The volume filling defects structure based on metals are widely used in modern nan-
otechnology, especially when creating high temperature sensors and structural elements 
based on metal foams [1]. The development of contactless and nondestructive methods for 
diagnosis and test control parameters of multiply connected matrix base material is a very 
important and interesting aspect of the application [2]. In a heat-resistant metal with the 
volume filling defects (VFD) (micro- and nanopores with complex topologies and sizes, 
see. Figure 1) it is primarily its strength and electrical and physical characteristics. Almost 
all rapid methods of such measurements are based on both electrical measurements data 
and on fundamental functional relationships establishing of the microstructure parameters 
and the dispersion medium carriers [3]. The influence of a disordered set of volume filling 
defects (VFD) (micro- and nano-pores of complex topology and various sizes, Figure 1.) is 
the unsolved problem on the electronic properties of the micro heterogeneous materials 
theory.
When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2060

Marenkov, V.I.

Electronic Sumy State University Institutional Repository

82                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I             FERMI LEVEL OF CARRIERS IN THE VOLUME FILLING DEFECTS STRUCTURE BASED  ON HEAT-RESISTANT METALS Volodymyr I. Marenkov   Odessa National I.I. Mechnikov University, Physics Department,  Dvorjanskaja 2, 65026, Odessa, Ukraine  ABSTRACT The volume filling defects structure based on metals are widely used in modern nan-otechnology, especially when creating high temperature sensors and structural elements based on metal foams [1]. The development of contactless and nondestructive methods for diagnosis and test control parameters of multiply connected matrix base material is a very important and interesting aspect of the application [2]. In a heat-resistant metal with the volume filling defects (VFD) (micro- and nanopores with complex topologies and sizes, see. Figure 1) it is primarily its strength and electrical and physical characteristics. Almost all rapid methods of such measurements are based on both electrical measurements data and on fundamental functional relationships establishing of the microstructure parameters and the dispersion medium carriers [3]. The influence of a disordered set of volume filling defects (VFD) (micro- and nano-pores of complex topology and various sizes, Figure 1.) is the unsolved problem on the electronic properties of the micro heterogeneous materials theory.  Key words: nanopores, electronic properties, materials with VFD.  PLASMA STATISTICAL APPROACH The new statistical “plasma” approach is proposed in this work.  This method is based on the modeling statistical concept of the heterogeneous plasma system (HPS) characteristics [3-5]. The main point of this approach is the concept of an electrically neutral cell (see Figure 2). This cell is the smallest area of the electrically inhomogeneous material released by a multiply connected surface 3extreme of instant self-consistent system electric potential [4]. The electronic component statistical equilibrium in volume filling defects of the heat-resistant metals of both nano- and mesoscopic sizes determines the level of electrochemical potential of a homogeneous volume of the sample in any its point.  Statistical equilibrium of the electronic component in FVD high-temperature metal nano- and mesoscopic size determines the level of electrochemical potential of a homogeneous volume of the sample in any its point.  Moreover, according to the principle of free energy minimum, F takes the smallest value. Equilibrium distribu-tion of the local density of the electronic component in the matrix base material and Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   83  VFD satisfies this condition and is determined by solving the effective electrostatic problem in an averaged cell zC[  [3, 5].    Fig. 1 – Nanoporous metal foams [1] Fig. 2 – Planar cell  of  the micro-hulled metal with VFD  Fig.3 – 3-D graph of the dependence F = F(Ɏ0)  RESULTS AND DISCUSSION The main point of this approach is the concept of an electrically neutral cell (see Figure 2). This cell is the smallest area of the electrically inhomogeneous material released by a multiply connected surface 3  extreme of instant self-consistent system electric potential [4]. The electronic component statistical equilibrium in volume filling defects of the heat-resistant metals of both nano- and mesoscopic sizes determines the level of electrochemical potential of a homogeneous volume of the sample in any its point.  Statistical equilibrium of the electronic component in FVD high-     pC rr                    0                    Cp rr  Y X O B A 84                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I             temperature metal nano- and mesoscopic size determines the level of electrochemical potential of a homogeneous volume of the sample in any its point. Moreover, according to the principle of free energy minimum, F takes the smallest value. Equilibrium distribution of the local density of the electronic component in the matrix base material and VFD satisfies this condition and is determined by solving the effective electro-static problem in an averaged cell zC[   [3, 5]. For the hulled metal sample with VFD this equation looks like 0)sinh(kTE~2rtg)F,( F0FFpp0  GNNNHD¸¸¹·¨¨©§ N ):  (1)  Here:  Ɏ0 is potential in the center of the cell; F is the Fermi level of the carriers; G,rp  is respectively, the size of the defect and matrix elements of metal, which belongs to zC[ ; 1F1,  NN  is   Debye  length  and  the  Fermi  length  of  the  electronic component; > @)E/WE/F1(/1)E/WE/F1(32~ 0F00F0F00F  D   is the parameter of the equation; 0FE   and  W0 is the Fermi energy and electron work function of metal; Hp is  metal dielectric permittivity; T is temperature of the sample. Equation (1) establishes a functional relationship of electrochemical potential of the carriers with the defining parameters of the sample: temperature, geometric characteristics and concentration of VFD, the electronic parameters of the base material, and particularly with the equilibrium value of the local electrostatic defects potential (Figure 3.) stabilized. The external electric field Ɏ0  influence on the electrons density distribution in the sample VFD was determined in the computer experiment. The possibility of creating of the sensitive temperature sensors based on heat-resistant metal with nano-VFD was discussed in details. REFERENCES [1] B.C. Tappan, S.A. Steiner, E.P. Luther, Nanoporous Metal Foams.- Angewandte Chemie.- International Edition, 2010, Vol. 49, No 27, P. 4544-4565.  [2] X. Ma, A.J. Peyton, Y.Y. Zhao, NDT & E International, 2005,Vol. 38, P. 359-367. [3] V.I. Marenkov, 24th Symposium on Plasma Physics and Technology, 14th-17th June, 2010, Prague, Czech Republic, P 130. [4] V.I. Marenkov, Ukrainian-German Symposium on Physics and Chemistry of Nanostructures and on Nanobiotechnology.- Beregove, The Crimea, Ukraine, 6th – 10th September, 2010, Book of Abstracts,P.143 [5] V.I. Marenkov, Ⱥ.Yu. Kucherskiy, 4th International Scientific and Technical Con-ference Sensors Electronics and Microsystems Technology (SEMST-4), Odessa, Ukraine, June 28 - July 2, 2010, Book of Absracts, P. 125-126. 

Fermi level of carriers in the volume filling defects structure based on heat-resistant metals

SocioEconomic Challenges Journal (Sumy State University)

82                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I            
 
FERMI LEVEL OF CARRIERS IN THE VOLUME FILLING 
DEFECTS STRUCTURE BASED  
ON HEAT-RESISTANT METALS 
Volodymyr I. Marenkov  
 
Odessa National I.I. Mechnikov University, Physics Department,  
Dvorjanskaja 2, 65026, Odessa, Ukraine 
 
ABSTRACT 
The volume filling defects structure based on metals are widely used in modern nan-
otechnology, especially when creating high temperature sensors and structural elements 
based on metal foams [1]. The development of contactless and nondestructive methods for 
diagnosis and test control parameters of multiply connected matrix base material is a very 
important and interesting aspect of the application [2]. In a heat-resistant metal with the 
volume filling defects (VFD) (micro- and nanopores with complex topologies and sizes, 
see. Figure 1) it is primarily its strength and electrical and physical characteristics. Almost 
all rapid methods of such measurements are based on both electrical measurements data 
and on fundamental functional relationships establishing of the microstructure parameters 
and the dispersion medium carriers [3]. The influence of a disordered set of volume filling 
defects (VFD) (micro- and nano-pores of complex topology and various sizes, Figure 1.) is 
the unsolved problem on the electronic properties of the micro heterogeneous materials 
theory. 
 
Key words: nanopores, electronic properties, materials with VFD. 
 
PLASMA STATISTICAL APPROACH 
The new statistical “plasma” approach is proposed in this work.  This method 
is based on the modeling statistical concept of the heterogeneous plasma system 
(HPS) characteristics [3-5]. The main point of this approach is the concept of an 
electrically neutral cell (see Figure 2). This cell is the smallest area of the 
electrically inhomogeneous material released by a multiply connected surface 3
extreme of instant self-consistent system electric potential [4]. 
The electronic component statistical equilibrium in volume filling defects of 
the heat-resistant metals of both nano- and mesoscopic sizes determines the level of 
electrochemical potential of a homogeneous volume of the sample in any its point.  
Statistical equilibrium of the electronic component in FVD high-temperature metal 
nano- and mesoscopic size determines the level of electrochemical potential of a 
homogeneous volume of the sample in any its point.  Moreover, according to the 
principle of free energy minimum, F takes the smallest value. Equilibrium distribu-
tion of the local density of the electronic component in the matrix base material and 
Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I                   83 
 
VFD satisfies this condition and is determined by solving the effective electrostatic 
problem in an averaged cell zC[  [3, 5].   
 
Fig. 1 – Nanoporous metal foams [1] Fig. 2 – Planar cell  of  the micro-hulled 
metal with VFD 
 
Fig.3 – 3-D graph of the dependence F = F(Ɏ0) 
 
RESULTS AND DISCUSSION 
The main point of this approach is the concept of an electrically neutral 
cell (see Figure 2). This cell is the smallest area of the electrically 
inhomogeneous material released by a multiply connected surface 3  extreme 
of instant self-consistent system electric potential [4]. 
The electronic component statistical equilibrium in volume filling defects 
of the heat-resistant metals of both nano- and mesoscopic sizes determines the 
level of electrochemical potential of a homogeneous volume of the sample in 
any its point.  Statistical equilibrium of the electronic component in FVD high-
 
    pC rr                    0                    Cp rr  
Y 
X 
O 
B A 
84                   Nanomaterials: Applications and Properties (NAP-2011). Vol. 2, Part I            
 
temperature metal nano- and mesoscopic size determines the level of 
electrochemical potential of a homogeneous volume of the sample in any its 
point. Moreover, according to the principle of free energy minimum, F takes 
the smallest value. Equilibrium distribution of the local density of the electronic 
component in the matrix base material and VFD satisfies this condition and is 
determined by solving the effective electro-static problem in an averaged cell 
zC[   [3, 5]. For the hulled metal sample with VFD this equation looks like 
0)sinh(
kT
E~
2
r
tg)F,( F
0
FFpp
0  GNN
NHD¸¸¹
·
¨¨©
§ N ):  (1) 
 
Here:  Ɏ0 is potential in the center of the cell; F is the Fermi level of the 
carriers; G,rp  is respectively, the size of the defect and matrix elements of metal, 
which belongs to zC[ ; 
1
F
1,  NN  is   Debye  length  and  the  Fermi  length  of  the  
electronic component; > @)E/WE/F1(/1)E/WE/F1(
3
2~ 0
F
00
F
0
F
00
F  D   is 
the parameter of the equation; 0FE   and  W
0 is the Fermi energy and electron work 
function of metal; Hp is  metal dielectric permittivity; T is temperature of the sample. 
Equation (1) establishes a functional relationship of electrochemical potential of the 
carriers with the defining parameters of the sample: temperature, geometric 
characteristics and concentration of VFD, the electronic parameters of the base 
material, and particularly with the equilibrium value of the local electrostatic 
defects potential (Figure 3.) stabilized. The external electric field Ɏ0  influence on 
the electrons density distribution in the sample VFD was determined in the 
computer experiment. The possibility of creating of the sensitive temperature 
sensors based on heat-resistant metal with nano-VFD was discussed in details. 
REFERENCES 
[1] B.C. Tappan, S.A. Steiner, E.P. Luther, Nanoporous Metal Foams.- Angewandte 
Chemie.- International Edition, 2010, Vol. 49, No 27, P. 4544-4565.  
[2] X. Ma, A.J. Peyton, Y.Y. Zhao, NDT & E International, 2005,Vol. 38, P. 359-367. 
[3] V.I. Marenkov, 24th Symposium on Plasma Physics and Technology, 14th-17th June, 
2010, Prague, Czech Republic, P 130. 
[4] V.I. Marenkov, Ukrainian-German Symposium on Physics and Chemistry of 
Nanostructures and on Nanobiotechnology.- Beregove, The Crimea, Ukraine, 6th – 
10th September, 2010, Book of Abstracts,P.143 
[5] V.I. Marenkov, Ⱥ.Yu. Kucherskiy, 4th International Scientific and Technical Con-
ference Sensors Electronics and Microsystems Technology (SEMST-4), Odessa, 
Ukraine, June 28 - July 2, 2010, Book of Absracts, P. 125-126. 


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Fermi level of carriers in the volume filling defects structure based on heat-resistant metals

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