Corresponding author: Andrei A. Kharchenko ( xaatm@mail.ru ) © 2019 Alexander K. Fedotov, Sergey L. Prishchepa, Alexander S. Fedotov, Vladzislaw E. Gumennik, Ivan V. Komissarov, Artem O. Konakov, Svetlana A. Vorobyova, Andrei A. Kharchenko, Oleg A. Ivashkevich.
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Citation:
Fedotov AK, Prishchepa SL, Fedotov AS, Gumennik VE, Komissarov IV, Konakov AO, Vorobyova SA, Kharchenko AA, Ivashkevich OA (2019) Effect of cobalt particle deposition on quantum corrections to Drude conductivity in twisted CVD graphene. Modern Electronic Materials 5(4): 165173. https://doi.org/10.3897/j.moem.5.4.52068

Graphene applications in electronics require experimental study of the formation of highquality Ohmic contacts and deeper understanding of electron transport mechanisms at metal/grapheme contacts. We have studied carrier transport in twisted CVD graphene decorated with electrodeposited Co particles forming Ohmic contacts with graphene layers. We have compared layer resistivity as a function of temperature and magnetic field R_{□}(T, B) for assynthesized and decorated twisted graphene on silicon oxide substrates. Experiments have proven the existence of negative (induction < 1 Tl) and positive (induction > 1 Tl) contributions to magnetoresistance in both specimen types. The R_{□}(T, B) functions have been analyzed based on the theory of 2D quantum interference corrections to Drude conductivity taking into account competition of hopping conductivity mechanism. We show that for the experimental temperature range (2–300 K) and magnetic field range (up to 8 Tl), carrier transport description in test graphene requires taking into account at least three interference contributions to conductivity, i.e., from weak localization, intervalley scattering and pseudospin chirality, as well as graphene buckling induced by thermal fluctuations.
graphene, graphene/metal structures, electron transport, magnetostriction
Graphenes have been intensely investigated in the last decade due to their specific physical properties such as high electrical and heat conductivities, welldeveloped surface, high mechanical strength, elasticity etc. In accordance with the graphene electronics development roadmap [
Carrier transport in metal/graphene nanostructures depends on multiple factors. These are primarily the synthesis method (mechanical debonding, CVD, epitaxy etc.) and graphene type (singlelayered, multilayered, twisted). Secondly one should take into account the type of dielectric substrate (quartz, glass, silicon oxide ctc.) onto which graphene is deposited or transferred. Finally important factors are the type, concentration and distribution of potential defects in graphene layers including polycrystalline ones as well as the properties of graphene / electric contact interfaces. These properties are mainly determined by deposited metal type and deposition technology [1–3,
In spite of extensive research into the galvanomagnetic properties of graphene layers and graphene/metal hybrid structures, there is still one more problem concerning understanding the main electrotransport mechanisms in graphene. Most of this research has dealt with micron sized graphene specimens produced either by debonding from graphite [12, 15–18] or cutting from single polycrystalline graphene grains [
Descriptions of lowtemperature electrotransport and magnetotransport in pure graphene available in literature most often adhere to interference mechanisms within the theory of quantum corrections to Drude conductivity under weak localization conditions [16–18,
The aim of this work was to study the effect of cobalt particles on magnetotransport mechanisms in metal/graphene composite structures synthesized by electrodeposition of cobalt particles on twisted CVD graphene.
We chose twisted graphene as the working layer for Co particle deposition since it is less affected by substrate as compared to singlelayer graphene [
The growth conditions of the experimental graphene layers were described in detail earlier [
The surface structure of the specimens on the copper foil and on the SiO_{2}/Si substrates was examined under a Hitachi S4800 scanning electron microscope (SEM) equipped with a Bruker QUANTAX 200 energy dispersive Xray spectrometer (EDXS) allowing elemental composition mapping. The quality of the graphene layer was also studied by Raman spectroscopy on a Confotec NR500 selected are Raman instrument with a 473 nm excitation wavelength and an approx. 3 cm^{1} spectral resolution [14, 33–36]. Additionally the thickness of graphene transferred to glass was measured by 400–800 nm light transmittance (PROSCAN MC121 spectrometer). The transmission ratio of graphene was > 94% at 550 nm, thus the average number of graphene layers was two.
The electrical resistivity of graphene as a function of temperature and magnetic field R_{□} (T, B) was measured with the fourprobe method on a Cryogenics Ltd. cryogenfree measurement system (CFMS) with a closed cycle cryostat. The R_{□} (T, B) functions were measured in the 2 < T < 300 K range in a transverse magnetic field of up to 8 Tl. The test specimens were placed on a contact pad as shown in Fig.
(a) Photo of specimen on contact pad and (b) schematic of measurement probe arrangement: (1 and 2) current contacts and (3 and 4) voltage contacts.
The layer conductivity of graphene was calculated as follows:
${\sigma}_{\square}\left(T\right)=\sigma \left(T\right)\left(\frac{L}{W}\right)$ (1)
where σ_{□} (Т) is the specimen conductivity, W is the conducting channel (graphene layer) width and L is the distance between the voltage contacts 3 and 4 in Fig.
$MR=100\frac{R\left(B\right)R\left(0\right)}{R\left(0\right)}$ (2)
where R (B) and R (0) are the resistivities in a magnetic field with induction B and without magnetic field, respectively. The error of MR and σ_{□} (T) was within 5% and was mainly induced by the dimension measurement errors for the specimen and the electric contacts.
Typical SEM images of the graphene specimens (Fig.
(a) Example of SEM image and (b) map of band intensity ratio I_{G}/I_{D} for CoG/SiO_{2} specimen, and histograms of Raman spectra band intensity ratio I_{G}/I_{D} for (c) G/SiO_{2} and (d) CoG/SiO_{2}.
The structures of the source twisted graphene and the CoGr/SiO_{2} specimen with deposited Co particles were studied using selected area Raman spectroscopy. Detailed analysis of the Raman spectra of the specimens was reported earlier [14, 33–36]. The spatial distribution of the I_{G}/I_{D} peak intensity ratio for the CoGr/SiO_{2} specimen is shown in Fig.
Figure
The presence of the linear portions in the σ_{□} (Log[T]) coordinates is usually attributed to an interference contribution to Drude conductivity under weak localization conditions [12, 15–18, 27, 37–40].
Figure
Raman scattering and SEM data suggest that Co particle deposition onto a twisted graphene layer increases the defect density of the CoG/SiO_{2} specimen in comparison with source G/SiO_{2}. Nevertheless comparison of Curves 1 and 2 in Fig.
Layer conductivity as a function of temperature σ_{□} (T) in semilogarithmic coordinates for (1) G/SiO_{2} and (2) CoG/SiO_{2}.
One can reasonably assume that cobalt particle deposition can similarly affect the carrier phase break length at the crossing with the graphene/Co particle interfaces. The phase break time determined for a CoG/SiO_{2} specimen from the σ_{□}(T) temperature functions [
To reveal other potential contributions to magnetotransport we analyzed the relative magnetoresistance as a function of magnetic field MR (В,Т) (Fig.
Relative magnetoresistance MR for (a) G/SiO_{2} and (b) CoG/SiO_{2} specimens as a function of magnetic field induction B at T = (1) 5 K, (2) 10 K, (3) 25 K, (4) 50 K, (5) 100 K, (6) 200 K and (7) 300 K.
These regularities of MR (В,Т) behavior at 2–300 K suggest that the test graphene specimens may exhibit not only weak localization corrections (providing negative magnetoresistance effect in fields of less than 1 Tl [
$\Delta {\sigma}_{\square}=\frac{{e}^{2}}{\pi h}\left[F\left(\frac{B}{{B}_{\phi}}\right)F\left(\frac{B}{{B}_{\phi}+2{B}_{i}}\right)2F\left(\frac{B}{{B}_{\phi}+{B}_{\square}}\right)\right]$ (3)
where
$F\left(x\right)=\mathrm{ln}\left(x\right)+\psi \left(0,5+{x}^{1}\right)$,
ψ is the digamma function. Here the х = B/В_{φ,}_{i}_{,*} parameter is determined by the ratio between the induction of the external magnetic field B and that of the characteristic field В_{φ,}_{i}_{,*} of scattering. The characteristic fields В_{φ,}_{i}_{,*} determine the carrier phase break times τ_{φ,}_{i}_{,*} for the respective process of elastic or quasielastic scattering. These phase break times are determined from the relationship
${\tau}_{\phi ,i,*}=\frac{\hslash c}{4eD}{B}_{\phi ,i,*}^{1}$ (4)
where D is the electron diffusion coefficient.
The first term in Eq. (3) with the index φ corresponds to scattering at lowenergy phonons, the second term with the index i corresponds to intervalley scattering and the third term with the index * corresponds to chirality violation and graphene buckling induced by thermal fluctuations.
To evaluate the characteristic times of the processes leading to the formation of quantum corrections to Drude conductivity (Eq. (4)) one should calculate the carrier diffusion coefficient D. Earlier, Tikhonenko [
$D={v}_{F}\frac{l}{2}$ (5)
where v_{F} is the Fermi carrier velocity, l is the free path equal to l = h/(2e^{2}k_{F}n), k_{F} is the Fermi pulse and n is the carrier concentration. It is assumed that only the carriers at the Fermi surface participate in conductivity. Thus this approach is the most correct for defectfree graphene at low temperatures.
Since quantum corrections exist in the test graphene layers at far above 25 K [
We represent a conducting specimen as a homogeneous medium and ignore the contribution of large defects, e.g. grain boundaries. We further assume that the carrier energy distribution is described by the FermiDirac function
$f\left(E\right)=\frac{1}{{e}^{\frac{E\mu}{kT}}+1}$
Then the carrier concentration can be described as follows:
$n=\int f\left(E\right)g\left(E\right)\mathrm{d}E$ (6)
where g (E) is the band density of states. We use the expression
$\sigma ={e}^{2}D{\left(\frac{\partial n}{\partial \mathrm{\mu}}\right)}_{T}$ (7)
borrowed from earlier work [
$\begin{array}{l}\sigma ={e}^{2}D{\int}_{\infty}^{+\infty}g\left(E\right)\frac{\partial}{\partial \mu}\left(\frac{1}{\frac{E\mathrm{\mu}}{{e}^{kT}}+1}\right)\mathrm{d}E=\\ =\frac{{e}^{2}D}{kT}{\int}_{0}^{\infty}g\left(E\right)\left(\frac{{e}^{\frac{E\mu}{kT}}}{{\left({e}^{\frac{E\mathrm{\mu}}{kT}}+1\right)}^{2}}\right)\mathrm{d}E=\\ =\frac{{e}^{2}D}{kT}{\int}_{0}^{\infty}g\left(E\right)f\left(E\right)(1f(E\left)\right)\mathrm{d}E\end{array}$ (8)
This latter expression yields the sought formula of the diffusion coefficient:
$D=\frac{\sigma kT}{{e}^{2}}{\int}_{0}^{\infty}f(E,\mu )[1f(E,\mu \left)\right]g\left(E\right)\mathrm{d}E$ (9)
Equation (9) allows comparing the average (effective) carrier diffusion coefficient.
The diffusion coefficient calculation method proposed herein gives the following important advantages: (a) possibility of evaluating D by changing the density of states g (E) for either singlelayer or twolayered graphene; (b) possibility of taking into account carrier energy distributions at temperatures far above LH; (c) possibility of taking into account Fermi level shift (chemical potential) µ upon application of an external electric field to specimen (e.g. for measurements with a third electrode).
The main limitation upon the use of this method is the fact that Eq. (8) which correlates σ and D is only valid if diffusion (drift) conductivity is dealt with. At low temperatures the experimentally measured conductivity σ can incorporate a hopping transport mechanism contribution. Therefore when evaluating the diffusion coefficient D one should make sure that there is no large hopping conductivity contribution in the specimen or it is possible to distinguish the hopping and drift (diffusion) conductivity contributions.
From the negative magnetoresistance effect as a function of magnetic field in accordance with Eqs. (3) and (4), one can determine the phase break time due to weak localization as a function of temperature τ_{φ}(Т) [15–18,
Phase break time τ_{φ}(Т) as a function of temperature for quantum correction contribution due to weak localization in (a) G/SiO_{2} and (b) CoG/SiO_{2} specimens. Dots: calculated from experimental ∆σ (В) functions; lines: linear approximation.
Unfortunately, deriving characteristic process times for other scattering types which give positive contributions to quantum corrections at positive magnetoresistance effect [
Temperature dependences of ratios between phase break time τ_{φ} due to lowenergy phonon scattering and phase break times for (a) intervalley scattering τ_{i} and (b) cxhirality violation τ_{*} in G/SiO_{2} and CoG/SiO_{2}. Dots: calculated from experimental ∆σ (В) functions; lines: linear approximation.
Noteworthy, the temperature dependence of these ratios also has the form of a power function τ_{i},τ_{*} ~ T–^{p} in the 2–10 K range as indicated by the linear portions of the curves in double logarithmic coordinates. After cobalt deposition the line slope increases for τ_{*} (from p ≈ 0.38 to p ≈ 0.77) and decreases for τ_{i} (from p ≈ 0.42 to p ≈ 0.29). This behavior agrees with earlier results for singlelayer graphene [
We showed that the G/SiO_{2} and CoG/SiO_{2} structures exhibit a competition between negative and positive magnetoresistance effects at low temperatures. Negative magnetoresistance effect is completely suppressed by weak magnetic fields (B ≤ 1 Tl), and Co particle deposition onto the graphene layer reduces the contribution of negative magnetoresistance effect. Lowtemperature electrotransport and magnetotransport at negative magnetoresistance effect are mainly caused by the localization quantum correction to Drude conductivity. In magnetic fields below 1 Tl (positive magnetoresistance effect) the dominating quantum correction contributions are those from intervalley scattering, chirality violation and graphene buckling. Cobalt particle deposition slightly increases the phase break time τ_{φ} due to weak localization whereas the characteristic phase break times due to intervalley scattering τ_{i} and chirality violation τ_{*}, on the contrary, decrease strongly.
The work was accomplished with financial support from the State Program for Photonics, Opto and Microelectronics (Assignment No. 3.3.01), the State Committee for Science and Technology of the Republic of Belarus (BRFFI Project No. F18PLSHG005) and the Joint Nuclear Research Institute (Russian Federation) Contract No. 08626319/18216117074. S.L. Prischepa and I.V. Komissarov are grateful to the National Nuclear Research University MIFI for financial support of the Competitiveness Upgrading Program. The Authors express gratitude to Ph.D. (Phys.) I.A. Svito, Belarus State University, for measuring electric properties and Postgraduate Student A.V. Pashkevich, Institute for Nuclear Physics, Belarus State University, for help with article preparation.