测 量 没 有 基 底 效 应 的 薄 膜 材 料 的 杨 氏 模 量 谢 存 毅 博 士 纳 米 压 痕 讲 座 录 像 链 接 : https://keysight.webex.com/mw0307l/mywebex/default.do?siteurl=keysight&service=6 1
问 题 所 在? Low-k film (440 nm) on silicon? Berkovich indenter CSM (1nm, 75 Hz) Oliver-Pharr analysis 2
解 决 方 案 : 考 虑 基 底 材 料 对 测 量 的 影 响 Low-k film (440 nm) on silicon Berkovich indenter CSM (1nm, 75 Hz) Oliver-Pharr analysis PLUS thin-film analysis Hay, J.L. and Crawford, B., "Measuring Substrate-Independent Modulus of Thin Films," Journal of Materials Research 26(6), 2011. It was fun to read. Prof. Gang Feng, Villanova University 3
薄 膜 和 基 底 材 料 都 对 测 试 结 果 有 影 响 Development of strain field during nano-indentation of a film-substrate system, from Modelling Simul. Mater. Sci. Eng. 12 (2004) 69 78. (Authors: Yo-Han Yoo, Woong Lee and Hyunho Shin) 4
历 史 回 顾 (1986) Doerner and Nix: Analytic model assuming linear transition from film to substrate and including an empirically determined constant. (1989) King: Form of Doerner-Nix model with no adjustable parameters. (1989) Shield and Bogy: Analytic model, but with physical problems. (1992) Gao, Chiu, and Lee: Simple approximate model. (1997) Mencik: Practical refinements to the Gao model. (1999-2006) Song, Pharr, and colleagues: Alternate version of Gao s approximate model. 5
The Song-Pharr model with Gao s weight function 1 m a (1 1 I 0 ) m s I m m shear modulus; E = 2m(1+n) 0 1 f a t film, m f substrate, m s 6
两 个 弹 簧 之 间 相 互 关 系 的 模 型 在 力 的 作 用 下, 两 个 不 同 刚 度 系 数 的 串 联 弹 簧 : 每 个 弹 簧 的 形 变 量 是 不 同 的, 刚 度 系 数 越 小, 弹 簧 变 形 量 越 大 较 柔 软 的 弹 簧 起 主 导 作 用 在 力 的 作 用 下, 两 个 不 同 刚 度 系 数 的 并 联 弹 簧 : 两 个 弹 簧 具 有 相 同 的 型 变 量 刚 度 系 数 较 大 的 弹 簧 其 主 导 作 用 7
如 何 解 决 薄 膜 的 横 向 支 撑? 很 明 显 是 串 联 效 应 并 联? 硬 膜 软 基 底 : 基 底 顶 层 的 变 形 趋 近 薄 膜 的 变 形 薄 膜 起 主 导 作 用. 8
薄 膜 的 作 用 既 有 串 联, 又 有 并 联 (Hay & Crawford, 2011) 压 痕 载 荷 压 痕 载 荷 薄 膜 薄 膜 基 底 薄 膜 基 底 旧 模 型 新 模 型 9
保 留 了 前 人 的 进 展 特 点 Gao s 权 重 函 数 随 着 压 痕 深 度 的 增 大 逐 渐 呈 现 每 个 弹 簧 的 影 响 Mencik s suggestion that t = t 0 h c. 有 效 泊 松 比 的 定 义 最 早 来 自 于 Song and Pharr. 10
薄 膜 - 基 底 交 互 作 用 的 新 模 型 Applied indentation force film film substrate 11
薄 膜 - 基 底 交 互 作 用 的 新 模 型 force m f : shear modulus, film m s : shear modulus, substrate D : relates stiffness to modulus; D=4a/(1-n a ) I 0 : Gao s weighting function; as a/t 0, I 0 1; as a/t, I 0 0 a : contact radius t : film thickness F : empirical constant; F = 0.0626 12
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 13
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 14
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 15
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 Gao, et al., 1992 16
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 Gao, et al., 1992 17
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 Gao, et al., 1992 Song & Pharr, 1999 18
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 Gao, et al., 1992 Song & Pharr, 1999 19
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 Gao, et al., 1992 Song & Pharr, 1999 20
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 Gao, et al., 1992 Song & Pharr, 1999 Gao, et al., 1992 21
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 Gao, et al., 1992 Song & Pharr, 1999 Menčίk et al., 1997 Gao, et al., 1992 22
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 Gao, et al., 1992 Song & Pharr, 1999 Menčίk et al., 1997 Gao, et al., 1992 23
Load on Sample/mN 有 限 元 模 拟 数 值 70.3 o E f-in t 0.2 0.15 0.1 0.05 Analytic model E out 0 0 50 100 150 Displacement/nm 24
Load on Sample/mN 有 限 元 模 拟 数 值 70.3 o E f-in t 0.2 0.15 0.1 0.05 Sneddon E out E apparent 0 0 50 100 150 Displacement/nm 25
Load on Sample/mN 有 限 元 模 拟 数 值 70.3 o E f-in t 0.2 0.15 0.1 0.05 Sneddon & Hay-Crawford E out E film 0 0 50 100 150 Displacement/nm 26
70 个 有 限 元 模 拟 (2D) 结 果 总 结. Simulation E s, GPa Maximum indenter displacement (h), nm 1-10 100 20 40 60 80 100 120 140 160 166 174 11-20 50 20 40 60 80 100 120 140 160 166 184 21-30 20 20 40 60 80 100 120 140 160 180 200 31-40 10 20 40 60 80 100 120 140 160 180 200 41-50 5 20 40 60 80 100 120 140 160 180 200 51-60 2 20 40 60 80 100 120 140 160 180 200 61-70 1 20 40 60 80 100 120 140 160 180 200 70.3 o E f = 10GPa 500 nm 27
70 个 有 限 元 模 拟 (2D) 结 果 总 结. Simulation E s, GPa Maximum indenter displacement (h), nm 1-10 100 20 40 60 80 100 120 140 160 166 174 11-20 50 20 40 60 80 100 120 140 160 166 184 21-30 20 20 40 60 80 100 120 140 160 180 200 31-40 10 20 40 60 80 100 120 140 160 180 200 41-50 5 20 40 60 80 100 120 140 160 180 200 51-60 2 20 40 60 80 100 120 140 160 180 200 61-70 1 20 40 60 80 100 120 140 160 180 200 70.3 o E f = 10GPa 500 nm 28
Young's Modulus [GPa] 模 拟 结 果 正 常 吗? 20 18 16 14 12 10 8 6 Ef=Es, apparent input film modulus for all simulations 4 2 0 0 10 20 30 40 Indenter Penetration / Film Thickness [%] 29
Young's Modulus [GPa] 模 拟 结 果 正 常 吗? 20 18 16 14 12 10 8 6 4 Ef=Es, apparent Ef=Es, film alone input film modulus for all simulations 2 0 0 10 20 30 40 Indenter Penetration / Film Thickness [%] 30
70 个 有 限 元 模 拟 (2D) 结 果 总 结. Simulation E s, GPa Maximum indenter displacement (h), nm 1-10 100 20 40 60 80 100 120 140 160 166 174 11-20 50 20 40 60 80 100 120 140 160 166 184 21-30 20 20 40 60 80 100 120 140 160 180 200 31-40 10 20 40 60 80 100 120 140 160 180 200 41-50 5 20 40 60 80 100 120 140 160 180 200 51-60 2 20 40 60 80 100 120 140 160 180 200 61-70 1 20 40 60 80 100 120 140 160 180 200 70.3 o E f = 10GPa 500 nm 31
Young's Modulus [GPa] 模 拟 : 软 膜 硬 基 底 20 18 16. 14 12 10 8 6 4 Ef/Es = 0.1, apparent input film modulus for all simulations 2 0 0 10 20 30 40 Indenter Penetration / Film Thickness [%] 32
Young's Modulus [GPa] 模 拟 : 软 膜 硬 基 底 20 18 16. 14 12 10 8 6 4 Ef/Es = 0.1, apparent Ef/Es = 0.1, film alone input film modulus for all simulations 2 0 0 10 20 30 40 Indenter Penetration / Film Thickness [%] 33
Young's Modulus [GPa] 模 拟 : 软 膜 硬 基 底 20 18 16. 14 12 10 8 6 4 2 0 Ef/Es = 0.1, apparent Ef/Es = 0.1, Film (Hay) Ef/Es = 0.1, Film (Song-Pharr) input film modulus for all simulations 0 10 20 30 40 Indenter Penetration / Film Thickness [%] 34
70 个 有 限 元 模 拟 (2D) 结 果 总 结. Simulation E s, GPa Maximum indenter displacement (h), nm 1-10 100 20 40 60 80 100 120 140 160 166 174 11-20 50 20 40 60 80 100 120 140 160 166 184 21-30 20 20 40 60 80 100 120 140 160 180 200 31-40 10 20 40 60 80 100 120 140 160 180 200 41-50 5 20 40 60 80 100 120 140 160 180 200 51-60 2 20 40 60 80 100 120 140 160 180 200 61-70 1 20 40 60 80 100 120 140 160 180 200 70.3 o E f = 10GPa 500 nm 35
Young's Modulus [GPa] 模 拟 : 硬 膜 软 基 底 20 18 16 Ef/Es = 10, apparent input film modulus for all simulations 14. 12 10 8 6 4 2 0 0 10 20 30 40 Indenter Penetration / Film Thickness [%] 36
Young's Modulus [GPa] 20 18 16 14 模 拟 : 硬 膜 软 基 底 Ef/Es = 10, apparent Ef/Es = 10, Film (Hay) input film modulus for all simulations. 12 10 8 6 4 2 0 0 10 20 30 40 Indenter Penetration / Film Thickness [%] 37
Young's Modulus [GPa] 模 拟 : 硬 膜 软 基 底 20. 18 16 14 12 Ef/Es = 10, apparent Ef/Es = 10, Film (Hay) Ef/Es = 10, Film (Song-Pharr) input film modulus for all simulations 10 8 6 4 2 0 0 10 20 30 40 Indenter Penetration / Film Thickness [%] 38
Determining the value of F (fudge factor) E f-in sim (P, h). E f-out E f = 2m f (1-n f ) F was determined as that value which minimized the sum of the squared relative differences (between output and input film moduli) over all 70 simulations. F : 70 d i 1 E f out E df f in / E f in 2 i 0 F = 0.0626 39
求 解 薄 膜 的 模 量 : m f = f(m a, m s, t 0, a, h c, F) Hay & Crawford, 2011 Sneddon, 1965, as implemented by Oliver and Pharr, 1992 Hay & Crawford, 2011 Gao, et al., 1992 Song & Pharr, 1999 Menčίk et al., 1997 Gao, et al., 1992 40
NanoSuite integration in CSM thin film methods 41
NanoSuite integration in ET thin film methods 42
Application: SiC on Si wafers Sample ID Description t nm 16 Silicon carbide (SiC) on Si 150 17 Silicon carbide (SiC) on Si 300 43
Experimental method Materials: o A set of 2 SiC films on Si Platform: Agilent G200 NanoIndenter with o DCM head o CSM option o Berkovich indenter o New test method: G-Series DCM CSM Hardness, Modulus for Thin Films.msm 44
Young's Modulus [GPa] 硬 膜 软 基 底 : SiC on Si 400 350 300 250 200 150 100 50 0 t=150nm, apparent citation of results 0 10 20 30 40 50 Indenter Penetration / Film Thickness [%] 45
Young's Modulus [GPa] 硬 膜 软 基 底 : SiC on Si 400 350 300 250 t=150nm, apparent t=150nm, film citation of results 200 150 100 50 0 0 10 20 30 40 50 Indenter Penetration / Film Thickness [%] 46
Young's Modulus [GPa] 硬 膜 软 基 底 : SiC on Si 400 350 300 250 t=150nm, apparent t=150nm, film t=300nm, apparent citation of results 200 150 100 50 0 0 10 20 30 40 50 Indenter Penetration / Film Thickness [%] 47
Young's Modulus [GPa] 400 350 300 250 200 150 100 50 0 硬 膜 软 基 底 : SiC on Si t=150nm, apparent t=150nm, film t=300nm, apparent t=300nm, film citation of results 0 10 20 30 40 50 Indenter Penetration / Film Thickness [%] 48
Young's modulus, h/t=20% [GPa] SiC on Si: Modulus at h/t = 20% 400 350 300 250 200 150 100 50 0 SiC on Si (t=150nm) Sample Film Apparent SiC on Si (t=300nm) Film modulus is about 25% higher than apparent modulus! 49
Application: low-k materials (on silicon) t 0 = 445 nm t 0 = 1007 nm Rapid Mechanical Characterization of low-k Films, http://cp.literature.agilent.com/litweb/pdf/5991-0694en.pdf 50
Experimental method Materials: o Two low-k films on Si Platform: Agilent G200 NanoIndenter with o DCM head o CSM option o Express Test option o Berkovich indenter Test Methods: o G-Series DCM CSM Hardness, Modulus for Thin Films o Express Test for Thin Films 51
Modulus of low-k film (t = 1mm) is 4.44±0.08GPa 52
Hardness of low-k film (t = 1mm) is 0.70±0.02GPa 53
Application: Ultra-thin films 54
Four samples Basecoat: sputter-deposited Al 2 O 3 (2600nm) Substrate: sintered Al 2 O 3 and TiC 55
Four samples PECVD SiO 2 (50nm) OR ALD Al 2 O 3 (50nm) Basecoat: sputter-deposited Al 2 O 3 (2600nm) Substrate: sintered Al 2 O 3 and TiC 56
Experimental method Agilent G200 with DCM II head and NanoVision Express Test Berkovich indenter Thin-film model applied to both basecoat and top layers. 57
Substrate independent modulus of 50nm films E = 146 GPa Application note: http://cp.literature.agilent.com/litweb/pdf/5991-4077en.pdf 58
In summary, the proposed model 新 模 型 已 经 被 有 限 元 模 拟 和 实 验 测 试 验 证 该 模 型 既 能 用 于 硬 膜 软 基 底, 又 适 用 于 软 膜 硬 基 底, 新 模 型 可 以 允 许 我 们 在 相 对 较 深 的 压 痕 深 度 获 得 没 有 基 地 效 应 的 薄 膜 材 料 的 杨 氏 模 量, 从 而 可 以 有 效 降 低 表 面 粗 糙 度 对 测 量 结 果 的 影 响 59
Thank you! 60
BASIC code for implementing Hay-Crawford thin-film model as an EXCEL function (Hay, J.L. and Crawford, B., "Measuring Substrate-Independent Modulus of Thin Films," Journal of Materials Research 26(6), 2011.) Public Function FilmModulus(ApparentModulus As Double, ContactDepth As Double, ContactArea As Double, FilmThickness As Double, E_s As Double, nu_s As Double, nu_f As Double) As Double 'Function which returns the true Young's modulus of a film when the apparent value is substantially ' influenced by the substrate. 'Required arguments ' ApparentModulus: Substrate-affected value of Young's modulus calculated by Oliver Pharr method. ' ContactDepth: Contact depth calculated by the Oliver-Pharr method. ' ContactArea: Projected contact area; the value returned by the empirical area function at the contact depth. ' FilmThickness: Film Thickness ' E_s: Young's modululus of the substrate ' nu_s: Poisson's ratio of the substrate ' nu_f: Poisson's ratio of the film 'Notes on units: ' ApparentModulus and E_s must have the same units (typically GPa) ' Returned value of FilmModulus has the same units as ApparentModulus and E_s. ' ContactDepth and FilmThickness must have the same units (typically nm) ' Units for ContactArea must be the square of those used for ContactDepth and FilmThickness (typically nm^2) F = 0.0626 'Factor mitigating parallel influence of film (Do not modify) Pi = 3.14159 ContactRadius = (ContactArea / Pi) ^ 0.5 'Contact radius t_a = (FilmThickness - ContactDepth) / ContactRadius ' t/a to characterize indentation size relative to film thickness. t_a2 = t_a ^ 2 mu_s = E_s / 2 / (1 + nu_s) 'Substrate shear modulus I1 = 2 * Atn(t_a) / Pi + t_a * Application.WorksheetFunction.Ln((1 + t_a2) / t_a2) / Pi ' Gao's weight factor I1 nu_app = 1 - (1 - nu_s) * (1 - nu_f) / (1 - (1 - I1) * nu_f - I1 * nu_s) 'Apparent Poisson's ratio I0 = 2 * Atn(t_a) / Pi + 0.5 / Pi / (1 - nu_app) * ((1-2 * nu_app) * t_a * Application.WorksheetFunction.Ln((1 + t_a2) / t_a2) - t_a / (1 + t_a2)) 'Gao's weight factor, I0 mu_app = ApparentModulus / 2 / (1 + nu_app) 'Apparent shear modulus 'Intermediate calculations A = F * I0 / mu_app B = mu_s / mu_app + I0-1 - F * I0 * I0 C = -I0 * mu_s ' Final Calculation mu_f = (-B + (B * B - 4 * A * C) ^ 0.5) / (2 * A) 'Shear modulus film FilmModulus = 2 * mu_f * (1 + nu_f) End Function 61