1 Copyright 2002 2008 PEGASUS Software Inc All
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1. はじめに Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 3
2. プラズマシミュレーションに用いられる計算手法 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 8
粒 子 モ デ ル Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 11
流 体 モ デ ル Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 20
運動方程式の簡略化(ドリフトー拡散モデル) 圧力勾配項 ▽nek. BTe 1 1 n e v. T 2 meneνm = ne ▽( 3νm ) = ne ▽( 1 De = ne ▽(ne. De)~ ne ▽ne e. E m e νm 外力(電界)項 n e τ m v. T 2 ) 3 = μe E μe = e m e νm 拡散係数 De = τ m v. T 2 3 フラックス Γe = - neμe E - De▽ne 移動度 = k. BTe m e νm = μek. BTe e Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 28
イオンの輸送パラメータ (2) 次の近似式からμを求める。 3 e|Z| π(mion+M) Nμ= 8 2 mion. Mk. BTeff 1/2 1 Ω(1, 1)(Teff) k. BTeff=k. BTn +(1/3)Mvd 2 Ω(1, 1)(Teff)= 1 (k T )-3∫ε∞ 2σ (ε)exp(-ε/k T )dε B eff m B eff 0 2 D= μk. BTeff e Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 37
ファラデーの法則 アンペールの法則 ガウスの法則 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 47
Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 48
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3. 気相シミュレーションの計算例 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 53
3. 1 対向ターゲットマグネトロンスパッタ装置 粒子モデル PIC/MCC DSMC Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 54
解析モデル 残留磁束密度: 1 T N Ar, O 2: 0. 25 Pa 200 S -400 V S N 80 100 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 55
磁力線と磁束密度 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 56
荷電粒子密度 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 57
O(-)密度、電子、電子温度 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 58
Ar(+), O 2(+)入射フラックス、Siスパッタ粒子フラックス Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 59
Si 密度、温度 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 60
Si 速度、堆積フラックス Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 61
3. 2 ドライエッチング装置のシミュレーション 参考文献:M. Shiozawa and K. Nanbu, "Coupling of plasma and flow in materials processing", Thin Solid Films, Vol. 457, pp. 48 -54, 2004 ハイブリッドモデル + DSMC Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 62
解析モデル 121 100 RF Cl2 385 ICPパワー: 500[W] 13. 56[MHz] Cl2流量 : 50[sccm] z r 250 15 78 174 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 63
電子に関する物理量、電位分布 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 66
Cl-、Cl+密度分布、 Cl-、Cl+生成率分布 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 67
Cl 2+密度、生成率分布、 Cl 2、 Cl分布 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 68
3. 3 大気圧沿面放電シミュレーション 流体モデル Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 69
解析モデル形状 N 2 1[atm], 300[K] 1 d 1 1 陽極:電圧V 陰極(接地) 誘電体 εr=3 0. 3 h 単位:[mm] Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 71
シミュレーション結果 (h=2 mm) 2 mm Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 75
シミュレーション結果 (h=0. 3 mm) 0. 3 mm Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 76
シミュレーション結果 (遠方接地) 誘電体表面において 表面電荷の蓄積を考 慮せず 0. 3 mm 100 mm Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 77
プラズマ成長/消滅の判断(h=2 mm, d=4 mmの例) 密度ピーク値の 時間変化 放電 消滅 電子密度分布 V=3200[V] V=3300[V] Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 79
密度ピーク値の経時変化(h=2 mm) d=0. 5 mm V=1200 V d=3. 0 mm V=3200 V d=1. 0 mm V=2100 V d=4. 0 mm V=3300 V d=1. 5 mm V=2700 V d=2. 0 mm V=3100 V d=5. 0 mm V=3500 V Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 80
電子密度の空間分布(h=0. 3 mm) d=1. 0 mm V=1500 V d=4. 0 mm V=1400 V d=2. 0 mm V=1500 V d=3. 0 mm V=1400 V d=5. 0 mm V=1500 V Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 81
電子密度の空間分布(h=2 mm) d=1. 0 mm V=2100 V d=4. 0 mm V=3300 V d=2. 0 mm V=3100 V d=3. 0 mm V=3200 V d=5. 0 mm V=3500 V Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 82
4. 形状ミュレーションに用いられる計算手法 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 83
Ar/Cl 2プラズマによる Poly-Si エッチング 参考文献: R. J. Hoekstra, M. J. Grapperhaus and M. J. Kushner, Kushner "An Integrated Plasma Equipment Model for Polysilicon Etch Profiles in an Inductively Coupled Plasma Reactor with Subwafer and Super wafer Topography“ J. Vac. Sci. Technol. A. 15, 1913 (1997) Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 87
Poly-Si:Ar/Cl 2プラズマ表面反応機構(1) Cl 2+ Cl+ Si. Cl 2 Si Si. Cl Cl+ Si. Cl 2+ Si. Cl 2 Ar+ Si. Cl 3 , Ar Ar+ Si. Cl 4 Si. Cl 2 , Ar Cl デポ反応 イオンアシスト エッチング反応 I* 高速中性粒子 Si. Cl 3 Cl, Cl+ バルク表面種 錯体 Cl Si. Cl 2+ Si. Cl 2 Cl 2+ Si. Cl 4 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 88
Poly-Si:Ar/Cl 2プラズマ表面反応機構(2) p 0 Si(s) +Cl(g) Si. Cl (s) Si. Cl(s) +Cl(g) Si. Cl2 (s) Si. Cl2(s)+Cl(g) Si. Cl3 (s) Si. Cl3(s)+Cl(g) Si. Cl4 (g) Si(s) +Si. Cl2(g) Si(s)+ Si. Cl2 (s) Si. Cl(s) +Si. Cl2(g) Si. Cl(s)+ Si. Cl2 (s) Si. Cl2(s)+Si. Cl2(g) Si. Cl2(s)+ Si. Cl2 (s) Si. Cl3(s)+Si. Cl2(g) Si. Cl3(s)+ Si. Cl2 (s) 0. 99 0. 20 0. 15 0. 0001 0. 8 0. 5 0. 3 0. 1 1/2 Si. Cl2(s)+Ar+(g) Si. Cl2(g)+ Ar (g) 0. 16 ( E/E 0 -1 ) Si. Cl3(s)+Ar+(g) Si. Cl3(g)+ Ar (g) 0. 16 ( E/E 0 -1 ) Si. Cl(s) +Cl+(g) 0. 13 ( E/E 0 -1 ) Si. Cl2(g) Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 1/2 89
Poly-Si:Ar/Cl 2プラズマ表面反応機構(3) p 0 Si. Cl2(s)+ Si(s) + Cl+(g) Si. Cl2(g)+ Si. Cl(s) Si. Cl3(s)+ Si(s) Cl+(g) Si. Cl4(g) +Cl 2+(g) Si. Cl2(g) Si. Cl(s) + Si(s) + Cl 2+(g) Si. Cl2(g)+ Si. Cl(s) Si. Cl2(s)+ Si(s) + Cl 2+(g) Si. Cl2(g)+ Si. Cl2 (s) Si. Cl3(s)+ Si(s) + Cl 2+(g) Si. Cl4(g)+ Si. Cl (s) 0. 16 ( E/E 0 -1 ) 0. 19 ( E/E 0 -1 ) 1/2 E/E 0. 13 ( 0 -1 ) 1/2 E/E ( ) 0. 16 0 -1 1/2 E/E 0. 16 ( 0 -1 ) 1/2 0. 19 ( E/E 0 -1 ) Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 90
Si 形状 (Cl, Cl+, Ar+, Cl 2+: 1. 6 x 106, 5 x 104, 1 x 104) Si T=200[s] T=600[s] Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. T=1000[s] 91
入射粒子、反応生成粒子の密度 Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 92
ボッシュプロセスによる Si エッチング Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 93
ボッシュプロセス SF 6/C 4 F 8 9[sec]/9[sec] 24回 流入サンプル数:エッチング ステップ F, Si. F_x(+): 3 x 106, 1. 5 x 105 デポジション ステップ Cx. Fy, I(+) : 1. 5 x 106, 3 x 105 # エッチングステップ 反応 Si + 4 F → Si. F_4 Si + Si. F_x(+) → Si. F_x Polymer + F → Cx. Fy # デポジションステップ 反応 Mask + Cx. Fy → Mask + Polymer + Cx. Fy → Polymer + I(+) → Cx. Fy + I Si + Cx. Fy → Si + Polymer Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 94
ボッシュプロセス 初期形状 Si 形状 ポリマー膜 Si Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 95
参考文献(追記) 1)菅井秀郎 プラズマエレクトロニクス オーム社、2000 2)M. A. Lieberman and A. J. Lichtenberg Principles of Plasma Discharges and Materials Processing, Second Edition Wiley-Interscience, John and Wiley and Sons, Inc. 2005 3)Kenichi Nanbu and Masakazu Shiozawa kinetic Modeling of Rarefied Plasmas and Gases in Materials Processing, AIP Conference Proceedings Vol. 663, Rarefied Gas Dynamics: 23rd International Symposium、2003 4)ミシガン大:Kushner教授のHP ハイブリッドモデル(静磁場有無) http: //uigelz. eecs. umich. edu/ Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 96
参考文献 [1]C. K. Birdsall and A. B. Langdon Plasma Physics via Computer Simulation Mc. Graw-Hill, New York, 1985 [2] Kenichi Nanbu Probability Theory of Electron-Molecule, Ion-Molecule, Molecule-Molecule , and Coulomb Collisions for Particle Modeling of Materials Processing Plasmas and Gases, IEEE Trans. Plasma Sci. Vol. 28, 971 (2000). [3]G. A. Bird. Molecular Gas Dynamics and the Direct Simulation of Gas Flow Clarendon Press Oxford, 1994. [4]南部健一 原子・分子モデルを用いる数値シミュレーション 第 3章 モンテカルロ法の基礎. コロナ社, 1996. Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 98
[5]E. W. Mc. Daniel and E. A. Mason: The Mobility and Diffusion of Ions in Gases Wiley, New York, 1973 [6]K. Okazaki, T. Makabe and Y. Yamaguchi Appl. Phys. Lett. Vol. 54, 1742 (1989) [7]T. Makabe, N. Nakano and Y. Yamaguchi Phys. Rev. A Vol. 45, 2520 (1992) [8]T. J. Sommerer and M. J. Kushner. Journal of Applied Physics, Vol. 71, pp. 1654 --1673, 1991. [9]真壁利明 プラズマエレクトロニクス 培風館, 2000. Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 99
[10]H. M. Wu, D. B. Graves and M. Kilgores. Plasma Source Sci. Technol. , Vol. 6, pp. 231 --239, 1997. [11]P. L. G. Ventzek, M. Grapperhaus, and M. J. Kushner. J. Vac. Sci. Technol. B 12(6), pp. 3118 --3137, 1994. [12]M. Shiozawa and K. Nanbu. Coupling of plasma and flow in materials processing. Thin Solid Films Vol. 457, pp. 48 --54, 2004. Copyright 2002 -2008 PEGASUS Software Inc. , All rights reserved. 100
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