沉積鈦薄膜於不同基材上之熱應力分析｜國立臺灣科技大學博碩士論文系統

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研究生：	安德魯 Glen - Andrew Porter
論文名稱：	沉積鈦薄膜於不同基材上之熱應力分析 Characteristics and Thermal Behavior of Sputtered Titanium Thin Films on Various Substrates
指導教授：	趙振綱 Ching-Kong Chao
口試委員:	黃榮芳 Rong-Fung Huang 褚晴暉 Ching-Hwei Chue 張瑞慶 Rwei-Ching Chang 楊鍚杭 Hsi-Harng Yang
學位類別：	博士 Doctor
系所名稱：	工程學院 - 機械工程系 Department of Mechanical Engineering
論文出版年：	2011
畢業學年度：	99
語文別：	英文
論文頁數：	193
中文關鍵詞：	鈦、薄膜、濺射、熱應力、X射線
外文關鍵詞：	sputtering, thermal stress, x-ray diffraction, thin films, titanium
相關次數：	點閱：269 下載：6
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Titanium films are growing in popularity, and are soon expected to replace copper for metallization purposes. However, the thermal stress behavior of titanium films had not been extensively studied, and therefore not clearly understood. Thus, the main goal of this work was to develop a systematic process to analyze and model the dσ/dT evolution between 20oC and 300oC, in sputtered, titanium thin films. A biaxial stress state has been legitimately assumed.

In the laboratory, titanium films, with a nominal thickness of 200 nm, were deposited on five different kinds of unheated substrates, by RF magnetron sputtering. These substrates included titanium plate, soda-lime glass and three kinds of p-type silicon wafers, having crystallographic orientations of (100), (110) and (111). X-ray diffraction was used to characterize the crystallographic evolution with respect to temperature. By utilizing a heating chamber and special tooling, the lattice spacings were measured in-situ, and the thermal stress behaviors were estimated with either the sin2ψ method or the d-spacing method.

All titanium films on silicon substrates displayed a stress that grew more compressive with a rise in temperature, largely due to the nature of their thermal expansions. The films deposited on silicon (111) appeared to be uniquely amorphous in the as-sputtered state, but at temperatures above 100oC, they resumed the same crystallographic orientations typically found in the other films. The stresses in the titanium films on the soda-lime glass and titanium plate substrates were both highly compressive, but the stress remained unchanged throughout the temperature cycle from 20oC to 300oC. The uneventful stress behavior was expected for films on these two substrates, since their differences in thermal expansion are nearly zero.

The results appear to support the following conclusions:

• The choice of a substrate has a great influence on the residual intrinsic stresses formed during deposition, and a smaller, although still significant, effect on the thermal stress evolution.
• The sputtering parameters (i.e., deposition temperature, bias voltage, working gas pressure), play a dominant role in the crystallographic texture and growth behavior, whereas, the substrate epitaxy plays only a minor role, with the one exception of titanium on silicon (111).
• The geometry of the sputtering chamber and the physical conditions of the deposition process have an extremely strong influence on the residual stress.
• Because of the anisotropy in stiffness, according to the individual grain orientations, certain grains appear to bear more strain under a compressive stress, whereas, other grains may remain in tension.
• The variance in the CTE has a much more powerful bearing on the stress behavior than any uncertainty surrounding the true value of the film modulus.
• The electrical resistance is reduced as a result of the thermal cycle, which indicates more crystallographic order after heating.
• Surface profiling indicated that the roughnesses of the films can exceed the film thicknesses, even at temperatures as low as 60°C, which implies that some amount of material transport is occurring, and that the Stoney method has a limited precision, especially for extremely thin films.

Out of all the film and substrate combinations covered by this study, the stress behavior of the titanium films on the silicon (100) substrates was investigated the most intensely. A modified stress rule from the literature was used to analyze the component stresses, and polynomial estimations of the CTE were used to enhance accuracy. A simple linear function of stress has been implemented to capture how the changes in the CTE affect the extrinsic stress estimation, and this effect has been termed, the “curl”.

A special behavior in the titanium films on silicon (100) substrates was identified to be an intrinsic stress relaxation. This behavior was considered to be a special occurrence of a strain-induced-restructuring, having an activation energy delivered by the extrinsic, thermal stress. Two scale models are suggested from different viewpoints, which both assume that the intrinsic stress is directly proportional to the concentration of lattice defects per unit area of film. The first model presumes a volumetric distortion, and thereby adopts an appropriate supporting clinical analysis (the differential thermal expansion method). The second model works from a thermodynamic standpoint (the defect diffusion coefficients and their associated free energies), and effectively explains the role of strain-induced-restructuring in the observed stress relaxation. Of these two models, the second offers the most ample insight to the nature of intrinsic stress relaxation.

Some specific conclusions regarding this phenomena are as follows:

• The residual, intrinsic stress is caused primarily by stacking defects on the atomic scale.
• The intrinsic stress relaxation behavior is not primarily viscoelastic.
• The geometry of thin films, which have a much greater surface-area-to-volume ratio than bulk materials, supplies unique opportunities for strain to cause restructuring and material transport to occur.
• The thermodynamic calculations show that the derivative of the thermal stress is equivalent to the negative entropy of the system, which implies that a thermally induced stress relaxation produces more crystallographic order.
• A Sherby-Hockett model of inelastic stress completely explains the thermal stress deviation above 220oC. The resultant curve-fitting fairly represents the average actual laboratory results.

Chapter 1	Introduction	1
	1-1	RESEARCH MOTIVATION	.	.	.	.	.	.	.	1
		1-1.1	Commercial Applications of Thin Films	.	.	. 	.	1
		1-1.2	Keypoints of the Research Frontier	.	.	.	.	.	1
			1-1.2.1	The Unique Geometry of Thin Films	.	.	.	.	2
			1-1.2.2	The Confusion Surrounding Inaccurate Generalizations	.	4
		1-1.2.3	The Current Absence of a Standard Quality Procedure for a Comprehensive Stress Analysis	5
	1-2	LITERATURE REVIEW	.	.	.	.	.	. 	.	6
		1-2.1	Sources of Stress	.	.	.	.	.	. 	.	6
		1-2.1.1	Intrinsic Stresses due to Epitaxial Mismatch Strain	. 	.	7
		1-2.1.2	Intrinsic Stresses due to Deposition (Residual Stress) 	.	7
			1-2.1.3	Extrinsic Stresses 	.	.	.	.	. 	.	9
			1-2.1.4	Thermal Effects 	.	.	.	.	. 	.	9
			1-2.1.5	The Comprehensive Stress Behavior	.	.	. 	.	10
		1-2.2	Development of Mathematical Models	.	.	. 	.	11
			1-2.2.1	Modeling the Intrinsic Stress	.	.	.	. 	.	11
				Satomi’s Deposition Rate Model	.	.	. 	.	11
				Hoffman’s “Grain Boundary Relaxation” (GBR) Model	.	12
				Windischmann’s “Volumetric Distortion” Model	. 	.	13
				Nix and Clemens’ “Island Zipping” Model	.	. 	.	14
				The Seel & Freund Zipping Model	.	.	. 	.	15
				Cammarata’s Island Growth Model	.	.	. 	.	16
				Floro’s Superposed Volmer-Weber Growth Model	. 	.	17
			1-2.2.2	Modeling the Extrinsic Stress	.	.	.	. 	.	18
	1-3	RESEARCH OBJECTIVES	.	.	.	.	.	. 	.	19
		1-3.1	A Physical Analysis of the Titanium Thin Films	. 	.	.	19
		1-3.2	A Standard Quality Procedure for a Comprehensive Stress Analysis	20
		1-3.2.1	The CTE Rule for Thermal Stress in Films	.	.	.	20
		1-3.2.2	The Factorization and Variable Reduction Analysis Strategy	20
		1-3.3	To Characterize the Thermal Stress Behavior of Titanium Thin Films	20
Chapter 2	Experimental Procedures	21
	2-1	MATERIALS AND THEIR PROPERTIES	.	.	.	. 	.	21
		2-1.1	Silicon Substrates	.	.	.	.	.	. 	.	23
			2-1.1.1	(100) Silicon	.	.	.	.	.	. 	.	24
			2-1.1.2	(110) Silicon	.	.	.	.	.	. 	.	24
			2-1.1.3	(111) Silicon	.	.	.	.	.	. 	.	24
		2-1.2	Soda Lime Glass Substrates	.	.	.	.	. 	.	24
		2-1.3	Titanium Substrates	.	.	.	.	.	. 	.	25
	2-2	PHYSICAL VAPOR DEPOSITION BY SPUTTERING	.	. 	.	27
		2-2.1	Choosing the Deposition Conditions	.	.	.	.	.	27
		2-2.2	Substrate Preparation 	.	.	.	.	.	.	.	27
		2-2.3	Deposition Parameters	.	.	.	.	.	.	28
	2-3	FILM CHARACTERIZATION	.	.	.	.	. 	.	29
		2-3.1	X-Ray Diffraction	.	.	.	.	.	. 	.	29
			2-3.1.1	The XRD Equipment and Heating Chamber	.	. 	.	31
			2-3.1.2	Experimental Procedures	.	.	.	. 	.	31
		2-3.1.3	The Suitability of XRD for Estimating the Mean Biaxial Film Strain	32
		2-3.2	Profilometry	.	.	.	.	.	.	. 	.	33
			2-3.2.1	Film Thickness Measurements	.	.	. 	.	34
			2-3.2.2	Substrate Curvature Measurements	.	.	. 	.	34
		2-3.3	Atomic Force Microscopy	.	.	.	.	. 	.	35
			2-3.3.1	Experimental Procedures	.	.	.	. 	.	36
		2-3.4	Electrical Properties	.	.	.	.	.	. 	.	36
			2-3.4.1	Experimental Procedures	.	.	.	. 	.	39
	2-4	STRESS MEASUREMENT	.	.	.	.	.	. 	.	40
		2-4.1	Using X-Ray Diffraction to Measure the Stress	.	. 	.	40
		2-4.1.1	Asymmetric X-Ray Diffraction	.	.	.	.	41
			2-4.1.2	The Relationship Between  dψ  and the CTE	.	.	.	42
			2-4.1.3	The Advantages of Using XRD to Measure the Stress	.	43
			2-4.1.4	The Limitations of Using XRD to Measure the Stress	.	44
		2-4.2	Stress Measurement via the  sin2ψ  Method	.	. 	.	.	45
			2-4.2.1	The Mathematical Derivation of the  sin2ψ  Method	. 	.	46
			2-4.2.2	The Limitations of the  sin2ψ  Method	.	.	.	47
		2-4.3	Stress Measurement via the  d-Spacing Method	.	. 	.	48
		2-4.3.1	The Relationship Between the Stress and the d-Spacing	.	48
			2-4.3.2	The Limitations of the d-Spacing Method	.	.	.	49
		2-4.4	Stress Measurement via the Stoney Method	.	.	. 	.	50
		2-4.4.1	The Relationship Between the Stress and the Curvature	.	50
			2-4.4.2	The Limitations of the Stoney Method	.	.	.	52
Chapter 3	Experimental Results	53
	3-1	X-RAY DIFFRACTION	.	.	.	.	.	. 	.	53
		3-1.1	The Ti / Si (100): L-series 	.	.	.	.	. 	.	53
		3-1.1.1	The Intensity vs 2θ, Major Peaks and Grain Orientation for the Ti / Si (100): L-series	53
		3-1.1.2	The Intensity vs. Temperature for the Ti / Si (100): L-series	.	54
		3-1.1.3	The Average Peak Shift vs. Temperature for the Ti / Si (100): L-series	56
		3-1.1.4	The FWHM for the Ti / Si (100): L-series	.	. 	.	56
		3-1.2	The Ti / Si (110): H-Series 	.	.	.	.	. 	.	57
		3-1.2.1	The Intensity vs 2θ, Major Peaks and Grain Orientation for the Ti / Si (110): H-Series	57
		3-1.2.2	The Intensity vs. Temperature for the Ti / Si (110): H-Series	57
		3-1.2.3	The Average Peak Shift vs. Temperature for the Ti / Si (110): H-Series	59
		3-1.3	The Ti / Si (111): H-Series 	.	.	.	.	.	.	59
		3-1.3.1	The Intensity vs 2θ, Major Peaks and Grain Orientation for the Ti / Si (111): H-Series	60
		3-1.4	The Ti / Soda-Lime Glass: L-Series	.	.	.	.	.	60
		3-1.4.1	The Intensity vs 2θ, Major Peaks and Grain Orientation for the Ti / Glass: L-Series	60
		3-1.4.2	The Intensity vs. Temperature for the Ti / Soda-Lime Glass: L-Series	62
		3-1.4.3	The Average Peak Shift vs. Temperature for the Ti / Soda-Lime Glass: L-Series	62
		3-1.5	The Ti / Ti: L-Series	.	.	.	.	.	. 	.	62
		3-1.5.1	The Intensity vs 2θ, Major Peaks and Grain Orientation for the Ti / Ti: L-Series	62
		3-1.5.2	The Intensity vs. Temperature for the Ti / Ti: L-Series	.	64
		3-1.5.3	The Average Peak Shift vs. Temperature for the Ti / Ti: L-Series	64
	3-2	PROFILOMETRY	.	.	.	.	.	.	. 	.	67
		3-2.1	Film Thickness	.	.	.	.	.	. 	.	67
		3-2.2	Substrate Curvature and Surface Roughness	.	.	. 	.	68
	3-3	ATOMIC FORCE MICROSCOPY 	.	.	.	.	. 	.	69
	3-4	ELECTRICAL RESISTANCE	.	.	.	.	. 	.	72
		3-4.1	L-Series Titanium on Silicon (100) Substrates	.	. 	.	72
	3-5	STRESS ANALYSIS	.	.	.	.	.	.	. 	.	73
		3-5.1	Data Collection and Analysis	.	.	.	.	. 	.	73
			3-5.1.1	Stress Analysis Using the  sin2ψ  Method	.	. 	.	73
			3-5.1.2	Stress Analysis Using the  d-Spacing Method	. 	.	74
		3-5.2	Thermal Stress Estimations	.	.	.	.	. 	.	75
		3-5.2.1	Thermal Stress in the Ti / Si (100) L-Series Films	. 	.	75
		3-5.2.2	Thermal Stress in the Ti / Si (110) H-Series Films	. 	.	76
		3-5.2.3	Thermal Stress in the Ti / Si (111), H-Series Films	. 	.	76
		3-5.2.4	Thermal Stress in the Ti / Soda-Lime Glass, L-Series Films	.	77
		3-5.2.5	Thermal Stress in the Ti / Ti, L-Series Films	.	. 	.	77
Chapter 4	Effects Arising from the Substrate and Deposition Conditions	81
	4-1	THE EFFECTS OF THE SPUTTERING PARAMETERS ON THE FILM CRYSTALLOGRAPHY AND GROWTH	81
		4-1.1	Overview of the Sputtering Process	.	.	. 	.	.	81
			4-1.1.1	Physical Vapor Deposition	.	.	.	.	.	81
			4-1.1.2	The Physics of Sputtering	.	.	.	.	.	82
			4-1.1.3	The Design of the Sputtering Chamber	.	. 	.	84
		4-1.2	The Deposition Process	.	.	.	.	. 	.	84
			4-1.2.1	Material Properties and Material States Affecting Deposition	84
			4-1.2.2	The Thornton Structure Zone Model	.	.	. 	.	86
			4-1.2.3	The Ion Flux Ratio	.	.	.	.	. 	.	87
	4-2	FILM CHARACTERISTICS ARISING FROM DEPOSITION CONDITIONS	88
		4-2.1	Film Crystallography	.	.	.	.	.	.	.	88
			4-2.1.1	Film Crystallography as Indicated by the XRD Intensity	.	88
			4-2.1.2	Grain Size as Indicated by the XRD FWHM	.	.	.	88
			4-2.1.3	Film Crystallography as Indicated by the Electrical Resistance	89
		4-2.2	Film Thickness Variation	.	.	.	.	.	.	90
			4-2.2.1	Film Thickness vs. the Substrate to Target Distance	.	.	90
			4-2.2.2	Film Thickness vs. the Sputtered Material	.	.	.	91
		4-2.3	Stress Generation	.	.	.	.	.	.	.	92
			4-2.3.1	Stress vs. Film Thickness	.	.	.	. 	.	93
			4-2.3.2	Stress vs. Deposition Energy	.	.	.	. 	.	95
			4-2.3.3	Stress vs. Deposition Pressure	.	.	. 	.	95
Chapter 5	Thermal Stress Modeling	99
	5-1	ANALYSIS STRATEGIES	.	.	.	.	.	. 	.	99
		5-1.1	The CTE Rule for Thermal Stress in Films	.	.	. 	.	99
		5-1.2	The Factorization and Variable Reduction Analysis Strategy (FAVRA)	104
			5-1.2.1	A Description of FAVRA	.	.	.	. 	.	104
			5-1.2.2	The Application of FAVRA to the Present Study 	.	.	105
	5-2	THE THERMAL STRESS ANALYSIS	.	.	.	. 	.	109
		5-2.1	Titanium Films on Silicon (100) Substrates	.	.	. 	.	109
			5-2.1.1	Residual Stress from Deposition	.	.	.	.	110
			5-2.1.2	Extrinsic Stress Development During Thermal Excursion	.	111
				5-2.1.3	Inelastic Stress at Elevated Temperatures	.	.	.	111
			5-2.1.4	Stress Evolution During Thermal Cycling	.	.	.	111
		5-2.2	Titanium Films on Silicon (110) Substrates	.	.	.	.	112
		5-2.3	Titanium Films on Silicon (111) Substrates	.	.	.	.	112
			5-2.3.1	Residual Stress from Deposition	.	.	.	.	113
			5-2.3.2	Extrinsic Stress Development During Thermal Excursion	.	113
				5-2.3.3	Inelastic Stress at Elevated Temperatures	.	.	.	114
		5-2.4	Titanium Films on Soda-Lime Glass and Titanium Plate Substrates	.	114
	5-3	REFINING THE THERMAL STRESS MODEL	.	.	. 	.	115
		5-3.1	Defining the Curl	.	.	.	.	.	. 	.	115
		5-3.2	Modeling the Curl	.	.	.	.	.	. 	.	117
			5-3.2.1	The Significance of the Modulus vs. the CTE	.	.	.	119
Chapter 6	Intrinsic Stress Relaxation	121
	6-1	STRAIN INDUCED RESTRUCTURING	.	.	.	. 	.	122
		6-1.1	An Introduction to Strain-Induced-Restructuring	.	. 	.	123
			6-1.1.1	The Effect of Geometry on the Strain-Induced-Restructuring	124
		6-1.1.2	Strain Facilitates Intrinsic Stress Recovery by Dispersing the Volumetric Distortion	125
		6-1.2	Evidence of Strain-Induced-Restructuring in Titanium Films	.	126
			6-1.2.1	Clinical Results Indicating Strain-Induced-Restructuring	.	126
			6-1.2.2	The Slope of the CTE Rule	.	.	.	.	.	126
			6-1.2.3	The Intrinsic Stress Relaxation is Not Primarily Viscoelastic	127
		6-1.3	The Thermodynamics of Strain-Induced-Restructuring	. 	.	127
		6-1.4	The Theorem of Strain-Induced-Restructuring	.	.	.	130

	6-2	THE DEFECT CONCENTRATION AS A MEASURE OF DISTORTION AND STRESS	132
		6-2.1	Measuring the Defect Concentration	.	.	.	. 	.	132
		6-2.1.1	The Differential Thermal Expansion Method	.	. 	.	133
		6-2.1.2	Estimation by X-Ray Diffraction	.	.	. 	.	133
		6-2.2	The Defect Concentration as a Function of the Film Thickness	.	134
		6-2.2.1	A Single Uniform Growth Layer with a Parabolic Defect Concentration	134
		6-2.2.2	Segregated Growth Layers	.	.	.	. 	.	135
		6-2.2.3	The Influence of Thickness on the Defect Concentration	.	137
		6-2.3	Modeling the Defect Concentration, CD 	.	.	. 	.	138
		6-2.3.1	The Diffusion Coefficient for Lattice Refinement,  DD 	.	138
			6-2.3.2	The Diffusion Coefficient for One Defect,  Dd	. 	.	140
		6-2.4	Conclusions Concerning the Intrinsic Stress Relaxation	.	.	142
	6-3	INTRINSIC STRESS MODELING	.	.	.	.	. 	.	143
		6-3.1	The Intrinsic Stress as a Function of the Defect Concentration	.	143
		6-3.2	Modeling the Intrinsic Stress Relaxation as a Function of the Defect Concentration	144
		6-3.2.1	Using the Defect Concentration as Calculated from the Differential Thermal Expansion	144
		6-3.2.2	Using the Defect Concentration as Calculated from the Diffusion Coefficients	146
		6-3.3	Conclusions on the Stress Relaxation Models	147
Chapter 7	Intrinsic Stress Evolution at Higher Temperatures	149
	7-1	SURFACE OXIDATION	.	.	.	.	.	. 	.	150
	7-2	DIFFUSION AT THE SUBSTRATE INTERFACE	.	.	. 	.	151
		7-2.1	Diffusion of Silicon into Titanium	.	.	.	. 	.	151
		7-2.2	Diffusion of Titanium into Silicon	.	.	.	. 	.	152
	7-3	PLASTICITY AND DEFORMATION 	.	.	.	. 	.	153
		7-3.1	Inelastic Strain	.	.	.	.	.	. 	.	153
			7-3.1.1	The Hockett-Sherby Model of Inelastic Strain	.	.	153
		7-3.2	Shear Stress Evolution	.	.	.	.	. 	.	154
	7-4	THE VARIABILITY OF MATERIALS PROPERTIES	.	. 	.	156
		7-4.1	The Curl is Non-Linear	.	.	.	.	. 	.	156
		7-4.2	The Graded Interface	.	.	.	.	.	. 	.	156
	7-5	COMPREHENSIVE INTERACTION	.	.	.	. 	.	157
Chapter 8	Conclusions 	159
	8-1	STRESS EFFECTS FROM THE MATERIALS AND DEPOSITION PARAMETERS	159
	8-2	GENERAL OBSERVATIONS OF THE THERMAL STRESS BEHAVIOR 	159
		8-2.1	Titanium Films on Silicon (100) Substrates	.	.	. 	.	159
		8-2.2	Titanium Films on Silicon (110) Substrates	. 	.	.	.	160
		8-2.3	Titanium Films on Silicon (111) Substrates	. 	.	.	.	160
		8-2.4	Titanium Films on Soda-Lime Glass and Titanium Substrates	.	161
	8-3	SPECIAL CONCLUSIONS ON THE STRESS BEHAVIOR	.	.	161
		8-3.1	Conclusions Concerning the Extrinsic Stress	.	.	.	.	161
			8-3.1.1	Conclusions Concerning the Stress Generated from Thermal 		Expansion 	162
			8-3.1.2	Conclusions Concerning the Inelastic Stress	.	.	.	162
		8-3.2	Conclusions Concerning the Intrinsic Stress	.	.	.	.	162
			8-3.2.1	Conclusions Concerning the Residual Stress from Deposition	162
			8-3.2.2	Conclusions Concerning the Intrinsic Stress Relaxation 			Phenomenon	163
References	165
Appendices	181
	A	Diffusion Applied to a Thin Film	.	.	.	.	. 	.	181
	B	The Defect Concentration Along the  z-Plane, CZ 	.	.	. 	.	184
	C	Estimating the Vibrational Frequency,  υ	.	.	.	. 	.	186
	D	Calculating the Geometrical Coefficient, γ	.	.	.	. 	.	187
	E	Approximations of  the Enthalpy, Entropy and the Internal Energy	. 	.	189
	F	Impurity Concentration Profiles in Semiconductors	.	.	. 	.	191
		Case A:  Constant Surface Concentration Diffusion	.	.	. 	.	192
		Case B:  Constant Total Dopant Diffusion	.	.	.	. 	.	192

                                

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