﻿ 石墨烯热电器件栅控特性研究
 光学仪器  2020, Vol. 42 Issue (6): 49-53 PDF

Research on characteristics of gate-controlled graphene thermoelectric device
MA Zhihao, WANG Ning, MENG Cong, GAO Cong, JIA Hongzhi
Shanghai Key Laboratory of Modern Optical System, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: In order to obtain a stable and controllable energy source, a gate-controlled graphene thermoelectric device was proposed in this paper. The effects of temperature and gate voltages on channel resistance were obtained by the carriers’ transport mechanism of graphene channels. According to the semiclassical Mott formula, the expression of graphene Seebek coefficient was derived. The conductivity and thermal conductivity models of graphene were also exhibited. Finally, the finite element analysis (FEA) method was used to obtain the device temperatures under different gate voltages. When back-gate voltage VB=0 V, the temperature difference between the hot and cold side of graphene thermoelectric devices is 30 K; when VB=6 V, the maximum temperature difference reaches 50 K; when VB=0 V, the minimum temperature difference is only 10 K. The results show that the gate voltage has obvious regulation on the performance of thermoelectric devices. This article provides a theoretical reference for the design of graphene thermoelectric devices.
Key words: thermoelectric devices    graphene    mobility    Seebeck coefficient

1 石墨烯热电器件模型

 图 1 石墨烯热电器件示意图 Figure 1 Schematic of graphene thermoelectric device
2 石墨烯热电器件仿真建模 2.1 石墨烯通道的载流子输运

 $\mu \left( {n,T} \right) = \frac{{{\mu _0}}}{{(1 + {{\left( {n/{n_{\rm{{ref}}}}} \right)}^\alpha })\left( {1 + {{\left( {T/{T_{\rm{{ref}}}} - 1} \right)}^\beta }} \right)}}$ (1)

 ${n_{\rm{B}}} = \frac{{({V_{\rm{B}}} - {V_{{\rm{B}},{\rm{Dirac}}}}) \cdot {C_{\rm{B}}}}}{e} = \frac{{({V_{\rm{B}}} - {V_{{\rm{B}},{\rm{Dirac}}}}) \cdot {\varepsilon _{\rm{o}}} \cdot {\varepsilon _{\rm{r}}}}}{{e \cdot {t_{\rm{B}}}}}$ (2)

 $n = \sqrt {4 \cdot n_0^2 + n_{\rm{B}}^2} = \sqrt {4 \cdot n_0^2 + {{\left( {\frac{{({V_{\rm{B}}} - {V_{{\rm{B}},{\rm{Dirac}}}}) \cdot {C_{\rm{B}}}}}{e}} \right)}^2}}$ (3)

 ${R_{{\rm{channel}}}}{\rm{ = }}\frac{{L(1 + {{\left( {n/{n_{{\rm{ref}}}}} \right)}^\alpha })\left( {1 + {{\left( {T/{T_{{\rm{ref}}}} - 1} \right)}^\beta }} \right)}}{{We{ \mu_0}\sqrt {n_0^2 + {{\left(\tfrac{{\left({V_{\rm{B}}} - {V_{{\rm{B}},{\rm{Dirac}}}}\right) \cdot {C_{\rm{B}}}}}{e}\right)}^2}} }}$ (4)

2.2 石墨烯热电器件性能参数

 $ZT = \frac{{{S^2}\sigma T}}{k}$ (5)

 $\begin{split} \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! S &= {\rm{ - }}\dfrac{{{ {\text{π}} ^2}k_{\rm{B}}^2T}}{{3e}}\dfrac{1}{G}\dfrac{{{\rm{d}}G}}{{{\rm{d}}E}}\left| {_{E = {E_{\rm{F}}}}} \right. = \dfrac{{{{\text{π}} ^2}k_{\rm{B}}^2T}}{{3e}}\dfrac{1}{R}\dfrac{{{\rm{d}}R}}{{{\rm{d}}n}}\dfrac{{{\rm{d}}n}}{{{\rm{d}}E}}\left| {_{E = {E_{\rm{F}}}}} \right. \\ &=\dfrac{{2{{\text{π}} ^{\frac{3}{2}}}k_{_{\rm{B}}}^2T}}{{3e\hbar {v_{_{\rm{F}}}}}}\left( {\dfrac{{{n_{\rm{B}}}\sqrt {{n_{\rm{B}}}} }}{{{n^ * }^2 + n_{\rm{B}}^2 + 4n_{\rm{{th}}}^2}}} \right) \end{split} \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!$ (6)

 $\sigma {\rm{ = }}\frac{{e{\mu_0}\sqrt {n_0^2 + {{(\tfrac{{({V_{\rm{B}}} - {V_{{\rm{B}},{\rm{Dirac}}}}) \cdot {C_{\rm{B}}}}}{e})}^2}} }}{{d(1 + {{\left( {n/{n_{\rm{{ref}}}}} \right)}^\alpha })\left( {1 + {{\left( {T/{T_{\rm{{ref}}}} - 1} \right)}^\beta }} \right)}}$ (7)

 $k = \left\{ {\begin{array}{*{20}{l}} {{k_0}\begin{array}{*{20}{c}} {} \end{array}\left( {T \leqslant 350{\rm{K}}} \right)} \\ {\dfrac{{{k_0}}}{{1 + 0.01\left( {T - 350} \right)}}\begin{array}{*{20}{c}} {} \end{array}\left( {T > 350{\rm{K}}} \right)} \end{array}} \right.$ (8)

3 结果与讨论

 图 2 背栅电压和温度与石墨烯热电参数的关系 Figure 2 Relationship between back gate voltage and temperature to graphene thermoelectric parameters

 图 3 不同背栅电压下石墨烯热电器件热端和冷端温度图 Figure 3 Charts of hot and cold side temperatures of graphene thermoelectric device at different back gate voltages.
4 结　论

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