Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. Simple analytical model
In this paper we have investigated thermoelectric effect in the epitaxial graphene on a semiconductor substrate using a simple model. We have obtained the expressions for static conductance and thermopower of the epitaxial graphene. The thermopower of the epitaxial graphene can be abnormally large...
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irk-123456789-1186672017-05-31T03:04:29Z Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. Simple analytical model Alisultanov, Z.Z. Электронные свойства проводящих систем In this paper we have investigated thermoelectric effect in the epitaxial graphene on a semiconductor substrate using a simple model. We have obtained the expressions for static conductance and thermopower of the epitaxial graphene. The thermopower of the epitaxial graphene can be abnormally large near the edges of the semiconductor band gap. 2013 Article Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. Simple analytical model / Z.Z. Alisultanov // Физика низких температур. — 2013. — Т. 39, № 7. — С. 767–770. — Бібліогр.: 22 назв. — англ. 0132-6414 PACS: 68.43.–h, 72.80.Vp, 65.80.Ck http://dspace.nbuv.gov.ua/handle/123456789/118667 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Электронные свойства проводящих систем Электронные свойства проводящих систем |
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Электронные свойства проводящих систем Электронные свойства проводящих систем Alisultanov, Z.Z. Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. Simple analytical model Физика низких температур |
| description |
In this paper we have investigated thermoelectric effect in the epitaxial graphene on a semiconductor substrate
using a simple model. We have obtained the expressions for static conductance and thermopower of the
epitaxial graphene. The thermopower of the epitaxial graphene can be abnormally large near the edges of the
semiconductor band gap. |
| format |
Article |
| author |
Alisultanov, Z.Z. |
| author_facet |
Alisultanov, Z.Z. |
| author_sort |
Alisultanov, Z.Z. |
| title |
Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. Simple analytical model |
| title_short |
Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. Simple analytical model |
| title_full |
Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. Simple analytical model |
| title_fullStr |
Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. Simple analytical model |
| title_full_unstemmed |
Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. Simple analytical model |
| title_sort |
thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate. simple analytical model |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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2013 |
| topic_facet |
Электронные свойства проводящих систем |
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http://dspace.nbuv.gov.ua/handle/123456789/118667 |
| citation_txt |
Thermoelectric effect in single layer epitaxial graphene
formed on semiconductor substrate.
Simple analytical model / Z.Z. Alisultanov // Физика низких температур. — 2013. — Т. 39, № 7. — С. 767–770. — Бібліогр.: 22 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT alisultanovzz thermoelectriceffectinsinglelayerepitaxialgrapheneformedonsemiconductorsubstratesimpleanalyticalmodel |
| first_indexed |
2025-07-08T14:25:06Z |
| last_indexed |
2025-07-08T14:25:06Z |
| _version_ |
1837089119239405568 |
| fulltext |
© Z.Z. Alisultanov, 2013
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 7, pp. 767–770
Thermoelectric effect in single layer epitaxial graphene
formed on semiconductor substrate.
Simple analytical model
Z.Z. Alisultanov
A.M. Prokhorov General Physics Institute of RAS, 38 Vavilov Str., Moscow 119991, Russia
Amirkhanov Institute of Physics of Daghestan Scientific Center of RAS
94 Yaragskovo Str., Makhachkala 367003, Russia
Dagestan State University, 43-a Gadzhiyev Str., Makhachkala 367000, Russia
E-mail: zaur0102@gmail.com
Received December 27, 2012, revised February 22, 2013
In this paper we have investigated thermoelectric effect in the epitaxial graphene on a semiconductor sub-
strate using a simple model. We have obtained the expressions for static conductance and thermopower of the
epitaxial graphene. The thermopower of the epitaxial graphene can be abnormally large near the edges of the
semiconductor band gap.
PACS: 68.43.–h Chemisorption/physisorption: adsorbates on surfaces;
72.80.Vp Electronic transport in graphene;
65.80.Ck Thermal properties of graphene.
Keywords: graphene, thermopower.
Introduction
Graphene, a two-dimensional allotrope of carbon, has a
unique band structure, in which electrons are described by
linear and gapless dispersion law [1]. Unusual spectrum
and geometry of the lattice lead to the unique transport
properties of graphene [1–3]. Effects of various factors
(impurities, vacancies, substrate, etc.) on the electronic
spectrum of graphene was investigated partially in [4–6].
The study of epitaxial graphene (EG) is one of the main
problems in the physics of graphene [6–9]. The properties
of EG sheets are of interest for several reasons. First of all,
graphene on the surface of metals and semiconductors can
be considered as an effective contact for devices [10]. On
the other hand, in order to make full use of the properties
of graphene in electronics, it is necessary to vary the struc-
ture, chemical composition, morphology, etc., that can be
done using a suitable substrate.
The study of thermoelectric properties provides com-
plementary information to the electronic structure of con-
densed matter. The Mott formula [11] is the main expres-
sion in the theory of thermoelectric effect. This formula
connects the differential thermopower with the logarithmic
derivative of the longitudinal conductivity
2
[ln ( , 0)]
3
xx B
d
S k T T
e d
, (1)
where T is temperature, ( , 0)T denotes conductance
at zero temperature, denotes chemical potential, Bk is
the Boltzmann constant.
Graphene has unique thermoelectric properties (see,
e.g., review [12]). In fact, the thermopower of graphene at
room temperature reaches about 100 mV/K (for compari-
son, the thermopower of metals is about 0.01 mV/K). Such
large values of the thermoelectric power were observed in
gapped graphene, when the chemical potential is close to
the edge of the band gap. In this paper, using a simple
model we investigated thermoelectric effect in the EG,
which formed on a semiconductor substrate.
mailto:zaur0102@gmail.com
Z.Z. Alisultanov
768 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 7
Model of epitaxial graphene
We investigate EG using the model which was pro-
posed by Davydov [13]. In [14–18], this model was ap-
plied to different cases: EG on metal, EG on semiconduc-
tor, EG on size-quantized film. In this model, the EG is
represented as carbon atoms adsorbed on the substrate and
arranged in a hexagonal structure [13]. In the Anderson
model for the Green function of single adatom, we have
0 1( ( ) ( ))i a cG i ,
where a is the energy of adatom level, ( )c
2| | ( )V denotes the half-width of adatom level,
1
( ) ( ) /( )cP d is the level shift function,
( ) is the density of states of substrate, “P” denotes the
principle value of the integral. Between carbon adatoms
arranged in a hexagonal structure occurs electron ex-
change. Consequently, Brillouin zone is formed in the ad-
sorbed layer. To determine the Green's function of the per-
turbed system, we use the Dyson equation:
0 0
ij i ij i il lj
l
G G G t G ,
where ilt t is the nearest-neighbor hopping energy (for
isolated graphene t ≈ 2.8 eV). Applying Fourier transform
to Dyson equation, given the symmetry of the crystal lat-
tice of graphene, and given that 0
0 ,iG G we get
1 1
0( ) ( ) ( )G G tf iqq , (2)
where
( ) 3 2cos ( 3 ) 4cos ( 3 /2)cos (3 /2),b x x yf q a q a q aq
a is the carbon–carbon distance (for isolated graphene
a ≈ 1.42 Å), q is the two-dimensional wave vector of the
electron, b is the band index: 1b corresponds to the
conduction band and 1b corresponds to the valence
band, is the energy damping of quasiparticle due to scat-
tering (by phonons, etc.). Near the Dirac point for the energy
spectrum, we obtain ( ) 3 | | /2btf tak k | |,b F k
where k is the wave vector measured relatively to the Dirac
points and F is the Fermi velocity (for electrons in of iso-
lated graphene 810 cm/s).F For the density of the states
of substrate, we use the Haldane–Anderson model:
0( ) (| | ), where is the band gap in the energy
spectrum of semiconductor. Then
2
0( ) | | (| | )c V
and
2
0( ) lnV .
Static conductance and thermopower of EG
Assuming an electric field applied in the x direction, the
frequency dependent (real part) conductivity is calculated
from the Kubo–Greenwood formula [19]
2 2 2
( , ) [ ( ) ( )]
2
F e d
T f f
NS
1 2, , 1
Im ( , ) Im ( , ) ,
b bk
G Gk k (3)
where ( )/ 1( ) (e 1)Tf is the Fermi–Dirac distribu-
tion function, 1b and 2b are the band indices for
( , )G k and ( , ),G k respectively, S denotes the area
of graphene. In (3), the number of bands, valley and the
spin degeneracy is taken into account. The Kubo–
Greenwood formula for the static conductance at zero tem-
perature reads
2
2
(0, 0)
2
e
T
1
1 2, 1 0
Im ( , ) Im ( , )
b
b b
k k k kd G G , (4)
where is the band width of graphene (ξ ~ t), is the
chemical potential of graphene. Performing the integration
in (4), we have
2 2 2 2 2
2 2 2
( ) ( ) 4
1
( ) 4
G S
e F
F
2 21 ( )
arctg arctg ,
2 2 2
F
(5)
where 2 2 2( ) ,F ( ),
(| | ) .c F The result (5) shows that, when
, 0c conductance has a universal value
22 /e inde-
pendent of the dilution concentration, in agreement with
earlier theoretical works and in agreement with the experi-
mental data on graphene. The dependence of the EG static
conductance on the chemical potential is shown in Fig. 1.
From Fig. 1 we see that near the edges of the band gap, de-
pendence has a resonant character. We believe, that
0.1 eV, 3 eV, 810 cm/sF and 1.5 eV
(for example, for SiC polytypes 1.55 eV). A resonant
character of the conductivity related to the fact that near the
edges of the band gap relaxation time of quasiparticles is
strongly dependent on energy. This dependence related to
the fact that in the vicinity edges of the substrate band gap
the band gap opens in spectrum of EG [13,17]. Latter is
caused by the fact that in the region of the substrate band
gap 0,c but 0. It needs to call the readers attention
Thermoelectric effect in single layer epitaxial graphene formed on semiconductor substrate
Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 7 769
to the evident analogy between the transport in gapped gra-
phene and in metal close to the electronic topological transi-
tion [20,21]. Indeed, in the vicinity of the critical point,
when the Fermi surface connectivity changes, the quasipar-
ticle relaxation rate also acquires a contribution depending
on energy in the form of step function. This generates the
well known kinks in conductivity [12,20,21].
A detailed study of the transport properties of epitaxial
graphene formed on the semiconductor substrate is given
in [22]. In this work, the dependence of static and dynamic
conductivity on temperature is also investigated.
Using the formula (1) we obtained the thermopower of
EG. The dependence of the EG thermopower on chemical
potential at constant temperature is shown in Fig. 2. From
Fig. 2 we see that near the edges of the band gap, thermo-
power is very high. The reason for the increasing of the
thermopower near the edge of the band gap is explained
above and in Refs. 12, 20, 21.
To get the dependence of the thermopower on tempera-
ture, it is necessary to know the temperature dependence of
the chemical potential, which is gives by expression
2
0
2
[ ( ) ( )]
( )F
n f f d , (6)
where n is the carrier concentration. If we use the formula
(6), then this leads to a deviation from the linear depen-
dence of the thermoelectric power on the temperature. This
conclusion is confirmed by the experimental results [9].
Conclusion
A simple model of EG used here was first proposed in
Ref. 13. Such phenomena as the charge exchange between
the graphene and the substrate, the occurrence of a gap in
the graphene by indirect interaction of its atoms through the
electron gas of the substrate, the occurrence of a gap in the
graphene formed on the semiconductor substrate, the effect
of external magnetic field on the charge exchange and other
phenomena have been investigated by S.Yu. Davydov and
Z.Z. Alisultanov [13–18,22]. Realized in these works nu-
merous comparison of analytical results with the experimen-
tal data and the data obtained from the first principles, show
that the model used is quite adequate and can be used for
qualitative calculations.
When designing the novel nanoelectronic devices it will
be possible to control their temperature regime using the
Peltier cooling effect, which is governed by the value of
the thermoelectric coefficient. Thermoelectric power in EG
can be tuned by choosing a suitable substrate, what looks
promising for practical applications.
Author thanks the Federal Lezghin National and Cul-
tural Autonomy (FLNCA) for the support and A.A. Var-
lamov for useful discussion.
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Fig. 1. The conductance (in units of e
2
/ ) of epitaxial graphene,
formed on the semiconductor substrate.
Fig. 2. The dependence of thermopower of epitaxial graphene on
chemical potential.
Z.Z. Alisultanov
770 Low Temperature Physics/Fizika Nizkikh Temperatur, 2013, v. 39, No. 7
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