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

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Thermoelectricity of Low-Dimensional Nanostructured Materials 305

nanodots as the superlattice period decreases. The values of ZT are found to

be higher than 4 and 6 for 5 nm-diameter PbSe/PbS and PbTe/PbSe

superlattice segmented nanowires.

The enormous prospects of quantum dot like systems for the

improvement of the thermoelectric performance of materials has been

confirmed recently by experiments. In particular, a high value of the

thermopower has been observed at room temperature in PbTe/PbSe

1-x

quantum dot superlattice structures, which have reached values of ZT = 2

[27].

Investigating the thermoelectric properties of PbTe nanostructures with

grain sizes of the order of 30–50 nm in [28, 29] a considerable

enhancement in the thermopower relative to bulk PbTe materials has been

demonstrated. The magnitude of the enhancement is similar to the

abovementioned result for PbTe/PbSe

1-x

quantum dot superlattices.

An other nanostructured material like PbTe and the system

AgPb

SbTe

2+m

[30] have been fabricated and shown to have a high

thermoelectric figure of merit ZT

max

of 2.2 at 800 K. The observed ZT

enhancement is explained by the presence of quantum “nanodots” in these

materials similar to those found in the PbSe/PbTe MBE–grown thin films

quantum dot system [27]

Conclusions

The paper reviews some recent investigations dealing with the ways of

radical improvement of the thermoelectric figure of merit ZT in low

dimensional solid state nanostructures. If the conditions of nanoscale size

effects are fulfilled the transport of the charge carriers and phonons can be

significantly modified and this can be used to improve the thermoelectric

energy conversion efficiency.

Recent studies have revealed a lot of new aspects of thermoelectric

transport in low dimensional structures, which show promising ways to

reach a large increase in ZT values. A number of approaches have been

proposed for thermoelectric nanostructures of different dimensionality:

quantum wells, superlattices, quantum wires and quantum dot systems.

A brief analysis of existing results in the research area of quasi-two

dimensional systems is presented, including some experimental data

confirming high power factor S

σ and other thermoelectric parameters in

the PbTe/PbEuTe and Si/SiGe systems. Recently, superlattices with quasi

two-dimensional

electron gases have been produced in the Bi

system

306 V. G. Kantser

(the best bulk thermoelectric material), which offers significantly higher Z

(more than twice of the bulk value) with the transport across the structure.

The report has outlined these new important results.

Quasi one-dimensional nanowire array composites are the most

promising systems for improving the thermoelectric properties by making

use of the quantum confinement effect and phonon transport engineering.

Due to the large anisotropy and other electronic peculiarities bismuth is a

very attractive material for low-dimensional thermoelectricity, when a

semimetal-semiconductor transition appears due to an anisotropy enhanced

quantum size effect leading to a large enhancement in the figure of merit.

An even more significant improvement of the thermoelectric performance

in nanowire systems was revealed by employing a mechanism based on the

reduction of thermal diffusivity. Some selected results in this area as well as

in the field of electronic properties engineering by the quantum

confinement in nanowire systems have been highlighted in the paper.

In the last part of the review some aspects of nanostructured bulk

materials and quantum dot systems have been discussed. A significant

improvement of the thermoelectric figure of merit ZT can be achieved in

such systems by a strong reduction of the lattice thermal conductivity as

well as by a scattering-induced enhancement of the thermopower, when the

nanostructure dimensions become less than the electron mean free path.

An important aspect of low dimensional nanostructured thermoelectric

materials outlined in the paper is its capability to be implemented into

microsystem devices and wafer based microelectronic technologies. They

can be used to solve some problems of heat removal and thermal

management of nanoscale devices, which become more important with

increasing amount of dissipated power.

Acknowledgments

This work has been supported by INTAS project N 0184 and National

Program of Nanotechnology of R.Moldova .

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Polychroniadis EK, Mercouri G, Kanatzidis I (2004). Science 303:818

Organic Semiconductors – More Efficient Material

for Thermoelectric Infrared Detectors

A. Casian

, Z. Dashevsky

, V. Dusciac

, R. Dusciac

Department of Computers, Informatics and Microelectronics,

Technical University of MoldovaMD-2004, Chisinau, Moldova.

Department of Materials Engineering,

Ben-Gurion University, Beer-Sheva 84105, Israel

Department of Physics,

State University of Moldova, MD-2012, Chisinau, Moldova

Abstract: The opportunities for the application of new quasi-one-dimensional

organic semiconductors as sensitive elements in nonselective

thermoelectric infrared detectors for the long wave length regime of

the spectrum are analyzed. It is shown that under certain conditions

the effective scattering probability for some carriers is considerably

reduced due to the interference of two main electron-phonon

interactions. As a result, a significant increase of the thermoelectric

power factor, which is the most important parameter of the materials

used for infrared detectors, is predicted.

Keywords: Infrared detectors, thermoelectric power factor, organic

semiconductors, detector sensitivity.

Introduction

In the last years, the demand for detectors of infrared radiation (IR) in the

long

wave length regime of the spectrum has increased considerably. In

this context, the attention of investigators has been focused on the

development of new, more sensitive nonselective thermoelectric detectors.

it is known, the photoelectric detectors are sensitive only up to the

wave

length of the order of 1.3 µm. On the other hand, the earth’s

309

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 309–317.

310 A. Casian, Z. Dashevsky, V. Dusciac, R. Dusciac

atmosphere has only several “windows” of sufficient transparency. Such

detectors can be applied for the measuring of radiation up to the most far

infrared region.

An important parameter of the materials used for the sensitive element of

such detectors is the thermoelectric power factor,

= , were

is the

electrical conductivity and S is the thermopower (Seebeck coefficient). As

large as possible values of P are desired for applications. However, the

requirements to realize in the same material high electrical conductivity and

high values of the thermopower are, in general, contradictory. Therefore,

the search and investigation of materials and structures with more

complicated energy spectrum giving the possibility to overcome these

contradictions and to realize higher values of the thermoelectric power

factor are of great importance not only from the theoretical point of view,

but also for the prospective practical applications.

Recently, it was shown [1] that it is possible to improve the

thermoelectric properties of some materials by preparing them in the form

of low-dimensional quantum-well (QW) superlattice structures. Several

types of such structures have been investigated [2–5]. In n-type

PbTe/PbEuTe quantum wells values of P as high as 62–66 µW/cmK

were

measured [2]. This is almost two times higher than the best measured value

of 38 µW/cmK

in the bulk PbTe, a material widely used in thermoelectric

applications. In our work [6, 7] it has been shown that the expected values

of P for (100) and (111) oriented QWs are

100

W/cmK 175

=P and

111

W/cmK 108

=P , which are, respectively, 4.6 and 2.8 times higher

than the above mentioned measured value in bulk PbTe. The application

potential of n-type PbTe/PbEuTe QWs in the most rigorous model has been

investigated in [8]. A high value of

W/cmK 160

=P , the highest

measured up to now, was observed in p-type PbTe/PbEuTe QWs [9],

although our calculations show that for certain parameters of QWs and hole

concentrations the power factor could achieve usually large values of the

order of

W/cmK 250

[10]. However, as it also has been established that

the technology for fabrication of such QW structures is very complicated

and expensive. Therefore, in spite of the great success in the realization of

QW nano-structures, the search and investigation of novel materials with

higher thermoelectric power factor continue to remain an important and

urgent problem.

Lately, organic materials attract more and more attention, since they are

less expensive and show a broad spectrum of physical properties [11]. In

the present paper we predict that in quasi-one-dimensional organic crystals

is possible to obtain, under certain conditions, an extremely high value

Organic Semiconductors – More Efficient Material 311

of the thermoelectric power factor at room temperature. These conditions

are determined by the interference and mutual compensation of two major

electron-phonon interaction mechanisms in such systems.

Quasi-One-Dimensional Organic Crystals

Initially, the interest in the synthesis and investigation of new Q1D organic

crystals was connected with the predicted possibility to find high

temperature superconductors. Superconductivity in such crystals was

indeed discovered, but the achieved critical temperatures are still quite low.

Simultaneously, it was established that the Q1D organic crystals have rather

diverse and often unusual physical properties, coming mainly from their

specific structure. They represent needle-like three-dimensional crystals

formed by linear stacks or chains of usually planar molecules (see Ref. 11,

Chap. V). Significant π-bonding along the stacks ensures band-like

conduction in the stack direction, whereas between the stacks the

conduction is hopping-like and is usually negligible. The Q1D conduction

takes place in the ion-radical salts of the tetra-thiofulvalene-

tetracyanoquinodimethane (TTF-TCNQ) type in a number of complexes by

charge transfer in crystal polymers

The crystal model considered here has been described in [12, 13]. It must

be mentioned that due to rather localized molecular orbitals the tight

binding and nearest neighbor approximations are applied for conduction

along the chains and the transversal hopping conduction is neglected for

simplicity. Two main electron-phonon interaction mechanisms are taken

into account simultaneously. One mechanism is deformation potential like

and is determined by the variation (caused by intermolecular acoustical

vibrations) of the transfer energy W (or transfer integral) of an electron

from one molecule to the nearest one along the chain. The coupling

constant is proportional to the derivative

′

of W with respect to the

intermolecular distance. The second mechanism is polaron-like and is

determined by the variation of the polarization energy of molecules

surrounding the conduction electron, due to the same intermolecular

vibrations. The coupling constant for this mechanism is proportional to the

average polarizability

of the molecule. As it was shown in [12–14], an

interference between these interactions can take place. As a result, these

interactions considerably compensate each other for some states in the

conduction band. For carriers in these states the effective scattering rate is

significantly reduced, and the mobility is considerably increased. Increased

mobility is favorable for the desired increase of the thermoelectric power

factor.

312 A. Casian, Z. Dashevsky, V. Dusciac, R. Dusciac

We are interested in the study of the electrical conductivity

and

thermopower S near room temperature. Usually, in the Q1D conducting

crystals there are different phase transitions to other, less conducting or

insulating phases. We will assume that the highest critical temperature of

these phase transitions is lower than room temperature. In this case, in order

to investigate the electronic transport it is possible [12, 15] (i) to neglect in

first order approximation the weak interaction between the 1D chains and to

consider a one-dimensional crystal model, and (ii) to use the Boltzmann

kinetic equation for the 1D model.

It was shown in Ref. 12 that near room temperature the scattering of

carriers on acoustical phonons can be considered elastic. However, in this

case the electron-phonon interactions can fully compensate each other for

some states in the conduction band. The mobility of carriers in these states

will be limited by the scattering on impurities or defects, which always

exist in the crystal. Therefore, it is necessary to take into account the

scattering on impurities, as well. The latter, for simplicity, are considered

neutral and point-like. The energy of the conduction electron is taken in the

usual form

)cos1(2)( kaWk

−

where k is the projection of the electron wave-vector, and a is the lattice

constant along the chains. The sign of W is chosen in such a way that

0>W for the s-type band, and 0

W for the p-type one. The dispersion

law of longitudinal acoustical phonons is taken in the standard form

2sin2

qaa

−

υω

where

is the sound velocity along the chains and q is the projection of

the phonon wave-vector in the chain direction.

Thermoelectric Power Factor

The kinetic equation is presented in Ref. 12. It has the form of a Boltzmann

equation and in the considered case can be solved exactly. For non-

degenerated charge carriers the thermoelectric power factor takes the form

)(

222

RTeRP = ,

(1)

Organic Semiconductors – More Efficient Material 313

where

()()exp

EE E dE

kT kT

∆



−

=−





∫

(2)

)()()()(

EEEeE

ρτυσ

= ,

(3)

e is the electron charge,

k is the Boltzmann constant,

E is the Fermi

energy,

∆ is the conduction band width, )()(

222

EEaE −∆=

−

the square of the carrier velocity as a function of charge carrier energy E,

)(E

is the relaxation time, which has the form of a Lorentzian

[

]

222

4)(

)(

DWEE

WTka

+−

−∆

⋅

′

(4)

TTD

WTka

MdIn

sim

222

′

(5)

Here, M is the mass of the molecule,

is a dimensionless parameter which

represents the ratio of the amplitudes of two above mentioned interaction

mechanisms,

γγ

)1(2

±= WE

is the Lorentzian resonance energy, D is

a dimensionless parameter which describes the impurity scattering,

n is

the linear impurity concentration, I and d characterize the effective height

and width of the impurity potential,

K300

T is the room temperature. In

(4) the phonon distribution function has been taken in the high T limit,

because in these materials the Debye temperature is of the order of 80–

100 K.

and 0=D , i.e. if only the first interaction mechanism is active,

the crystal model coincides with that used in [16]. If

is small, 1<<

, the

resonance energy

is placed into the forbidden band and the

interference of above mentioned interactions is weakly pronounced. In this

case the usual results for a narrow 1D conduction band are obtained. If

1≥

proves to be in the allowed band, and if 1

<D , the electronic

states near

will be characterized by very high values of the relaxation

time. This situation changes essentially the behavior of

, S and P.

314 A. Casian, Z. Dashevsky, V. Dusciac, R. Dusciac

For nondegenerate carriers the transport integrals

R and

R in (1) can

be calculated analytically, but the respective expressions are very

cumbersome and cannot be presented here. They will serve for the

comparison with the approximate or numerical calculations. Obviously,

most interesting is the case when the Lorentzian from the relaxation time

(4) is placed in the conduction band (

) and is very sharp ( 1<<D ). In

this case

R and

R can be calculated approximately by decomposing the

Lorentzian in series on D. For the calculation of

R and

R one can take

only the first term from the decomposition, corresponding to the

replacement of the Lorentzian by delta-function. As a result we obtain

232 ,

00F

332

(1)

exp

TEE

DT kT

πγ





−−

=−









(6)

)( REER

−= ,

(7)

where

depends only on crystal parameters

)(

TkWa

WMre

′

(8)

After the substitution of (6) and (7) in (1), we obtain

232, 2

00 00F

0F0

332 2

(1) ( )

exp ( )

()

kTEE

EEkT

eDT kT

πσ γ

−−







=⋅−−









(9)

It is seen that P can take high values, because

D appears in the

denominator and

<<D . However, P also depends strongly on the

difference (

EE− ). It is evident from (9) that the optimal value, which

corresponds to the maximum of P, is

0F0

EEkT−= . On the other hand,

for the non-degenerate case it is necessary that

E is at least equal

3 Tk− . Therefore (9) is not valid for the determination of

max

P , but still

can serve for the evaluation of P near the maximum value. Numerical

calculations following the exact expression (1) are necessary in order to

determine P for a larger interval of the parameters. Unfortunately, not all

Organic Semiconductors – More Efficient Material 315

parameters in (1) are known for any Q1D organic crystal. We shall

consider a hypothetical crystal with parameters close to those of TTF chains

(p-type band) in the TTF-TCNQ crystals:

107.3 ×= (

m is the mass

of the electron),

eV 075.0=W ,

-1

eVÅ 2.0=

′

W , cm/s102

×=

Å 3.12=a , Å 82.3=b , Å 47.18=c (b is the direction of chains),

acr 2= . Let’s put 5.1=

and

3 TkE

−

, then

9.1 TkE

= . From

(9) we obtain

W/cmK 1.7

−

⋅= DP . For

−

=D we will then have

W/cmK 225

=P , a very promising result.

Fig. 1. Thermoelectric power factor P as a function of the parameter

D values

used for the various curves: 1 – 10

-3

; 2 – 10

-2

We do not know the polarizability

of the TTF molecule. But in order

to obtain

5.1

it is necessary to have

Å5.8=

, which is not a very

for the TTF molecule

in the TTF-TCNQ crystal is of the order of

Å16 . This value of

would

correspond to

8.2=

and, respectively, to

W/cmK 5.58

=P for

−

=D . This is also a promising result. At the same time, it is seen that

P decreases quickly, when

grows. Estimations show that in order to

achieve

10~

−

D the crystal purity must be high, but quite reasonable.

012345678910

100

200

300

P, µW/cm

⋅

-1

high value. Note, that the calculated value [17] of

; 3 – 10 .

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

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