Supplemental Material
Mid infrared Response of Reduced Graphene Oxide and its High
Temperature Coefficient of Resistance
Haifeng Liang a)
Key Laboratory for Optical Measurement and Thin Films of Shaanxi Province, Xi’an
Technological University, 710032, China
a) Author to whom correspondence should be addressed. Electronic mail:
hfliang2004@gmail.com
1 Optical band gap
The optical band gap was calculated from UV-vis absorption spectra using the following form
of Tauc’s expression1:
 2  (  Eg )2
Where  is absorption intensity,
(1)
 (2  c  ) is the angular frequency of incident light,  is
reduced Planck constant, and E g is the optical band gap. In figure 4(a)
hv is plotted against
 (hv) near absorption edge for two samples of as-deposited GO and after-annealed GO. It is
apparent in Figure s1 that the absorption edge in the tail followed by an absorption which is
represented by a straight line showing that in this region of 
  (  Eg ) 2 . If we extrapolate
2
this line, we obtained at annealing of 900℃ Eg=1.69 eV, and as-deposited Eg=3.65eV.
Figure S1 Tauc plot for as-deposited GO and RGO annealed at 900℃
2 Spectral radiance
Wavelength dependent Planckian radiation power can be described thus3:
B (T ) 
2hc 2

1
5
e
hc
k B T
(3)
1
Where B denotes spectral radiance with unit of W/m3, T its absolute temperature with unit of K, kB
the Boltzmann constant, h the Planck constant, and c the speed of light. Figure 1(b) showed the
results of spectral radiance at temperature of 473.17K. The radiation wavelength mainly covers mid
and far infrared range (from 3 to 25µm).
3 Absorption power.
3.1 Light radiation
The set-up of photocurrent experiment was shown in Figure 1(a), along with geography
parameters. Thus, the total radiation power of blackbody (with the type of ES1000-100 ) with
aperture of 24.5mm at working temperature of 473.15K can be approximated numerically by using
Stefen-Boltaman law as follows4,5.
Pradiation  AT 4
(4)
Where
Pradiation
(watts) is the radiated power from a body of area (here is area of output aperture)
A (0.50671×10-3m2) at temperature T of 473.15K.  is emissivity of 0.99.  is the StefanBoltzmann constant, 5.67x10-8 W/(m-2K-4). So the result of
Pradiation
is 1.4399 W by substituting
the value of all of parameters into this expression.
Received power by RGO films can be calculated by taking a product of radiated power with solid
angle6, and then times the average absorption index of films (15%), which is expressed as follows.
Pabsoption  P    
Where,
Pabsoption
(5)
is the received power from the blackbody with 50mm away from my sample. 
is average absorption index of 0.15 covering wavelength from 3 to 25µm, which was derived from
the transmittance difference of samples with and without RGO films.  is solid angle denoted as
area of output aperture divided by the square of mutual distance between aperture and sample, i.e.,
  A d 2  0.203 . As well, Pabsoption was determined to 43.78mW by substituting the values into
that equation.
3.2 Joule heating
Applied voltage Joule heating power could be derived by,
PJ o u le I b2 a c k R, R  V / I b a c k
(6)
Where, I back is background current of 1.1mA,
R is resistance without light, V is applied
voltage of 3V. So PJoule was determined to 3.3 mW.
4 Temperature coefficient of resistance (TCR) and films’ temperature
The TCR is the relative change of a physical property when the temperature is changed by 1 Kelvin.
In the following formula, let R be the physical property to be measured and T be the temperature
at which the property is measured. T0 is the reference temperature. Finally, TCR is the temperature
coefficient. Given these definitions, the physical property is7:
TCR 
R (T )  R (T0 )
R (T0 )  (T  T0 )
(7)
In our work, TCR of RGO films annealed at 900℃ with temperature up and down showed a
fluctuation from 1.49 to 6 K-1 (shown in Figure 2(b)). Thus, average TCR was determined to -3%
K-1 by taking an average value of all the TCR from 20 to 55℃。
In light of definition of TCR, temperature increment of films could be easily worked out in using
following expressions
T 
 R
TCR

 0.06
 2K
 0.03( K 1 )
(8)
Where, T is temperature increment,  R is rate of resistance change before and after light
radiation. In this case, resistance changes from 2.553KΩ to 2.40KΩ after 2 minutes (figure 2(a)).
Thus,
 R 
2.4  2.553
 0.06 .
2.553
Reference
1
J. Tauc, Mater. Res. Bull. 1968, 3, 37.
2
Y. Shen, S.B. Yang, P. Zhou, Q.Q. Sun, P.F. Wang, L. Wan, J. Li, L.Y. Chen, X.B. Wang, S.J. Ding,
D. W. Zhang, Carbon, 2013,62, 157.
3
http://en.wikipedia.org/wiki/Planck's_law
4
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/radfrac.html
5
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
6
http://en.wikipedia.org/wiki/Steradian
7http://en.wikipedia.org/wiki/Temperature_coefficient