Gross R., Sidorenko A., Tagirov L. Nanoscale Devices

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284 D. V. Shamshur, D. V. Shakura, R. V. Parfeniev, S. A Nemov

≅ 10 mkA (z = 0.8) to ~ 100 mkA (z = 0.7) due the increasing size of the

links between SC islands in the samples. The weak link critical current was

suppressed by low external magnetic fields.

Fig. 6. Temperature dependence of the resistivity in (Pb

1-Z

)

0.8

TeIn

0.2

solid solu-

tions with Pb contents z = 0.5- 0.9 and fixed x = 0.2.

Fig. 7. Temperature dependence of the resistivity in Pb

0.8

0.2

)

0.8

0.2

Te measured-

for different applied currents showing a nonlinear current dependence.

Superconductor-Insulator Transition in a Pb

1-Z

Te:In Solid Solution 285

Fig. 8. Current–voltage characteristics in (Pb

1-Z

)

0.8

0.2

Te (z = 0.7, 0.8, 0.9).

In contrast to the x = 0.2 series the samples with the lower In content

(x = 0.16) exhibit on the SC side of the S-I transition (z = 0.6) a threshold

type current increase near zero bias similar to that observed for S-I-S junc-

tions (see Fig. 9). Fig. 9 shows the voltage and dV/dI as a function of the

bias current in the sample (z = 0.8, x = 0.16) with a residual resistance at

low temperatures after the SC transition. A salient feature of the dV/dI

curve at T = 1.2 K is a zero bias differential resistivity peak corresponding

to the pair tunneling through probable S-I-S interface in the SC-Sm system.

The role of SC clusters decreases when the lead content z increases and, in

turn, the SC step in the

ρ (T) dependence decreases for the sample with

z > 0.6.

The features of the SC-Sm mesoscopic system are more remarkable in

the magnetoresistance (MR) near the critical temperature. In the SC region

the MR sharply increases and the negative MR in H > 1 kOe transforms

into a positive MR in (Pb

0.7

0.3

)

0.84

0.16

Te. In this case the low temperature

positive MR is sensitive to the tunneling conductance between SC clusters.

It changes in the x = 0.16 series from a positive value at z = 0.7 (destruction

of S-I-S interfaces) to a negative MR at z = 0.9 (weak localization in the Sm

matrix) at the same temperature (see Fig. 10).

286 D. V. Shamshur, D. V. Shakura, R. V. Parfeniev, S. A Nemov

Fig. 9. Voltage-current characteristic (left) and dV/dI as a function of bias current

(right) in (Pb

0.6

0.4

)

0.84

0.16

Te at T = 1.2 K.

Fig. 10. Magnetoresistance as a function of applied magnetic field at T = 1.4 K for

(Pb

1-Z

)

0.84

0.16

Te solid solutions with Pb content z = 0.7, 0.8, 0.9.

Superconductor-Insulator Transition in a Pb

1-Z

Te:In Solid Solution 287

Conclusions

The optimal composition and In doping level to achieve the highest SC pa-

rameters in solid solutions based on the PbSnTe:In system has been deter-

mined.

The filling of the In impurity band located against the background of the

heavy hole band is responsible for the high SC parameters in the PbSnTe:In

system. The higher the concentration of the In doping level the wider the

range of the Pb content for which high SC parameters can be obtained in

the PbSnTe:In system.

A superconducting to insulating state transition was found in the low

temperature conductivity of the PbSnTe:In compounds with varying com-

positions.

At low currents we have observed a transition from a SC mesoscopic

system to a SC – Sm system with the dielectric state of the semiconductor

matrix. The anomalous magnetoresistance in the vicinity of the S – I transi-

tion consists of negative and positive parts associated with a transition from

a SC mesoscopic system to a semiconductor with the weak localization ef-

fect in the normal state for a random fluctuating potential.

The studied material is of interest for the development of SC bolometers

and nanoscale devices due to observed high sensitivity of the normal and

SC properties to temperature variations.

Acknowledgments

The authors acknowledge support of the Presidium of RAS grants, RFBR

04-02-16638 grants and “Leading scientific school” – 2200.2003.2 grant.

References

1. Kaidanov VI, Ravich YuI (1985). Sov Phys Usp 28:31

2. Berezin AV, Nemov SA, Parfeniev RV, Shamshur DV (1993). Phys Solid

State 35:28

3. Nemov SA, Parfeniev RV, Shamshur DV, Stepien-Damm J (1996). Czecho-

slovak Journal of Physics, Suppl S2 46:863

4. Nemov SA, Ravich Yu I (1998). Usp Fiz Nauk 169:817

5. Hulm JK, Jones CK (1968). Phys Rev 169:388,

Hein RA, Meijr PHE (1969). Phys Rev 179:497

6. Tahar MZ, Popov DI, Nemov S (2003). Physica C 388-389, 581

288 D. V. Shamshur, D. V. Shakura, R. V. Parfeniev, S. A Nemov

7. Chernik IA, Kaidanov VI, Ishutinov EM (1968). Sov Phys – Semiconductors

2:995

8. Shelankov AL (1987). Solid St Commun 62:327

9. Mott NF (1974). Phil Mag 19:835

ADVANCED SENSORS OF ELECTROMAGNETIC

RADIATION

Thermoelectricity of Low-Dimensional

Nanostructured Materials

V. G. Kantser

International Laboratory of Superconductivity and Solid State Electronics,

Academy of Sciences of Moldova, Chişinau

Abstract: Efficient thermoelectric technologies of power generation, heat

removal and thermal management by refrigeration require

solid-state materials and structures with significantly improved

thermoelectric characteristics. The achievements in physics of

low dimensional structures and the development in the

corresponding fabrication techniques has recently reopened the

field of thermoelectricity in order to engineer solid-state

systems with high thermoelectric performance. Some aspects

of thermoelectricity and technology of low dimensional

nanostructured materials are highlighted in the present paper.

As illustration of the ways to improve the figure of merit and

others thermoelectric parameters some recent achievements in

the investigation of solid-state nanostructures with quantum

wells, wires, and dots are reviewed.

Keywords: thermoelectricity, nanostructures, size quantization, nanowires,

electron and phonon transport

General Considerations on Thermoelectricity

The motion of charges in solid-state materials and structures is

accompanied also by energy and heat transport. Therefore, this opens the

possibility of solid-state thermoelectric thermal management, heat removal

and

energy conversion, which transforms heat directly into electricity, or

heat transport, when the energy is transferred from one to the other side

291

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 291–307.

292 V. G. Kantser

of materials. At present there is growing interest stimulated by application

demands in developing of novel thermoelectric materials and structures for

efficient solid-state cooling and energy conversion devices. In particular,

heat removal and thermal management becomes extremely important for

further development of electronic industry as the feature size of the devices

decreases and the dissipated power increases. For these purposes it is

important to have the possibility of selective spot cooling of chips with high

heat flow extraction and decreasing of electric power input.

Solid-state power generation and cooling are based on thermoelectric

effects, which are known as the Seebeck effect (for power generation) and

the Peltier effect (for cooling and heat pumping). The Seebeck effect is

associated with the generation of a voltage along a conductor when it is

subjected to a temperature difference and this effect is the principle for

thermocouples. Charged carriers (electrons or holes) diffuse from the hot

side to the cold side, creating an internal electric field that opposes further

diffusion. The Seebeck coefficient S is defined as the voltage generated per

degree of temperature difference between two points [1]

VST

−∆

(1)

Conversely, when carriers flow through a material they carry heat and

this phenomenon is described by the Peltier effect. The heat current

Q is

proportional to the charge current

QPJ

(2)

and the corresponding coefficient

is the Peltier coefficient , which is

connected to the Seebeck coefficient by the Kelvin relation

(3)

The dc transport of electrical current

J and heat

J are described by

(

)

JEST

−∇ ,

JTEKT

−∇,

(4)

where

is the electrical conductivity and K is the thermal conductivity.

Equations (4) under the conditions

lead to the following

expressions for the heat current

JSTJKT

−∇

(5)

Thermoelectricity of Low-Dimensional Nanostructured Materials 293

(

)

'1 'KK ZT=−

−

The last parameter

Z is the thermoelectric figure of merit – the central

issue of thermoelectricity as well as the power factor

(6)

Thermal conductivity

K enters Z in the denominator of Z because in

thermoelectric coolers or power generators the thermoelectric elements also

act as the thermal insulation between the hot and the cold sides.

On the basis of continuity relation of one dimensional model

∂

and heat balance equation

0 JKT

+∇

the temperature distribution along axes x can be obtained [1]

() ()

Tx T T xL x

=+∆+ −,

() ()

KT L

Jx SJTx J x

∆



=−−−





() ()()

Vx JL ST xL x

=+∆+ −,

TT T

∆

=−

The last allow to show that thermoelectric refrigerator efficiency and

generator efficiency are directly related to the material figure of merit

Z .

The refrigerator efficiency is described by the ratio.

294 V. G. Kantser

The efficiency of refrigerator is defined as

. The rate of heat

(

()

Qc Q c

KT L

JJ SJT J

∆

==−−) removed from the cold source is

divided by the input power,

(

)

JJLST

+∆ . These quantities depend

on the current

J . One maximizes the efficiency by varying J . This

maximum of efficiency is called the coefficient of performance (COP):

()

COP

−

∆

1 ZT

=+ ,

()

TTT=+

The COP value increases by increasing

Z and achieves the Carnot limit

COP T T→∆ in the case when Z →∞.

A similar analysis can be done for generators. The COP is defined as

= , the power divided by the heat flow from hot source

()

Qh Q h

KT L

JJLSJT J

∆

==−−

The COP coefficient η is optimized by varying the current and the COP

has the form

(

)

max

∆

−

Again the ideal Carnot efficiency of

∆

is obtained in the case when

ZT→∞.

Comparison of COP and efficiency of different cooling and power

generation technologies, inclusive thermoelectric one for different ZT

values shows [2] ,that solid-state thermoelectric cooler and power

generators can become competitive with other energy conversion methods

provide values of ZT parameters are larger than 3-4. The present state of

established thermoelectric materials and of emerging TE materials are

plotted in Fig. 1.

Gross R., Sidorenko A., Tagirov L. Nanoscale Devices - Fundamentals and Applications

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