Conductivity of transparency

In physics the conductivity of transparency describes the combination of the sheet resistance and the transparency and utilizes the properties of graphene as the reference.

Description

The properties of electroconductive and transparent materials can be described by the sheet resistance and the transparency (at 550 nm). The conductivity of transparency was introduced on the basis of graphene to compare different materials without the use of two independent parameters.[1]

Conductivity of Transparency

${\displaystyle \sigma _{gt}={\frac {\epsilon _{graphene}}{-\lg \left({\frac {I}{I_{0}}}\right)\rho _{sample}}}}$

${\displaystyle \sigma _{gt}}$

conductivity of transparency based on graphene;

${\displaystyle \epsilon _{graphene}}$

absorption coefficient of graphene;

${\displaystyle \rho _{sample}}$

sheet resistance of the sample;

I

intensity of light after absorption;

${\displaystyle I_{0}}$

intensity of light before absorption.

Derivation

The absorption of a single graphene layer was published in 2008. So graphene absorbs 2.3% of white light.[2] Hence, assuming that the ideal inter-layer distance of two graphene sheets is ${\displaystyle d_{graphite}=0.335\ \mathrm {nm} }$, as in graphite, one can calculate the absorption coefficient of graphene according to the Bouguer-Lambert law to ${\displaystyle 301655\ \mathrm {cm} ^{-1}}$.

Applied Bouguer-Lambert law:

${\displaystyle -\lg \left({\frac {I}{I_{0}}}\right)=\epsilon ^{*}cd;\epsilon ^{*}c=\epsilon _{graphene}}$

${\displaystyle \epsilon _{graphene}={\frac {-\lg \left({\frac {I}{I_{0}}}\right)}{d_{graphite}}}={\frac {-\lg \left({\frac {97.7\%}{100\%}}\right)}{3.35\times 10^{-8}\ \mathrm {cm} }}=301655\ \mathrm {cm} ^{-1}}$

The outcome of this is the general formula to determine the conductivity of transparency of arbitrary electroconductive and transparent materials, utilizing graphene as the reference:

Formula to determine the Conductivity of Transparency

${\displaystyle \sigma _{gt}={\frac {301655\ \mathrm {cm} ^{-1}}{-\lg \left({\frac {I}{100\%}}\right)\rho _{sample}}}}$

So, to determine the conductivity of transparency it is necessary to measure the transmission (at 550 nm) and the sheet resistance of the sample. The sheet resistance can be obtained by four-point probe measurement (Sheet resistance, Van der Pauw method). Contrary to the electrical conductivity it is not necessary to determine the thickness of the sample, because graphene is utilized as the reference by using the transparency.

Examples

Materials	I (%)	ρ (Ω)	${\displaystyle \sigma _{gt}}$ (S/cm)	references
graphene	97.7	6000	4975	Blake et al.[3]
graphene oxide	96	3.0×10^11	5.7×10^−5	Becerril et al.[4]
reduced graphene oxide	87	1×10^5	50	Eda et al.[5]
nanographene (1100 °C)	56	1600	749	Wang et al.[6]
graphene (CVD)	90	350	1.8×10^4	Li et al.[7]
SWCNTs	70	30	6.5×10^4	Wu et al.[8]
ITO	77	100	2.7×10^4	Sigma–Aldrich catalog no. 639281 [9]

References

1. S. Eigler (2009). "A new parameter based on graphene for characterizing transparent, conductive materials". Carbon. 47 (12): 2936–2939. doi:10.1016/j.carbon.2009.06.047.
2. R. R. Nair; P. Blake; A. N. Grigorenko; K. S. Novoselov; T. J. Booth; T. Stauber; N. M. R. Peres; A. K. Geim (2008). "Fine Structure Constant Defines Visual Transparency of Graphene". Science. 320 (5881): 1308. arXiv:0803.3718. Bibcode:2008Sci...320.1308N. doi:10.1126/science.1156965. PMID 18388259.
3. P. Blake; P. D. Brimicombe; R. R. Nair; T. J. Booth; D. Jiang; F. Schedin; L. A. Ponomarenko; S. V. Morozov; H. F. Gleeson; E. W. Hill; A. K. Geim; K. S. Novoselov (2008). "Graphene-Based Liquid Crystal Device". Nano Letters. 8 (6): 1704–1708. arXiv:0803.3031. Bibcode:2008NanoL...8.1704B. doi:10.1021/nl080649i. PMID 18444691.
4. H. A. Becerril; J. Mao; Z. Liu; R. M. Stoltenberg; Z. Bao; Y. Chen (2008). "Evaluation of Solution-Processed Reduced Graphene Oxide Films as Transparent Conductors". ACS Nano. 2 (3): 463–470. doi:10.1021/nn700375n. PMID 19206571.
5. G. Eda; G. Fanchini; M. Chhowalla (2008). "Large-area ultrathin films of reduced graphene oxide as a transparent and flexible electronic material". Nature Nanotechnology. 3 (5): 270–274. doi:10.1038/nnano.2008.83. PMID 18654522.
6. X. Wang; L. Zhi; N. Tsao; Z. Tomovic; J. Li; K. Müllen (2008). "Transparent Carbon Films as Electrodes in Organic Solar Cells". Angewandte Chemie International Edition. 47 (16): 2990–2992. doi:10.1002/anie.200704909. PMID 18330884.
7. X. Li; Y. Zhu; W. Cai; M. Borysiak; B. Han; D. Chen; R. D. Piner; L. Colombo; R. S. Ruoff (2009). "Transfer of Large-Area Graphene Films for High-Performance Transparent Conductive Electrodes". Nano Letters. 9 (12): 4359–4363. Bibcode:2009NanoL...9.4359L. doi:10.1021/nl902623y. PMID 19845330.
8. Z. Wu; Z. Chen; X. Du; J. M. Logan; J. Sippel; M. Nikolou; K. Kamaras; J. R. Reynolds; D. B. Tanner; A. F. Hebard; A. G. Rinzler (2004). "Transparent, Conductive Carbon Nanotube Films". Science. 305 (5688): 1273–1276. Bibcode:2004Sci...305.1273W. doi:10.1126/science.1101243. PMID 15333836.
9. Sigma–Aldrich catalog no. 639281|