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Determination of intervalley electron‐phonon deformation potential constants in n ‐silicon by analysis of high electric field transport properties
1.H. D. Rees, J. Phys. Chem. Solids 30, 643 (1969).
2.The g‐‐type intervalley phonon transitions occur between valleys whose major axes are collinear and f‐type transitions between valleys whose major axes are perpendicular.
3.James G. Nash and James W. Holm‐Kennedy, Appl. Phys. Lett. 24, 139 (1974).
4.For a detailed discussion see P. Norton, T. Braggins, and H. Levinstein, Phys. Rev. B 8, 5632 (1973).
5.J. C. Portal, L. Eaves, S. Askenazy, and R. A. Stradling, Solid State Commun. (to be published).
6.Intervalley phonons are referenced according to their activation energy θ in degrees Kelvin. Thus where ℏω is the phonon activation energy in electron volts and k is Boltzmann’s constant.
7.This doping concentration was taken to be 4% lower than that given in Ref. 3 to give a better fit between experimentally and theoretically determined current density vs applied field (Fig. 3).
8.Esther M. Conwell, High‐Field Transport in Semiconductors (Academic, New York, 1967), Vol. 9.
9.Harvey Brooks, Advances in Electronics and Electron Physics, edited by L. Marton (Academic, New York, 1955).
10.D. Long and J. Myers, Phys. Rev. 120, 39 (1960).
11.L. J. Neuringer and W. J. Little, in Proceedings of the International Conference on the Physics of Semiconductors, Exeter, 1962 (The Institute of Physics and Physical Society, London, 1962), p. 614.
12.R. A. Stradling and V. V. Zhukov, Proc. Phys. Soc. Lond. 87, 263 (1966).
13.E. M. Gershenzbn, Yu A. Gurvich, and N. A. Serebryakova, Fiz. Tverd. Tela. 12, 2306 (1970)
13.[E. M. Gershenzbn, Yu A. Gurvich, and N. A. Serebryakova, Sov. Phys.‐Solid State 12, 1841 (1971)].
14.R. Ito, H. Kawamura, and M. Fukai, Phys. Lett. 13, 26 (1964).
15.Kazuo Murase, Katsuhisa Enjouji, and Eizo Otsuka, J. Phys. Soc. Jpn. 29, 1248 (1970).
16.A. G. Kazanskii and O. G. Koshelev, Fiz. Tekh. Poluprovodn. 6, 953 (1972)
16.[A. G. Kazanskii and O. G. Koshelev, Sov. Phys.‐Semicond. 6, 826 (1972)].
17.The result of Kazanskii and Koshelev (Ref. 15) is not directly applicable here because in their experiment at 4. 2 K conditions were such that electron‐phonon scattering was dominated by spontaneous emission of acoustic phonons. Their value of would increase considerably for equiparition of lattice energy according to Gurvich, Fiz. Tverd. Tela 6, 2107 (1964)
17.[Gurvich, Sov. Phys.‐Solid State 6, 1661 (1965)].
18.This difference is probably caused by the remnants of electron‐electron scattering.
19.Use of the parameters in Table I gives a room‐temperature Ohmic mobility of which is in very good agreement with the value of found by Norton et al., (Ref. 4).
20.We have made an attempt to include two 220 K TA phonons as a two‐phonon process in our analysis [a possibility suggested by Paul Norton and Kai Ling Ngai (private communication)], but were not successful in obtaining a good fit whether the two‐phonon process was treated as f or g. Thus it appears that the two‐phonon coupling strength is weaker than those listed in Table I.
21.The work of Norton et al., was based on Ohmic mobility versus temperature measurements which do not directly give the type of phonon involved. However, assuming that their 670 K phonon is f type and their 190 K is g type , their relative coupling strengths of are equivalent to and
22.M. H. Jorgenson, N. O. Gram, and N. I. Meyer, Solid State Commun. 10, 337 (1972).
23.James W. Holm‐Kennedy and K. S. Champlin, J. Appl. Phys. 43, 1878 (1972).
24.We use coupling strength here rather than the deformation potential constant because the coupling strength is a more accurate indicator of the magnitude of the electron‐phonon interaction. The coupling strength W is proportional to where for g‐type scattering and for f‐type scattering.
25.Any change in the theoretical repopulation due to use of deformation potential constants other than those given in Table I results in an almost equal change in the theoretically calculated conductivity ratio of Fig. 1 since it is controlled essentially by the amount of repopulation. Thus, it is appropriate to use repopulation to determine the effects different sets of deformation potential constants will have on transport.
26.The choice of coupling strength here was such that the Ohmic room‐temperature mobility would not be greatly altered.
27.Further underst and ing of intervalley scattering may require greater resolution in the magnitude of acoustic scattering anisotropy.
28.The experimental repopulation shown here is slightly different from that given in Ref. 3 because here anisotropy was not included, whereas in Ref. 3 it was included according to the results of Long and Myers (Ref. 10).
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