We study the Einstein relation for the diffusivity to mobility ratio (DMR) in quantum wires (QWs) of III-V, ternary, and quaternary materials in the presence of light waves, whose unperturbed energy band structures are defined by the three band model of Kane. It has been found, taking n-InAs, n-InSb, n-Hg1xCdxTe, n-In1xGaxAsyP1y lattice matched to InP as examples, that the respective DMRs exhibit decreasing quantum step dependence with the increasing film thickness, decreasing electron statistics, increasing light intensity and wavelength, with different numerical values. The nature of the variations is totally band structure dependent and is influenced by the presence of the different energy band constants. The strong dependence of the DMR on both the light intensity and the wavelength reflects the direct signature of the light waves which is in contrast as compared to the corresponding QWs of the said materials in the absence of photoexcitation. The classical equation of the DMR in the absence of any field has been obtained as a special case of the present analysis under certain limiting conditions and this is the indirect test of the generalized formalism. We have suggested an experimental method of determining the DMR in QWs of degenerate materials having arbitrary dispersion laws and our results find six applications in the field of quantum effect devices.

1.
H.
Kroemer
,
IEEE Trans. Electron Devices
25
,
850
(
1978
).
2.
R. W.
Lade
,
Proc. IEEE
51
,
743
(
1964
).
3.
G. D.
Hatchel
and
A. E.
Ruchli
,
IEEE Trans. Electron Devices
15
,
437
(
1968
);
4.
P. T.
Landsberg
,
Eur. J. Phys.
2
,
213
(
1981
).
5.
P. T.
Landsberg
,
Thermodynamics and Statistical Mechanics
(
Oxford University Press
,
Oxford
,
1978
);
In Recombination in Compounds
(
Cambridge University Press
,
Cambridge
,
1991
).
6.
P. T.
Landsberg
,
J. Appl. Phys.
56
,
1696
(
1984
).
7.
P. T.
Landsberg
and
S. A.
Hope
,
Solid-State Electron.
20
,
421
(
1977
).
8.
S. A.
Hope
,
G.
Feat
, and
P. T.
Landsberg
,
J. Appl. Phys.
61
,
4909
(
1987
).
9.
P. T.
Landsberg
,
Proc. R. Soc. London, Ser. A
213
,
226
(
1952
).
10.
J. P.
Bouchaud
and
A.
Georges
,
Phys. Rep.
195
,
127
(
1996
).
11.
R. K.
Jain
,
Phys. Status Solidi A
42
,
K221
(
1977
).
12.
A. H.
Marshak
,
Solid-State Electron.
30
,
1089
(
1987
).
13.
A. H.
Marshak
and
K. M. V.
Vliet
,
Proc. IEEE
72
,
148
(
1984
).
14.
K. M. V.
Vliet
and
A.
Van der Zeil
,
Solid-State Electron.
20
,
931
(
1977
).
15.
A. N.
Chakravarti
and
B. R.
Nag
,
Int. J. Electron.
37
,
281
(
1974
).
16.
B. R.
Nag
and
A. N.
Chakravarti
,
Solid-State Electron.
18
,
109
(
1975
).
17.
B. R.
Nag
,
A. N.
Chakravarti
, and
P. K.
Basu
,
Phys. Status Solidi A
68
,
K75
(
1981
).
18.
B. R.
Nag
and
A. N.
Chakravarti
,
Phys. Status Solidi A
67
,
K113
(
1981
).
19.
A. N.
Chakravarti
and
D. P.
Parui
,
Phys. Lett.
40
,
113
(
1972
);
A. N.
Chakravarti
and
D. P.
Parui
,
Phys. Lett.
43
,
60
(
1973
).
20.
D.
Mukherjee
,
A. N.
Chakravarti
, and
B. R.
Nag
,
Phys. Status Solidi A
26
,
K27
(
1974
).
21.
B. R.
Nag
,
Electron Transport in Compound Semiconductors
(
Springer-Verlag
,
Berlin
1980
).
22.
A. N.
Chakravarti
,
K. P.
Ghatak
,
A.
Dhar
,
K. K.
Ghosh
, and
S.
Ghosh
,
Appl. Phys. A: Solids Surf.
26
,
169
(
1981
).
23.
M.
Mondal
and
K. P.
Ghatak
,
Phys. Scr.
30
,
217
(
1984
).
24.
M.
Mondal
and
K. P.
Ghatak
,
J. Magn. Magn. Mater.
62
,
115
(
1986
);
M.
Mondal
and
K. P.
Ghatak
,
J. Phys. C
20
,
1671
(
1987
);
M.
Mondal
and
K. P.
Ghatak
,
Ann. Phys.
46
,
502
(
1989
).
25.
M.
Mondal
and
K. P.
Ghatak
,
Thin Solid Films
148
,
219
(
1987
).
26.
K. P.
Ghatak
,
A. K.
Choudhury
,
S.
Ghosh
, and
A. N.
Chakravarti
,
Appl. Phys.
23
,
241
(
1980
).
27.
M.
Mondal
,
N.
Chattopadhyay
, and
K. P.
Ghatak
,
J. Low Temp. Phys.
73
,
321
(
1988
).
28.
K. P.
Ghatak
,
N.
Chattopadhyay
, and
M.
Mondal
,
J. Appl. Phys.
44
,
305
(
1987
);
K. P.
Ghatak
,
N.
Chattopadhyay
, and
M.
Mondal
,
J. Appl. Phys.
63
,
4536
(
1988
);
K. P.
Ghatak
,
B.
Mitra
, and
M.
Mondal
,
Ann. Phys.
48
,
283
(
1990
);
K. P.
Ghatak
and
S. N.
Biswas
,
J. Appl. Phys.
70
,
4309
(
1991
).
29.
B.
Mitra
and
K. P.
Ghatak
,
Phys. Lett. A
135
,
397
(
1989
).
30.
B.
Mitra
and
K. P.
Ghatak
,
Solid-State Electron.
32
,
810
(
1989
).
31.
S. N.
Biswas
and
K. P.
Ghatak
,
Int. J. Electron.
73
,
287
(
1992
).
32.
K. P.
Ghatak
, “
Influence of Band Structure on Some Quantum Processes of tetragonal semiconductors
,” D.Eng. thesis,
Jadavpur University
,
1991
.
33.
K. P.
Ghatak
,
B.
Mitra
, and
B.
Nag
,
Phys. Status Solidi B
199
,
95
(
1997
).
34.
S.
Choudhury
,
L. J.
Singh
, and
K. P.
Ghatak
,
Nanotechnology
15
,
180
(
2004
).
35.
H.
Sasaki
,
Jpn. J. Appl. Phys.
19
,
94
(
1980
).
36.
P. M.
Petroff
,
A. C.
Gossard
,
R. A.
Logan
, and
W.
Weigmann
,
Appl. Phys. Lett.
41
,
635
(
1982
).
37.
I.
Miller
,
A.
Miller
,
A.
Shahar
,
U.
Koren
, and
P. J.
Corvini
,
Appl. Phys. Lett.
54
,
188
(
1989
).
38.
F.
Sols
,
M.
Macucci
,
U.
Ravaioli
, and
K.
Hess
,
Appl. Phys. Lett.
54
,
350
(
1980
).
39.
C. S.
Lent
and
D. J.
Kirkner
,
J. Appl. Phys.
67
,
6353
(
1990
).
40.
C. S.
Kim
,
A. M.
Satanin
,
Y. S.
Joe
, and
R. M.
Cosby
,
Phys. Rev. B
60
,
10962
(
1999
).
41.
S.
Midgley
and
J. B.
Wang
,
Phys. Rev. B
64
,
153304
(
2001
).
42.
T.
Sugaya
,
J. P.
Bird
,
M.
Ogura
,
Y.
Sugiyama
,
D. K.
Ferry
, and
K. Y.
Jang
,
Appl. Phys. Lett.
80
,
434
(
2002
).
43.
B.
Kane
,
G.
Facer
,
A.
Dzurak
,
N.
Lumpkin
,
R.
Clark
,
L.
PfeiKer
, and
K.
West
,
Appl. Phys. Lett.
72
,
3506
(
1998
).
44.
C.
Dekker
,
Phys. Today
52
(
5
),
22
(
1999
).
45.
A.
Yacoby
,
H. L.
Stormer
,
N. S.
Wingreen
,
L. N.
Pfeiffer
,
K. W.
Baldwin
, and
K. W.
West
,
Phys. Rev. Lett.
77
,
4612
(
1996
).
46.
Y.
Hayamizu
,
M.
Yoshita
,
S.
Watanabe
,
H. A. L.
PfeiKer
, and
K.
West
,
Appl. Phys. Lett.
81
,
4937
(
2002
).
47.
S.
Frank
,
P.
Poncharal
,
Z. L.
Wang
, and
W. A.
Heer
,
Science
280
,
1744
(
1998
).
48.
I.
Kamiya
,
I. I.
Tanaka
,
K.
Tanaka
,
F.
Yamada
,
Y.
Shinozuka
, and
H.
Sakaki
,
Physica E (Amsterdam)
13
,
131
(
2002
).
49.
A. K.
Geim
,
P. C.
Main
,
N.
La Scala
, Jr.
,
L.
Eaves
,
T. J.
Foster
,
P. H.
Beton
,
J.-W.
Sakai
,
F. W.
Sheard
,
M.
Henini
,
G.
Hill
, and
M. A.
Pate
,
Phys. Rev. Lett.
72
,
2061
(
1994
).
50.
A. S.
Melinkov
and
V. M.
Vinokur
,
Nature (London)
415
,
60
(
2002
).
51.
K.
Schwab
,
E. A.
Henriksen
,
J. M.
Worlock
, and
M. L.
Roukes
,
Nature (London)
404
,
974
(
2000
).
52.
L.
Kouwenhoven
,
Nature (London)
403
,
374
(
2000
).
53.
S.
Komiyama
,
O.
Astafiev
,
V.
Antonov
, and
H.
Hirai
,
Nature (London)
403
,
405
(
2000
).
54.
E.
Paspalakis
,
Z.
Kis
,
E.
Voutsinas
, and
A. F.
Terziz
,
Phys. Rev. B
69
,
155316
(
2004
).
55.
J. H.
Jefferson
,
M.
Fearn
,
D. L. J.
Tipton
, and
T. P.
Spiller
,
Phys. Rev. A
66
,
042328
(
2002
).
56.
J.
Appenzeller
,
C.
Schroer
,
T.
Schapers
,
A.
Hart
,
A.
Froster
,
B.
Lengeler
, and
H.
Luth
,
Phys. Rev. B
53
,
9959
(
1996
).
57.
J.
Appenzeller
and
C.
Schroer
,
J. Appl. Phys.
87
,
3165
(
2000
).
58.
P.
Debray
,
O. E.
Raichev
,
M.
Rahman
,
R.
Akis
, and
W. C.
Mitchel
,
Appl. Phys. Lett.
74
,
768
(
1999
).
59.
P. M.
Solomon
,
Proc. IEEE
70
,
489
(
1982
);
T. E.
Schlesinger
and
T.
Kuech
,
Appl. Phys. Lett.
49
,
519
(
1986
).
60.
H.
Heiblum
,
D. C.
Thomas
,
C. M.
Knoedler
, and
M. I.
Nathan
,
Appl. Phys. Lett.
47
,
1105
(
1985
).
61.
O.
Aina
,
M.
Mattingly
,
F. Y.
Juan
, and
P. K.
Bhattacharyya
,
Appl. Phys. Lett.
50
,
43
(
1987
).
62.
I.
Suemune
and
L. A.
Coldren
,
IEEE J. Quantum Electron.
24
,
1178
(
1988
).
63.
D. A. B.
Miller
,
D. S.
Chemla
,
T. C.
Damen
,
J. H.
Wood
,
A. C.
Burrus
,
A. C.
Gossard
, and
W.
Weigmann
,
IEEE J. Quantum Electron.
21
,
1462
(
1985
).
64.
R.
Bisaro
,
G.
Laurencin
,
A.
Friederich
,
M.
Razeghi
,
Appl. Phys. Lett.
40
,
978
(
1982
).
65.
R. C.
Alferness
,
C. H.
Joyner
,
M. D.
Divino
,
M. J. R.
Martyak
, and
L. L.
Buhl
,
Appl. Phys. Lett.
49
,
125
(
1986
).
66.
T. E.
Bell
,
IEEE Spectrum
20
,
38
(
1983
).
67.
P. Y.
Lu
,
C. H.
Wang
,
C. M.
Williams
,
S. N. G.
Chu
, and
C. M.
Stiles
,
Appl. Phys. Lett.
49
,
1372
(
1986
).
68.
N. K.
Taskar
,
I. B.
Bhat
,
K. K.
Parat
,
D.
Terry
,
H.
Ehsani
, and
S. K.
Gandhi
,
J. Vac. Sci. Technol. A
7
,
281
(
1989
).
69.
E.
Weiss
and
N.
Mainzer
,
J. Vac. Sci. Technol. A
7
,
391
(
1989
).
70.
F.
Koch
,
Two Dimensional Systems, Heterostructures and Superlattices
,
Springer Series in Solid State Science
, edited by
G.
Bauer
,
F.
Kuchar
, and
H.
Heinrich
, Vol.
53
(
Springer-Verlag
,
Berlin
1984
).
71.
D. H.
Daw
,
D. S.
Caoand
, and
G. B.
Stringfellow
,
J. Appl. Phys.
69
,
2552
(
1991
).
72.
M. L.
Timmons
,
S.
Bedair
,
M. R. J.
Markunas
, and
J. A.
Hutchby
,
Proceedings of 16th IEEE Photovoltaic Specialists Conferences
(
IEEE
,
San Diego, CA
,
1982
), Vol.
666
.
73.
M. K.
Lee
,
D. S.
Wu
, and
H. H.
Tung
,
J. Appl. Phys.
62
,
3209
(
1987
).
74.
G. L.
Hansen
,
J. L.
Schmit
, and
T. N.
Casselman
,
J. Appl. Phys.
63
,
7099
(
1982
).
75.
S. K.
Sutradhar
,
D.
Chattopadhyay
, and
B. R.
Nag
,
Phys. Rev. B
25
,
4069
(
1982
).
76.
K.
Seeger
,
Semiconductor Physics
, 7th ed. (
Springer-Verlag
,
Berlin
,
2006
).
77.
B. R.
Nag
,
Physics of Quantum Well Devices
(
Kluwer
,
Dordrecht
,
2000
).
78.
M.
Abramowitz
and
I. A.
Stegun
,
Handbook of Mathematical Functions
(
Dover
,
New York
,
1965
).
79.
B.
Mitra
and
K. P.
Ghatak
,
Phys. Scr.
42
,
103
(
1990
).
80.
W.
Zawadzki
,
Two—Dimensional Systems, Hetrostructures and Superlattices
,
Springer Series in Solid-State Science Vol. 53
, edited by
G.
Bower
,
F.
Kuches
, and
H.
Haiunich
(
Springer
,
Berlin
,
1984
), p.
79
;
K. P.
Ghatak
and
M.
Mondal
,
J. Appl. Phys.
66
,
3056
(
1989
).
81.
I. M.
Tsidilkovskii
,
Band Structures of Compounds
(
Pergamon
,
London
,
1982
);
B.
Mitra
and
K. P.
Ghatak
,
Phys. Lett. A
141
,
81
(
1989
).
82.
A. K.
Sreedhar
and
S. C.
Gupta
,
Phys. Rev. B
5
,
3160
(
1972
).
83.
K. P.
Ghatak
,
J. P.
Banerjee
,
M.
Mitra
, and
B.
Nag
,
Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. B: Nonlinear Opt.
16
,
193
(
1996
);
B.
Nag
and
K. P.
Ghatak
,
J. Phys. Chem. Solids
58
,
427
(
1997
).
84.
S.
Adachi
,
J. Appl. Phys.
58
,
R11
(
1985
).
85.
R.
Dornhaus
and
G.
Nimtz
,
Springer Tracts in Modern Physics
(
Springer
,
Berlin
,
1976
),
78
, p.
1
.
86.
W.
Zawadzki
,
Handbook of Semiconductor Physics
, edited by
W.
Paul
(
North-Holland
,
Amsterdam
,
1982
), Vol.
1
, p.
719
.
87.
I. M.
Tsidilkovski
, Ph.D. thesis, Electronic Properties of Degenerate Semiconductors,
Leningrad University
,
1955
.
88.
E. V.
Rozenfeld
,
Yu. P.
Trkhin
, and
P. G.
Guletskii
,
Sov. Phys. Solid State
29
,
1314
(
1988
).
89.
K. P.
Ghatak
and
M.
Mondal
,
Z. Naturforsch. Teil A
41A
,
881
(
1986
);
K. P.
Ghatak
and
M.
Mondal
,
Z. Phys. B: Condens. Matter
69
,
471
(
1988
).
90.
K. P.
Ghatak
and
M.
Mondal
,
Solid-State Electron.
31
,
1651
(
1988
).
91.
A. S.
Filipchenko
,
I. G.
Lang
,
D. N.
Nasledov
,
S. T.
Pavlov
, and
L. N.
Radaikine
,
Phys. Status Solidi B
66
,
417
(
1974
).
92.
M.
Wegener
,
Extreme Nonlinear Optics
(
Springer-Verlag
,
Berlin
,
2005
).
93.
P. K.
Chakraborty
,
S.
Bhattacharya
, and
K. P.
Ghatak
,
J. Appl. Phys.
98
,
053517
(
2005
).
94.
J. N.
Schulman
and
Y. C.
Chang
,
Phys. Rev. B
24
,
4445
(
1981
).
95.
V. V.
Mitin
,
V. A.
Kochelop
, and
M. A.
Stroscio
,
Quantum Heterostructures
(
Cambridge University Press
,
Cambridge
,
1999
).
96.
S.
Datta
,
Electron Transport in Mesoscopic Systems
, (
Cambridge University Press
,
Cambridge
,
2001
).
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