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標題: | 雙層薄石墨片於高磁場及高電場下之電性與熱電傳輸性質研究 Electric & Thermoelectric transport phenomena in bilayer Graphene under High Magnetic & Electric Fields |
作者: | Wen-Sen Lu 呂文森 |
指導教授: | 張慶瑞(Ching-Ray Chang) |
關鍵字: | 熱電效應,石墨片,石墨烯,量子霍爾效應,雙閘極, thermopower,graphene,Quantum Hall effect,Bandgap, |
出版年 : | 2011 |
學位: | 碩士 |
摘要: | 本論文旨在探討雙原子層薄石墨片(bilayer graphene,BLG),於高磁場或高電場下之電性、熱電傳輸性質。本論文第一部分針對高磁場下,BLG呈現量子霍爾效應時,其橫向熱電導率之峰值隨溫度、磁場、藍道能階(Landau level)之關係進行探討。第二部分則藉雙閘極結構,針對垂直電場下,BLG之熱電效應增益進行研究。
第一部分我們藉由量測電導率、橫向電導率、thermopower及Nernst coefficient,進一步計算出熱電導率與橫向熱電導率。根據Girvin及Johnson的理論預測,當二維電子系統處於量子霍爾領域、且費米面位於藍道能階上時,其橫向熱電導率將呈現一峰值α_(xy,peak),且該峰值與樣品所在溫度、磁場、及費米面所在之藍道能階均無關,為一常數4×ln2 ((k_B e)⁄h)。本部分實驗我們先在高垂直磁場底下,對BLG進行電性量測,觀察並確認其處於量子霍爾領域。接著進行熱電效應量測並計算其電導率與橫向熱電導率。藉由調整底閘極電壓,我們得以調整其費米面之位置,並觀察其橫向熱電導率與費米面、藍道能階位置之關係。根據實驗結果我們發現,α_(xy,peak)不隨磁場、藍道能階而有變化,但和樣品中雜質導致之disorder width及樣品所在溫度有關。當溫度 k_B T<0.2W_L 時,α_(xy,peak) 和溫度成線性關係;而當溫度 k_B T>0.5W_L 時,α_(xy,peak)為一和溫度無關之常數,實驗上我們得到此常數約為 8.5±1 nA⁄K,與Girvin及Johnson的理論預期4×ln2 ((k_B e)⁄h)~9.24 nA⁄K 相近。此外,實驗中我們在電荷中性點(Charge Neutrality Point,CNP)附近發現能斯特效應與蒙特關係式(Mott relation)之理論預期不同,顯示在雙原子層石墨片中,CNP附近之額外簡併態對熱電效應應有之額外貢獻,可能與所觀察到之自旋簡併態分裂、自旋極化邊界電流有關,其機制有賴日後研究進一步探討。 第二部份,我們藉由雙閘極之結構,在樣品垂直紙面方向上施加強電場並觀察雙原子層石墨薄片之能隙(bandgap)變化,及其產生能隙後熱電效應之增益。根據郝雷等人之理論計算,具有能隙之BLG其thermopower將較無能隙之BLG為大,且該增益隨能隙變大而增加。本實驗先藉由電性量測結果,決定出BLG在垂直電場施加後之能隙大小,再在同電場施加下進行熱電效應量測。由電性實驗結果我們觀察到電阻率隨電場成指數關係,符合具有能隙之半導體其電阻隨熱激發(thermal excitation)之載子數量之關係。熱電量測結果則顯示,其thermopower增益隨電場變大而上升,在溫度15K與電場大小 0.7 V⁄nm 時,該增益約可達零電場底下thermopower之四倍。與郝雷等人之理論計算結果比較後,實驗所得之增益較理論計算為小,我們認為其原因應與實驗樣品中潛在的electron-hole puddle有關。若考慮樣品中局部存在不等量之電子與電洞,則此將對thermopower之產生相互抵消之貢獻,進而導致實驗量測到之thermopower較小。這部分的實驗我們發現具有能隙之BLG其thermopower增益隨垂直電場增加而變大,我們認為雙閘極之BLG有望成為一極具發展潛力之熱電材料。 Electric and thermoelectric properties on bilayer graphene (BLG) under either high magnetic field or perpendicular electric field are investigated experimentally. For BLG under high magnetic field, the transverse thermoelectric conductivity αxy is determined from four transport coefficients which are measured experimentally. αxy(Vbg) attains a peak value of αxy,peak whenever the chemical potential μ, which can be tuned by Vbg, lies in the center of a Landau level. The results show that the temperature dependence of αxy,peak is dictated by the disorder width WL. For kBT/WL ≤ 0.2, peak value αxy,peak is basically linear in temperature, which gives a slope αxy,peak /T=0.019±0.03 nA/K2 and is independent of the magnetic field, temperature, and Landau-level index. At kBT/WL ≥ 0.5, αxy,peak saturates to a value close to the predicted universal value of 4(ln2) kBe/h from the theory of Girvin and Jonson. In addition to the universality of αxy,peak, we also find two anomalies around charge neutrality point (CNP) which cannot be explained by the generalized Mott relation. We attribute the failure of Mott relation to the proposed phase of counter propagating edge channels with opposite spin which presents when spin degeneracy is lifted, as indicated from the observed double peaks feature in the longitudinal conductivity σxx near CNP in our device. Considering the long spin diffusion length in graphene system, the proposed spin polarized counter propagating edge channels in the spin degeneracy lifted BLG around CNP is very interesting for spintronics application. For the BLG under perpendicular electric field, a full electric-field tuning of thermoelectric power (TEP) in a BLG device is demonstrated experimentally with dual-gated geometry. Under a strong electric field bias along the out of sample plane direction, a band-gap is opened in BLG. Resistance and TEP signal are then measured at different biased fields readily tuned by the dual-gated geometry for temperature ranging from 15K to 300K. The TEP exhibits an enhancement as biased field increases, and grows larger at lower temperature. At 15K and a biased field of 0.7V/nm, the TEP reaches a value of 48μV/K and is four-fold increased compared to the unbiased BLG. We suggest that with the introduction of material with high dielectric constant serves as the dielectrics, the enhancement could be enhanced further by increase the biased field further. This enhanced TEP at low temperature makes dual gated BLG device an idea candidate for the thermoelectric application at low temperature such as the power source for spacecrafts. We also find evidences indicating the band structure deformation when larger biased field applied, suggesting redistribution of states near the CNP. Further experiments could be made to confirm this scenario. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/45086 |
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