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Self-diffusion in InSb
PHYSICS LETTERS
Volume 71A, number 2,3
30 April 1979
SELF-DIFFUSION IN InSb H. SIETHOFF Physikalisches Institut, Universitdt Würzburg, D-8700 Wurzburg, Germany
Received 21 February 1979
The activation energy and the preexponential factor of self-diffusion in InSb have been derived from plastic deformation 2/s, respectively. These values may be ascribed to the slowest diffusing element.
techniques to be 1.5 eV and 3 x 10~cm
Self-diffusion in InSb has been studied by several authors [1—51. The first measurements were per.
formed by Boltaks and Kulikov [1], but most likely their results were influenced by grain boundaries [5]. Eisen and Birchenall [2] found the activation energies for In and Sb self-diffusion to be 1.82 eV and 1.94 eV, respectively; theelements. preexponential factor D0 wasof5 Cu X 102 2/s for both From investigations cm diffusion [3] and S diffusion [4] in InSb activation energies of 1.84 eV and 2.0 eV were derived for the self-diffusion of In and Sb, respectively, in excellent agreement with the above values. All these measurements [2—4]were mterpreted in terms of vacancy diffusion. On the contrary, Kendall and Huggins [5] reported on measurements yielding an activation energy of 4.3 eV for both, In and Sb diffusion, 2/s and with 3.1 preexponential factors of 1.8 X 1013 cm X 1013 cm2/s, respectively. They interpreted their results in terms of a divacancy mechanism. The striking discrepancies between the different authors, though discussed to some extent by Kendall and Huggins [5], are not understood. One reason may be found in the extremely small temperature region (480 to 520°C) suitable for tracer diffusion measurements in InSb, which may lead to erroneous Arrhenius plots; Self-diffusion parameters can be also deduced from plastic deformation experiments at high temperatures. During plastic deformation besides dislocations also point defects are created, which may become rate controlling at high temperatures. Two mechanisms have been discussed in this connection: the climb of edge dislocations and the dragging ofjogs on screw
dislocations. It has been shown [6,7] that both pro-
cesses are rate controlling at the beginning of stage III (stress r 111, strain rate of the dynamic deformation test in Si and Ge. For the climb mechanism it was found that the shear stress normalized by the shear modulus, r111/G, as a function of the strain rate and ofequation, the temperature T isoriginally compatible with the following which was developed for the interpretation of steady-state creep experiments [8] and which is transformed here for the purpose of the dynamic deformation test: • SD
a111)
a111
(r
11 1/G)’1
=
(kTa1j1/AD0Gb) exp(Q /kT).
(1)
Here b is the Burgers vector, k is Boltzmann’s constant and D0 and QSD are the preexponential factor and the activation constants nenergy andA of areself-diffusion, correlated byrespectively. the empiricalThe relation [9] n3.0+0.3Iog 1oA.
(2)
This method has been successfully applied to evaluate self-diffusion parameters from i-111-measurements in Si [6] and Ge [7]. Schafer et al. [10] performed r111-measurements in InSb with deformation temperatures varying between 280 and 5 10°C.The data have been re-evaluated and are presented in fig. 1 in a normalized plot according to eq. (1). Such normalized plots have the advantage, that all data points fit to a single curve for each material, if an appropriate value for the activation energy QSD has been taken into account. The curve for JnSb is characterized by QSD = 1.5 ôV and n = 3.7. For 265
Volume 71A, number 2,3
PHYSICS LETTERS
30 April 1979
measurements in InSb are comparable to those of Eisen and Birchenall [2]and may be also interpreted in
In
~
+~c +
,—~
~
—
• —
__________________________________________ ui” 1010 1O~ 108 iO~ l0~ 10~° lO~’ 10° ârn~exP(~)[cm2u15}
Fig. 1. Modulus-corrected stress at the beginning of stage III of the dynamic deformation test as a function of the temperature-compensated strain rate in InSb [11] with QSD = 1.5 eV and in Ge [7] with QSD = 3 eV.
comparison the results of Ge (QSD = 3.0 eV, n = 3.7) are included in fig. 1. (The deviations from linearity of both curves at high stresses are not compatible with eq. (1) and may be better described by the jog-dragging theory [6,7].) The preexponential factor D0 for InSb can be estimated by the following way: According to eq. (2) and taking into account the same n-values for Ge and InSb, the constantA is the same for both materials. Then it follows from eq. (1) that both curves in fig. 1 differ only by their D0both for 2/s [11], theD0-values. difference Taking between Ge to be 10 cm curves is characterized by D 2/s for 0 = =3 X InSb. From this value and QSD 1.5l0~cm eV the diffusion coefficient at the melting point can be calculated to be 10—13 cm2/s. These diffusion parameters deduced from r~-
266
terms of vacancy diffusion. This view is supported by applying the analysis of diffusion data of Sherby and Simnad [12], which QSD =to1.7 eV for InSb. The Till-method doesyields not allow discriminate between In and Sb diffusion. However, as the diffusion of the In and Sb atoms is a sequential process for the climb (and for the jog-dragging) mechanism the diffusion parameters derived by the r111-method may be ascribed to the slowest diffusing element. References [1]B.I. Boltaks and G.S. Kulikov, Soy. Phys. Tech. Phys. 2 (1957) 67.
[2]F.H. Eisen and C.E. Birchenall, Acta Metail. 5 (1957) 265. [3] HJ. Stocker, Phys. Rev. 130 (1963) 2160. [41G.I. Rekalova, U. Këbe and L.A. Mezrina, Soy. Phys. Semiconductors 5 (1971) 685. [5] D.L. Kendall and R.A. Humins, J. Appl. Phys. 40 (1969) 2750.
[6] H. Siethoff and W. Schröter, Phil. Mag. A37 (1978) 711. [7]H.G. Brion, W. SchrOter and H. Siethoff, Defects and
radiation effects in semiconductors Conf. Ser. No. 46, to be published.
(1978),
Inst. Phys.
[8] i.E. Bird, A.K. Mukherjee and J.E. Dorn, in: Quantitative relation between properties and microstructure, eds. D.G. Brandon and A. Rosen (Israel U.P., Jerusalem, 1969)Stocker p. 255.and M.F. Ashby, Scr. Metall. 7 (1973) 115. [9] R.L. [10] S. Schafer, H. Alexander and P. Haasen, Phys. Stat. So!. ~ (1964) 247. [11]H. Widmer and G.R. Gunther-Mohr, Helv. Phys. Acta 34 (1961) 635. [12] O.D. Sherby and M.T. Simnad, Trans. Am. Soc. Met. 54 (1961) 227.
Volume 71A, number 2,3
30 April 1979
SELF-DIFFUSION IN InSb H. SIETHOFF Physikalisches Institut, Universitdt Würzburg, D-8700 Wurzburg, Germany
Received 21 February 1979
The activation energy and the preexponential factor of self-diffusion in InSb have been derived from plastic deformation 2/s, respectively. These values may be ascribed to the slowest diffusing element.
techniques to be 1.5 eV and 3 x 10~cm
Self-diffusion in InSb has been studied by several authors [1—51. The first measurements were per.
formed by Boltaks and Kulikov [1], but most likely their results were influenced by grain boundaries [5]. Eisen and Birchenall [2] found the activation energies for In and Sb self-diffusion to be 1.82 eV and 1.94 eV, respectively; theelements. preexponential factor D0 wasof5 Cu X 102 2/s for both From investigations cm diffusion [3] and S diffusion [4] in InSb activation energies of 1.84 eV and 2.0 eV were derived for the self-diffusion of In and Sb, respectively, in excellent agreement with the above values. All these measurements [2—4]were mterpreted in terms of vacancy diffusion. On the contrary, Kendall and Huggins [5] reported on measurements yielding an activation energy of 4.3 eV for both, In and Sb diffusion, 2/s and with 3.1 preexponential factors of 1.8 X 1013 cm X 1013 cm2/s, respectively. They interpreted their results in terms of a divacancy mechanism. The striking discrepancies between the different authors, though discussed to some extent by Kendall and Huggins [5], are not understood. One reason may be found in the extremely small temperature region (480 to 520°C) suitable for tracer diffusion measurements in InSb, which may lead to erroneous Arrhenius plots; Self-diffusion parameters can be also deduced from plastic deformation experiments at high temperatures. During plastic deformation besides dislocations also point defects are created, which may become rate controlling at high temperatures. Two mechanisms have been discussed in this connection: the climb of edge dislocations and the dragging ofjogs on screw
dislocations. It has been shown [6,7] that both pro-
cesses are rate controlling at the beginning of stage III (stress r 111, strain rate of the dynamic deformation test in Si and Ge. For the climb mechanism it was found that the shear stress normalized by the shear modulus, r111/G, as a function of the strain rate and ofequation, the temperature T isoriginally compatible with the following which was developed for the interpretation of steady-state creep experiments [8] and which is transformed here for the purpose of the dynamic deformation test: • SD
a111)
a111
(r
11 1/G)’1
=
(kTa1j1/AD0Gb) exp(Q /kT).
(1)
Here b is the Burgers vector, k is Boltzmann’s constant and D0 and QSD are the preexponential factor and the activation constants nenergy andA of areself-diffusion, correlated byrespectively. the empiricalThe relation [9] n3.0+0.3Iog 1oA.
(2)
This method has been successfully applied to evaluate self-diffusion parameters from i-111-measurements in Si [6] and Ge [7]. Schafer et al. [10] performed r111-measurements in InSb with deformation temperatures varying between 280 and 5 10°C.The data have been re-evaluated and are presented in fig. 1 in a normalized plot according to eq. (1). Such normalized plots have the advantage, that all data points fit to a single curve for each material, if an appropriate value for the activation energy QSD has been taken into account. The curve for JnSb is characterized by QSD = 1.5 ôV and n = 3.7. For 265
Volume 71A, number 2,3
PHYSICS LETTERS
30 April 1979
measurements in InSb are comparable to those of Eisen and Birchenall [2]and may be also interpreted in
In
~
+~c +
,—~
~
—
• —
__________________________________________ ui” 1010 1O~ 108 iO~ l0~ 10~° lO~’ 10° ârn~exP(~)[cm2u15}
Fig. 1. Modulus-corrected stress at the beginning of stage III of the dynamic deformation test as a function of the temperature-compensated strain rate in InSb [11] with QSD = 1.5 eV and in Ge [7] with QSD = 3 eV.
comparison the results of Ge (QSD = 3.0 eV, n = 3.7) are included in fig. 1. (The deviations from linearity of both curves at high stresses are not compatible with eq. (1) and may be better described by the jog-dragging theory [6,7].) The preexponential factor D0 for InSb can be estimated by the following way: According to eq. (2) and taking into account the same n-values for Ge and InSb, the constantA is the same for both materials. Then it follows from eq. (1) that both curves in fig. 1 differ only by their D0both for 2/s [11], theD0-values. difference Taking between Ge to be 10 cm curves is characterized by D 2/s for 0 = =3 X InSb. From this value and QSD 1.5l0~cm eV the diffusion coefficient at the melting point can be calculated to be 10—13 cm2/s. These diffusion parameters deduced from r~-
266
terms of vacancy diffusion. This view is supported by applying the analysis of diffusion data of Sherby and Simnad [12], which QSD =to1.7 eV for InSb. The Till-method doesyields not allow discriminate between In and Sb diffusion. However, as the diffusion of the In and Sb atoms is a sequential process for the climb (and for the jog-dragging) mechanism the diffusion parameters derived by the r111-method may be ascribed to the slowest diffusing element. References [1]B.I. Boltaks and G.S. Kulikov, Soy. Phys. Tech. Phys. 2 (1957) 67.
[2]F.H. Eisen and C.E. Birchenall, Acta Metail. 5 (1957) 265. [3] HJ. Stocker, Phys. Rev. 130 (1963) 2160. [41G.I. Rekalova, U. Këbe and L.A. Mezrina, Soy. Phys. Semiconductors 5 (1971) 685. [5] D.L. Kendall and R.A. Humins, J. Appl. Phys. 40 (1969) 2750.
[6] H. Siethoff and W. Schröter, Phil. Mag. A37 (1978) 711. [7]H.G. Brion, W. SchrOter and H. Siethoff, Defects and
radiation effects in semiconductors Conf. Ser. No. 46, to be published.
(1978),
Inst. Phys.
[8] i.E. Bird, A.K. Mukherjee and J.E. Dorn, in: Quantitative relation between properties and microstructure, eds. D.G. Brandon and A. Rosen (Israel U.P., Jerusalem, 1969)Stocker p. 255.and M.F. Ashby, Scr. Metall. 7 (1973) 115. [9] R.L. [10] S. Schafer, H. Alexander and P. Haasen, Phys. Stat. So!. ~ (1964) 247. [11]H. Widmer and G.R. Gunther-Mohr, Helv. Phys. Acta 34 (1961) 635. [12] O.D. Sherby and M.T. Simnad, Trans. Am. Soc. Met. 54 (1961) 227.