dissolve already existing nuclei or precipitates if these are not yet large enough to survive the high temperature [2]. The precipitation and evolution of nuclei and precipitate size distribution depend in a complicated way on the annealing temperatures, time, initial Oi and earlier temperature history of the crystal and wafers [6
8,102,104]. Initial Oi has a major effect on precipitation, which effect can be studied by performing various annealings to test wafers, and measuring either the amount of oxygen consumed to precipitates or bulk microdefect (BMD) concentration related to precipitates. The loss of oxygen into precipitates in annealing of lightly doped test wafers is quantified by measuring Oi of the same wafer before (Oi,initial) and after annealing (Oi, final) by using infrared absorption technique. The amount of precipitated oxygen is the difference ΔOi 5 Oi,

initial 2 Oi,final

assuming that out-diffusion of oxygen is negligible compared to the precipitated amount [101]. Figure 3.22 shows the results of a precipitation test for wafers with exceptionally high initial Oi, for simple onestep heat treatment. The resulting curve (ΔOi vs. initial Oi) shows an “S” shape, as typical. The threshold for Oi to start clear precipitation is quite high in this particular example, around 14
15 ppma. At the highest Ois, ΔOi approaches Oi, indicating that, the majority of oxygen is in precipitates while the remaining interstitial oxygen Oi, final is only few parts per million atoms. Theoretically, not all of the oxygen can be precipitated even at the highest Oi’s because some oxygen remains soluble, as interstitials, depending on the temperature used for the precipitation. Other type of annealing processes result in different thresholds, and many examples of S curves can be found in the literature [7,101]. The radial variation of ΔOi largely originates from the radial profile of initial Oi, see Figures 3.22 and 3.23. Therefore, if even oxygen precipitation is needed, relatively even Oi(r) (i.e., low oxygen gradient) is preferred. Various annealing procedures are used to study oxygen precipitation [101]. The annealing parameters (number of steps, their temperatures and times) are often selected to describe the phenomena taking place in the actual, more complicated device fabrication process, allowing the results to be used in the optimization of the device process and/or in setting of the oxygen specification for the wafers. Sometimes wafers directly from the device process line are taken for oxygen precipitation analysis. Typical simple annealing tests consist of either one-step annealing only, two steps (lowhigh), or three steps (high-low-high). In the low-high

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FIGURE 3.23 Radial variation of initial Oi and ΔOi for a high-oxygen 6 in. p ,100. wafer, for a one-step treatment at 950 C for 20 h. The radial variation of initial Oi explains most of the radial variation of ΔOi.

18 16 14 Oi,initial and Δ Oi (ppma)

12 Oi,initial 10

ΔOi

8 6 4 2 0

–75

–50

–25

0 Radius (mm)

25

annealing process, the initial low-T annealing (typically at 600
800 C for a few hours) is used for nucleation, to allow or accelerate precipitation during the proceeding high-T annealing. The nucleation step may generate new nuclei or increase the size of nuclei formed already during crystal growth. Because of the very small size of the nuclei, they consume only minor fraction of Oi. The high-T annealing, after the nucleation step, is typically performed at 950
1200 C for at least a few hours, and grows nuclei into much larger precipitates. The two-step annealing (or, more generally, annealing process which has a nucleation step in the beginning, before one or more high-T steps) is favorable if a large number of precipitates in needed, typically for IG. The disadvantage of the two-step annealing is that oxygen precipitates are formed everywhere in the wafer, thus also in the surface region where the devices typically are processed, which may cause failure of devices. The three-step annealing (high-low-high) has an initial high-T annealing at around 1100
1200 C, before nucleation and growth steps, and causes out-diffusion of oxygen from the wafer surfaces, resulting in an oxygen-poor layer at the surfaces. Thus, much reduced nucleation and oxygen precipitation will take place near the surface versus bulk during the second and third annealing step, respectively, and a defectfree DZ is formed at the surface, while precipitation further in the bulk takes place and is useful for IG [9]. A DZ allows devices processed on the wafer surfaces to function properly without deterioration due to defects. The thickness and quality of DZ depends on the initial Oi and annealing parameters, and is typically around 10 μm to a few tens of micrometers. After the three-step treatment, the thermal donor formation in the DZ as well as in the bulk containing precipitates will

50

75

be weaker than initially because of the reduced Oi in both regions [59,61]. Another effect of the first high-T annealing in the highlow-high process is that it may dissolve the nuclei formed already during crystal growth, if the annealing temperature is high enough, preferably at least 1100C [2]. New nuclei are then formed in a more controlled manner during the low-T step, while the nucleation is no longer much contributed or assisted by the thermal history of crystal growth. Thus, for the three-step annealing, the precipitation of wafers taken from different length positions of the crystal become more similar and predictable, assuming that also the initial Oi is about the same. For example, according to Ref. [7], a three-step DZ-IG heat treatment, where the first annealing was performed at 1150 C for 4 h, resulted in very uniform precipitation for all length positions of the body, for constant Oi. Contrary to this, for a two-step (low-high) treatment, the wafers from the beginning of the body started to form precipitates already at Oi even up to about 3 ppma lower compared with wafers from the end of body [7]. However, the disadvantage of the additional initial annealing step, if applied to real device process, is that it makes the total process time longer and increases the cost.

3.9.3 Bulk Microdefects Oxygen precipitation in the bulk of wafers, and the variation of precipitation with depth from wafer surface is generally studied by cutting the annealed wafer into half, polishing the edge and using suitable etchant (e.g., Wright etch) to reveal the BMDs related to oxygen precipitates. Notice that the BMD density of as-grown crystal is very

Properties of Silicon Crystals Chapter | 3

FIGURE 3.24 BMD density in highly Sbdoped n 1 wafers and lightly doped p 2 wafers vs initial oxygen concentration, for either a one-step treatment at 1000 C for 32 h or after a two-step treatment of 700 C/ 4 h 1 1000 C/32 h. The oxygen concentration of Sb-doped crystal was determined by using GFA method. The dashed lines are only guides for the eye, and indicate trends for Sbdoped cases. (BMD densities of n 1 samples with initial oxygen less than 8 ppma were below detection limit of 100 cm22, and are not included in the figure.)

1.E+07 6 in. p<100>/<111> (1000°C/32 h) 6 in. Sb<111> (1000°C/32 h) 1.E+06

6 in. p<100>/<111> (700°C/4 h + 1000°C/32 h) 6 in. Sb<111> (700°C/4 h + 1000°C/32 h)

BMD density (cm–2)

79

1.E+05

1.E+04

1.E+03

1.E+02

1.E+01 8

9

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11

12

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14

Initial oxygen (ppma)

low. It is also possible to directly use the front surface of a wafer for the studies, to detect defects at or near the surface if these defects in the active region are of main concern. The defects can be counted by using the microscope, and a value for the BMD density can be obtained. The resulting density can be presented either as the number of BMD per area or per volume [105]. This BMD counting method can also be used for p 1 and n 1 wafers, contrary to infrared absorption measurement of ΔOi. According to Refs. [8,106], relatively large density of precipitates, greater than 108 cm23, is necessary for good IG of transition metals, but the required minimum density also depends on the size of precipitates. Typically this requirement can only be fulfilled if the amount of precipitated oxygen exceeds 0.1 ppma while the optimized values for IG are often higher, even up to several ppma’s. Figure 3.24 shows a BMD density (number of BMD’s per area) comparison between highly Sb-doped n 1 wafers (resistivity  15 mΩ-cm) and lightly borondoped wafers, for two different treatments. The defects inside the bulk were revealed as described above, and counted by using a microscope. The BMD density can be seen to increase by many orders of magnitude with the increase of the initial oxygen, the exact correlation depending on the heat treatment parameters. For very low initial oxygen levels, below about 8
9 ppma in Figure 3.24, not much BMD formation takes place. Large BMD densities greater than 104 cm22 are reached at oxygen levels above 11 ppma if initial nucleation at 700 C is used, while without the nucleation step the densities remain much lower.

As an approximate general rule, we can say that practically no precipitation or BMD formation takes place in lightly doped wafers, in reasonable wafer annealings, if the initial Oi is below 8 ppma (in new ASTM units), and up to about 10 ppma precipitation is quite weak. Low Oi is, thus, beneficial if the target is to strongly avoid BMD’s (or oxygen donors). Clear oxygen precipitation and BMD formation often start to take place at Oi $ 12
15 ppma but this limit is quite sensitive to annealing process. Wafers with initial Oi . 18 ppma have an extremely strong tendency to oxygen precipitation but such high Oi values are not often used. Exact size distribution, density and shape of oxygen precipitates depend in a complicated way on the initial Oi, the thermal history of crystal and heat treatments of wafers [8,101,104]. Depending on the application, suitable, realistic oxygen specification is defined for the wafers to optimize the result. If IG is used to capture harmful metal impurities, for example, Fe, Cu or Ni, during the device processing, a relatively high Oi of at least 13 ppma is preferred, in lightly doped wafers, depending on the process. On the other hand, if a low oxygen-related defect density is necessary (e.g., in certain MEMS applications or in solar cells), or if formation of thermal donors is to be avoided (e.g., in very high-resistivity wafers), a lower Oi is better. Too low Oi may, however, increase the risk of slip formation [4,5]. Especially the FZ wafers, which have Oi  0 ppma, are mechanically weaker versus CZ wafers. On the other hand, too strong oxygen precipitation, forming large precipitates and/or decreasing the remaining Oi to very low values, may decrease the mechanical strength [6,8]. For example, according to Ref. [8], oxygen

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PART | I Silicon as Mems Material

FIGURE 3.25 Recombination lifetime of minority carriers in 6 in. p ,100. and 6 in. p ,111. wafers versus the amount of precipitated oxygen (ΔOi). The data is for various one- or two-step heat treatments, and a μ-PCD method was used for lifetime measurements. The line is a fit to the data for ΔOi . 1 ppma, see Eq. 3.7.

1000

Lifetime (µs)

100

10

1

0.1 0

2

4

6

8

10

12

14

16

18

ΔOi (ppma)

precipitates of sizes above 200 nm are potential nuclei of slip dislocations. Free vacancies are known to make the precipitation of oxygen easier [67]. However, most of the vacancies in the vacancy-rich (COP-rich) crystals, with no OISF ring, are consumed to voids during crystal growth and the catalyzing effect of few remaining vacancies is typically only relatively marginal. Modification of free vacancy concentration of the wafers by using suitable, special annealing has been suggested as a method to enhance and control oxygen precipitation [67], but is not commonly used in MEMS.

3.9.4 Oxygen Precipitation in Highly-doped Wafers The precipitation of oxygen is enhanced in boron-doped p1 wafers (e.g., at  5
10 mΩ-cm) and it is retarded in Sb-doped n1 wafers [8,43,94,105,107,108], while precipitation behavior is independent of the dopant type and concentration at lower dopant concentrations below 5 3 1016 cm23 [107]. The effect of high concentrations of boron or antimony seems to be valid even for samples that have similar initial oxygen concentrations as the lightly doped reference wafers have, although the differences in the oxygen concentrations between these products often contribute considerably to the precipitation behavior seen in practice. According to our own tests, the density of BMD’s formed by oxygen precipitation annealings in Sb-doped n1 wafers becomes similar to the density formed in lightly doped p2 reference wafers if the Sb-doped wafers have, depending on the annealing

process, about the same or slightly higher oxygen concentration versus that in lightly doped wafers, Figure 3.24. We can conclude that the main reason for the weak precipitation in Sb-doped n 1 wafers is the typically low oxygen level in these crystals, while also the direct effect of Sb may contribute to some extent. Also, for n 1 doped with arsenic or phosphorus, the precipitation is typically retarded [8,105,109]. The nucleation mechanisms in phosphorus-doped n1 wafers are discussed in Ref. [110]. The precipitation in p1 wafers, although enhanced in principle, has also been found to have a dependence on resistivity (boron concentration), among other factors [8,94]. Oxygen precipitation in p 1 wafers is enhanced especially/mainly at resistivities around 5
10 mΩ-cm. On the other hand, Ref. [41] suggests a considerable reduction of oxide precipitate density in p1 for resistivity below a threshold of 7 mΩ-cm compared with resistivities slightly above this threshold. However, the exact behavior of p1 can be quite sensitive to detailed material and process parameters [92].

3.9.5 Effect of Precipitation on Lifetime and OISFs Recombination lifetime of minority carriers is sensitive to oxygen precipitation (see, e.g., Ref. [111]), and the μ-PCD lifetime can decrease to very low values, for example, to 1
10 μs in p-type wafers, for strong precipitation. Lifetime degrades also in n-type silicon but possibly not as much as in p-type [112]. Figure 3.25 shows the dependence of the minority carrier lifetime of lightly doped 6 in. p ,100. and 6 in. p ,111. wafers on the

Properties of Silicon Crystals Chapter | 3

amount of precipitated oxygen ΔOi. Although the data includes various heat treatments, it shows a common trend. Already precipitation of ΔOi 5 1 ppma leads to a drastic lifetime reduction in p-type wafers, from the initial value of around 1000 μs to  20 μs, and lifetime decreases further with increase of ΔOi. This effect is among the reasons why oxygen precipitates should often be avoided in regions where the devices are located. (For solar cells the active device region practically covers the whole bulk of the wafer, and the efficiency of the cell decreases if the lifetime becomes too low, for example, due to oxygen precipitates, especially if the precipitates become decorated with metal impurities such as Fe [113].) By fitting the data points of Figure 3.25, for ΔOi . 1 ppma, to the dependence suggested in Ref. [111], the following approximate relation is obtained for p-type wafers: τðμsÞ  36½ΔOi ðppmaÞ21:49

(3.7)

The standard OISF test [82,83] has an oxidation step at 1100 C. Although the treatment can cause some precipitation of oxygen, it is not very effective with this respect because the treatment has no nucleation step at lower T. The resulting OISF densities of lightly boron- or phosphorus-doped wafers or highly-doped n 1 wafers, measured from wafer surface, are typically relatively low, and do not show much dependence on Oi either. (Notice, however, that our resolution of the OISF counting,  10 cm22, limits the accuracy of analysis at the low densities.) For example, for vacancy-rich (COP-rich) 6 in. p ,100. wafers of semiconductor grade, the OISF density is typically around 10 cm22 or lower, for any reasonable Oi. Only for exceptionally high Oi, for example, $ 20 ppma, the OISF density of 6 in. p ,100. wafers increases for the standard OISF test. The increase is probably due to strong oxygen precipitation not only in the bulk but also near the surface of the wafers, causing or strengthening the formation of SFs probably because silicon selfinterstitials are injected from the oxygen precipitates during their growth and/or because oxygen precipitates may behave as nuclei for OISF’s [8]. However, in p 1 ,100. wafers, the enhanced oxygen precipitation (due to high boron concentration) [8,94] may cause the OISF density of a standard OISF test to increase already at intermediate oxygen concentration, depending though much on the resistivity and details of thermal history of crystal and that during wafer fabrication, before the OISF test. As already discussed more thoroughly in Sections 3.7 and 3.8, an OISF ring is formed if the v/G ratio during the crystal growth corresponds to a certain critical value. The ring is formed because of enhanced oxygen precipitate formation at the ring position during the crystal growth

81

[64,67,68,88], although this phenomenon becomes weaker if the oxygen concentration is very low. These precipitates survive the oxidation temperature of 1100 C, and may grow further. The stacking faults are able to nucleate to these defects during the oxidation, resulting in a dense, easily detectable OISF ring. However, the OISF ring is usually avoided by using optimized crystal growth process, and should thus not be a major quality concern in semiconductor-grade wafers used, for example, for MEMS.

3.10 CONCLUSIONS We have covered the major properties of CZ silicon crystals in this chapter. The focus has been on those impurities and defects that have the greatest effect on device performance and/or that have proven to be of the greatest importance and interest in the industrial development of the crystal growth process and crystal quality. By understanding the crystal properties and their connection to the growth process, as well as the inherent limitations of the CZ silicon crystals, it is possible to better specify the crystal properties needed and to improve the growth process, as well as the resulting material quality. Improved or more suitable material increases the yield of devices processed on the wafers. The proper CZ silicon used for wafer fabrication is always dislocation-free, contains only relatively insignificant concentrations of harmful impurities such as carbon and transition metals, has a reasonably controlled or predictable defect formation behavior, and its resistivity and oxygen concentrations are suitable for the intended application. Typical high-quality CZ material has such a low carbon concentration that it has almost no effect on oxygen precipitation behavior and, similarly, also the amount of various harmful transition-metal impurities (e.g., iron) in the as-grown crystal is typically clearly within acceptable limits. Furthermore, the radial and axial uniformity of the properties is important and has been discussed in this review. The radial variation of oxygen and resistivity depends on the dopant, resistivity level, and/or crystal orientation, although other process parameters also influence the result. In practice, various applications can have quite different requirements for the crystal and the optimization of certain product-specific properties may be of major concern and challenge. For example, in MEMS wafers, the highest oxygen concentrations are typically avoided to keep the bulk defect-free and to make sure that the structures, formed by etching, are of high quality. On the other hand, some other applications may benefit from relatively high oxygen concentration, mainly if strong metal impurity gettering by oxygen precipitates is needed during device processing. Furthermore, the cost of the material is a relevant issue and should be minimized without compromising the quality. For example, an unnecessarily narrow resistivity specification leads to a lower commercial crystal yield and,

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PART | I Silicon as Mems Material

thus, increases the cost per wafer unless the rejected material has some other commercial use. The customers’ requirements for the impurities and defects of the crystals and wafers are expected to continue to develop in the future as the processed device structures and their complexity, structural dimensions, and processing methods, as well as targets for device performance, yield, and total cost evolve. The major challenge for crystal growth is to answer these expectations.

ACKNOWLEDGMENTS Colleagues at Okmetic Oyj, especially the present and former members of the crystal growth R&D group and other crystal team members, as well as the laboratory staff, are gratefully acknowledged for their long-term cooperation and contributions to this work, and O. Anttila also for his comments to Section 3.9.

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