Investigation of structure and phase transformations in silicon implanted with 12C+ at room temperature

.__ __ l!iB N.FT

Nuclear Instruments and Methods in Physics Research B 103 (1995) 161-174

NOMB

M

Beam Interactions with Materials 8 Atoms

ELSEVIER

Investigation of structure and phase transformations in silicon implanted with “C+ at room temperature K.Kh. Nussupov

*, N.B. Bejsenkhanov,

J. Tokbakov

High Energy Physics Institute, National Academy of Sciences of Republic of Kazakhstan, 480082 Almaty, Kazakhstan

Received 20 September 1993; revised form received 28 April 1995 Abstract The methods of Auger-electron spectroscopy and of X-ray diffraction are applied to an investigation of C+ ion implanted silicon layers. The ion energies are 40, 25, 17, 10, 6 and 3 keV for creation of a linearly decreasing profile of carbon in silicon or only 40 keV to obtain a concentration distribution which is approximately Gaussian. The microstructure and the phase composition of the implanted layers are studied experimentally to determine the dependence upon annealing temperature. The mechanism for creation of complicated multilayer structures during annealing is shown graphically. Formation of SIC crystallites begins at the sample middle layer and spreads to the surface layer and substrate as the annealing temperature increases. Crystallization of silicon amorphized by implantation begins both near the substrate and the sample surface and propagates to the middle of the layer with the Gaussian carbon distribution while in the layer with the linear distribution the crystallization comes about from the sample interior to its surface. After annealing at 125O”C, nearly 35% of the total volume of polycrystalline Si passes to c-Si from the substrate side for the samples with the Gaussian distribution and 45-50% for the samples with the linear distribution of carbon, respectively.

1. Introduction Synthesis of Sic by high-dose carbon ion implantation into silicon is of considerable interest due to opportunities to apply the material widely in the field of microelectronics. Formation of Sic by ion-implantation is favoured for its low contamination and relatively low temperature of formation [ 1,2]. In the majority of analogous studies, Sic synthesis was carried out by implantation of carbon ions of some specified energy and dose into a silicon substrate at room temperature [l-7]. Inhomogeneities in the carbon-atom concentration have been found to cause, in a number of cases, structure variations in the composition of the implanted layers. In particular, as a result, multi-layer structures with alternating layers of different composition and structure states [3,4,6,7] can be created. Akimchenko et al. [3] have shown that the structure and the composition of a silicon layer implanted with carbon (E = 40 keV, D = 4.3 X 1017 cm-‘) after annealing at 900°C varied in depth as follows: a mixture of amorphous Sic and P-Sic crystallites in the surface layer and recrys-

l

Corresponding

author. E-mail [email protected].

tallized silicon regions at the film/substrate interface. Subsequently Akimchenko et al. [4] reported a multilayered structure consisting of different phases after a high temperature anneal. This structure contained the following regions: a) a thin surface layer of single-crystalline Si; b) polycrystalline P-Sic and amorphous material at the boundary; c) intermediate solid solution of l*C in Si and d) polycrystalline textural Si. The ion energy and dose were 310 keV and 5.5 X 10” cm-‘, respectively and the anneal conditions were 1100°C for 30 min in a vacuum of about lo-’ Torr. Implantation with carbon ions (E = 100 keV, D = (1.1-2) X 10’s cm-‘) resulted in the creation [6] of P-Sic in layers with comparable concentrations of carbon and silicon, Sic-microcrystallites surrounded by crystalline Si in the regions where N,/Nsi = 0.7 and graphite and Sic in regions where N,/Nsi = 4.2. The assumption was made that the majority of implanted carbon atoms are included in P-Sic in the regions where the carbon concentration is lower than the silicon one, whereas in the regions with the opposite relation (N, > Nsi) carbon cluster formation is observed. Srikanth et al. [7] carried out a layer-by-layer analysis of the structure of a silicon surface layer containing a Gaussian distribution of implanted carbon atoms (E = 100

0168-583X/95/$09.50 0 1995 El sevier Science B.V. All rights reserved SSDI 0168-583X(95)00591-9

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Instr. and Meth. in Phys. Rex B 103 (1995) 161-I 74

Fig. 1. The profiles of “C atom distribution in Si obtained by the ion-implantation technique (Table 1, the linearly decreasing profile). Dotted line: the calculated profile (curve 1) obtained using R, and AR, given by Burenkov et al. [lo]; dashed line: the profile N,/Nsi (curve 2) calculated using the LSS theory [13]; solid line: the experimental profile N,/Nsi after annealing of sample at 1250°C for 30 min (curve 3) obtained from the data on Auger spectroscopy; open dots: the experimental profile No/Nsi (curve 4).

D = 10” cm-*) using spectroscopic ellipsometry for three cases: (i) just after implantation, (ii) after annealing at 8OO”C, and (iii) after annealing at 1000°C. It was shown that the implanted layer which does not undergo annealing, consists of: silicon dioxide (45 A), amorphous silicon (13 A), a mixture of c-Si and Si,.,C,., (2360 A), Si,,,C,,,(870 A) above the c-Si substrate. After annealing at 800°C the following multi-layer structure was observed: SiO, (46 A), a mixture of Sic and c-Si (2050 A), a mixture of Si,.,&,, and Sic (1230 A) above the c-Si substrate. Annealing at 1000°C resulted it a strong rearrafgement of the impltnted layer: SiO, (58 A), c-Si (1690 A), S$&,,, (22 A), a mixture of c-S&,,, and Sic,,, (1160 A) above c-Si. A few authors have reported the creation of multi-layer

structures after carbon ion implantation into a heated silicon substrate [8,9]. Investigation of the relationship between the implanted structure and the conditions of implantation and post-implantation annealing is of considerable scientific interest. In this paper an attempt is made to explain the observed layer structure nonhomogeneity as a result of a nonuniform distribution of the implanted carbon. The layers with a linearly decreasing and Gaussian depth profiles of ‘*C in Si are considered as an example. The effect of the carbon concentration and distribution profile shape on layer crystallization and the volumes of the polycrystal phases of Si and P-Sic is considered. Experimental studies have been carried out by the

Table 1 The values of R,, AR,, and Gibbons et al. [13]

Table 2 energy and dose used to produce The values of “C-ion linearly decreasing and Gaussian profiles of carbon in Si

keV,

and S,, given by Burenkov

Burenkov et al. [lo] :eV] 40 30 20 10 5 3

R

P

120.4 90.23 59.96 30.28 16.05 10.51

AR

P

46 37.8 28.3 16.9 10.2 7.2

s

k

-0.4 -0.3 -0.1 0.1 0.2 0.3

et al. [lo]

Gibbons et al. [13]

Linearly decreasing

%

E. lkeV1

89.8 67.7 45.4 23.3

AR, 28.2 23.3 17.6 10.6

40 2.5 17 10 6 3

profile

D: 110” at/cm21 2.018 1.285 1.054 0.720 0.427 0.322

Gaussian profile E [keV]

D [lo”

40

2.6

at/cm’]

the

RKh. Nussupou et al. /Nucl.

Ins@. and Meth. in Phys. Res. B 103 (1995) 161-l 74

163

Fig. 2. The same as Fig. 1 but for the Gaussian profile.

techniques troscopy.

of X-ray diffraction

and Auger-electron

spec-

2. Experimental After cleaning and removing the native surface oxide in a chemical etch, silicon samples of the (100) orientation and of the size 12 X 7 X 0.3 mm3 were mounted in the ion accelerator target chamber. Ion implantation was carried out under completely oil-free conditions. Carbon implanta-

tion was made at room temperature into the samples with resistivities of 4-10 L! cm. In order to prevent sample heating during implantation, the ion current density was kept at a level of less than 4 PA/cm’. The linearly decreasing profile was obtained by means of multiple implantation in such way that the carbon concentration was close to stoichiometry in the surface vicinity and decreased approximately linearly with depth (N,/Nsi = 1 + 0). To realize such profiles experimentally, the appropriate calculated profile of carbon in silicon was preliminarily constructed (curve 1 in Fig. 1). When calcu-

I-

Fig. 3. Microdensitometric intensity curve of X-ray radiation obtained from carbon implanted silicon samples (see Fig. 1, curve 3) after annealing at 1250°C for 30 min.

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K.Kh. Nussupor

et al./Nucl.

Ins&. and Meth. in Phys. Res. B IO3 (1995) 161-l 74

Table 3 The number of lines (rings) of Si, P-Sic and SiO, appearing the X-ray diffraction patterns after annealing for 30 minutes temperatures ranging from T,,,, to 1270°C T [“Cl

Linearly decreasing Si

Troom 800 900 1000 1100 1200 1250 1270

P-Sic

in at

profile Gaussian profile

SiO,

-

1

-

1 1

3 3

_

5

7

1

Si

S-Sic

SiO,

_

_

_

‘QZ

1

-Q-

1

_

21 31 3 4

2 3

_ _

4

3

1

60 -

YO-

to -

1 800

1 900

1 /OOO T,.C

I l/O0

I 1200

lating the profile, the values of the mean projectile range, R,, the root-mean-square (RMS) deviation, AR,,, and the momentum, S,, (see Table 1) were taken from Burenkov et. al. [lo] (the underlying assumptions were discussed by Burenkov et al. in 1981 [ll]). The chosen energy values of carbon ions and of corresponding dose values were calculated by the technique described in Ref. [12] and presented in Table 2. Using these values a carbon profile in silicon was calculated and constructed (curve 2 in Fig. 1) on the data of R, and AR, from LSS [13] (see Table 1). The Gaussian profile was produced by C+ implantation at an energy of 40 keV and dose 2.6 X 1Or7 cm-*, when the carbon concentration at the distribution peak is lower than the value appropriate for stoichiometric Sic. Post-implantation isochronal annealing was carried out in flowing argon for 30 minutes at temperatures from 600 to 1250°C with temperature steps of 50 or 100°C. The profiles of the implanted ion distribution were measured using Auger-electron spectroscopy and the implanted layer structure was studied by the X-ray diffraction technique. The X-ray diffraction patterns were obtained with the help of a collimated (0.1 X 1.5 mm*) monochromatic X-ray beam, directed at an angle of 5” relatively to the sample

surface. The intensity of the diffraction lines was measured using the microdensitometer MD-100. The average sizes of crystallites were calculated from the widths of X-ray diffraction lines according to Jones’ method [14]. As is known [14], diffraction maxima undergo broadening, in addition to physical factors, as a result of instrumental factors, including imperfect focusing, doubling of the K,-radiation and collimator slit sizes. To determine instrumental broadening a standard sample

Fig. 4. The dependence of the integral intensity of the line (111) for Sic (curve 1) and Si (curve 2) on the annealing temperature for the linear profile.

Fig. 6. The X-ray diffraction patterns obtained from the silicon layer with the linear profile of the implanted carbon distribution after annealing at temperatures: (a) 1000°C; (b) 1250°C.

Fig. 5. The dependence of the average size of Si crystallites (curve l), p-Sic (curve 2) and SiO, (m) in silicon implanted with carbon upon the annealing temperature (the linear profile).

of carbon-implanted

silicon

with

a total

dose sufficient

for

si Wf)

K.Kh. Nussupou et al. / Nucl. Instr. and Meth. in Phys. Res. B 103 (1995) 161-l 74

&a; SiC(;ff)

165

(220)(3jf)

Fig. 7. The same as Fig. 6 but for the Gaussian profile. T,: (a) 1000°C; (b) 1270°C; (c) 1250°C; (d) 1270°C. X-ray chamber: RKD-57 ((a), (b)) and RKU-114Ml (cc), cd)).

substrate amorphisation was prepared. The implantation was carried out with carbon ions of varying energy values ranging from 3 to 40 keV with the purpose of constructing a homogeneous amorphous silicon layer with a rectangular profile of carbon [12]. The low value of carbon concentration (N 4 at.%) in the implanted layer permitted complete

I

9

I

I

13

I

I

47

I

I

recrystallization of the layer on annealing at 1250”. Really, as the annealing temperature increases diffraction lines from the silicon polycrystalline phase narrowed and disappeared at T = 1250°C [12]. Line widths at half way to peak intensity (FWHM) after annealing at 1200°C were taken as the instrumental components of the diffraction maxima

1

I

$4

21

I

1

29

I

1

33

8, Fig. 8. The same as Fig. 3 but for the Gaussian profile. T, = 1270°C.

I

I

37

I

K.Kh. Nussupov et al. /Nucl. instr and Mefh. in Phys Res. B 103 119951 161-174

166

T,‘C Fig. 9. The same as Fig. 4 but for the Gaussian profile

widths. Calculation of average crystallite sizes was carried out using the ratio D = RA/P

Fig. 10. The annealing temperature of which polycrystalline phase of Si (curve 1) and p-Sic (curve 2) occur versus the carbon relative concentration, N, /Ns, [12].

cos 0,

where R is the chamber radius, A is the wave length of CuK, radiation, 0 is the Bragg angle, and p is the line physical broadening obtained by using the Jones method (see Ref. [14]).

3. Results Figs. 1 (curves 1 and 2) and 2 (curves 1 and 2) show the calculated profiles of carbon in samples implanted with the energies and doses listed in Table 2. These profiles have been calculated in the manner discussed by Nussupov et al. [12], and measured experimentally by Auger-electron spectroscopy for the linearly decreasing profile (Fig. 1, curve 3) and for the Gaussian profile (Fig. 2, curve 3), respectively. The experimental curve 3 in Fig. 1 which was obtained after annealing at 1250°C for 30 minutes is similar to curve 1 in the layer at depths greater than 100 nm, where the carbon concentration is relatively small (N,/Nsi < 0.5). Closer to the sample surface, where the carbon concentra-

Fig. 11. The linear profile of carbon distribution

tion is high, the ratio N,/Nsi is close to one (curve 2), calculated using the data of LSS [13]. The thermal oxide layer produced on annealing at temperatures above 1200°C leads to a decrease in the carbon concentration to very low values in the subsurface layer at depths less than 40 nm. The ratio No/Nsi = 2 in this layer (curve 4 in Fig. 1) was sufficient for the formation of a SiO, phase. Moreover, the X-ray diffraction pattern (Fig. 6) shows the appearance of the SiO, polycrystalline phase. As seen from Figs. 3 and 6 (and Fig. 6 in Ref. [12]), the SiO, line width is comparable to the0 line width of Sic and Si. The calculation gives about 60 A for the average size of SiO, crystallites. Several diffraction lines usually appear from any polycrystalline phase, however, only one SiO, line is observed from this sample. It is thus necessary to carry out more detailed studies devoted to this problem. The Gaussian concentration profiles, curves 1, 2 and 3 in Fig. 2, have peak values of (Nc/NSi)max = 0.45, 0.76 and 0.51, respectively. The X-ray diffraction pattern (see

in silicon after annealing

at 1250°C for 30 min.

K.Kh. Nussupou et al. / Nucl. Instr. and Meth. in Phys. Res. B 103 (1995) 161-I 74

;e...o, 40

.o.

80

,o*,*

167

(

s,nm

izo

m

x

Fig. 12. For structure analysis of silicon implanted by carbon, after annealing at T, = 1250°C during 30 min.: 1 - the linear profile of C-distribution in Si; 2 - O-distribution in Si; 3 - the distribution (N, + No/2)/Nsi; 4 - the recrystallization curve (1 - N,,i/Nsi); 5 - the layer with N,/Nsi = 0.04 (X = 190 nm).

Fig. 7 or 8) shows the appearance of a broad diffusion line which corresponds to the almost amorphous Sip, phase. In this case the calculation gives about 25 A for the average size of SiO, crystallites. In Table 3 the data on the number of the diffraction lines (rings) corresponding to the polycrystalline phases of Si and P-Sic versus the annealing temperatures are presented. It is evident that after annealing at temperatures lower than 900°C diffraction lines are not observed in the diffraction patterns. Annealing at 900°C and higher leads to the appearance of lines which are characteristic of polycrystalline phases of Si and P-Sic. In the case of the linearly decreasing profile, seven S-Sic lines and five Si lines corresponding to reflections from the planes with the indices (ill), (2201, (311) etc., (see Fig. 3) have been revealed after annealing at 1250°C. In Fig. 4 the variation of the integral intensity of the lines (111)SiC (curve 1) and (111&i (curve 2) with annealing temperature is shown. The dependence of the average size of Si, SIC and SiO, crystallites in the (111) plane on the annealing temperature is given in Fig. 5. In Fig. 6 the X-ray diffraction patterns illustrating the data given in Table 3 and Fig. 4 are presented. From Figs. 4, 5 and Table 3 it follows that continuous improving of the structure of the crystallites of Si and SIC as well as continuous growth of the volume of both polycrystalline phases takes place as the annealing temperature increases. The data shown in Fig. 4 suggests that after annealing the implanted layer is composed mainly of silicon carbide. The increase of the Sic phase volume after annealing at 1250°C may be considered as near to complete. In Table 3 the lines associated with the phases of Si, SiO, and S-Sic, which appear in the diffraction patterns on annealing of the sample with an implanted Gaussian distribution of carbon, are presented. The table demonstrates that continuous improvement of the crystallite Si and p-Sic structure holds as the annealing temperature increases. In Fig. 7a-d the diffraction patterns on annealing of samples at 1000, 1250, 127O”C, obtained using

RKD-57 and RKU114Ml X-ray chambers, are given. In Fig. 8 the intensity variation of the diffraction pattern (T= 127O”C), which includes a strong peak from the surface SiO, layer (at 0 = 10.5”), is shown. In Fig. 9 the variation of the integral intensity of the lines (1ll)SiC (curve 1) and (111)Si (curve 2) with annealing temperature for the Gaussian profile is shown.

4. Discussion Previous results which showed the dependences of the layer microstructure on the annealing temperature and on the implanted carbon concentration are used to facilitate the interpretation of the new data presented here [12]. Let us describe briefly these data to ensure a better understanding of the interpretation. In the earlier paper [12] it was shown that formation of the polycrystalline phases of Si and P-Sic occurs in different ways and depends on the value of the relative carbon concentration, NC/N,,. In Fig. 10 the dependence of the temperature at which the lines of the polycrystalline phases of Sic (curve 2) and Si (curve 1) appear, is plotted against the value of NJN,,. The figure shows the linear dependence upon temperature at which Si crystallites are produced. The greater the carbon concentration, the higher is the annealing temperature needed to form Si crystallites, for example at 800°C the value of N,/Nsi is 0.04 whilst at 1000°C the value of NJNs, is 0.7. When NJNsi > 0.7, the silicon recrystallization processes in the layer bordering the matrix leads to Si-texturing. The most intense formation of the polycrystalline P-Sic phase during annealing is observed for carbon concentration values Nc/Nsi = 0.4 to 0.7. The P-Sic crystallites, being produced at 900°C already on annealing at 1000°C possess good structure, whereas in the samples with N,/Nsi = 1.4 and 0.06 P-Sic crystallite formation is observed only after annealing at 1250°C. After annealing at 1250°C the largest volume of polycrystalline P-Sic is

observed in layers with N,/Nsi ranging from 0.7 to 1.0, while for polycrystalline Si the same is true when N,/Nsi = 0.25. This behaviour is explained by the effects of Si-C bonds and carbon clusters on atomic microdiffusion within the implanted layers. The above data has been used for the analysis of the crystallization process in silicon layers both with a linearly decreasing profile and a Gaussian profile. 4.1. Structural analysis of silicon layer having the linear profile of carbon atoms To carry out layer-by-layer analysis of the implanted structures we shall make the following construction. For analysis of the linear profile, showed in the Fig. 1 (curve 31, we shall draw a straight line parallel to the absciss axis at the ordinate point N,/Nsi = 1.0, i.e. corresponding to the stoichiometric composition of Sic (Fig. 11). The perpendicular to the absciss axis at any point X intersects both the stoichiometric straight line and the profile curve. The distance between the absciss axis and the profile curve, 1X4 1,points to the carbon atom number per silicon atom, Nc/Nsi, at a depth X from the sample surface, whereas the distance between the profile and the stoichiometric line, 1AC I, corresponds to the fraction of silicon atoms, 1 - NJNsi, that cannot form SIC due to the lack of carbon atoms. On multiplying these quantities by the length element, dx, we obtain (N,_Ns,)dx and (1 - N,/Nsi)dx. As is known, crystallization during annealing causes formation of Si and Sic crystallites in the implanted layer. Let us consider an ideal case when all carbon atoms are bonded to silicon to form SIC crystallites. It is assumed that the excess silicon atoms form Si crystallites. Then, taking in mind the relation between the number of excess Si-atoms in the layer of thickness dx and the area, (1 N,/N,,)dx, one can depict schematically (shaded region) the amount of the polycrystalline phase of Si in the layer dx and, further, compare the obtained values with the X-ray diffraction data. The number of Si-atoms combined into poly-Si may be approximately evaluated from the expression: N poly-SI = k/{ (1 - Nc/Ns,)/S,}

dx = k/S,jds

= ks/S,,

where: ds is the area of shaded region ACDE; the coefficient k is the number of Si atoms, which correspond to the unit area S,. The area of the rectangle with vertices X, C, D, X f dx (Fig. 1 l), where dx = 1 nm, is adopted as a unit area (S,). From the expression p,AX one can determine approximately that this unit (S,) corresponds to the number of Si atoms: ksi = 5 X 10” cme3 X lo-’ cm = 5 X 10” silicon atoms/cm’. The shaded region of (N,/Nsi)dx (the region X, A, E, X + dx) corresponds to the number of implanted carbon atoms in the layer dx, (N,); or to the number of silicon atoms bonded with carbon atoms after annealing to

form Sic, N,,(C) = Nsi - Npa,y_Si(the distribution of Si(C) atoms is equal to the distribution of C-atoms); or to a half of the expected amount of Sic, because of N, = N,,(C) = {N, + Nsi(C)}/2 = Nsic/2. Thus, one can estimate the total number of Si and C atoms incorporated into polycrystalline Sic on doubling the area of shaded region ( N,/‘Nsi)d x. For example, for the composition N,/Nsi = 0.33 we have 33 atoms of carbon which are bonded to 100 silicon atoms (Fig. 11). After annealing one should expect of 33 two-atoms molecules of SIC and 67 Si atoms which are not able to bond to form Sic, where the values are equivalent in terms of the total number of atoms [12]. In this paper [12] the equality of the phase volumes of Si and SIC determined by X-ray diffraction techniques was shown. Fig. 11, in agreement with previous reasonings, shows that the area of (1 - N,/N,,)dx = 0.67 dx is twice the area of (N,/N,,)dx = 0.33 dx. This is consistent with the structural characteristics of Si and SiCb as the volume of the elementary cell of Si (aii = 160.1 A31 is twice that of Sic (a& = 82.9 A3’,. The region above the stoichiometric line (Fig. 1, curve 2) points to an excess of carbon atoms with respect to Si atoms. Following from the data reported in Ref. [6], a large number of carbon clusters can be expected in this layer. One can evaluate approximately the possible maximum ratio of the volumes of Sic to Si in the implanted region. Suppose, carbon implantation into silicon with a net dose of N, = EiD, = 5.836 X 10” atoms/cm2 (see Table 1) has resulted in silicon amorphization at depths from 0 to 190 nm. The number of silicon atoms in this layer equals: Nsi = psiAX= 9.5 X 1017 atoms/cm2, where psi = 5 X 1O22 atoms/cm3 is the volume concentration, AX= 190 nm is the thickness of the amorphous layer. In the course of crystallization, N,,(C) = 5.836 x 10” silicon atoms/cm’ bond with carbon atoms to form polySic, i.e. NpO,y_sic= N, + N,,(C) = 2N, = 11.672 x lOI atoms/cm*. The remaining free silicon atoms, NP,Y_si = Nsi -N,,(C) = 3.664 X 1017 atoms/cm2, can create Sicrystallites. As a result, the numbers of silicon and silicon carbide atoms are in the following ratio: N poly-Sic ’ Npoly-Si

=

11.672:3.664=

1:0.31.

(1)

As for the experiment (Fig. 4), the ratios of the polycrystalline phases of SIC to Si for several temperatures, within the temperature interval lOOO-125O”C, are as follows:

: Zi,,t(Si) = 0.312 : 0.084 = 1: 0.27,

1000°C

Z,,(SiC)

1100°C

Zint(SiC) : Zint(Si) = 0.477 : 0.130 = 1 : 0.33,

1200°C

Z&Sic)

1250°C

Z,,,(SiC) : Z&Si)

: Zi,,(Si) = 0.642: 0.217 = 1: 0.34,

Over this temperature ZiJSiC)

= 0.688 : 0.239 = 1: 0.35.

interval the ratio is assumed to be,

: Z,,,(m) = 1: (0.33 + 0.02),

(2)

K.Kh. Nussupov et al. /Nucl.

Instr. and Meth. in Phys. Res. B 103 (1995) 161-l 74

where 0.33 is the average value for poly-Si, 0.02 is the appropriate RMS deviation. Let us consider the experimental Auger-profile (Fig. 1, curve 3) obtained after annealing at 125O’C. The peculiarity of this data is the occurence of the SiO, layer near the sample surface resulting in a decrease of the total number of carbon atoms in the implanted layer, as well as epitaxial silicon recrystallization from the substrate leading to the decrease of the polycrystalline Si volume. Assuming that the crystallization process is almost complete after annealing at 125O”C, we shall define, by the technique described above, the ratio of the polycrystalline phase atom numbers of P-Sic to Si. In Fig. 12 we have drawn a dashed line (N, + N,/2)/Nsi (curve 3). This curve shows the distribution of bonded silicon atoms N,,(b) which is the sum N,,(C) + Nsi(0) of silicon atoms bonded to atoms of carbon, N,,(C), and oxygen, Nsi(0), for the formation of Sic and SiO,. After annealing the number of atoms is evaluated as N,,(b) = N,;(C) + Nsi(0) = N, + N,,/2, where one atom of carbon or two atoms of oxygen are bonded to each atom of silicon for the formation of SIC or SiO, molecules. The area of the region I is bounded by the curve 3, the stoichiometric line and the perpendicular 5 which intersects the absciss axis at the point X= 190 nm (Fig. 12) and, thus, represents the number of free silicon atoms which do not interact with atoms of carbon or oxygen and are able to produce Si-crystallites during annealing. The area of the region II, bounded by curve 1, and the same perpendicular, represents half of the total number of Si and C atoms which combine to form Sic-crystallites. The regions beyond x = 190 nm (Figs. 11 and 12) are not considered because the implanted layer is assumed to be amorphous only when N,/Nsi > 0.04 [12]. On measuring the areas, we obtain: S,, = 66.6; 5, = 81.8. N poly-Sic : Npoly-Si =2&r:&=

133.2:81.8=

1:0.61.

(3)

The overestimated value of the polycrystalline Si fraction in Eq. (3), in comparison with Eq. (l), can be explained by the decrease of the Sic quantity during annealing at 1250°C as a result of the replacement of the carbon rich silicon surface layer by a silicon dioxide layer. If the silicon dioxide surface layer is ignored then the experimental curve 3 in Fig. 1 can be approximated to the sample surface in such way that the area under curve 3 (S,,, which shows total carbon atoms in the layer, i.e. the net dose of N, = CiDi = 5.836 X lo*’ atoms/cm*) must be equal to the values S,, of calculated curves 1 and 2 in the same figure, as both the experimentally obtained curve 3 and calculated curves 1 and 2 were constructed with the same values of ion energies and doses. On measuring these values (S,,), we obtain 2S,, : S, = 1: 0.35, which is comparable with Eq. (1) calculated for the applied ion doses CDi (Table 1). It is noted that at lower anneal temperatures silicon dioxide formation is not observed (see Fig. 6a).

169

Fig. 13. The experimental dependence of the fraction (q = I%‘,.,~/CNPolY_si+ N,.,,)) of the total volume of polycrystalline Si, converting to c-Si, on N, /Nsi after annealing at T, = 1250°C.

Let us compare Eq. (3) and the results of X-ray measurements when it follows, from Fig. 4, that the ratio of the polycrystalline Sic to Si at 1250°C is as follows: &(SiC)

: Z&Si)

= 0.688 : 0.239 = 1: 0.34.

(4)

The quantity of poly-Si is almost half the value derived from Eq. (3) although both equations were obtained for the same temperature point (1250°C). The difference can be explained by a transition of part of the polycrystalline silicon phase volume to c-Si at the annealing temperature above 1100°C. Previously, it has been shown (Fig. 15 in Ref. [12]) that the increase of the annealing temperature from 900 to 1250°C leads to the transition of 80 percent of the poly-Si volume into c-Si in the layer with N=/Ns, = 0.125. In Fig. 13 the fraction ((Ye) of the total amount of poly-Si converted to c-Si after annealing at 1250°C plotted against N,/Nsi is shown. This dependence is based upon experimental data from Nussupov et al. [12]. This figure demonstrates that during an anneal at this temperature part of the poly-Si volume converts into c-Si in the silicon layers with carbon concentration N,/Nsi < 0.5. Thus, it can be expected (for the curve 1 in Fig. 12) that during annealing at 1250°C part of the poly-Si phase volume converts into c-Si in the layer at depths between 100 and 190 nm, where NC/N,, < 0.5. Justifying this assumption one can note that, as a consequence of the low carbon concentration in this layer, Sic crystallites are surrounded by crystalline Si [6]. During a high temperature anneal Si crystallites increase their average size (Fig. 5). This process may be accompanied by compounding of Si crystallites or incorporation with the substrate. For instance, silicon atoms at depth X (Fig. 12) are incorporated into Si or Sic crystallites or into the substrate. Let us consider the crystallization process graphically. In Fig. 12, curve 4 “the recrystallization curve” is constructed as follows. Suppose, N,/Nsi = 0.125 corresponds to the point A of the profile curve. Then the value (1 -NC/N,,) = 0.875 represents the relative number of

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Instr. and Meth. in Phys. Res. B 103 (1995) 161-I 74

silicon atoms incorporated into poly-Si. After annealing at 1250°C 80 per cent of these atoms are incorporated in c-Si.

c-Si (Fig. 12), N,.si = a,(1 - N,/Ns,)Nsi is the number of silicon atoms at a depth X passing to c-Si. In this case

1 - Nc/Nsi

o, = S,.si/‘(

= (I - Nc/Nsi )poiy-si + (1 - Nc/Nsi)c_si=0.175

+ 0.7.

=

Let us draw the perpendicular at the point A to the stoichiometric straight line and define the point B satisfying the following conditions: 1AB I= 0.175; 1BC ( = 0.7; 1AX I= 0.125. Making use of Fig. 13, we obtain, in the same manner, the remaining points of the recrystallization curve 4. From the equation 1BC 1= N,,,/N,, we obtain I XB 1= 1 - N,.,JN,,. The recrystallization curve (1 Nc_si/Nsi) labelled 4 is the distribution of silicon atoms which are not included into c-Si. Really, all atoms of silicon are included into c-Si at the depths x > 200 nm and I XB I= 0. Further, all atoms of silicon are incorporated into Sic, or SiO,, or poly-Si at the depths x < 100 nm and I XB I = 1. The curve 4 divides the region I into two parts: “poly-Si” and “c-Si”. The area of the region restricted by the curves 3 and 4 is proportional to the number of poly-Si atoms. In fact, the area measurements show that in this case N poly-Sic

. Npoly-si

=

2S,, : (1 - ‘y&S, = 133.2 : 43.8

= 1: 0.33,

(5)

being close to Eq. (4). The coefficient (Y, = N,_,,/(N,,,,,, + N,.si) shows the fraction of the poly-Si atoms passing to

Sp,y.si

+

S,.,i)

=

S,.si/'S,

=

38/'81.8

0.464.

Thus, for the profile considered, the transition of 45-50% of the free (being not incorporated into Sic or SiO,) silicon atoms into c-Si during an anneal at 1250°C is observed. After annealing at temperatures < 1200°C layer recrystallization is assumed to be incomplete and a significant fraction of Si- and C-atoms do not form crystallites of Sic or Si. In the following section the evolution of the structures over the temperature range 900°C to 1250°C is described and is represented diagramatically in Figs. 14a14d. As is seen from Fig. 10, formation of the P-Sic polycrystalline phase takes place at 900°C in layers with the concentration NJNsi ranging from 0.4 to 0.7. On finding this range on the ordinate axis (Fig. 14a), let us draw the lines parallel to the absciss axis and intersecting the distribution profile curve. It is clear from Fig. 14a that P-Sic crystallites occurs at a certain depth from the implanted layer surface with a layer thickness of about 25 nm (region II in Fig. 14a). Also, it follows from Fig. 10 that annealing at 900°C results in Si polycrystalline phase formation in the layer with the concentration N,/Nsi = 0.04 to 0.35. Constructions analogous to the previous case show (Fig. 14a) that S&crystallite formation occurs in the layer

_

- -x;nm

4

40

80

i20 x,nm

460 200

Fig. 14. Schematical representation of layer-by-layer 900°C; (b) 1000°C; k) 1100°C; (d) 1250°C.

crystallization

of the silicon layer with the linear profile of C-distribution.

T,: (a)

K.Kh.

Nussupo~~

et al. /Nucl.

Instr. and Meth. in Phys. Res. B 103 (1995) 161-l 74

(Fig. 14~). The layer containing Si-crystallites grows in the direction to the surface reaching a thickness of - 120 nm. Structurely, the ion-implanted layer differs only slightly from the previous one (T= 1OOO’C). On annealing at 1100°C one should expect the growth of the line number and intensity at the expense of more complete incorporation of Si- and C-atoms into Si and P-Sic crystallites, as well as an increase of the polycrystalline layer thickness. However, the line number remains unchanged (Table 3), whilst the line intensity and crystallite size growth (Figs. 4 and 5) becomes slower, pointing to a slowing down in the process of crystallite structure ordering. Seemingly, it is caused by the presence of carbon clusters decaying at 1200-1250°C [2,15]. Annealing at 1250°C results in Sic-crystallite formation in the layer with N,/Nsi = 0.06 to 1.4 and Si-crystallite formation in the layer with N,/Nsi = 0.04 to 1.0 (see Fig. 10). Decay of carbon clusters occurs at this temperature resulting in an increase in the volume of Sic. Subsequent ordering of the Si and P-Sic crystallites produced at lower temperatures (Table 3) and a growth in size is observed (Fig. 5). The processes described occur through the entire thickness of the implanted layer resulting in the layer structure being composed, mainly, of a mixture of P-Sic and Si-crystallites. From the substrate side, complete and partial silicon recrystallization (Fig. 14d) will occur. The experimental data shows a significant growth of the line intensity and number: 7 P-Sic lines, 5 Si lines and a SiO, line (Table 3, Fig. 6b). Surface oxidation during anneals at 1250°C has led to substitution of the surface carbon atoms by oxygen atoms, resulting in X-ray diffraction patterns showing a polycrystalline SiO,-line (Fig. 6b) with an average SiO,-particulate size d = 60 A. The formation of SiO, at the sample surface during anneals at T > 1200°C may be caused by oxygen contamination of the flowing argon. In this point of view Sic-film annealing is preferable under high vacuum. It isOinteresting that the average size of SiO, crystallites (60 A) is comparable with the size of Sic-crystallites obtained after annealing samples at 1200°C. Thus the

of the thickness - 60 nm, adjacent to the substrate (region I in Fig. 14a). However, the X-ray diffraction patterns from annealed samples (900°C) contain only one weak-intense line from polycrystalline P-Sic and have no Si-lines. The latter can be explained by a small thickness of polycrystalline Si. Crystallization is not terminated at this temperature, so the area of the shaded region in Fig. 14a is not to be related to the amount of polySi and Sic. In total, beginning with the sample surface and up to matrix we have obtained a multilayer structure having, approximately, the following structure: amorphous Si1,0-C1,2_,,7 mixture (O-84 nm); Sic-crystallites + amorphous Si,-C, mixture (84-108 nm); amorphous Sit,+,,,, mixture (108-132 nm); amorphous Si,-C, mixture + Si crystallites (132-190 nm) and c-Si. Increasing the annealing temperature up to 1000°C (Fig. 10) leads to polycrystalline P-Sic formation in the layer with N,/Nsi = 0.12 to 1.0 and polycrystalline Si in the layer with N,/Nsi = 0.04 to 0.63. Repeating the construction for samples annealed at these higher temperatures, we find that the P-Sic polycrystalline region grows both towards the substrate and the surface (Fig. 14b). The thickness of the layer containing P-Sic crystallites is evaluated to be - 130 nm. The region of polycrystalline Si increases from the matrix to the sample surface, reaching a thickness - 100 nm. In total the multilayer structure is composed of the following layers: amorphous Si,,,C i,z_t,e mixture (O-50 nm); Sic crystallites + amorphous Si,-C, mixture (50-92 nm); Sic crystallites + Si crystallites + C-atoms and Si (92-176 nm); Si crystallites + amorphous Si,-C, mixture (176-190 nm) and c-Si. The increase of the volumes of polycrystalline P-Sic and Si has led to the appearance of three Sic lines and one Si line in the X-ray diffraction pattern (Table 3, Fig. 6a) accompanied by an increase of the line intensities. Annealing at 1100°C results in the formation of P-Sic and Si crystallites in layers with concentrations ratios (NJN,,) ranging from 0.1 to 1.2 and from 0.04 to 0.9, respectively (Fig. 10). The layer containing P-Sic crystallites becomes wider reaching a thickness of about 170 nm

I.0

I

171

l

-0,0-

x

0,6: f w- -----_

5

Jr02 &2

-

X,

nm

Fig. 15. The same as Fig. 12 but for the Gaussian profile. T, = 1270°C.

K.Kh. Nussupooet al./Nucl. Instr. and Meth. in Phys. Rex B 103 (1995) 161-174

172

Sic-crystallites have been replaced by the SiO,-crystallites of the same size. However, more detailed studies are necessary to justify this assumption. The composition of the multi-layer structure is (Fig. 14d): polycrystalline SiO, layer (O-40 nm); Sic-crystallites + Si-crystallites (40-100 nm); Si-crystallites + Sic-crystallites + c-Si (loo-190 nm) and c-Si. 4.2. Structural analysis of silicon layer having the Gaussian profile of carbon atoms In this section crystallization in the implanted layer with a Gaussian carbon distribution is discussed. Let us evaluate the possible maximum ratio of the volumes of Sic to Si in the implanted region. The carbon atom number in the layer is: N, = D = 2.6 X 1017 carbon atoms/cm* (Table 1). Then NPO,Y_sic = 2N, = 5.2 X 1017 is the total number of atoms atoms/cm*, where N,,,,, incorporated into polycrystalline silicon carbide. The number of atoms entering poly-Si is as follows: Npoty-si =Nsi -N,,(C)

= psiAX_Nc

= 7.4 X 1Or7 atoms/cm2, where psi = 5 X lo** silicon atoms/cm3; (Fig. 15). Then N poly-Sic

: Npoly-Si

AX = 200 nm

=5.2:7.4=1:1.42.

(6)

For the temperature range 1000 to 1270°C the experimental data gives the following ratios for polycrystalline Sic to Si (Fig. 9): 1000°C

Zi,((SiC) : Zint(Si) = 0.073 : 0.19 = 1: 2.60,

1100°C

Zi,,(SiC) : Zint(Si) = 0.11: 0.22 = 1: 2.00,

1200°C

Zint(SiC) : Z&Si)

1250°C

Zi,,(SiC) : Zint(Si) = 0.28 : 0.29 = 1: 1.04,

1270°C

Zi,t(SiC) : Z&Si)

Over this temperature ratio is

= 0.23 : 0.27 = 1: 1.17,

= 0.29 : 0.265 = 1: 0.91.

interval

the average

value of the

Zi,r(SiC) : Zint(Si) = 1: (1.72 f 0.60),

(7)

where 1.72 is the average value and 0.60 is the RMS deviation. The significant variation of the ratio Z&Sic): Zi,,(Si) from 1: 2.60 at 1000°C to 1: 0.91 at 1270°C is caused, seemingly, by the Gaussian profile of carbon in silicon and the particular value of the implanted carbon dose. In these samples the number of silicon atoms in the implanted layer, Nsi = psiAX = 1 X 10” cm-‘, exceeds the number of carbon atoms, N, = 2.6 X 10” cm-* . The average concentration of carbon atoms (NC/N,,) is 0.26 and the formation of Si-crystallites occurs at a lower temperature (Fig. 10) than the formation of Sic crystallites. From this point of view, one can expect that the Si phase volumes at T= 1000°C is much greater than that of polycrystalline Sic. The composition of the near surface layer of thickness m 40 nm in these samples greatly differs from the previous samples with a linear profile. The concentration of silicon atoms in these layer (curves 1 and 2 in Fig. 2), exceeds the carbon concentration. After annealing at temperatures from 900 to 1200°C this layer consists, mainly, of Si-crystallite. After annealing at 1250-1270”$ the layer transformates to nearly amorphous (d N 25 A) SiO, resulting in a decrease of the polySi volume in the implanted layer. This fact together with recrystallization of the silicon layer adjacent to the substrate and the Sic volume growth at high temperatures

40 0,8 9 0,6 \ 2 U O,Y 0,2 40

/so

80

200

r,nm

I,

nm

d)

C)

40

60

r20

X,nfn

160 200

40

80

120

t60

200

x,nm

Fig. 16. The same as Fig. 14 but for the Gaussian profile. T,: (a) 900°C; (b) lOOO”C, (c) 1100°C; (d) 1270°C.

K.Kh. Nussupov et al./Nucl.

Instr. and Meth. in Phys. Res. B 103 (1995) 161-l 74

explains, in our opinion, the significant decrease of the polySi fraction at high temperatures. By making the assumption that the crystallization process is almost complete after annealing at 1270°C the ratio of the atomic numbers of Sic to Si in the polycrystalline phases can be defined. In Fig. 15 the graphical constructions analogous to Fig. 12 but for the Gaussian profile are presented. Taking into account the recrystallization processes from the substrate side (curve 4), we can obtain by means of the technique described above for area measurements as follows: S,, = 44.5; S, = 110.3; a, = S,.JS, = 39.2/110.3 = 0.356. N ply-Sic

: Nply-Si

=

2S,, : (1 - o&

= 89 : 70.8 = 1: 0.80. (8)

This ratio is comparable experiments I,,,(SiC)

: Ii,,

with the results from the X-ray

= 0.29 : 0.265 = 1: 0.91

(9)

The value of the coefficient (Y, shows that - 35% of the total volume of polycrystalline Si regrows from the substrate side to form c-Si. In Fig. 16a-16d, the crystallization process is represented schematically for the annealing temperatures 900°C lOOO”C, 1100°C and 1270°C. Using the data of Fig. 10, one can show by the technique stated above (Section 4.1) that Si-crystallite formation at 900°C begins in the surface layer and in the layer adjacent to the substrate (regions 1 in Fig. 16a). S-Sic crystallite formation at this temperature begins in the central part (region II in Fig. 16a) because the carbon concentration through the entire central layer satisfies the condition 0.4
173

carbon solid solution in silicon (200-220 nm) and c-Si. Two Si lines and a Sic line (Table 3) are observed in the X-ray diffraction pattern with a certain increase in intensities (Fig. 9). Annealing at 1100°C results in the Sic volume growth (Fig. 9), however, noticeable ordering of the crystallite structure is not observed (Table 3). It seems to be related to the presence of carbon clusters which annihilated at higher temperatures. Decay of certain forms of carbon clusters provide the Sic volume growth, whereas the more stable forms of carbon clusters prevent the crystallite structure from further ordering. For the Si polycrystalline phase, besides the volume growth, occurrence of the reflection planes with the indices (311), in addition to the planes (111) and (220), is observed. Fig. 16c shows that crystallites of Si and Sic are distributed almost throughout the whole thickness of the implanted layer. After annealing at 1200°C a second Sic line with the indices (220) is observed which seems to be caused by both strengthened atomic microdiffusion and carbon cluster decay which starts to arise at this temperature [2,15]. Annealing at 1250°C and 1270°C has resulted in further structure ordering of the Si and Sic crystallites. The third Sic line and the fourth Si line appear, pointing to a good crystallite structure. The observed decrease of the silicon volume (Fig. 9) is related to silicon oxide formation at the surface (Figs. 2, 7b and 7d) and to recrystallization processes at the boundary with the substrate as well. The implanted layer structure is to be as follows (Fig. 16d): microdisperse SiO, layer (O-40 nm); Sic-crystallites + Sicrystallites (40-120 nm); Si-crystallites + Sic-crystallites + c-Si (120-200 nm); carbon solid solution in c-Si (200220 nm) and c-Si. To summarize, for the Gaussian profile (D = 2.6 X lOI cm-‘) and over the temperature interval 900-1270°C Sic crystallization begins at the peak of the carbon distribution and propagates both toward the substrate and the sample surface, whereas Si crystallite formation begins in the vicinity of the surface and the substrate and then propagates to the central part as the annealing temperature increases.

5. Conclusion

The dependence of the structure of a C+ implanted layer upon annealing temperature and implanted carbon concentration has been quantified in a study of the crystallization processes of C + implanted Si. It is found that in layers with a nonhomogeneous carbon distribution the appearance of several layers which differ both in composition and structure orderliness takes place. The main conclusions from an experimental investigation of C+ implanted silicon layers with linearly decreasing concentra-

174

K.Kh. Nussupoc~ et al./Nucl. Instr. and Meih. in Phys.Res. B 103 (1995) 161-l 74

tion-depth profile and with a Gaussian profile are summarized as follows. 5.1. Linear profile 1) The experimental curve of the 12C-distribution in Si after annealing reveals a certain similarity with the curve calculated according to Burenkov et al. [lo] when the carbon concentration is relatively small (NJ&& < 0.5). Closer to the sample surface, where the carbon concentration is close to the stoichiometric composition of Sic, the experimental curve is similar to that calculated according to LSS [13]. 2) Crystallite formation starts at 900°C for P-Sic and at 1000°C for Si. As the annealing temperature increases up to 125O”C, continuous growth of the volume of the polycrystalline phases of Si and P-Sic as well as crystallite structure ordering is observed. At the temperature 1250°C an increase of the rate of growth of crystallite size and of structure ordering by carbon cluster decay takes place. Formation of a SiO, layer at the surface is observed at this same temperature. The average size of SiO, crystallites near the sample surface is about 60 A. 3) Crystallization of P-Sic is assumed to begin at the centre of the layer and to propagate to the sample surface and towards the substrate as the annealing temperature increases. The regrowth front of silicon amorphized by the implantation advances from the substrate towards the surface. After annealing at 1250°C nearly 45-50% of the total volume of polycrystalline Si has converted to c-Si from the substrate side. 5.2. The Gaussian profile 1) The experimental C-concentration-depth profile in Si for a dose (D) of 2.6 X 10” cm- ’ has a peak concentration that is within 10% of the value calculated according to Burenkov et al. [lo]. 2) Formation of Si and P-Sic crystallites begins at 900°C. Annealing up to 1250°C results in the phase volume growth. Within the temperature interval 1200-1270°C noticeable improvement of Sic crystallite structure together with significant increase of the phase volume due to carbon cluster decay is observed. 3) Formation of Sic crystallites is assumed to begin at

the layer middle and to propagate to the surface and inside as the annealing temperature increases. Amorphous silicon crystallization occurs near the substrate and the sample surface and propagates to the layer middle. Annealing at 1270°C leads to a decrease of the Si amount as a result of SiO, production in the surface vicinity. About 35% of the remaining volume of polycrystalline silicon has converted to c-Si from the substrate side.

References [l] J.A. Borders, S.T. Picraux and W. Beezhold, Appl. Phys. Lett. 18 (19711 509. [2] T. Kimura, Sh. Kagiyama and Sh. Yugo, Thin Solid Films 94 (1982) 191. [3] I.P. Akimchenko, K.V. Kisseleva, V.V. Krasnopevtsev, Yu.V. Milyutin, A.G. Touryansky and V.S. Vavilov, Radiat. Eff. 33 (1977) 75. [4] I.P. Akimchenko, K.V. Kisseleva, V.V. Krasnopevtsev, A.G. Touryanski and V.S. Vavilov, Radiat. Eff. 48 (1980) 7. [5] T. Kimura, Sh. Kagiyama and Sh. Yugo, Thin Solid Films 81 (1981) 319. 161 T. Kimura, Sh. Kagiyama and Sh. Yugo, Thin Solid Films 122 (1984) 165. [7] K. Srikanth, M. Chu, S. Ashok, N. Nguen and K. Vedam, Thin Solid Films 163 (1988) 323. [8] P.A. Alexandrov, E.K. Baranova, A.E. Gorodethky, K.D. Demakov, O.G. Kutukova and S.G. Shemardov, Physics and Technics of Semiconductors 22(41 (1988) 731. [9] K.J. Reeson, J. Stoemenos and P.L.F. Hemment, Thin Solid Films 191(l) (1990) 147. [lo] A.F. Burenkov, F.F. Komarov, M.A. Kumakhov and M.M. Temkin, Spatial Distribution of Energy Released in: Atom Collision Cascade in Solids (Energoatomizdat, Moskva, 198.5) in Russian. [ll] A.F. Burenkov, F.F. Komarov and M.M. Temkin, Phys. Status Solidi B 105 (1981) 201. [12] KKh. Nussupov, V.O. Sigle and N.B. Bejsenkhanov, Nucl. Instr. and Meth. B 82 (1993) 69. [13] J.F. Gibbons, W.S. Johnson and S.W. Mylroie, Projected Range Statistics, 2nd Ed. (Dowden, Hutchinson and Ross, Stroudsburg, PA, 1975). [14] A. Taylor, X-ray Metallography (Metallurgiya, Moskva, 1965) in Russian (translated by V.G. Lyutsau et al. from: A. Taylor, X-ray Metallography (Pittsburg, 19611). [15] W.N. Reynolds, Chemistry and Physics of Carbon, Vol. 2 (Dekker, New York, 1968).