Journal of Alloys and Compounds, 209 (1994) 181-187 181 JALCOM 1059

Solid solutions of silicon in boron-carbide-type crystals

H e l m u t W e r h e i t , U d o K u h l m a n n and M i c h a e l L a u x Solid State Physics Laboratory, University of Duisburg, D-47048 Duisburg (Germany)

R a i n e r Te l l e Institut fiir Gesteinshiittenkunde, RWTH Aachen, D-52064 Aachen (Germany)

(Received November 16, 1993)

Abstract

The optical absorption spectrum of silicon-doped boron carbide in the spectral range of the absorption edge and its low-energy tail, obtained from transmission measurements between 0.25 and 4 eV, is compared with that of undoped boron carbide (B4.3C) with comparably low distortions. Silicon is proved to be an effective dopant of boron carbide, because the edge absorption spectrum and the plasma edge are considerably changed. However, the conduction remains p-type for the sample investigated. The IR phonon spectrum of silicon-doped boron carbide is similar to that of boron-rich boron carbide, which contains a considerable amount of chainless unit cells. It is shown that the Si atoms occupy these cells, forming a two-atom chain. From a comparison of the Raman spectrum with those of similar structures and theoretical calculations, it can be estimated that the force field constant in such chains varies linearly with the distance between the atoms.

1. Introduction

The tailoring of ceramics for specific applications is a difficult problem in general. In the case of boron carbide, this problem has to be solved for different aspects. On the one hand, the utilization of its excep- tional hardness is restricted by its poor sinterability, low toughness and low oxidization resistance. On the other hand, its unique thermoelectric properties make it a very promising semiconductor for thermoelectric energy conversion; however, it is p-type throughout the whole homogeneity range and a corresponding n-type material is required to realize this application.

Doping and the formation of ternary compounds, respectively, are suitable procedures to solve such prob- lems. Telle [1] has described in detail the formation, sintering and reaction kinetics of solid solutions of silicon in the boron carbide structure, and has discussed the structure modifications compared with that of boron carbide as known at that time. Meanwhile, the con- centrations of the different structural elements in the unit cells of boron carbide (B12 and BloC icosahedra, C-B-C and C-B--B chains and, particularly, the con- centration of chainless unit cells) have been quanti- tatively determined throughout the homogeneity range [2, 3]. Moreover, the relationship between the aniso- tropic distortion of the icosahedron, when a carbon atom substitutes for boron, and the anisotropic change

of the unit cell parameters has been discussed in detail [4]. These aspects lead to new considerations with respect to the possible accommodation of silicon atoms in the unit cells of boron carbide. These considerations are supported by investigations of the IR-active and the Raman-active lattice vibrations, and their inter- pretation based on group theoretical results. To obtain some insight into the electronic effect of this silicon doping of boron carbide, qualitative investigations on the optical interband transitions and on the Seebeck coefficient have been performed.

2. Structural aspects

The change in the unit cell parameters of boron carbide could be easily described [4] by the effect of chainless unit cells, whose concentration increases from zero at the carbon-rich limit of the homogeneity range (B4.3C) to more than 50% close to the boron-rich limit [2, 3], Compared with other interstitial sites in the unit cells of boron carbide, discussed with respect to the accommodation of silicon atoms, chainless cells offer by far the largest holes in the structure. This suggests them to be preferential for the accommodation of foreign atoms.

It can be assumed, according to the structure of B2.8Si, that two silicon atoms can be arranged on the

0925-8388/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSDI 0925-8388(93)01059-D

182 H. Werheit et al. / Solid solutions o f Si in boron carbides

t - " l

c- o (9 U3

f13 8 ' ' ' ' ' I'

2

8 10 12 14 16 18 Carbon Content Iat.%l

t ' - I

6 ~

."Z_ t'--

G)

c-

c- O c--

2,0

03

b5

0

Fig. 1. Si content in the homogeneity range of boron carbide, depending on its carbon content (I-q, • ) (data taken from Table 1 in ref. 1). The sample with excess carbon is shifted to the carbon-rich limit B4.3C of the homogeneity range. Also shown is the number of silicon sites in undoped boron carbide, if (according to the compound B2.sSi [7, 8]) two possible sites per chainless unit cell [2, 3] are assumed (O). • marks the sample whose specific properties are discussed in the paper•

trigonal axis in the rhombohedral unit cell. In Fig. 1, the number of such sites in the chainless unit cells of the boron carbide structure determined in refs. 2 and 3 are compared with the silicon content in the silicon- doped boron carbide given in Table 1 of ref. 1. The very good agreement over a large portion of the ho- mogeneity range of boron carbide confirms that the silicon atoms are accommodated in the chainless unit cells of undoped boron carbide of the relevant chemical composition. Only close to the boron-rich limit of the homogeneity range do other mechanisms discussed be- low obviously prevent any further increase in the ac- commodation of silicon atoms on these sites•

Based on this result, the modifications of the unit cell parameters caused by the silicon atoms can easily be explained, when the parameters of a-rhombohedral boron and B2.sSi (Table 1) are used for comparison• As discussed earlier [4] in some detail, the increase in

TABLE 1. Uni t cell parameters of some representatives of the t~-rhombohedral boron structure group

a c c/a V Ref. (A) (A) (A ~)

et-rhombohedral B 4.927(3) 12.564(7) 2.55 264.1 5-7 B4.3C 5.602 12.075 2.16 328.2 4 B2.8Si 6.319 12.713 2.01 439.6 7, 8

the a and the c axes starting from the carbon-rich limit is caused by the tendency of the chainless unit cells to approach the cell parameters of ot-rhombohedral boron•

The strong, largely covalent bonds between the end atoms of the C-B-C or C-B-B chains and the equatorial atoms of the icosahedra are directed approximately perpendicular to the c axis [2, 3]. Therefore, in this direction, the chainless unit cells have only a small effect on the average cell parameters measured by X- ray diffraction, because the effect is largely suppressed by the large number of unit cells retaining their re- spective C-B-C or C-B-B chains. However, parallel to the c axis, the effect of these bonds is much weaker, because, in this direction, they are stressed on bending and, therefore, the average elongation of the c axis is considerable. The same arguments also hold in the case of silicon doping, helping to explain the even larger changes in the c axis in this case, since the unit cell parameters of B2.sSi greatly exceed those of o~-rhom- bohedral boron (Table 1). Moreover, it must be taken into account that silicon doping obviously means that the chainless unit cells in undoped boron carbide of the same composition are completed; hence, the dis- torted structure is stabilized in this way. This may be the reason why, in silicon-doped boron carbide, the elongation of the c axis extends over a part of the

H. Werheit et al. / Sofid solutions of Si in boron carbides 183

rn

12.4

5.g

v

• --- 5.8 x <

5.7

5.6 , I 6 8

A

A

A

A

doped D O O

_

undoped u I , I

10 12

doped Z

A

&

undoped /

12 14 16 18 20 C Content(at.%)(Si neglected)

12.3

,,< 12.2 .- x

<

12.1

Fig. 2. Unit cell parameters of silicon-doped boron carbide compared with the averaged slopes of the cell parameters derived for undoped material [5]. The arrows indicate the shift to the carbon-rich limit of the homogeneity range (see ref. 3).

range in which the structure would collapse in the case of such distortions in undoped boron carbide.

Valuable qualitative conclusions can also be derived from the behaviour close to the boron-rich limit of the homogeneity range. Despite the chainless unit cells exceeding 50%, the solubility of silicon atoms in the structure decreases. From this fact, it can be concluded that the controlling role of even this comparably low partition of complete boron carbide unit cells cannot be suppressed by the larger partition of (BllC) Si2 unit cells. Hence, the bonding forces of the Si2 chains in these cells must be considerably weaker than those of the C-B-B chains in the unchanged (BllC)C-B-B unit cells (for experimental confirmation, see below). There- fore, an increasing number of chainless unit cells is energetically more favourable than is a high degree of occupation of these cells by silicon atoms.

3. Electronic properties

To obtain some qualitative insight into the effect of silicon doping on the electronic properties of boron carbide, the absorption edge and its low-energy tail have been measured for one sample. This was composed of 78.7 wt.% B4C, 16.3 wt.% B and 5 wt.% Si. Assuming that this composition also holds for the prepared sample, it contains 16.5 at.% C in the boron carbide structure (silicon content neglected) and 2.0 at.% Si. These data are included in Fig. 1 (symbol, B).

Optical measurements were performed with a Per- kin-Elmer Lambda 9 double-beam spectrometer. The sample compartment of this spectrometer is behind the monochromator. Hence, optical excitation by the meas- uring beam can be largely excluded, and the results correspond to the thermal equilibrium of the sample. The absorption coefficient was determined from trans- mission measurements, taking reflectivity and multiple reflections in the sample into account.

For these transmission measurements, a plane parallel sample was required, whose thickness did not exceed several micrometres, because of the high absorption level of boron carbide in this spectral range [9]. The sample was first polished on one side, then cemented to a quartz glass support by an organic glue, before it was finally polished on the second side. Grinding and polishing leads to convex surfaces, making it difficult to determine reliably the thickness. The absolute un- certainty is only a few micrometres, but, relatively, it may be up to about 25%. This is also the absolute uncertainty of the optical absorption coefficient in Fig. 3, where the silicon-doped sample is compared with high quality undoped boron carbide of approximate c o m p o s i t i o n B4.3C [9]. This was prepared from extremely fine powder (H.C. Starck) by hot isostatic pressing (at 2100 °C and 30 MPa for 30 min in vacuo) in the MPI Stuttgart.

The effect of silicon-doping on the electronic prop- erties of boron carbide is considerable. While the steep absorption edge is flattened, a strong absorption band

184 H. Werheit et al. / Solid solutions o f Si in boron carbides

7000

6000

5000

E 4 0 0 0

3 0 0 0

/ - / -

j - j f undoped (high quality)

/ -

/ t

/ /

/ /

/ / /

/ /

/ /

f . . . . . - 2000 ;-:=:~\ . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . .

j , ~ ~ . / Si-doped (2 at.%) /

. /

10000 , , , , I . . . . I . . . . I . . . . I 2 3 4

(eV) Fig. 3. Absorption coefficient vs. photon energy in the absorption edge range and its low-energy tail of boron carbide doped with 2 at.% Si atoms, compared with high quality undoped material [9]. The absorption bands at 0.4 eV do not belong to boron carbide but are C - H vibrations of the organic glue by which the thin samples were adhered to a quartz glass support.

develops at low photon energies. Obviously, silicon evokes a high density level in the band gap, and strong interband transitions are largely cancelled or shifted towards higher photon energies outside the range of our spectrometer.

The Seebeck coefficient remains positive but greatly exceeds that in pure boron carbide. Hence, p-type conductivity also prevails in silicon-doped boron carbide.

For a quantitative evaluation of the effect of silicon- doping on the electronic properties of boron carbide, more detailed and systematic investigations are nec- essary.

4. IR spectra

For the optical measurements on the sample men- tioned above in the mid-IR and far-IR spectral range, a Bruker Fourier transform (FT) IR spectrometer (IFS) l13v was used. The reflectivity spectrum measured was transformed to the absorption spectrum by a Kra- mers-Kronig transformation. The extrapolation to zero frequency required was based on the obvious assumption of a semiconducting material.

The reflectivity spectrum (Fig. 4) and the absorption spectrum (Fig. 5) are characterized by the typical phonon bands of boron-rich boron carbide. However, the com- parison with B4.3C at low frequencies (inset in Fig. 4) shows that silicon doping causes the plasma edge of

boron carbide to shift towards higher frequencies, in- dicating an increasing carrier concentration. The broad maximum at about 2000 cm -1 is probably the result of the contribution of the rear reflection to the signal measured. The IR and far-IR absorption spectra show that the phonon bands are considerably broadened and slightly shifted towards lower frequencies, as is known from undoped boron-rich boron carbide; the shoulder in the phonon band at 1580 cm -1 results from the isotope effect, which is more pronounced in this range of chemical composition, where it is almost only C-B-B chains that have remained in the structure [2, 3]. In the IR spectrum, there is no indication of the Si2 chains existing in about 20% of the unit cells (Fig. 1 and refs. 3 and 4). This is in agreement with group theory [10, 11], which shows that a two-atom chain in the D3d symmetry of the boron carbide structure is not IR active.

5. Raman spectrum

The Raman spectrum of the sample mentioned was measured with Bruker FT-Raman equipment using an Nd-YAG laser (1.06/zm-1.16 eV) for excitation. Av- eraging of about 4000 interferograms was necessary to obtain reliable Raman spectra of the boron carbide.

The most significant feature of the Raman spectrum of silicon-doped boron carbide (Fig. 5) is that the signal

H. Werheit et al. / Sofid solutions o f Si in boron carbides 185

0.45

0.4

0.35 ..~

rr 0.3

0.25

0.2 0

I ' ' ' ' I ' ' ' ' 1 ' ' ' ' 1 . . . . I ' ' ' '

0.8 . . . . i . . . . I . . . . i . . . . I . . . .

0.7

0.60,5 ~ ~ + 2 a t . % S l

0.3

0 100 200 300 400 500]

I

I , , , t I t , , , I , , , , I I , I , I

500 1000 1500 2000 2500 3000 Wave Number [cm "1]

Fig. 4. Reflectivity spectrum of silicon-doped boron carbide in the mid-IR and far-IR spectral range. In the inset, the low-frequency part of the spectrum is compared with undoped B4.3C. The broad maximum with a peak at 1850 cm -1 is probably caused by the reflection from the rear of the thin sample.

2.51, , , I . . . . ] . . . . [ . . . . I . . . . I . . . .

x ID c

c- o

. i

..,_, im l _

o i n

..Q <

1.5

0.5

• ) II I I

I

C ) + 2 at.% Si

0 ~ 0 500 1000 1500 2000 2500 3000

Wave Number [cm -1] Fig. 5. Spectrum of the absorption index of silicon-doped boron carbide, determined by a Kramers-Kronig transformation from the reflectivity spectrum in Fig. 4.

strongly increases towards high frequencies in the Stokes range, exhibiting the steepest slope at an absolute photon energy of about 0.75 eV. This radiation obviously results from luminescence and confirms the existence of an

electron transition identified in the absorption spectrum [9]. Electrons, which were excited by the laser radiation to the conduction band, undergo subsequent transitions to the silicon-induced states in the band gap, which

186 H. Werheit et al. / Solid solutions o f Si in boron carbides

are responsible for the strong absorption band with maximum at 1.2 eV in Fig. 3. The narrow peak at -865 cm-a (absolute energy, 1.27 eV) and the broad peak at - 240 cm -1 (absolute energy, 1.195 eV) in the anti-Stokes range also result from electron transitions, with the broad peak being in agreement with the analysis of the absorption edge of boron carbide [9]. While the peak at -865 cm-1 is found in the Raman spectra of silicon-doped but not in undoped boron carbide, it is the only one that can be attributed without doubt to the effect of the silicon atoms in the boron carbide structure. For the interpretation of the other transitions of electrons affecting the Raman spectrum in Fig. 6, the formation of the electron-trapping levels in boron carbide discussed in ref. 12 in more detail must be taken into account.

The enlarged spectrum of the Raman-active phonons in silicon-doped boron carbide is outlined in the inset in Fig. 6. Since the Raman phonon spectrum reacts much more sensitively to structural distortions than does the IR phonon spectrum, the almost complete disappearance of the intra-icosahedral Raman-active phonon bands in the spectrum compared with the Raman spectrum of the undoped material [12] confirms that the structure is more distorted than that of undoped boron carbide with the same carbon content. The strongest Raman phonon band at 1080 cm -1 belongs to the intericosahedral B-B vibrations. A second distinct Raman band is seen at 570 cm -~. We attribute this

to the Raman-active vibration of the Si-Si chains in the structure.

Based on this assumption, the Raman spectra of the representatives of the t~-rhombohedral boron structure group yield information on the forces in two different bonds within each structure, i.e. the intericosahedral B-B bond and the bond between the atoms forming the chains. The Raman spectra of numerous icosahedral boron structures [13] confirm that the intericosahedral B-B vibration depends only slightly on the individual structure. Therefore, this vibration can be used to normalize the Raman-active vibration of the two-atom chain.

Neglecting the contribution of the five neighbours of the B atoms involved in the intericosahedral two- centre B-B vibration, and that of the equatorial atoms of the neighbouring icosahedra bonded to the silicon atoms on the stretching vibration of the Si-Si chain, because in both cases only the comparably weak bending forces are stressed by these vibrations, the relationship between the force field constants of the Si-Si and the B-B vibration can be estimated according to

t°sl-s___2 : /'~si-si/ ( m . / ah~-B \ ka-a ] \ msU

leading to

ksi--si = 0.72 kB-B

0.9 0.12 l i ' ' i i i ' ' '

0 . 8 -

" 0 . 1

0.7- c -

D 0.6 -°'°8 ~D

0 . 5 - 0 . 0 6

" ~ ,

o.4- S .0.04

c 0.3- E " 0.21-100300 500 700 1300

0.1

-1000 -500 0 500 1000 1500 2000 2500 3000 3500 Raman Shift I-cm "13

Fig. 6. Raman spectrum of silicon-doped boron carbide in the Stokes and in the anti-Stokes range. The enlarged spectrum of the Raman-active lattice vibrations is shown in the inset. The narrow peaks at 1500 and 3000 cm -1 are caused by the exciting Nd-YAG laser.

H. Werheit et al. / Solid solutions of Si in boron carbides 187

2.5

•2.0 J~ x

c 1.5 o

~ 1.0 ±

m ° 0.5

theory ~ - experiment

\ boron carbide X-B-X chllTn k(BX)/k(BB) vs. distance X-)~

[3/B6P (theory)

_ ~ 4 2 ~ A s (theory)

BsSi (exp./Raman)

B60 (exp./Raman)

0.0 ' i i ' 2.2 2.4 2 6 2 8 3 3.2 X-X Distance (Chain) [~3

Fig. 7. Ratio of the force field constants of the intericosahedral X-X vibration and the B--B force field constants in different (B12)X2-type structures. The theoretical results on B6P and B6As of Beckel and Yousaf [14] are shown, as are the experimental results for B6Si (this work) and B60 [13]. Data for the three- atom chain in boron carbide are shown for comparison: theoretical results of Beckel and Yousaf [14], and experimental results of Kuhlmann and Werheit [2, 3, 12].

In Fig. 7, this result is compared with the corre- sponding value for the O-O vibration derived from the Raman spectrum of B4202 [13] and with the data calculated by Beckel and Yousaf for (B12)P2 and (B12)As2 [14]. The ratios of the force field constants are plotted v s . the atomic distances X - X of both atoms in the chains of the different compounds (see ref. 7 and references therein). All these results can be satisfactorily fitted by a linear dependence on the distance X-X, as expected in the case of a linear force law. Obviously, the kind of atoms forming the chains in the (B12)X: structure has no significant effect on the bonding forces in opposition to the distance between both atoms.

The ratio of k~_x in the three-atom X-B-X chain and k~a of boron carbide (theoretical data [14], as well as experimental data derived from IR spectra [2, 3, 12]) are included in Fig. 7 for comparison. This information shows that the three-atom chain in boron carbide stabilizes the structure more than does any two-atom chain; in particular, much more than the Si-Si chain in the compound under discussion. This may support the above discussion that the (B12)Si2 unit cells are not able to determine the whole structure of

silicon-doped boron carbide. Probably, the three-centre bonds in the chainless a-rhombohedral boron-like unit cells are strong enough to contract the structure per- pendicular to the c axis to drive the silicon atoms out of the structure. In addition, the strong distortions caused by Si2 chains in a large portion of unit cells may make the whole structure unstable. This would explain the decreasing solubility of silicon atoms towards the boron-rich limit of the homogeneity range of boron carbide.

Acknowledgment

Some of this work was performed as part of a project supported by the Minister of Research and Technology of Germany under Contract 317-4003-0328845A.

References

1 R. Telle, Structure and properties of Si-doped boron carbide, in R. Freer (ed.), The Physics and Chemistry of Carbides, Nitrides and Borides, Kluwer, Dordrecht, 1990, p. 249.

2 U. Kuhlmann and H. Werheit, Solid State Commun., 83 (1992) 849.

3 U. Kuhlmann, H. Werheit and K.A. Schwetz, J. Alloys Comp., 189 (1992) 249.

4 H. Werheit, U. Kuhlmann and T. Lundstr6m, J. Alloys Comp., 204 (1994) 211.

5 B. Morosin, A.W. Mullendore, D. Emin and G.A. Slack, Rhombohedral crystal structure of compounds containing boron-rich icosahedra, Boron-Rich Solids AIP Proc., 140 (1986) 70.

6 G. Will, B. Kiefer, B. Morosin and G.A. Slack, NovelRefractory Semiconductors, Mater Res. Soc. Symp. Proc., 97 (1987) 151.

7 T. Lundstr6m, Structural aspects of some boron-rich refractory compounds related to B4C , Boron-Rich Solids, AlP Proc., 140 (1986) 186.

8 B. Magnusson and C. Brosset, Acta Chem. Scand., 16 (1962) 449.

9 H. Werheit, M. Laux, U. Kuhlmann and R. Telle, Phys. Status Solidi, B, 172 (1992) K 81.

10 H. Binnenbruck and FI. Werheit, Z. Naturforsch. A, 34 (1979) 787.

11 H. Werheit and H. Haupt, Z. Naturforsch. A, 42 (1987) 925. 12 U. Kuhlmann and H. Werheit, J. Alloys Comp., 205 (1994)

87. 13 U. Kuhlmann and H. Werheit, J. Phys. Chem. Sol., in press. 14 C.L. Beckel and M. Yousaf, Lattice vibrations of icosahedral

boron-rich solids, Boron-Rich Solids, AIP Proc., 231 (1990) 177.