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Hall effect measurements on silicon inversion layers
Volume 66A, number 1
PHYSICS LETTERS
17 April 1978
HALL EFFECT MEASUREMENTS ON SILICON INVERSION LAYERS J.P. THOMPSON Cavendish Laboratory, Cambridge, UK Received 2 February 1978
Hail mobility measurements have been made in the region of activated conductivity. The results are inconsistent with the mechanism being activation to a mobility edge, but agree with a new model of correlation-dominated transport, developed by Adkins.
In the two-dimensional electron gas at an inversion for low carrier concentrations and at temperatures up to 20K, the conductivity a can be seen to vary as [1]
—~
2
layer,
a=a mm exp(—W/kfl. This has been interpreted as conduction by excitation of carriers from localised states in the tail of the band to the extended states at the mobility edge, the activation energy W being the energy difference between the Fermi level and the mobility edge which separates locaused and extended states. The conduction is due to behave as free electrons even though they will have a these electrons above the mobility edge, which should short mean free path. Hence, according to this model, we would expect to see an activated carrier concentration and a constant mobility equal to tl~ievalue at the mobility edge. Hall measurements were made in order to test these predictions. Hall voltages were measured across samples with an applied source-drain field of less than 30 Vm’. An ac method was used as this removed thermal e.m.f.s. and reduced offsets significantly in comparison with dc methods. Measurements were made between 4 K and 20 K in fields up to 0.9 T. The measured Hall mobility ~H is defined by =
OH/B = (EH/E~)(1/B),
where °H is the Hall angle, B is the magnetic field strength, EH is the measured Hall field and E~is the
n,iO1cm 2.3
o
U) q~ ~
W/meV
-
\\\NN~
0 01 —
~
—
\
6 0
0-1
K/I
0-2
Fig. 1. Variation of device conductivity with temperature,
showing activated behaviour and a constant minimum metallic conductivity in agreement with the independent particle model of Mott. The carrier concentration n is calculated from the oxide capacitance and the gate voltage.
source-drain field applied to the device. Figs. 1 and 2 show typical results obtained with an n-channel insulated gate field effect transistor. The behaviouredge of the conductivity is consistent thea mobility model of Mott [21 and wouldwith imply value of minimum metallic conductivity of 3.6 X l0~ S in good agreement with theOretical estimates [3]. 65
Volume 66A, number 1
PHYSICS LETTERS
found from the Hall measurements (given by n = I IRHe = u/e~H) is temperature independent and equal, with-
10
-2
\\
a
n/b
cm
-
\\
=
~&
2 0
~
0
WimeV 1•3 2.2 10
2 i~0
17 April 1978
I
01
o2
in the accuracy of the measurements, to the total density of carriers in the channel. Similar results have been reported in p-channel devices [4]. These results, namely, that the activated conductivity is due to an activatedmobiity, and that the carrier concentration is temperature independent, are contrary to the independent particle model of excitation to a mobility edge. They are, however, in agreement with a new model proposed by Adkins [5], where localisation occurs in the Wigner sense rather than the Anderson, and conduction occurs by a process of correlated, fluid-like motion of the carriers. According to this model, the carriers behave like a classical liquid, showing liquid-like viscosity, which accounts for the activated mobility, and virtually all carriers contribute to the Hall effect.
K/T Fig. 2. Variation of Hail mobility with temperature. The resuits show an activated mobility, the activation energy being equal, within the accuracy of the experiments, to the activation energy in the conductivity for the same carrier concentration.
However, the Hall mobility is not constant but shows activated behaviour with the same activation energy as the conductivity, and the carrier concentration
References Ill
C.J. Adkins, S. Poilitt and M. Pepper, J. Physique 37 (1976) C4-343. [21 N.E. Mott et al., Proc. Roy. Soc. A345 (1975) 169.
[31 D.C.
4157.
Licciardello and D.J. Thouiess, J. Phys. C8 (1975)
[41 E. Arnold, Appi. Phys. Lett. 25 (1974) 705. [51 C.J. Adkins, J. Phys. Cli (1978).
PHYSICS LETTERS
17 April 1978
HALL EFFECT MEASUREMENTS ON SILICON INVERSION LAYERS J.P. THOMPSON Cavendish Laboratory, Cambridge, UK Received 2 February 1978
Hail mobility measurements have been made in the region of activated conductivity. The results are inconsistent with the mechanism being activation to a mobility edge, but agree with a new model of correlation-dominated transport, developed by Adkins.
In the two-dimensional electron gas at an inversion for low carrier concentrations and at temperatures up to 20K, the conductivity a can be seen to vary as [1]
—~
2
layer,
a=a mm exp(—W/kfl. This has been interpreted as conduction by excitation of carriers from localised states in the tail of the band to the extended states at the mobility edge, the activation energy W being the energy difference between the Fermi level and the mobility edge which separates locaused and extended states. The conduction is due to behave as free electrons even though they will have a these electrons above the mobility edge, which should short mean free path. Hence, according to this model, we would expect to see an activated carrier concentration and a constant mobility equal to tl~ievalue at the mobility edge. Hall measurements were made in order to test these predictions. Hall voltages were measured across samples with an applied source-drain field of less than 30 Vm’. An ac method was used as this removed thermal e.m.f.s. and reduced offsets significantly in comparison with dc methods. Measurements were made between 4 K and 20 K in fields up to 0.9 T. The measured Hall mobility ~H is defined by =
OH/B = (EH/E~)(1/B),
where °H is the Hall angle, B is the magnetic field strength, EH is the measured Hall field and E~is the
n,iO1cm 2.3
o
U) q~ ~
W/meV
-
\\\NN~
0 01 —
~
—
\
6 0
0-1
K/I
0-2
Fig. 1. Variation of device conductivity with temperature,
showing activated behaviour and a constant minimum metallic conductivity in agreement with the independent particle model of Mott. The carrier concentration n is calculated from the oxide capacitance and the gate voltage.
source-drain field applied to the device. Figs. 1 and 2 show typical results obtained with an n-channel insulated gate field effect transistor. The behaviouredge of the conductivity is consistent thea mobility model of Mott [21 and wouldwith imply value of minimum metallic conductivity of 3.6 X l0~ S in good agreement with theOretical estimates [3]. 65
Volume 66A, number 1
PHYSICS LETTERS
found from the Hall measurements (given by n = I IRHe = u/e~H) is temperature independent and equal, with-
10
-2
\\
a
n/b
cm
-
\\
=
~&
2 0
~
0
WimeV 1•3 2.2 10
2 i~0
17 April 1978
I
01
o2
in the accuracy of the measurements, to the total density of carriers in the channel. Similar results have been reported in p-channel devices [4]. These results, namely, that the activated conductivity is due to an activatedmobiity, and that the carrier concentration is temperature independent, are contrary to the independent particle model of excitation to a mobility edge. They are, however, in agreement with a new model proposed by Adkins [5], where localisation occurs in the Wigner sense rather than the Anderson, and conduction occurs by a process of correlated, fluid-like motion of the carriers. According to this model, the carriers behave like a classical liquid, showing liquid-like viscosity, which accounts for the activated mobility, and virtually all carriers contribute to the Hall effect.
K/T Fig. 2. Variation of Hail mobility with temperature. The resuits show an activated mobility, the activation energy being equal, within the accuracy of the experiments, to the activation energy in the conductivity for the same carrier concentration.
However, the Hall mobility is not constant but shows activated behaviour with the same activation energy as the conductivity, and the carrier concentration
References Ill
C.J. Adkins, S. Poilitt and M. Pepper, J. Physique 37 (1976) C4-343. [21 N.E. Mott et al., Proc. Roy. Soc. A345 (1975) 169.
[31 D.C.
4157.
Licciardello and D.J. Thouiess, J. Phys. C8 (1975)
[41 E. Arnold, Appi. Phys. Lett. 25 (1974) 705. [51 C.J. Adkins, J. Phys. Cli (1978).