crystal res 40 jk

8/20/2019 Crystal Res 40 JK

http://slidepdf.com/reader/full/crystal-res-40-jk 1/6

See discussions, stats, and author profiles for this publication at: http://www.researchgate.net/publication/264354560

Lattice parameter measurements of borondoped Si single crystals

ARTICLE in CRYSTAL RESEARCH AND TECHNOLOGY · APRIL 2005

Impact Factor: 0.94 · DOI: 10.1002/crat.200410361

CITATIONS

14

READS

55

2 AUTHORS:

Jacek Kucytowski

8 PUBLICATIONS 38 CITATIONS

SEE PROFILE

K. Wokulska

University of Silesia in Katowice

27 PUBLICATIONS 149 CITATIONS

SEE PROFILE

Available from: K. Wokulska

Retrieved on: 08 October 2015

http://www.researchgate.net/profile/Jacek_Kucytowski?enrichId=rgreq-044ed82c-ebc2-4497-b80b-8faf79615a9f&enrichSource=Y292ZXJQYWdlOzI2NDM1NDU2MDtBUzoxNTM5OTQ4NjEyMjM5MzZAMTQxMzcyNjY0NDc2Mw%3D%3D&el=1_x_4


http://www.researchgate.net/?enrichId=rgreq-044ed82c-ebc2-4497-b80b-8faf79615a9f&enrichSource=Y292ZXJQYWdlOzI2NDM1NDU2MDtBUzoxNTM5OTQ4NjEyMjM5MzZAMTQxMzcyNjY0NDc2Mw%3D%3D&el=1_x_1

http://www.researchgate.net/profile/K_Wokulska?enrichId=rgreq-044ed82c-ebc2-4497-b80b-8faf79615a9f&enrichSource=Y292ZXJQYWdlOzI2NDM1NDU2MDtBUzoxNTM5OTQ4NjEyMjM5MzZAMTQxMzcyNjY0NDc2Mw%3D%3D&el=1_x_7

http://www.researchgate.net/institution/University_of_Silesia_in_Katowice?enrichId=rgreq-044ed82c-ebc2-4497-b80b-8faf79615a9f&enrichSource=Y292ZXJQYWdlOzI2NDM1NDU2MDtBUzoxNTM5OTQ4NjEyMjM5MzZAMTQxMzcyNjY0NDc2Mw%3D%3D&el=1_x_6






http://www.researchgate.net/?enrichId=rgreq-044ed82c-ebc2-4497-b80b-8faf79615a9f&enrichSource=Y292ZXJQYWdlOzI2NDM1NDU2MDtBUzoxNTM5OTQ4NjEyMjM5MzZAMTQxMzcyNjY0NDc2Mw%3D%3D&el=1_x_1

http://www.researchgate.net/publication/264354560_Lattice_parameter_measurements_of_boron_doped_Si_single_crystals?enrichId=rgreq-044ed82c-ebc2-4497-b80b-8faf79615a9f&enrichSource=Y292ZXJQYWdlOzI2NDM1NDU2MDtBUzoxNTM5OTQ4NjEyMjM5MzZAMTQxMzcyNjY0NDc2Mw%3D%3D&el=1_x_3

http://www.researchgate.net/publication/264354560_Lattice_parameter_measurements_of_boron_doped_Si_single_crystals?enrichId=rgreq-044ed82c-ebc2-4497-b80b-8faf79615a9f&enrichSource=Y292ZXJQYWdlOzI2NDM1NDU2MDtBUzoxNTM5OTQ4NjEyMjM5MzZAMTQxMzcyNjY0NDc2Mw%3D%3D&el=1_x_2



Cryst. Res. Technol. 40, No. 4/5, 424 – 428 (2005) / DOI 10.1002/crat.200410361

© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Lattice parameter measurements of boron doped Si single crystals

J. Kucytowski and K. Wokulska*

Institute of Materials Science, University of Silesia, ul. Bankowa 12, 40-007 Katowice, Poland

Received 18 May 2004, accepted 29 July 2004Published online 1 March 2005

Key words silicon single crystals, lattice parameter, boron, oxygen.

PACS 82.80.EJ, 81.05.Cy, 83.85.Hf

The influence of boron dopants and oxygen impurity on lattice parameters of Si single crystals is studied.Concentrations of boron and oxygen were determined by the Bond method. A linear contraction of the crystallattice was observed due to high boron doping of Si single crystals. Lattice parameters of Si single crystals

increased below the lower limit boron concentration N B = 2.1 × 1016 cm-3. This proves the presence oxygen atlow boron concentrations. In highly boron-doped Si single crystals no oxygen influence on lattice parameterchange was observed.


1 Introduction

Silicon is the best-known and most frequently used semiconductor as a substrate of various electronic devices.

Despite intensive efforts, basic questions about point defects in silicon crystals are still unanswered and hotly

disputed. An attempt to examine the influence of boron impurities on Si single crystals lattice parameter was

undertaken in this study using the Bond method [1], known from previous determination of lattice parameters

of standard Si single crystal with precision ∆a/a = 10-6 [2]. However, to be studied single crystals should have

a high degree of structural perfection. Doping of Si single crystals is known to lead to changes in lattice

parameters [3-8]. Impuritie atoms of radii smaller than the covalent atomic radius of Si (B or P) cause crystal

lattice contraction, while atoms of larger atomic radii (Sb) cause its expansion. Numerous studies have been

carried out on lattice parameter changes due to impurities, their diffusion as well as on the influence of oxygen

micro-precipitations generated during single crystals growing on lattice parameters changes. Several authors

measured the effect of boron doping on silicon lattice deformations [3-8]. The analysis of data for various

boron concentrations in silicon shows that the reported values of the lattice contraction coefficient β lie

between 4.5 × 10-24 cm-3 and 5.5 × 10-24 cm-3. Table 1 surveys the empirical values of lattice contraction

coefficient β of Si crystals in the presence of boron dopants.

Boron atoms most frequently substitute the silicon atoms. As boron atoms are smaller than the covalent

silicon radius, they locally contract the lattice and ultimately cause changes in the relative averaged lattice

parameters:∆a/ap = β N B, (1)

where: ∆a/ap is the relative change in the lattice parameter under the influence of impurity, ap is the lattice

parameter of pure and perfect Si single crystal ap = 0.543098367 ± 5.2 × 10-8 nm (under normal atmospheric

pressure and 20°C) [9], and N B is the boron concentration (cm-3).

The influence of boron atom radius 0.088 nm as compared with the covalent radius of silicon atom 0,117

nm, on the lattice constant and unit cell volume change was considered by Celotti et al. [4]. In fact, the boron

atom radius is equal to (0.084 ±0.001) nm and the covalent silicon radius to (0.118 ±0.001) nm. Such values

were obtained by Becker [7] from silicon lattice parameter determined with a high accuracy ∆a/a = ± 1 × 10-7 ____________________

* Corresponding author: e-mail: [email protected]



Cryst. Res. Technol. 40, No. 4/5 (2005) / www.crt-journal.org 425


by the double crystal X-ray technique. He found the lattice contraction coefficient β = - 5.6 × 10-24 cm-3 on the

basis of unit cell volume previously determined by Siegert et al. [10] for high-purity silicon single crystals.

Using a high resolution double-crystal technique Holloway and McCarthy [8] determined coefficient β = (-5.19

± 0.09) × 10-24 cm-3 in epitaxial layers of silicon doped with boron (Si:B).

Table 1 Empirically based β coefficients of relative lattice changes in Si single crystals due boron doping.

Material Boron concentration N B [cm-3] Coefficient β [10-24 cm-3] Reference

Single crystal of silicon ≤ 4x1020 -4.7 [3]



Epitaxial silicon layers < 1x1020 -6.2 [6]

Single crystal of silicon > 1x1018 -5.6 [7]

Silicon epilayers 1.7x1019-1.2x1020 -5.19 [8]

Si single crystals are first of all obtained by two methods: the floating zone and the Czochralski method [11].

Dopants as well as trace amounts of undesirable impurities are introduced to them during the growth. High-

purity single crystals – both p and n types – are frequently obtained by the floating zone method. The resistivityof Si single crystals obtained by this method is not less than 1000 Ωcm. In this case the concentration of

impurities such as oxygen and carbon does not exceed 5 × 1016 cm-3, while for other metals it does not exceed 5

× 1013 cm-3.

Definitely worse Si single crystals are obtained by the Czochralski method. In this case it was found that

oxygen is incorporated to the pulled crystal from molten phase as an impurity. At that time the oxygen

concentration is around 1017 - 1018 cm-3, and the resistivity of such crystals falls to approximately 10-20 Ωcm.

The aim of this paper was to investigate the relation between concentrations of boron dopant moreover

oxygen impurity and the lattice parameter of Si single crystals using the Bond method.

2 Experimental

A series of 19 p-type (001) oriented Si:B single crystals obtained by the Czochralski method, which differed inresistivity ρ between 0.03 Ωcm and 40 Ωcm, was studied. Lattice parameters were measured on an asymmetric

reflection 444 CuK α1, λ = 0.15405929 ± 5x10-7 nm [12], using the method of precise measurement of lattice

parameter for perfect crystals – the Bond method [1]. For each of them a series of ten measurements of lattice

parameters was made. Statistical analysis of measurement results was carried out. Relative error was δa/a = ± 1

× 10-6. Lattice parameters were adjusted to 20°C, using a linear coefficient of thermal expansion [13]:

α = [2.51 + 0.0087(T – 293.0) K ± 0.05] × 10-6 K -1. (2)

Analysis of systematic errors was carried out according to ref. [14]. The contribution of the following factors

causing a shift of the peak position of measuring curve with respect the Bragg angle was considered: X-rays

refraction, X-ray beam horizontal and vertical divergence, absorption in the crystal and others. These

aberrations result in a change in lattice parameters and affect the accuracy of measurements. The total value of

obtained corrections was Σ∆a = 6.13 × 10-6

nm.

3 Results

The interaction of boron atoms with the Si crystal lattice is the basis of effective change in lattice parameters of

the examined Si:B single crystals. The concentration N B of boron atoms in silicon was determined using

relation (1). The coefficient of lattice changes β from the values of silicon and impurity atomic radii was

determined from the relation:

,

B Si

Si

R R

R N β

−

=

⋅

(3)



426 J. Kucytowski and K. Wokulska: Lattice parameter measurements of doped Si single crystals


where: RSi is the Si covalent atomic radius = 0.118 nm [10], R B is the B covalent atomic radius = 0.084 nm [7],

and N is the density of lattice sites = 4.99 × 1022 cm-3. The calculated value of the coefficient β = -5.77 × 10-24

cm-3 is close to the literature data (Table 1).

Table 2 presents results of lattice parameter measurements for Si:B single crystals and the calculated boron

concentrations N B and boron concentrations determined from resistivity measurements. The comparison of the

results shows excellent agreement between our findings and boron concentrations obtained on the basis of theresistivity measurements. While determining the boron concentration the lattice parameter of ideal Waso 9

single crystal Si was taken as the standard value, ap = 0.543098367 ± 5.2 × 10-8 nm, referred to 20°C and

normal atmospheric pressure [9]. This single crystal had a perfect structure and lack any of impurities. The

dependence of Si single crystal lattice parameter changes versus boron doping is presented in Fig. 1.

It was ascertained that the lattice parameter falls linearly with increasing boron concentration (between N B

= 2.1 × 1016 cm-3 and 2.3 × 1019 cm-3). This proves a strong influence of boron on the silicon crystal lattice and

lack of any defects such as another impurities, striations or agglomerations of point defects. When comparing

relative changes in the lattice parameter ∆a/a p this trend becomes even clearer. Similar relationship for boron-

doped silicon up to N B = 1 × 1019 cm-3 was observed by Baribeau and Rolfe [6]. For single crystals of lattice

parameter values close to pure Si measuring points on the diagram a = f(NB) become inseparable. Below the N B

= 5 × 1016 cm-3 the changes in lattice parameter values are imperceptible.

Table 2 Boron concentrations in silicon single crystals derived from the measured lattice parameter and resistivitymeasurements.

Crystal a ±1x10-6 [nm] N B concentration from

Bond method [cm-3]∆a/ a p

N B concentration fromresistivity measurements [cm-3]

High pure Si p [9] 0.543098367±5.2x10-8 - -

1 0.5430245 2.3 × 1019 -1.4 × 10-4 3.62 × 1019 - 2.01 × 1019

2 0.5430387 1.9 × 1019 -1.1 × 10-4 2.61 × 1019 - 1.62 × 1019

3 0.5430492 1.5 × 1019 -9.1 × 10-5 2.01 × 1019 - 1.34 × 1019

4 0.5430720 8.4 × 1018 -4.9 × 10-5 1.23 × 1019 - 8.49 × 1018

5 0.5430798 5.9 × 1018 -3.4 × 10-5 9.08 × 1018 - 5.97 × 1018

6 0.5430811 5.5 × 1018 -3.2 × 10-5 6.65 × 1018 - 4.47 × 1018

7 0.5430897 2.7 × 1018 -1.6 × 10-5 4.89 × 1018 - 3.02 × 1018

8 0.5430949 1.1 × 1018 -6.4 × 10-6 2.33 × 1018 - 1.40 × 1018

9 0.5430977 2.1 × 1017 -1.2 × 10-6 1.46 × 1018 - 9.14 × 1017

10 0.5430982 5.3 × 1016 -3.1 × 10-7 9.46 × 1017 - 5.89 × 1017

11 0.5430979 1.5 × 1017 -8.6 × 10-7 6.05 × 1017 - 3.88 × 1017

12 0.5430983 2.1 × 1016 -1.2 × 10-7 4.25 × 1017 - 2.77 × 1017

Fig. 1 Lattice parameters as a function ofboron concentration.



Cryst. Res. Technol. 40, No. 4/5 (2005) / www.crt-journal.org 427


Starting from Si crystal no 13 (Table 3), further increase in the lattice parameter was observed as against the

parameter of standard single crystal Sip = 0.543098367 ± 5.2x10-8 nm. This should be connected with the

presence of oxygen in single crystals examined. Results for Si single crystals no 13-19 and the oxygen

concentration N O determined from relation (1) are presented in Table 3. To determine the oxygen concentration

N O, the lattice expansion coefficient β O = 4.4 × 10-24 cm-3 for oxygen given by Windisch and Becker [9] was

used.

As shown in Table 3 and Fig. 2, the increase in lattice parameters results from the increase in oxygen

concentration in single crystals studied here.

Table 3 The oxygen concentrations in silicon single crystals derived from the lattice parametermeasurements.

Crystal a ± 1x10-6 [nm] N O [cm-3] ∆a/ a p

High pure Si p[9] 0.543098367 ± 5.2 × 10-8 - -

13 0.5430989 2.2 × 1017 9.8 × 10-7

14 0.5430993 3.9 × 1017 1.7 × 10-6

15 0.5431019 1.5 × 1018 6.5 × 10-6

16 0.5431006 9.3 × 1017 4.1 × 10-6

17 0.5431011 1.1 × 1018 5.0 × 10-6

18 0.5431010 1.1 × 1018 4.9 × 10-6

19 0.5431005 8.9 × 1017 3.9× 10-6

Fig. 2 Relationship betweenchange of the lattice parameterand the oxygen concentration.

As in highly boron-doped Si single crystals no influence of oxygen on lattice parameter changes was observed,

and at lower concentration the crystal lattice expanded as compared with the standard single crystal, it proves

the reactions proceeding during the crystallisation. Abe et al. [15] found that during the growth of single

crystals obtained by the Czochralski method oxygen is incorporated to the crystal from the molten phase as animpurity originating from quartz crucible. Oxygen from the quartz crucible transfers to the molten Si up to the

solubility limit. At the same time silicon monoxides and other oxides of dopants (B, Sb) evaporate, depending

on their partial pressures. In highly boron-doped Si single crystals, boron can react with SiO thereby enhancing

the evaporation of SiO when pulling Si crystal. This results in a reduction of the oxygen concentration, which

leads to values undetectable in lattice parameters measurements by the Bond method (Table 2).

While comparing the results in Table 2 one aspects that lattice parameter measurements of high boron

concentration Si single crystals by the Bond method are more accurate than the resistivity measurements. For

the determination of boron concentration from the silicon resistivity the results obtained by the American

Society for Testing and Materials ASTM [16] were used. Only close to the threshold of impurities detectability

by the Bond method (i.e. below the concentration of 5 × 1016 cm-3) the NB values predicted by the Bond

method are lower than those from resistivity measurements.



428 J. Kucytowski and K. Wokulska: Lattice parameter measurements of doped Si single crystals


4 Summary

On the basis of precise and accurate measurements of lattice parameters of the boron and oxygen

concentrations in Si single crystals obtained by Czochralski method was determined. It is concluded that the

cause of the lattice contraction within the range a = 0.5430245 ÷ 0.5430983 nm is immediately attributed to

the presence of substitutional boron in the silicon crystal lattice.

A prevailing nonintentionally impurity in silicon crystals, oxygen, may also contribute to alter the lattice

parameters. In this case the oxygen is incorporated into the silicon lattice occupying interstitial sites and

causing a lattice expansion. It has been ascertained that in highly boron-doped Si single crystals no oxygen

influence on lattice parameter change was observed. Only below the boron concentration N B = 2.1 × 1016 cm-3

the presence of oxygen within the range N O = 2.2 × 1017÷ 1.5 × 1018 cm-3 was observed.

Acknowledgements The authors wish to thank Mrs B. Surma from the Institute of Electronic Materials Technology inWarsaw for supplying the single crystals and for fruitful discussions.

References

[1] W. L.Bond, Acta Cryst. 13, 814 (1960).[2] J. Härtwig, J. Bąk-Misiuk, H. Berger, H.- G. Brühl, Y.Okada, S. Grosswig, K. Wokulska, and J. Wolf, Phys. Stat.

Sol. (a) 142, 19 (1994).[3] S. Kishino, Adv. X-ray Anal. 16, 367 (1973).[4] G. Celotti, D. Nobili, and P. Ostoja, J. Mater. Sci. 9, 821 (1974).[5] A. Fukuhara and Y. Takano, Acta Cryst. A 33, 137 (1977).[6] J. Baribeau and S. Rolfe, Appl. Phys. Lett. 58, 2129 (1991).[7] P. Becker in Proc. VII Intern. School on Defects in Crystals, World Scientific, Singapore 1987, p. 118.[8] H. Holloway and S. L. McCarthy, J. Appl. Phys. 73, 103 (1993).[9] D. Windisch and P. Becker, Phys. Stat. Sol. (a) 118, 379 (1990).

[10] H. Siegert, P. Becker, and P. Seyfried, Z. Physik B 56, 273 (1984).[11] J. Żmija, Fundamentals of Single Crystals Growth Theory, PWN, Warszawa, 1987.[12] G. Hölzer, M. Fritsch, M. Deutsch, J. Härtwig, and E. Förster, Phys. Rev. A 56, 4554 (1997).[13] Y. Okada and Y. Tokumoru, J. Appl. Phys. 56, 314 (1984).[14] J. Härtwig and S. Grosswig, Phys. Stat. Sol. (a) 115, 369 (1989).[15] K. Abe, K. Terashima, T. Matsumoto, S. Maeda, and H. Nakanishi, J. Cryst. Growth 186, 557 (1998).[16] Standard Practice for Conversion between resistivity and dopant density for boron-doped and phosphorus-doped

silicon, Annual Book of ASTM, F 723-81, 590 (1982).

crystal res 40 jk

Documents