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.

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:

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

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.