AbstractThe potential distribution in a deformed ZnO nanowire relies upon its piezoelectric and semiconductive properties. Here we systematically investigate the influence of different parameters on the equilibrium potential distribution. In particular we calculate the electric potential distribution when thermodynamic equilibrium among free charge carriers is achieved for nanowires under different doping concentrations (n or p type), different applied forces, and different geometric configurations. We show that doping concentration is the parameter that mostly affects the magnitude and distribution of the piezoelectric potential

D’Amico, A.

Falconi, C.

Gao, Y.

Mantini, G.

Wang, Z.L.

Elsevier - Publisher Connector 

Potential distribution in deformed ZnO nanowires 

Mantini G

Gao Y

Wang ZL

D'AMICO, ARNALDO

FALCONI, CHRISTIAN

Potential distribution in deformed ZnO nanowires

D’Amico A

Falconi C

Archivio della Ricerca - Università di Roma Tor vergata

Procedia 
Chemistry  
www.elsevier.com/locate/procedia
 
Proceedings of the Eurosensors XXIII conference 
Potential distribution in deformed ZnO nanowires 
G. Mantinia,b,*, Y. Gaoa, Z. L. Wanga, A. D’Amicob,c, C. Falconib,c 
aSchool of Material Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0245, USA 
bDepartment of Electronic Engineering, University of Tor Vergata, Via del Politecnico 1, 00133 Roma,Italy 
cCNR IDAC, Via Fosso del Cavaliere 100, 00133 Rome, Italy  
 
 
 
Abstract 
The potential distribution in a deformed ZnO nanowire relies upon its piezoelectric and semiconductive properties. Here we 
systematically investigate the influence of different parameters on the equilibrium potential distribution. In particular we 
calculate the electric potential distribution when thermodynamic equilibrium among free charge carriers is achieved for 
nanowires under different doping concentrations (n or p type), different applied forces, and different geometric configurations. 
We show that doping concentration is the parameter that mostly affects the magnitude and distribution of the piezoelectric 
potential. 
 
Keywords: Nanowire; ZnO; Nanogenerator 
1. Introduction 
Nano-devices for energy harvesting may become critical components of self-powered nanodevices for different 
applications such as implantable microsystems for medical applications and for nodes of wireless sensors networks. 
Piezoelectricity is a very promising method to harvest mechanical energy from the environment. Body movement, 
muscle stretching, acoustic waves and blood flow can all be sources of mechanical energy, that can be converted 
into electricity by means of the piezoelectric effect. 
Piezoelectric nanogenerators using nanowires (NWs) have been recently demonstrated for converting nanoscale 
mechanical energy into electricity1,2. The principle of nanogenerators is that an applied external force exerted at the 
top of the ZnO nanowire generates a piezoelectric potential due to elastic deformations. The resulting potential can 
drive the flow of charge carriers through an external load. The flowing direction of charge carriers is controlled by 
the Schottky barrier formed at the junction of the nanowire with an external electrode. 
A continuum model for the electrostatic potential in a bent piezoelectric nanowire has been presented3 and 
applied to a variety of piezoelectric nanowires and nanowalls4. This model and its calculations were based on the 
Lippman theory5, which can be employed when the doping concentration is extremely low, thus allowing to neglect 
the electrical conductivity of the material. By applying those calculations to a deformed nanowire, it has been 
demonstrated that the compressed side of the NW exhibits a negative potential, while the stretched side presents a 
 
* Corresponding author. Tel.: +39-06-7259-7347. 
 E-mail address: g.mantini@ing.uniroma2.it 
  
1876-6196/09  © 2009 Published by Elsevier B.V. 
doi:10.1016/j.proche.2009.07.350
 Procedia Chemistry 1 (2009) 1403–1406
Open access under CC BY-NC-ND license.
 positive potential. The voltage drop created across the section of the nanowire when it is laterally deflected, is at the 
base of the nanogenerator theory. 
A new model, including the statistics of electron/holes, has been presented6 in order to obtain a more accurate 
estimation of the piezoelectric potential in deflected nanowires with moderate conductivity (i.e. normal doping 
range). The same model has been used7 in order to investigate the influence of various parameters on the electric 
potential distribution in a laterally bent semiconductive nanowire. Previous works3,4,6 only considered n-type doping, 
because as-grown ZnO nanowires are typically n-type; the piezoelectric potential of deflected p-type nanowires has 
been shown8 for a certain doping concentration; here we show how the electrical potential distribution depends on 
applied force, geometric parameters, and doping (including various p-type doping concentrations). 
Calculations6 take into account both the piezoelectric constitutive equation and the redistribution of electrons 
under thermodynamic equilibrium (Fermi-Dirac statistics).  
 
2. Calculations and Results 
The Finite Element Method (FEM) was used to solve the nonlinear partial differential equations describing the 
piezoelectric constitutive equation and the redistribution of electron under thermodynamic equilibrium. A ZnO 
nanowire, epitaxially grown along the c axis, is laterally bent by a force exerted at the top.  
The material constants for ZnO used in the calculations are chosen as follows6: Young’s modulus E=129 GPa; 
Poisson’s ratio ν=0.349; relative dielectric constants κ∞=7.77, κ||= 8.91; piezoelectric constants e31= -0.51 C/m2, e33= 
1.22 C/m2, e15= -0.45 C/m2; other physical parameters are adopted from Gao et al.6 
The nanowire is modeled as a cylinder and the force is uniformly applied at the top surface of the nanowire, 
perpendicular to its axis, in order to avoid punctual deformations. 
Figure 1a shows the influence of the donor concentration on the equilibrium piezoelectric potential for different 
donor concentrations between 0.05x1017 cm-3 and 5x1017 cm-3. The length of the nanowire is 600 nm and the radius 
is 25 nm. The force exerted at the top is 80 nN. The stretched side (y<0) shows a small positive electric potential (as 
explained before); the compressed side (y>0) instead has a negative potential; the electrons are therefore 
accumulated in the stretched side (positive potential) so that the stretched side (y<0) is more conductive and, 
therefore, the voltage difference in this region is smaller than in the (depleted) compressed side (y>0). The positive 
potential in the stretched side is almost zero for high donor concentration (above 1017 cm-3). 
Figure 1b shows the same calculation carried out for a p-type nanowire, with acceptor concentration between 
0.1x1017 cm-3 and 5x1017 cm-3. In this case, analogously, holes are accumulated in the compressed side (negative 
potential) so that the compressed side (y<0) is more conductive and, therefore, the voltage difference in this region 
is smaller than in the (depleted) stretched side (y>0). The negative potential in the compressed side is almost zero 
for high acceptor concentration (above 1017 cm-3). 
 
 
Fig. 1. (a) Piezoelectric potential for different donor concentrations; (b) Piezoelectric potential for different acceptor concentrations. 
G. Mantini et al. / Procedia Chemistry 1 (2009) 1403–1406 1404
 Figure 2 shows the influence of the applied force on the equilibrium potential. The geometric parameters are the 
same as before, with donor concentration equal to ND=1x1017 cm-3. The force is increased in the range 40 nN to 140 
nN. As explained above, during the simulations, the force was applied at the top surface of the nanowire in order to 
avoid punctual deformations. When increasing the applied force, the electric potential in the compressed side 
increases as well. 
 
 
Fig. 2.  Piezoelectric potential for different forces exerted at the top of the nanowire. 
The influence of geometric parameters of the nanowire on the equilibrium potential is shown in figure 3. Figure 
3a shows that the length of the nanowire does not induce changes in the piezoelectric potential. In this case the 
radius of the nanowire has been kept constant at 25 nm, and the length has been varied in the range 200 nm to 1000 
nm. The donor concentration and the applied force have been kept constant at 1x1017 cm-3 and 80nN, respectively. 
Figure 3b shows the influence of the radius dimension on the piezoelectric potential, when all other parameters 
are kept constant. The effect of the variation of the radius has been investigated in the range 25 nm < a < 100 nm. 
The electric potential is almost neutralized for a radius of 100 nm. 
 
 
 
Fig. 3. (a) Piezoelectric potential for different lengths of the nanowire; (b) Piezoelectric potential for different radius dimension of the nanowire. 
 
 
G. Mantini et al. / Procedia Chemistry 1 (2009) 1403–1406 1405
 3. Conclusions 
The influence of different parameters on the equilibrium piezoelectric potential distribution in a deformed ZnO 
nanowire has been systematically investigated. The doping concentration was the parameter most affecting the 
potential distribution. 
Acknowledgements 
       The authors acknowledge the U.S.-Italy Fulbright Commission for awarding a Fulbright Scholarship to 
Giulia Mantini.  
References 
1. Wang ZL, Self-powered nanotech. Scientific American 2008; 82-87 
2. Wang ZL, Towards self-powered nanosystems: from nanogenerators to nanopiezotronics. Adv Func Materials 2008;18:3553-3567. 
3. Gao Y, Wang ZL. Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerators and nanopiezotronics. 
Nano Lett 2007;7:2499-2505 
4. Falconi C, Mantini G, D’Amico A, Wang ZL. Studying piezoelectric nanowires and nanowalls for energy harvesting. Sens Actuators 
B:Chem;2009;139:511-519. 
5. Landau LD, Lifshitz EM, Pitaevskii LP. Electrodynamics of continuous media. 2nd ed. New York: Pergamon; 1984. 
6. Gao Y, Wang ZL. Equilibrium potential of free charge carriers in a bent semiconducting nanowire. Nano Lett 2009; 9(3):1103-1110 
7. Mantini G, Gao Y, D’Amico A, Falconi C, Wang ZL. Equilibrium piezoelectric potential distribution in a deformed ZnO nanowire. Nano 
Research; accepted for publication 
8. Lu MP, Song J, Lu MY, Chen MT, Gao Y, Chen LJ, Wang ZL. Piezoelectric nanogenerator using p-type ZnO nanowire arrays. Nano Lett 
2009; 9(3): 1223-1227 
G. Mantini et al. / Procedia Chemistry 1 (2009) 1403–1406 1406


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Potential distribution in deformed ZnO nanowires

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