Mattiessen’s rule에 의하면 Probability Theory에 의해 1τ = τ1
T +τ1
I 로 Scattering 확률은 Lattice Vibration에 의한 확률과 Impurity Scattering 에 의한 확률로 나타낼 수 있다. 여기서, µ= eτm이므로 1µ = µ1
L +µ1
I이며
τT ∝ T1 에 의해 그래핀의 비저항은
ρ= 1
enµd = 1
enµL + 1
enµI =AT +B (Mattiessen′s rule)
로 나타낼 수 있다. 질소도핑 그래핀의 경우 온도에 비례하지 않는Impurity
Scattering이 증가하여 온도에 의한 영향이 순수 그래핀에 비해 작을 것
으로 예상되었지만 작은 온도 범위 내에서는 기존의 탄소들의 Lattice Vibration이 Scattering의 주 원인이기 때문에 온도에 의한 영향이 큰 차 이를 보이진 않았다. 더 넓은 온도 영역에서 실험하려 시도하였으나 앞에서 설명하였듯이 너무 고온으로 가게 되면 Substrate와 Graphene의 접촉력 변화에 의해 Graphene의 성질에 영향을 끼치게 되기 때문에 실험하는 과정에서 repeatability가 다소 떨어져서 실험을 중지하였다. 추후 고온에 서도 실험을 개선하여 더 넓은 온도에서의 결과를 비교해 볼 필요성이 있다.
그림 5.1 Electrical Conductivity of Pristine Graphene
그림 5.2 Electrical Conductivity of N-doped Graphene
표 5.1 순수 그래핀의 전기 전도도 및 Mobility
Conductivity(mS) Slope µh(cm2/Vs) Slope µe(cm2/Vs) 23℃ 0.106569 0.0057 6.334213 0.0107 11.89054 50℃ 0.107654 0.0053 5.889707 0.0104 11.55716 100℃ 0.114103 0.0047 5.222948 0.0091 10.11252 165℃ 0.116097 0.0040 4.445062 0.0071 7.889985
표5.2 질소 도핑 그래핀의 전기 전도도 및Mobility
Conductivity(mS) Slope µh(cm2/Vs) Slope µe(cm2/Vs) 14℃ 0.202423 0.0108 10.13632 0.0156 14.64136 50℃ 0.203108 0.0097 9.103921 0.0154 14.45365 100℃ 0.206283 0.0083 7.789953 0.0133 12.4827 150℃ 0.208562 0.0051 4.786598 0.0113 10.6056
제 6 장 결론
Gate Voltage를 가해주면서 순수 그래핀과 질소도핑 그래핀의 온도에 따른 전기전도도의 변화를 연구하였다. 두 그래핀 모두 온도가 상승함에 따 라Dirac Point에서의 최소 전기전도도는 증가하였고,Mobility는 감소하였 다. 이는 고온에 따라 전자가 에너지를 받아서Charge Carrier Density가 높 아짐에 따라Dirac Point에서의 전기전도도가 증가하고Lattice Vibration 이 증가하여Scattering이 증가하여Mobility가 감소하였다. 질소도핑 그래 핀의 경우Dirac Point가 왼쪽으로 이동하여N type소자 개발의 가능성을 확인하였다. 추후 Sample Quality와 실험과정을 개선하여 더 넓은 온도 범위에서 재측정하여 비교를 하여야 하며 전기전도도 뿐만 아니라 제벡계 수와 열전도도 측정 이후 열전소자 평가계수 ZT를 산출해내어 질소도핑 그래핀의 열전소자 활용 가능성을 확인해보도록 한다.
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Abstract
Temperature Dependence of Electrical Conductivity of N-doped & Pristine
Graphene
Gyumin Lim Department of Mechanical and Aerospace Engineering College of Engineering Seoul National University
In our work, we measured electrical conductivity of N-doped graphene &
pristine graphene while changing the temperature. In order to use 4 point method, we patterned metal electrodes with Au & Cr on FET substrate composed of Si and SiO2. Graphene was synthesized by CVD(Chemical Vapor Deposition) method on Cu foil and transferred to target substrate