The effects of the applied current and the measurement temperature on the negative differential resistance behaviour of carbonized xerogel

Chemical Physics 524 (2019) 85–91

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The effects of the applied current and the measurement temperature on the negative differential resistance behaviour of carbonized xerogel

T

I. Najeh , L. El Mir ⁎

Laboratory of Physics of Materials and Nanomaterials Applied at Environment (LaPhyMNE), Gabes University, Faculty of Sciences in Gabes, Gabes, Tunisia

ARTICLE INFO

ABSTRACT

Keywords: Nanoporous carbon Electrical properties Electric field Negative differential resistance Percolation phenomenon

Electrical properties of carbonised organic xerogel based on resorcinol–formaldehyde (RF), prepared by pyrolysis at 675 °C in nitrogen atmosphere for two hours, were investigated. In this temperature an insulator to semiconductor-like transition occurs. The voltage–current (V–I) characteristics indicate the presence of nonlinear conductivity depending on the measurement temperature. The origin of the non-linearity in the electrical conductivity is discussed using different theoretical models. The obtained results reveal that this non-linear conductivity starts above a threshold current, which is illustrated by the presence of negative differential resistance (NDR) region. The properties of the obtained NDR are controlled by the applied current and are attributed to a percolation phenomenon in the carbonised sample. The obtained result is very promising for many applications in power electronic technology specially for the development of some negatronic devices.

1. Introduction The expanding number of researchers, who are as of now working in the field of electrically conducting organic materials, is a result of the interesting properties appeared in these materials, both for potential innovative applications and in fundamental research. Since the carbon aerogels in light of resorcinol–formaldehyde (RF) was prepared by R.W. Pekala in 1989 [1], porous carbons, called also activated carbons, have been widely considered for the last decades [2–8]. Presenting a large specific surface area, high porous carbons have been utilized as a part of wide variety of technological applications, such as for gas storage, gas sensors, cathodes of supercapacitors, chromatographic packing, catalyst supports, diabetic detector and others [9–15]. Be that as it may, no methodical examination was researched to outline electric conductivity in this material specially in the transition zone [10,11]. We report in this paper, an easy systematic work in light of the gelation of resorcinol–formaldehyde (RF) xerogel using picric acid as activator, for the elaboration of electrical conducting carbon (ECC) structures. Conductivity of the obtained structures shows an indistinguishable conduct from electron transport paths in various polymer composite frameworks [16–20]. Electrical transport properties are of current intrigue and they give distinctive aspects of the conduction process, nature of carriers and their properties. In the bibliography, the electrical properties of nu-

⁎

merous organic semiconducting materials are studied [21]. Escalated look into studies on semiconducting like materials have prompted bits of knowledge into the chemical composition and physical properties. In association with that, we elaborated ECCs pyrolysed to make a semiconductor like material and explore its electrical properties. The motivation behind the present work is to explore the dependence of the temperature to the electrical conductivity of ECCs over a large range of temperature. After the synthesis of the samples based on resorcinol–formaldehyde (RF) xerogel using El Mir et al. process [22,24]; some investigations on the evolution of electrical properties as function of measurement temperature and applied electric field were carried out. Particular interest was given to the sample prepared at 675 °C (RF-675) to show some links between the structure and the electrical properties. This specific pyrolysis temperature is very close to the critical temperature corresponding to the electrical transition temperature from insulating to conducting behavior which is attributed in this work to the in-situ formation of metallic filaments like conducting paths in the porous carbon host matrix. In the present paper, we report the nonlinear conductivity in RF-675 [22–24]. This behavior is well pronounced in the voltage–current (V–I) characteristics by the appearance of a negative differential resistance (NDR) when the applied current exceeds a threshold value (Ith).

Corresponding author. E-mail address: [email protected] (I. Najeh).

https://doi.org/10.1016/j.chemphys.2019.04.032 Received 27 February 2019; Received in revised form 5 April 2019; Accepted 30 April 2019 Available online 09 May 2019 0301-0104/ © 2019 Elsevier B.V. All rights reserved.

Chemical Physics 524 (2019) 85–91

I. Najeh and L. El Mir

(a)

(b)

Fig. 1. TEM micrographs of the samples; (a): Xerogel and (b): RF-675.

2. Experimental 2.1. Sample preparation

(101)

Intensity (a. u.)

The experimental details of the preparation process of the xerogel and the ECC pyrolyzed at 675 °C have been described elsewhere [22]. 2.2. Characterization techniques The TEM images were recorded on JEOL-100C transmission electron microscope. The X-ray diffraction (XRD) patterns of the samples were obtained using a Bruker D5005 diffractometer with Cu Kα radiation operated at 40 kV. The electrical analyses were obtained over by an Agilent 4294A impedance analyser with excitation voltage amplitude of 50 mV.

(002)

(b)

(a)

30

3. Results and discussion 3.1. TEM micrographs and XRD spectrum diffractogram

2θ (degree)

60

Fig. 2. XRD spectra of the samples; (a): Xerogel and (b): RF-675.

Fig. 1 displays TEM micrographs of the xerogel prepared at 150 °C and the ECC after pyrolysis at 675 °C. The xerogel prepared at 150 °C contains complex aggregates of hydrocarbons. This xerogel turn into a porous solid, at 675 °C. So, the liquid released from the thermal treatment left holes in the solid. The sample RF-675 is formed by the pores in the range of 50–200 nm. It’s clear that the porosity becomes more pronounced after the heat treatment. It is believed that the large number of pores in ECC contributes to an interfacial polarization. A similar response has been observed in other porous materials. XRD patterns obtained from the samples ECCS are given in Fig. 2. The xerogel prepared at 150 °C is amorphous; after pyrolysis at 675 °C, it becomes partly crystalized with the appearance of two small bands centered at around 25° and 44°, respectively corresponding, to (0 0 2) and (1 0 1) hkl plans of the graphite phase.

100 80 K 100 K 120 K 140 K 160 K 180 K 200 K 220 K 240 K 260 K 280 K 300 K

Voltage (v)

80 60 40 20 0 -20 -40 -60 -80

3.2. Electrical characteristics

-15

Generally, the systems which show differential negative resistance are divided into two classes: the current-controlled S-type and the voltage-controlled N-type. Thus, in our sample RF-675 we observe the current-controlled S-type behavior. However, the negative differential resistance (NDR) gives rise to three broad mechanisms: the conduction by heated electrons, the set up semi-permanent of space-charge distributions and the atomic rearrangement in the insulator. In the S-type the electron mobility can rise suddenly, which means that the electrons have sufficient energy. The changes of the distribution of the filaments or paths characterize the NDR. Thus, the atoms with incompletely saturated bonds rise from the increase in conductivity, give an S-type characteristic. However, the Joule effect heating of the filament

-10

-5

0

Current (mA)

5

10

15

Fig. 3. V (I) characteristics of RF-675 for different measurement temperatures (80–300) K.

undergoes a fracture beyond its critical point. In this model, the formation of current filaments is unstable. The Fig. 3 shows that the V–I curves are linear for current less than the threshold value Ith = 30 mA (I < Ith = 30 mA). However, above Ith the conduction is strongly non-linear. These results depicts that, a lattice is formed by a random mixture of conductors and insulators. So, in this case the non-linearity 86

Chemical Physics 524 (2019) 85–91

I. Najeh and L. El Mir

100

R (kΩ)

range of temperatures (80–300 K). The Mott’s law for VRH (Eq. (4)) is well respected in the region of 80–200 K for I ≤ 1 mA:

80 K 100 K 120 K 140 K 160 K 180 K 200K 220 K 240 k 260 K

10

0.01

0.1

1

10

I (mA)

Fig. 4. R (I) curves of RF-675 for different measurement temperatures (80–300) K.

occurs when each conducting bond in the lattice is assumed to possess a nonlinear I–V relation (Fig. 4). In this case the evolution of the voltage and the resistance are given by Eqs. (1) and (2): [23]. (1)

and

R=

dV = R (T) dI 0

I

1

(2)

The non-linear phase is characterised by a negative differential resistance (NDR) phase. In this region, V–I curves, follow the relationship in Eq. (3):

V=

R = R 0 exp

(3)

I

R0 (KΩ)

R(T, E) = R(T, 0)exp

Experimental values Fit

1

-0.25

T

0.30 -0.25

(K

(5)

eRE kT

(6)

where R(T,0) is the conductivity for E → 0, R is the mean hopping distance, γ is a factor of the order of unit. Consequently, the influence of electric field on the activation energy is well illustrated. Here, an external electric field causes the filaments to align parallel to the field. This align shortens the hopping range and decreases the activation energy of the charge carrier. The resistance is activated in the insulating phase and activation energy vanishes at the transition because in this zone the number of filaments increases which induces to direct contacts between the aligned filaments. [28]. Accordingly, the sample presents metallic and semiconductor behaviors at high current at the same time [29–31]. For I = 100 mA, the expression for the resistance can then be written as given by Eq. (10) [32]:

10

0.27

Ea kT

where Ro is the resistance prefactor, Ea is the activation energy, and k is the Boltzmann constant. For I = 0.1 mA; the low-temperature domain is described by relatively low activation energy Ea = 50 meV, while at high temperature it’s about 90 meV. The changes of the activation energies take place at about 200 K, which may suggest that we have to deal with some changes of conduction mechanism at this temperature. For I = 30 mA; the low-temperature domain is described by relatively low activation energy Ea = 2 meV, while at high temperature is about 50 meV. Under the effect of the electric field applied to the material, the activation energy decreases. According to N. F. Mott et al. [27], the influence of electric field on the resistance is described by the Eq. (6):

where α = 22.5 V.Aβ and β = 0.32 according to Fig. 3. However, the NDR is due to the presence of metallic filaments. When I > Ith, the metallic filaments will provide parallel paths of conduction. This corresponds to the decrease of voltage. Thus, The Joule heating is probably considered for the non-linear conduction. This phenomenon implies the appearance of a metallic state accompanied by a large number of mobile charges [25]. 1 Fig. 5 shows the plots of R0 versusT 4 in semi-logarithmic scale. The obtained straight line indicates that the VRH model describes the conduction mechanism in the studied material. It is clear that for I ≤ 1 mA, the resistance is slightly dependent on current in the whole

100

(4)

where R00 = 8.41 × 10 Ω the pre-exponential factor and T0 = 2.74 × 107 K denotes material parameter related to the distribution of localized electronic states. For I < 1 mA, the measured data of the RF-675 sample agree well with the variable range hopping (VRH) model. The dc resistance versus measurement temperature at different currents 0, 30, 50 and 100 mA are presented in Fig. 6. For I > 1 mA there is a significant deviation of R(T) from the Mott’s law. Here, the variation of the resistivity versus the temperature is a signature of a change from the non-metal to the metal behavior. This transition is widely seen in networks of metallic conductors since the charge carriers must crossing barriers of different types; at low temperatures and when thermal energy becomes lower than barrier energies, a reversion to non-metallic behavior occurs [26,27]. At I = 100 mA the RF-675 undergoes a transition from a non-metallic state (dR/dT < 0) at low temperatures to a metallic state (dR/ dT > 0) at high temperatures. So, the R(T) shows an extremum value at 180 K, explained by the existence of a metastable state where the transition occurs. At high temperature, the conduction is assumed to be ohmic. Similar results were obtained recently on scattering by lattice vibrations. Here, the weakest points in a filament determine the filamentary resistance, when their temperature exceeds some critical value, the filaments remain spaced and disordered [26,27]. Fig. 7 shows two different mechanisms of the carrier transport in the RF-675. For T > 200 K appears a thermally activated process; in which the electrical resistance can be expressed by Eq. (5):

100

V = R 0. I + I

1 4

−6

1

1E-3

T0 T

R 0 = R 00exp

0.33

)

R = R 0 + AT + R 00 exp

Fig. 5. The resistance R0 versus measurement temperature (T−1/4) for RF-675 sample.

T0 T

where R0 = 122, A = 0.17 K 87

0.25

(10) −1

6

, R 00 = 0.034 and T0 = 5.69 × 10 K. In

Chemical Physics 524 (2019) 85–91

I. Najeh and L. El Mir 2100 0.25 0.20

R (kΩ)

R (MΩ)

0.15

10mA

1400

1mA

0.10

700

0.05 0.00

0 60

80

100 120 140 160 180 200 220 240 260 280

T (K)

70

140

0.176

T (K)

210

0.174

100mA

0.172

50mA

0.170

R (kΩ)

R (kΩ)

0.8

0.4

0.168 0.166 0.164 0.162 0.160

0.0

140

210

60

80

100 120 140 160 180 200 220 240 260 280

T (K)

T (K)

Fig. 6. Variation of resistance as a function of temperature for RF-675 sample at different currents:1, 10, 50 and 100 mA.

0.2

Ea = 2 meV Ea = 50 meV

0.8

R (kΩ)

0.7

100

-0.2 -0.4

Ea = 50 meV

30 mA 0.1 mA

0.6

10

0.5 Ea = 90meV

S (V/K)

0.9

0.0

R(kΩ)

1

1

0.4

675°C 0.1 mA 1 mA 10 mA

-1.0 -1.2 -1.4

60

80

100

120

140

-1.8

160

-2.0 50

-1

1/kT (eV ) Fig. 7. Variation of dc resistance as function of 1/kT for RF-675 at different currents 0.1 and 30 mA.

100

150

200

T (K)

250

300

Fig. 8. The thermoelectric power S versus measurement temperature (T) for RF675 at different currents 0.1, 1, and 10 mA.

accordance with this equation; both of the hopping and the ohmic transports are dominating at all measurement temperatures. So, metallic behaviors can be distinguished from insulator ones by the variation of R versus measurement temperature T. Metals are defined as materials in which R decreases as T decreases (dR/dT > 0), whereas the insulators are materials in which R increases as T decreases (dR/ dT < 0). Consequently, the conduction in the sample pyrolysed at 675 °C takes place through filamentary chains. These filaments will rupture when high local temperature is attained. Here, the distribution of the filaments depends on the intensity of the applied electric current and of the measurement temperatures. The thermoelectric power (TEP) S is important electrical characteristic; S is defined by Eq. (11): [33].

dV dT

-0.8

-1.6 40

S=

-0.6

S=

k Ec EV +1 e 2kT

(12)

where Ec and Ev are respectively the energy edges of conduction and valence bands. The temperature dependence of the TEP is plotted in Fig. 8. The results indicate that the electrical properties of RF-675 change from semiconductor behavior to metallic one as the measurement temperature is increases. Usually, S is considered as an intrinsic property of the material, independent of the dimension of the system. Here, at high temperature, the concentration of the carriers is almost independent of the temperature and the accumulation of the charges comes from a fast diffusion of the hot electrons and a slow diffusion of the cold electrons [34]. However, at low temperature the semiconductor’s carrier concentration depends on temperature. Fig. 9 shows that this TEP coefficient is related to the energy difference between the Fermi level and the edge of the transport band. Therefore, the Seebeck coefficient measurement is a powerful tool for characterizing semiconductors.

(11)

where, the temperature dependence of thermopower, S(T), is described by the well-known Eq. (12):

88

Chemical Physics 524 (2019) 85–91

I. Najeh and L. El Mir

120

100

80

40

Ea S

20

(V)

1 mA

-0.6 -0.9

Vth

60

-1.2

150

T (K)

200

60 40

50 40

20

30

-1.5

20

-1.8 100

60

70

-0.3

(mA)

80

0.0

80

V I

90

0.3

S (v/K)

Ea (meV)

100

Ith

0.6

0

10 60

250

80

100

120

140

160

180

200

220

240

260

280

T (K)

Fig. 9. The temperature dependence of the activation energy and the thermopower S(T).

Fig. 10. The temperature dependence of the Vth and Ith.

100

It is important to remember that these particular semiconductors have transport properties somewhat different from those of organic semiconductors because of the essential role played by the defects and disorder [35]. Indeed in conventional semiconductors, the conduction of charges is done by a band transport. However, in these semiconductors are performed rather by hopping between localized states. Generally, the NDR state might be attained in several ways, including thermal and electronic. For a long time the principal issue of the mechanism of the NDR is: whether the mechanism is primarily thermal or electronic. In general, the electrothermal the mainly controls the bulk specimens, while the electronic mechanism controls thin films [35–38]. The effects of excitation current on the current-voltage curves of polycrystalline samples of RF-675 were investigated. We measured Sshaped I–V characteristics. Here, the proposed NDR mechanism is characterized by the non-equilibrium carrier density excess caused by the presence of the applied electric field. This model is in agreement with the experimental results, particularly, with the threshold field temperature dependence. The Fig. 8 shows that an abrupt jump of the voltage and a huge increase in the temperature of the sample. This result is compatible with the model Joule self-heating. The nonlinearity of the I-V curves, observed for RF-675, is thus explained by the opening of the metallic-filament paths because of a percolation process due to the melting of the insulating phase into the metallic one. At I = Ith, this current path will decrease the voltage across the sample for a given current. As the current increases, presumably more such channels plug in leading up to a further decrease in voltage. This will present itself in the V–I curves with a region of NDR. Usually, the amorphous materials contain dipoles dispersed randomly. As the electric field is applied, these dipoles tend to orient in the direction of the field. As the temperature of the percolation path increases its viscosity decreases, which leads to an increase in the orientation processes up to threshold switching point [35–38].

80

Vth (V)

60

40

20

40

60

80

100

120

140

160

-1

1/KT (ev ) Fig. 11. Variation of VTH as function of 1/kT for RF-675.

the threshold voltage decreases, while the threshold current increases for RF-675. The dependence of Vth versus 1/kT was plotted in semi-logarithmic scale as shown in Fig. 11. The relation between the threshold voltage and the ambient temperature can be described by Arrhenius formula (Eq. (13)):

VTH = V0. exp

(13)

KB.T

where V0 is constant and ε the threshold voltage activation energy. The values obtained for ε are equal to 23 meV at low temperature and equal to 30 meV at high temperature. Also, the ratio of the activation energy of switching to that of conduction ε/Ea, equal to 0.46 at low temperature and equal to 0.3 at high temperature. This behaviour has good agreement with the values 0.5 obtained for thermal breakdown processes in other amorphous matter [39,40]. The strong temperature dependence of the ε characterizes the Joule-heating effect. Accordingly, the temperature rise in the heated region, which initiate the switching process. For the Joule-heating model, the temperature difference (ΔT = Tm -T s) between that of the middle of the specimen Tm and that of the surface Ts, is described by the Eq. (14) [40–42]:

3.3. Switching phenomenon However, there may be another reason for the non-linearity. Indeed, if the charge carriers do not have enough time to give up quickly the energy received from the field to the lattice, their temperature rises and exceeds that of the phonons. The overheating leads to the violation of the Ohm’s law. The curve current–voltage shows two distinct regions. Thus, switching consists in a transition from a state of high resistance (OFF) to that of low resistance (ON), the transition being generated by the application of a specific voltage, as the threshold voltage Vth. The effect of temperature on the switching parameter (Ith, Vth) is illustrated in Fig. 10. It is clear from the figure that as the temperature increases,

Tbreakdown = Tb =

kB. T 2 Ea

(14)

The case of steady state breakdown (dT/dt = 0), the difference 89

Chemical Physics 524 (2019) 85–91

I. Najeh and L. El Mir 2.0

1mA 10mA 50mA 100mA

1.0

0.5

10

-1 -1

20

-1

σ (ms)

1.5

λ (mWm k )

σ λ

λ (mWk )

1mA

20

10

0

0.0 100

150

T (K)

200

250

140

T (K)

210

Fig. 12. The thermal conductivity λ and the dc conductivity σ of carbon xerogels pyrolized at 675 °C versus measurement temperature T.

ΔT = Tm- Ts between the temperature at the middle of the sample Tm and that at the surface Ts is given as [40–42]:

Tb =

V2th V .I = th th 8 2T . d

0.4

0.3

(15)

1mA

=

Vth. Ith 2T . Tb. d

ZT

So (16)

Fig. 12 shows the thermal conductivity λ of carbon xerogels pyrolized at 675 °C versus measurement temperature T. For 1 mA the conductivity increases linearly with the temperature up to 30 mWK1 −1 m . This is a signature of weakly metallic, conduction. At high current λ is almost constant (λ = 0.5 mWK-1m−1). The composite becomes thermally insulating which reflects a change in behavior. Generally in semiconductors, the experimental data were fitted with a linear superposition of a phonon, electronic and radiative heat transfer:

=

ph

+

rad

+

el

0.1

0.0 70

= aT

140

T (K)

210

Fig. 13. The merit factor of carbon xerogels pyrolized at 675 °C versus measurement temperature T.

(17)

where λ ph and λ el are the phonon and electron contributions, respectively. rad the radiative thermal conductivity. For RF-675 at 1 mA, the solid thermal conductivity can be expressed in a first order approximation by the electronic contribution el . The electronic thermal conductivity for metals and semimetals can be described by the Wiedemann-Franz law given by equation (18) [43]. el

0.2

ZT =

S2 . T.

(19)

where S is the Seebeck coefficient, σ is the electrical conductivity, T is the temperature and λ is the thermal conductivity of the material. The Seebeck coefficient and the electrical conductivity are not independent of each other, and vary in opposite way with the charge carrier concentration: the best thermoelectric powers will be obtained in materials of low concentration in carriers, whereas the better electrical conductivities will be in materials with high concentration of carriers. By compromise, the best thermoelectric materials will, therefore, belong to the class of semiconductors. The best materials currently used in thermoelectric conversion devices have ZT merit factors close to 1. The optimization of thermoelectric efficiency represents a complex problem that affects as much the fields of chemistry, physics as science of materials. This return is usually quantified using the merit factor: ZT. A good thermoelectric, is characterized by a high ZT factor. For example, increased carrier density improves electrical conductivity, but also decreases Seebeck coefficient and increases thermal conductivity [47]. An ideal thermoelectric material (with a very high ZT) would allow a thermoelectric system with a yield approaching that of Carnot, the maximum yield predicted by thermodynamics. Nevertheless, the current situation is very far from this limit. Despite considerable efforts, the best thermoelectric was limited until the end of the 20th century to ZT of about 1, reducing their yield to only fractions.

(18)

where a = . L ;σ is the electrical conductivity and L is the Lorentz number. The fit parameter is a = 10-4 Wm-1K−2 for RF-675 at 1 mA. The value of a is probably explained by the fact that RF-675 is a semiconductor that exhibits the behavior of a semi-metal. Usually λ in carbon materials is dominated by phonons [44]. So, the strong covalent sp2 bonding resulting in heat transfer by lattice vibrations. However, λel can become significant in doped materials. Experimental studies revealed that λ in diamond-like carbon is mostly governed by the structural disorder of sp3 phase [45]. For sp3 amorphous, λ scales are linear with the sp3 content. Indeed, the amorphous carbon is likely the material with the highest λ among amorphous solids [46]. Fig. 13 shows the merit factor of carbon xerogels pyrolized at 675 °C versus measurement temperature T. The merit factor of carbon xerogels pyrolized at 675 °C increases up to 0.4 at 100 K and then decreases when the temperature increases. A good thermoelectric material will therefore simultaneously have a high Seebeck coefficient, good electrical conductivity (i.e., low electrical resistivity), and low thermal conductivity [47]. This optimization of materials involves the optimization of their electrical and thermal transport properties in order to maximize their merit factor. The expression of the merit factor can then be written as Eq. (19) [47].

4. Conclusion In this paper, we have investigated the effect of pyrolysis 90

Chemical Physics 524 (2019) 85–91

I. Najeh and L. El Mir

temperature on the structural, morphological and electrical properties of organic matrix based on resorcinol and formaldehyde prepared by sol-gel method. After thermal treatment, the XRD analysis show the presence of the graphite structure in the FR-675 sample. The TEM micrographs confirm that the samples are formed of a porous structure which becomes more pronounced after the heat treatment. The electrical characterizations, show that the conduction in the samples is controlled almost entirely by filaments of metallic nature like. Moreover the conduction is strongly non-linear, which supports the idea of the metallic behavior of the filaments. Accordingly, the nonlinear behavior in the electric conductivity of the organic sample pyrolysed at 675 °C, was attributed to the change in the distribution of the filaments and to the effect of annealing on such distributions. The obtained values of the ratio ε/Ea agree with that obtained theoretically on the basis of the electrothermal model. Accordingly, The formation of crystalline conductor phases, is attributed to the electrothermal model based on Joule heating effect.

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