Graphene, a material for high temperature devices – intrinsic carrier
density, carrier drift velocity, and lattice energy
Yan Yin1,*, Zengguang Cheng2, Li Wang1, Kuijuan Jin1, Wenzhong Wang3
1
The Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China. 2National
Center for Nanoscience and Technology, Beijing 100190, P. R. China. 3Minzu University of China,
Beijing 100081, P. R. China.
*Correspondence should be addressed to Y. Y. (yan.yin@aphy.iphy.ac.cn)
Supplementary information:
1. The reasons we use a different method to obtain  value for device B.
We don’t have an accurate E0 value for device B, an error in E0 will result in an error in a2. An
error in a2 will introduce an amplified error both in b1 and . Also, the high bias (Vsd ≥ 6 V) data
range of device B doesn’t have any temperature overlaying area with I. Calizo et al.’s
measurement, in fact, there is a gap about 600 K in temperature separation between I. Calizo et
al.’s measurement (only top at 373 K) and the data point for device B at Vsd = 6 V. Because above
reasons, it is invalid to process the limited data from device B with the same method for device A.
2. Comments on D. Chae et al.’s paper - Nano Letters 10, 466-471 (2010).
D. chae et al. reported similar measurements, but ignored the effect of intrinsic carrier
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density. D. Chae et al. reported the G mode energy of an about 2μm long graphene device as a
function of the G mode phonon number temperature; they also measured another graphene
flake with a heated substrate. Their data shows huge G mode energy differences at same
temperatures but between two different heating methods. Such big differences are the result of
rising intrinsic carrier density in a biased graphene device blue shifting the G mode, in contrast to
a substrate heated graphene, which doesn’t have the external field needed to separate the heat
generated electrons and holes and Fermi level stays at around zero. The temperatures we
calculated from G mode energy shift in Fig. 4a are very similar to the G mode temperatures D.
Chae et al. directly measured from phonon numbers, this supports the accuracy of our data
analysis. In addition, our G mode temperature is obtained from the G mode energy change which
is the result of bonding energy change between atoms, therefore our G mode temperature is
indeed the lattice temperature.
3. The linear relationship between temperature and device voltage.
In the paper, we use an assumption, a linear relationship between graphene device lattice
temperature and device driving voltage. We notice this linear relationship from the analysis of
our data. This linear assumption can be independently verified by the reported data from another
team. Figure 1 shows a linear relationship between the graphene device G mode temperature TG
and device voltage Vc. The data points and error bars are obtained from Figure 1.a (insert figure),
I-V curve, and Figure 3, TG vs. I·Vc, of the reported paper, Nano Letters 10, 466-471 (2010). The red
line is a linear fitting to all the data points, and this linear fitting gives an adjusted R-square 0.99.
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Only the zero voltage point shows some distance from the linear line, this is because zero voltage
is way off from high field condition. This supports that the linear relationship between graphene
device lattice temperature and device voltage holds very well under high field condition.
Figure 1. A linear relationship between the graphene device G mode temperature TG and device
voltage Vc. The data points and error bars are obtained from Figure 1.a (insert figure), I-V curve,
and Figure 3, TG vs. I·Vc, of the reported paper, Nano Letters 10, 466-471 (2010).
4. Matching of our measured lattice temperature and G mode temperature from phonon number
measurement in Nano Letters 10, 466-471 (2010).
The Raman system we used is based on edge filters and can’t measure anti-Stokes modes.
However, our temperature values can be independently verified by other team reported data.
Figure 3(b) of Nano Letter 10, 466 (2010) shows the matching of G mode energy shift and G
mode temperature from phonon number measurement (the Stoke and anti-Stoke ratio
measurement). In their figure, the G mode energy drops 6.7cm-1 (from 1586.1 to 1579.3) when G
mode temperature raises 1254K (from 312K to 1567K). In Figure 4(a) of our manuscript, G mode
energy is 1585.7cm-1 at room temperature (upward scan), and G mode energy is 1580.0cm-1 (the
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closest data point to 1579.3 cm-1) when Vsd =11V (upward scan). Our data analysis (using
=101.5K/V) gives a lattice temperature increases of 1117K from room temperature for Vsd =11V.
Our lattice temperature (1117K+room temperature) from G mode energy shift is 137K lower than
the reported G mode temperature (1254K+room temperature) from G mode phonon number
from Ref. 9. In general, the two temperatures are within close range, and the difference is smaller
than 10%. This difference might be from a slightly higher G mode phonon temperature than the
overall lattice temperature.
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