四族元件傳導之研究

藍偟翔

doi:10.6342/NTU.2013.10967

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四族元件傳導之研究

The Carrier Transport Study of Group IV MOSFETs

藍偟翔 , Ph.D　　Advisor：劉致為　　

英文 DOI： 10.6342/NTU.2013.10967

應變；鍺錫矽合金；金氧半電晶體；遷移率；彈道電流；經驗贗勢方法； Strain ； GeSnSi alloys ； MOSFETs ； Mobility ； Ballistic current ； Empirical pseudopotential method.

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Abstract 〈TOP〉

四族材料具有極高潛力應用於未來的金氧半電晶體元件，除了有與當前矽製程兼容的優勢外，還具有比矽通道高的載子遷移率。其中，鍺通道具有高於III-V族材料的電洞遷移率。但對電子遷移率而言，因為四族材料為間接能隙材料和III-V族的直接能隙材料相比，造成四族材料電子遷移率相對較低。然而應變技術可用以提高四族材料的電子和電洞遷移率。應變會改變的原本四族材料的能帶特性，包括等效質量和能隙。本論文的前部分，我們將透過光激發光量測和模擬計算以分別探討應變和四族材料對能隙的影響。而後半部則著重於四族材料應用於場效電晶體通道時的傳導特性研究。而這兩部分，也希望未來能夠加以整合，進一步延伸到超微奈米尺度通道的量子傳輸的計算上。
我們先透過光激發光量測 (100), (110), 和 (111) 鍺基板受到雙軸伸張應變時, 直接能隙光躍遷的變化。直接能隙的光躍遷的增強，來自於在 Γ 能谷的電子數目增加。對於(100)和(110)鍺基板而言，最低 L 能谷 和 Γ 能谷之間的能量差的減少是造成 Γ 能谷的電子數目增加的原因。然而對(111)鍺基板， 最低 L 能谷和 Γ 能谷之間的能量差卻是增加，我們利用能隙理論計算將實驗結果與理論結合說明直接能隙的光躍遷增強的原因。接下來，我們透過經驗贗勢方法來模擬鍺錫矽合金材料的能帶與能隙特性。在錫濃度超過 6.5%時，鍺錫合金會形成直接能隙材料。透過一定的矽和錫比率，鍺錫矽合金的晶格常數剛好匹配與鍺晶格常數，透過文獻上實驗得知此直接能隙可以有 0.9 到 1.4 eV 的調變範圍，我們將利用經驗贗勢方法成功的模擬出文獻上實驗的結果並探討矽濃度和雙軸壓縮應變對鍺錫矽能隙的影響。
我們更進一步透過金氧半電晶體元件製作和理論模擬以探討 n 型和 p 型鍺通道金氧半電晶體的載子遷移率。在模擬計算中，我們考慮聲子、庫倫和介面粗糙三種散射機制。由於減少介面的庫倫散射，鍺電子遷移率的高峰值可高於矽電子遷移率。然而，在實驗上我們發現當電場高於 0.3 MV/cm 時，鍺電子遷移率將會快速下降低於矽電子遷移率，另一方面，鍺電洞遷移率在高電場時卻仍然保有比矽通道高的電洞遷移率，我們將透過遷移率模擬進一步說明二氧化鍺氧化層和鍺通道之介面有著嚴重的介面粗糙散使得鍺通道電子和電洞的遷移率減低。接下來，我們整合實驗和模擬來研究鍺(001)和(111) n 型金氧半電晶體受到伸張應力時電子遷移率的改變。我們發現鍺(111)之電子遷移率也受到嚴重的介面粗糙散，並鍺(001)受到單軸應變時電子遷移率會有比較大的增加量相對於鍺(111)。另一方面，鍺電洞遷移率受到單軸應變時的增加量，理論上會比矽通道來的少。然而，我們將解釋如果鍺通道先受到雙軸壓縮應變，再進一步施加單軸應力時可以使其電洞的遷移率增加量高於矽通道。
	最後，我們將使用經驗贗勢方法所得到的鍺錫能帶結果來計算雙閘極n型鳍型電晶體的電子彈道電流，並計算 Γ 能谷非拋物線的能帶特性以考慮在反轉層的量子侷限中。隨著錫濃度增加可以提高電流特性，然而，雖然鍺錫材料在高錫濃度時已為直接能隙材料，但彈道電流特性仍然受到在反轉層時其他間接能谷中載子的影響。我們研究施加單軸應力在不同側邊方向的鳍型電晶體結構，使載子分佈到有利於彈道電流的某間接能谷中進一步增加電流特性。對鍺錫通道p型平型電晶體而言，我們先以理論與目前文獻上實驗結果做比較，發現電洞遷移率亦受到嚴重的介面粗糙散影響，與受到聲子散射之結果不同，並進一步發現隨著錫濃度電洞遷移率並不會有顯著的改變。
關鍵字 : 應變，鍺錫矽合金，金氧半電晶體，遷移率，彈道電流，經驗贗勢方法

Parallel Abstract 〈TOP〉

Group IV materials have high potential applications for the future CMOS devices, not only the compatible with current Si industry, but also the higher carrier mobility than Si channel. For hole mobility, Ge has the highest hole mobility even compared with group III-V materials. But for electron mobility, the indirect band gap of group IV materials is the disadvantage compared with III-V direct band gap materials to give lower electron mobility of group IV than one of III-V channel. Strain technology is the most important technique to improve electron and hole mobilities. Strain will change the origin band structures of group IV materials including the changes of effective mass and band gaps. In the first part of the dissertation, we will investigate the strain effects and group IV alloy materials on Ge by photoluminescence measurements and band gap simulations, respectively. For the rest part of the dissertation, the transport properties including mobilities and electron ballistic current of group IV channel materials are studied. We hope we can combine and extent these studied to simulate the quantum transport of nano-scale devices in the future. 
	We will investigate the strain effects on the enhanced photoluminescence of direct transition observed on (100), (110) and (111) Ge under biaxial tensile strain. The enhancement is caused by the increase of electron population in the Γ valley. The shrinkage of energy difference between the lowest L valleys and the Γ valley is responsible to the population increase on (100) and (110) Ge. On the contrary, for (111) Ge, the small density of states due to the two-fold degeneracy of the lowest L valleys make the population increase in the Γ valley. This is responsible to the enhanced photoluminescence on strained (111) Ge. Next, we investigate the band structures and band gaps of Ge1-xSnx and SiyGe1-x-ySnx on Ge by band structure calculations of the nonlocal empirical pseudopotential method. The indirect-direct transition of Ge1-xSnx is at Sn content of 6.5%. The simulated energy of direct band gap of Si4xGe1-5xSnx lattice matched with Ge can be tuned from 0.9 to 1.4 eV in consistent with the previous experimental results. We find that adding Si content will result more increasing of energy difference between the indirect valleys and the Γ valley than biaxial compressive strain on SiyGe1-x-ySnx and not easy to form direct band gap of SiyGe1-x-ySnx on Ge (001).
The carrier concentration dependence on phonon and interface roughness scattering of hole and electron mobilities are analyzed comprehensively for metal-oxide-semiconductor field-effect transistors (MOSFET) with GeO2/Ge gate stacks. Phonon scattering, coulomb scattering, and interface roughness scattering are taken into account. The Ge peak electron mobility exceeding Si universal in our device by a factor of 1.3 is due to the reduction of coulomb scattering of the interface states. As compared to Si, the faster roll-off of the Ge electron mobility at the effective field larger than 0.3 MV/cm is due to larger interface roughness scattering. We also found both hole and electron mobilities of Ge at high carrier concentration (high electrical field) are limited by the interface roughness scattering at GeO2/Ge interface. With reducing the roughness at insulator/Ge interface, the enhanced Ge hole mobility can be shown and dominated by phonon scattering at high carrier concentration.
	Next, we combine the experiment and simulation results to study the strain responses of Ge n- MOSFETs on (001) and (111) substrates. We found the electron mobility of Ge (111) is also limited by the serious interface roughness scattering, and Ge (001) has higher strain response than Ge (111) under uniaxial tensile stress. On the other hand, the hole mobility of strained-Ge channel on relaxed Si0.6Ge0.4 substrate were simulated and compared with previous data. Strained-Ge has higher mobility enhancement than Si under uniaxial compressive stress along [110] direction due to the enhancement of conductivity mass reduction of strained -Ge.
	Finally, we simulate the ballistic currents of Ge1-xSnx channel double gate (DG) n-FinFETs. The effective mass and non-parabolic coefficient (α) of Ge1-xSnx are simulated from nonlocal empirical pseudopotential method. The α influences the subband energy shift of Γ valley under quantum confinement in the inversion layer. The electron ballistic current of DG FinFETs (110)/[-110] will increase by adding Sn content up to 20% due to the increasing of injection velocity of Γ valley. After applying uniaxial stress at Sn content of 20%, DG FinFETs (00-1)/[1-10]has the largest mobility enhancement due to the carrier located into the small conductivity mass and large density of state benefit for the ballistic current.
The hole mobility of Ge1-xSnx p- MOSFETs will be investigated under 6×6 k．p Schrodinger and Poisson self consistently solutions. The mobilities of strained-Ge1-xSnx on Ge (111) and (001) are fitted compared with previous experimental results. The serious interface roughness scattering dominate the previous experimental mobility trend of (111) > (001) in opposite to the phonon-limited mobility ((001) > (111)). Furthermore, we found that the variation of Sn content does not affect the hole mobility of relaxed Ge1-xSnx channel except introducing strain into Ge1-xSnx channel due to the lattice mismatch from substrate or S/D region.

Keywords: Strain, GeSnSi alloys, MOSFETs, Mobility, Ballistic current, Empirical pseudopotential method.

Note that the related four journal papers are as below:
1. H. -S. Lan, Y.-T. Chen, Hung-Chih Chang, J.-Y. Lin, William Hsu, W. -C. Chang, and C. W. Liu, "Electron scattering in Ge metal-oxide-semiconductor field-effect transistors," Appl. Phys. Lett., Vol. 99, 112109, 2011.
2. Y.-T. Chen, H.-S. Lan, W. Hsu, Y.-C. Fu, J.-Y. Lin, and C. W. Liu, "Strain response of high mobility germanium n-channel metal-oxide-semiconductor field-effect transistors on (001) substrates," Appl. Phys. Lett., Vol. 99, 022106, 2011.
3. H. -S. Lan, S. -T. Chan and T. -H. Cheng, C. -Y. Chen and S. -R. Jan and C. W. Liu, “Biaxial tensile strain effects on photoluminescence of different orientated Ge substrates” Appl. Phys. Lett., Vol. 98, 101106, 2011.
4. T. -H. Cheng, K. -L. Peng, C. -Y. Ko, C. -Y. Chen, H. -S. Lan, Y. -R. Wu, C. W. Liu, and H. -H. Tseng, “Strain-enhanced photoluminescence from Ge direct transition,” Appl. Phys. Lett., Vol. 96, 211108, 2010.

Reference ( 151 ) 〈TOP〉

References (chapter 1)
[1] The website of Intel Corp: http://newsroom.intel.com/docs/DOC-2032
[3] Jay Deep Sau and Marvin L. Cohen, “Possibility of increased mobility in Ge-Sn alloy system”, Phys. Rev. B, vol. 75 , pp.045208-1 (2007)
[4] T. -H. Cheng, K.-L. Peng, C.-Y. Ko, C. -Y. Chen, H. -S. Lan, Y. -R. Wu, C. W. Liu and H. -H. Tseng, “Strain-enhanced photoluminescence from Ge direct transition”, Appl. Phys. Lett., 96, 211108 (2010)
[5] H.-Y. Yu, D. Kim, S. Ren, M. Kobayashi, D. A. B. Miller, Y. Nishi, and K. C. Saraswat, “Effect of uniaxial-strain on Ge p-i-n photodiodes integrated on Si”, Appl. Phys. Lett., 95, 161106 (2009)

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