Evidence of phonon-assisted tunnelling in electrical conduction through DNA molecules
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Research article
Evidence of phonon-assisted tunnelling in electrical conduction through DNA molecules
Povilas Pipinys and Antanas Kiveris*
Address: Department of Physics, Vilnius Pedagogical University, Studentu 39, LT 08106 Vilnius, LithuaniaEmail: Povilas Pipinys - [email protected]; Antanas Kiveris* - [email protected]* Corresponding author
Abstract
We propose a phonon-assisted tunnelling model for explanation of conductivitydependence on temperature and temperature-dependent
I-V characteristics indeoxyribonucleic acid (DNA) molecules. The capability of this model for explanation ofconductivity peculiarities in DNA is illustrated by comparison of the temperaturedependent
I-V data extracted from some articles with tunnelling rate dependences ontemperature and field strength computed according to the phonon-assisted tunnellingtheory.
PACS Codes:
Introduction
Conductance properties of DNA have recently attracted a lively interest for theoreticians as wellas experimenters [1]. Understanding the charge carriers transfer mechanism along DNA doublehelix is important for possible applications of DNA molecules in nanoelectronic circuit technol-ogy [1-6].Direct conductivity measurements have shown a very wide range of conducting propertiesranging from no conduction [5,7,8] to a good linear conductor [2,9,10], while in other experi-ments semiconducting conductivity behaviour emerges [3,6,11-14].The wide range of charge transport behaviour seems to arise from different experimental con-ditions in which the measurements are carried out. These include the nature of the devices usedto measure the conductivity, the sequence and length of the DNA, the type of contacts, the envi-ronment in different experiments, etc., all can greatly effects the conductivity of the DNA mole-cules. For instance, Kasumov et al. [4] have shown that strongly deformed DNA molecules
Published: 19 February 2008
PMC Physics B MC Physics B (page number not for citation purposes) deposited on a substrate, whose thickness is less than half the native thickness of the molecule,are insulating, whereas molecules keeping their native thickness are conducting down to very lowtemperature with a non-ohmic behaviour characteristics of a one dimensional (1D) conductor.Extensive experimental and theoretical work over the past decade has led to substantial clari-fication of charge transport mechanisms in DNA. The dominant mechanisms appear to be short-range quantum mechanical tunnelling [14-18] or long-range thermally activated hopping[10,13,19-24]. But these mechanisms are not capable to explain all the field- and temperature-behaviour of experimental data associated with conduction of the DNA molecules. Indeed, thehopping models confronted with difficulties in explaining the observed strong conductivitydependence on the temperature along λ -DNA double helix at high temperatures and a very weekdependence at low temperatures [9]. The tunnelling mechanism was excluded in the case of tem-perature-dependent results [9,11].We affirm that in many cases the temperature-dependent conductivity of DNA moleculescould be explained by the quantum mechanical tunnelling theories in which the impact of pho-nons on tunnelling rate is included. In the event, "pure" tunnelling can be observed at low tem-peratures when the vibrations modes of the molecule are frozen. At moderate temperatures theinput of phonon energy to the process of tunnelling must be taken into account and contempo-rary phonon-assisted tunnelling theories (PhAT) [25-27] realise this.Recently, it has been shown that the PhAT describes well not only the nonlinear I-V curves,but also the temperature-dependent conductivity in conducting polymers [28,29]. Therefore, weinvoke the PhAT theory to describe some the temperature-dependent experimental data on elec-trical transport through DNA molecules presented by other authors.
Model and comparison with experimental data
We suggest that the thermoactivated current through the DNA molecules is caused by the chargecarriers released from localised states located between HOMO and LUMO levels of DNA ones[11]. In the dc case, the said levels are continuously filled from the electrode. Assuming that theelectrons are released from these states due to phonon-assisted tunnelling, we will compare thecurrent (the same as the conductance) dependence on the temperature and field strength withthe tunnelling rate dependence on these parameters, computed using the PhAT theory. For thispurpose we explore the equation (18) in [27] derived by Makram-Ebeid and Lannoo for the pho-non-assisted tunnelling of the electrons from the impurity centre. Taking into consideration thefact that this theory has been evaluated using the Condon approximation, it is more suitable forthe molecular structures than other ones. For the tunnelling rate dependence on field strength E and temperature T this theory gives: MC Physics B (page number not for citation purposes) whereHere p o = ε T / ħ ω , ħ ω is the phonon energy, ε T is the centre depth, I P is the modified Bessel func-tion and S is the Huang-Rhys coupling constant.In the first instance, the comparison of the I-V data measured in the temperature range from43 K to 294 K for poly(dA)-poly(dT) DNA molecules (from Fig 2a in [11]) with theoretical
W(E,T) dependences is presented in Fig. 1. The
W(E,T) dependences were calculated using centredepth ε T to be 0.21 eV (the value is slightly higher than the value of the activation energy esti-mated in Table 1, which is offered in Ref. [11]), and for the electron effective mass the value of W E T RW p e Tp pp oo ( , ) ( ), = + =−+ ∑ ε ω (cid:61) (1) R pkBT S kBT I S kBT p = −⎛⎝⎜ ⎞⎠⎟ ⎛⎝⎜ ⎞⎠⎟ exp ( / , (cid:61) (cid:61) (cid:61) w w w (2) W eFm T me E e T T ( ) ( ) / exp ( ) / / ε ε ε = ∗⎛⎝⎜⎜ ⎞⎠⎟⎟ − ∗⎡⎣⎢⎢ ⎤⎦⎥⎥
22 1 2 4 2 1 23 (cid:61) .. (3) Comparison of
I – V dependences in poly(dA)-poly(dT) DNA molecules extracted from figure 2 (a) in [11] (sym-bols) with theoretical
W (E,T) against E dependences (solid curves) calculated for the same T as in the experiment (from top to bottom) using the following parameters: ε T = 0.21 eV, m* = 1.5 m e , ω = 43 meV and S = 12 Figure 1
Comparison of
I – V dependences in poly(dA)-poly(dT) DNA molecules extracted from figure 2(a) in [11] (sym-bols) with theoretical
W (E,T) against E dependences (solid curves) calculated for the same T as in the experiment (from top to bottom) using the following parameters: ε T = 0.21 eV, m* = 1.5 m e , ħ ω = 43 meV and S = 12. -4 -2 0 2-4-3-2-10 0 2 4 6 1617181920 l n I ( n A ) lnV (V)
294 K223 K161 K143 K89 K43 K
Yoo et al., 2001dA-dT Fig1a l n W ( s - ) lnE (MV/m) MC Physics B (page number not for citation purposes) m e [30] was used. For the phonon energy, the value of 43 meV was selected. This value is sim-ilar to the value of 348 cm -1 used for the calculation of the DNA IR active modes in [31]. The cou-pling constant S was chosen in order to get the best fit of the experimental data with thecalculated dependences on the assumption that the field strength for tunnelling is proportionalto the applied voltage. As is seen in Fig. 1, the theoretical W(E,T) dependences fit well with theexperimental data for entire range of the measured temperatures. The field strength for theoreti-cal curves ranges from 0.16 MV/m to 500 MV/m, which is close to the field strength estimatedfrom the sample thickness (about 20 nm).The judgment on the carriers transfer mechanism is often carried out considering the conduct-ance dependence on the temperature. The conductance measured by Yoo et al. for poly(dA)-poly(dT) was strongly temperature-dependent around room temperature and slightly tempera-ture-dependent at low temperatures [11]. The authors explain such dependence within smallpolaron hopping model. We note that the
W (E,T) versus E characteristics at temperatures below100 K are weakly dependent on the temperature, and this feature is in excellent agreement withthe experimental observation. This circumstance is also evident in Fig. 2 (solid lines) from theplot of ln W (E,T) versus calculated using the same parameters as in Fig. 1 and for E = 135MV/m. The symbols in Fig. 2 represent the experimental data extracted from figure 2(c) in [11].One can see that the theoretical dependences of the phonon-assisted tunnelling rate are in goodagreement with the experimental data.Tran et al. [9] using the resonant cavity technique studied conductivity and its temperaturedependence along the λ -DNA double helix at microwave frequencies. They observed similar Experimental σ (T) against dependence for poly(dA)-poly(dT) DNA molecules extracted from figure 2 (c) in [11] (symbols) fitted to W (E,T) against dependence, calculated using the same parameters as in Fig. 1
Figure 2
Experimental σ (T) against dependence for poly(dA)-poly(dT) DNA molecules extracted from figure 2 (c) in [11] (symbols) fitted to W (E,T) against dependence, calculated using the same parameters as in Fig. 1. l n (cid:86) ( (cid:58) - ) /T (K -1 ) poly(dA)-poly(dT) l n W ( s - ) Yoo et al., 2001Fig.2c
MC Physics B (page number not for citation purposes) behaviour of the conductivity on the temperature as in [11], i.e. a strong temperature dependenceof conductivity at high temperatures, whereas at low temperatures the conductivity in λ -DNAexhibits a very weak temperature dependence. They explain the temperature-dependent conduc-tivity suggesting two transport mechanisms, i.e. ionic conduction at low temperatures and tem-perature driven hopping transport processes at high temperatures. The underlying physics of theweak temperature dependence at low temperatures was not understood. The calculation in [32]has also shown that transport through DNA does not have a purely hopping character.In Fig. 3 the experimental data extracted from Fig. 3 in [9] for λ -DNA (symbols) fitted to thePhAT rate dependences on for the λ -DNA in buffer (solid curve) and for the dray λ -DNA(dashed curve), are depicted. In this case the theoretical W(T) dependences reflect also the exper-imental data well.
Conclusion
In conclusion, the PhAT model is able to explain the peculiarities of field- and temperature-dependent current observed in DNA molecules in a wide region of the electric field strength. Astrong temperature dependence of conductivity observed at high temperatures and a very weaktemperature dependence at low temperatures of DNA molecules is comprehensible in the frame-work of the PhAT model. It is worth to note that the
W(E,T) dependences at both low and hightemperatures are calculated using the same set of parameters, i.e. ε T , m*, T, E, ħ ω and S . Fromthese ones only the Huang-Rhys coupling constant S is the fitting parameter estimated from the Experimental σ (T) against dependences for the λ -DNA in buffer and for the dray λ -DNA extracted from figure 3 in [9] (symbols) fitted to theoretical W (E,T) against dependences calculated for the following parameters: ε T = 0.21 eV, E = 290 MV/m, S = 12 (solid line) and for parameters ε T = 0.17 eV, E = 315 MV/m, S = 8 (dashed line) Figure 3
Experimental σ (T) against dependences for the λ -DNA in buffer and for the dray λ -DNA extracted from figure 3 in [9] (symbols) fitted to theoretical W (E,T) against dependences calculated for the following parameters: ε T = 0.21 eV, E = 290 MV/m, S = 12 (solid line) and for parameters ε T = 0.17 eV, E = 315 MV/m, S = 8 (dashed line). l n (cid:86) (( (cid:58) c m ) - ) /T (K -1 ) Dray (cid:79) -DNA (cid:79) -DNA in buffer 100Hz
Tran et al., 2000Fig.3 l n W ( s - ) MC Physics B (page number not for citation purposes) best fitting of the experimental data and theory. Other parameters are known from experimentsor from literary sources. An advantage of the PhAT model over the other models used is the pos-sibility to describe the behaviour of the I-V data measured at different temperatures with the sameset of parameters characterizing the material.Thus, the PhAT mechanism, in some cases, could be dominant in the conductance of the DNAmolecules.
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