Tunneling Conduction in Nano Particles

6.1.3.3. Tunneling Conduction in Nano Particles

The present materials are very similar to ‘granular metals’, which represent a physical system for studying ‘percolation conductivity’ [9]. The microstructural features of these “glass-conducting nano ganules” system clearly show that the electrical transport due to tunneling mechanism between the isolated conduting particles will influence their DC conductivity behaviour [10]. For low electric fields, Abeles et al [9] have shown that the resistivity of granular metals, when the particles are isolated from each other, is given by :

(6.3) In this equation, ρ 0 is a constant and the value of the other constant is given by :

ρ =ρ exp[2(C/kT) 1/2 0 ]

(6.4) where, the parameter χ is expressed as :

C=χSE 0 c

(6.5) where, m denotes the electron mass, φ the effective barrier height and h is the Planck’s constant, S is the

χ = (2mφ/h 2 ) 1/2

separation between the grains, and E 0 c is the energy required to generate a pair of fully dissociated positively and negatively charged grains. This energy is given by :

(6.6) where, K is expressed as :

E c 0 = 2e 2 /Kd

(6.7) where, ε is the dielectric constant of the insulating medium, and d is the size of the nano particles.

K = ε[1 + (d/2S)]

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) cm

Lg (

4.0 4.5 2 1/2 –1/2 5.0 5.5 10 / T (K )

Figure 6.6 : DC resistivity data of glass 1 plotted as log ρ against 1/T 1/2

The DC resistivity data of bismuth and selenium containing glasses are plotted as log ρ against 1/T 1/2 in Figures 6.6 and 6.7. The linearity of the curves for temperatures below 120°C give us informa- tion on the ‘tunneling’ mechanism between conducting metallic islands.

The value of C belonging to different glasses are calculated from the slope of these curves. By taking χ = 10/nm [10] and S = 5 nm, the values of E 0 c are estimated from equation (6.4) for different compositions. The results are tabulated in Table 6.5. The values of E 0 c are also calculated from equa- tion (6.7) by taking ε = 4 [6] being the dielectric constant of the base glass and taking suitable values of

d as found from the TEM micrographs. All these values are also given in Table 6.5. The calculated values of the energy are in reasonable agreement with those deduced from log ρ against 1/T 1/2 plots, except for glass 8. This discrepancy is thought to be due to an ‘uncertainty’ in the value of S, which is taken approximately as 5 nm for the calculation. The inter-particle separation in this glass composition is expected to be less than 5 nm, which was the ‘resolution limit’ of the electron microscope used in this work [1, 2].

ELECTRICAL PROPERTIES

p i 10.0 (

10 /T (K –1/2 )

Figure 6.7 : DC resisvity data of selenium glasses plotted as log ρ against 1/T 1/2 .

Table 6.5 : Values of C and E 0 c for different glasses.

Glass No.

C (eV)

E c 0 (eV)

d (nm)

E c 0 (eV) Calculated

Both the real and imaginary parts of the dielectric permittivity of glass 1 are plotted against frequency in Figure 6.8 in the temperature range, where the ‘tunneling’ mechanism has been shown to

be operative. In Figure 6.9, these data are represented by the Cole-Cole diagrams [11]. It is evident from these plots that a ‘distribution’ of relaxation mechanism is present in this glass 1 containing bis- muth. The activation energy for dielectric relaxation is obtained by plotting log of the frequencies at which the ‘loss maximum’ occurs as a function of 1/T. The results are shown in Figure 6.10. From the slope of the linear plots, an activation energy value of 0.14 ev is calculated. This is also in reasonable

agreement with the values of E 0 c , as shown in Table 6.5. Therefore, the observed dielectric relaxation is attributed to the ‘tunneling’ of charge carriers between the ‘islands’ of nano particles of bismuth within the glass matrix.

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The current-voltage (I-V) trace on a Tektronix Oscilloscope for an 'ion-exchanged' glass 8 is shown in Figure 6.11. The width of the electrodes on the specimen surface and their separation are as shown in the figure. A thresold switch is observed at around 1.1 V from a low-resistance state (i.e. ≈

12.5 Ω) to high-resistance state (i.e. ≈ 100 Ω). This switching is found to occur reversibly over several hundred cycles. Such effects are believed to be due to the presence of nano-crystalline selenium parti- cles between the silver droplets precipitated in the glass matrix, after an ion-exchange and reduction treatments. The switching to a lower conductance-state by the application of a voltage seems to arise due to the formation of a high-resistance amorphous layer normal to the current path between the electrodes due to the ‘localised’ melting of crystalline selenium.

Figure 6.8 : Real and imaginary parts of dielectric permittivity for glass 1 at different temperatures against frequency : Circle = 16°C, Triangle = 59°C, Square = 118°C.

Such type of behaviour is termed as ‘reversible switching’, which has also been reported in the bulk crystalline selenium near the melting point [12]. The very low switching field of ≈ 1.1 V/cm observed in this study is ascribed to the presence of silver particles [2] in the system.

It has been shown that ‘nano granular’ metals represent an interesting system for studying the ‘percolation’ conductivity [9]. Such type of work was restricted either to computer simulation experi- ments [13, 14] or to simplified systems such as conducting papers with punched holes [15]. It is thought that the materials of the type described above could also be used for the same purpose [1].

ELECTRICAL PROPERTIES

Figure 6.9 : Cole-Cole plots for dielectric permittivity data for glass 1 at different temperatures : (a) 16°C, (b) 59°C, (c) 118°C.

kHz) in x ( 4.0

f ma g lo

3.0 2.5 3.0 3.5 3 10 /T (K ) –1

Figure 6.10 : Lof f max against 1/T for glass 1 giving activation energy.

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A 60.0 I (m

Figure 6.11 : V-I characteristics of the surface layer of an ion-exchanged and reduced sample of glass 8 : electrode width = 3 mm, electrode separation = 1 mm.