Bulge testing of single and dual layer thin films a
Dryver R. Huston*ab, Wolfgang Sauterac, Patricia S. Bunt ac, Brian Esserab Univ. of Vermont, b Burlington Advanced Technology LLC, cIBM Microelectronics ABSTRACT
The bulge testing technique determines the mechanical properties of solid thin films by measuring the deformation that forms in response to the application of a controlled differential pressure to a thin film window. By comparing the pressuredisplacement relation with a mechanical model, the elastic modulus and residual stress in the film can be measured. While the bulge testing technique can be quite effective, the technique is not routinely used because of difficulties that often arise with using this technique. The difficulties include specimen preparation and mounting, automated bulge height measurement and the correlation of bulge deformation with the mechanical properties of the thin film. This paper describes developments in the bulge testing technique that alleviate many of these difficulties, as well as presenting results from the testing of single and dual layer thin films. Single film tests were conducted on samples of B-doped-Si, SiC, and diamond-like carbon. A total of 135 windows with three different window aspect ratios and two different thicknesses were investigated. In a preliminary study to determine the feasibility of extending the technique to the testing of multilayer films, the mechanics of a dual layer system were measured. The dual layer system was an Al layer on top of B-doped-Si. The results from the single film test were that the elastic moduli of the B-doped-Si were close to nominal bulk values and the diamond-like carbon was about half that of diamond. The SiC elastic moduli measurements were inconclusive because of the large prestress. Elastic moduli measurements from nanoindentation were about 50% higher. It should be noted that neither the variation of the aspect ratio nor the variation of the film thickness led to different results. The measured prestresses agreed quite well with wafer curvature measurement. The dual-layer measurements yielded values for the elastic modulus of thin film Al that were within 5% of the nominal bulk values. Keywords: bulge tester, thin film, dual layer, automated
1. INTRODUCTION Bulge testing is a method of measuring the mechanical properties of solid thin films. Solid thin films appear in practical applications as either thin films bonded directly on a thick substrate, or as freestanding structures, such as the thin film windows that are used in Next Generation Lithography masks and certain MEMS devices. The bulge testing method measures the mechanical properties of a thin film by isolating it in a thin film window. Thin film windows are fabricated by removing the thick substrate out from underneath a thin film. The thin film window has such a small thickness to span ratio that it usually deforms as a membrane in response to differential pressure. The bulge testing technique has been known for almost a century. However, bulge testing has not enjoyed widespread use due to difficulties in understanding and interpreting the data, and sample preparation and mounting. Despite these obstacles, bulge testing has certain advantages over other more standard measurement tools, especially when testing ultrathin films. The advantage of having thin films detached from the substrate allows for more precise measurements than those attained with conventional methods. Current alternative tools are nanoindentation for measuring the elastic modulus and wafer curvature measurement for measuring the residual stress in a film. Both the nanoindentation and wafer curvature techniques fail when the film thickness becomes extremely small and the prestress level is very low. *
[email protected]; phone 1 802 656-1922; fax 1 802 656-1929; Mechanical Engineering Department, University of Vermont, Burlington, VT 05405-0156
A key step in the application of bulge testing is to correlate the bulge pressure and bulge center displacement to the stress, strain, and material properties in the film. Several methods have been proposed [1-4]. Different bulge testing equations can be derived for different window geometries, Figure 1. Most of these equations can be cast in the general form
p = Ah3 + Bh A = A( E, ν, t , a) B = B(σ 0 , t ,a )
(1)
Where p is the differential pressure applied to the membrane, h is the height of the center of the membrane, E is the elastic modulus of the membrane, ? is Poisson’s ration, t is the membrane thickness, a is a characteristic lateral dimension of the membrane, and s 0 is the membrane prestress. For a square membrane (1) becomes
p=
1
( 0.801 + 0.061ν )
3
Et σ t h3 + 3.4 02 h a (1 −ν ) a 4
(2)
For a long rectangular membrane (1) becomes
p=
8 Et 2tσ h3 + 2 0 h 2 4 6(1 − ν ) a a
(3)
Figure 1: Bulge Geometry
The mechanical properties of a thin film are extracted from pressure v. height data by fitting a cubic polynomial in the form of (1). The polynomial coefficients A and B are then manipulated to yield the unknown mechanical properties E, ?, and s 0 . The testing with either a square or rectangular membrane allows the determination of only two out of the three unknown mechanical properties – usually E and s 0 . The determination of the third property, such as Poisson’s ratio requires combining data from tests on membranes with two different aspect ratios. However, it can be shown that the measurement of Poisson’s ratio by this method is very sensitive to measurement errors and is therefore unreliable. If the residual stress in the film reaches a magnitude such that it dominates the strain behavior of the film, it is extremely difficult to determine the Young’s modulus with accuracy. Figure 2 shows a graph of a silicon carbide film with very high
residual stress (on the order of 210 MPa). According to the bulge pressure-displacement equations (1)-(3), the residual stress of the film can be determined from the linear portion of the pressure-displacement graph, and the Young’s modulus can be determined from the cubic behavior of the curve. The line graph in Figure 2 is the pressure-displacement, the upper dotted line is the linear component contributing for the residual stress, and the upper dotted line is the elastic strain. For a case as the one shown in Figure 2, the influence of the elastic strain is almost negligible compared to the influence of the residual stress.
Figure 2: Pressure-Displacement Graph for SiC Film with high Residual Stress
In order to increase the influence of the elastic strain, the cubic term in the bulge pressure-displacemtn equation has to be considered. Effective determination of the cubic coefficient, A, requires that it be large enough for the pressure-displacement relation to curve appreciably. This can be expressed by the criterion:
Ah3 Ah2 = > Ccrit Bh B
(4)
An analysis of a series of experiments indicated that acceptable results were obtained for
Ccrit > 0.1 . For a square
membrane this means that
E ( 0.801 + 0.061ν ) a 2 (1 −ν ) > 0.1 (5) σ0 h2 Note that equation (5) depends on h . By increasing the pressure and further inflating the bulge, h becomes larger and the 3
dependence between Young’s modulus and the residual stress can become smaller, i.e., the residual stress can be higher.
2. BULGE TESTER SYSTEM Some of the key issues in bulge testing are related to the ease of using the instrument. A bulge tester has several key components. These are: samples, sample holders, differential pressure control, a bulge height measuring system, and data analysis. Figure 3 shows the set-up and components of a custom built bulge tester. A significant improvement in bulge testing was made with the development of a stiction-based stress-free wafer mount. This enabled the testing of multiple windows on a single wafer. Wafer holders for 4-inch and 8-inch wafers allow the examination of full wafers without dicing the wafer into individual sample pieces. Wafers can be taken out of a production line, inspected without causing damage, and still be used. It is important that the sample must not be clamped or glued on a wafer holder, otherwise the introduction of additional stresses is unavoidable.
Figure 3: Bulge Tester System
Another method of improving the ease of using the bulge tester is to automate many of the testing operations. The bulge tester used a mass-flow controller to apply differential air-pressure. A precision electronic pressure gage measured the differential pressure. A laser Michelson interferometer determined the height of the bulge. Automated fringe counting was developed in an effort to automate the height measurement system. However, the automated fringe counting was complicated by the appearance of secondary fringes that werre quite similar to the primary fringes, Figure 4. This spawned a study aimed at identifying and controlling the secondary fringes. The primary cause of the secondary fringes was due to self interference of the light reflected off of the sloped sections of the bulge, Figure 5. Self interference or diffraction causes secondary fringes that appear concentric to the primary fringes, as in Figure 5. The diffraction also causes secondary fringes to form in a pattern that is rotated 45 degrees relative to the orientation of a square bulge. The geometric explanation of the 45 degree secondary fringes appears in Figure 6. A detailed examination of the 45 degree secondary fringes indicates that these are caused by a reflection from part of the bulge that is flat near to the edge. This flat geometry is attributed to stiffness effects in the bulge. Stiffness effects do not appear to be necessary for inclusion in the bulge height v. pressure analysis, but are important in describing the entire deformation surface of the bulge. Secondary Fringes
Primary Fringes
Figure 4: Interference Pattern Showing Primary and Secondary Fringes
Figure 5: Self Interference as a Cause for Secondary Fringes
Figure 6: Explanation of 45° Rotated Pattern of Secondary Fringes
3. SINGLE LAYER TESTS The samples were fabricated on 4-inch silicon wafers with microlithographic techniques. A total of 135 windows were investigated. The samples included 4 different materials with 3 different window aspect ratios and 2 different thicknesses of films made out of nominally the same material. Figure 7 shows multiple results for the elastic modulus (black, [GPa]) and the film residual stress (grey, [MPa]) for nine windows on one wafer. The chart titles denote the membrane size. The analyzed film is B-doped-Si. As can be seen, the repeatability of the bulge test experiment is very good. In order to assure the accuracy of the obtained results, the films were also investigated with a nanoindenter and a wafer curvature measurement tool. For the residual stress results, as shown in Figure 8, the bulge testing method yields the same results as the wafer curvature measurement, but possesses the obvious advantage that localized rather than averaged stress measurement can be performed. The measurement can be performed quickly and easily with only one measurement (as supposed to two measurements with the wafer curvature method. The bulge tester can also be used for very thin films with low residual stress, at which other methods fail to give good results. The results for the elastic modulus as determined with bulge testing versus results obtained with nanoindentation, the standard method in industry, are shown in Figure 9. As can be seen, results from nanoindentation are about 50% higher than results from bulge testing. Yet the obtained results are in a very reasonable range and it remains unclear which method delivers better results. It should be noted that neither the variation of the aspect ratio nor the variation of the film thickness led to different results. For the silicon carbide film used for this test with an upper limit on pressure of 4,000 Pa, equation (5) becomes:
E 0.1 > ≈ 2210 σ 0 0.0000452
This relationship does not hold for the silicon carbide film and indicates that the prestress is too large for the measurement of the elastic modulus.
2.5x2.5
2.5x2.5
2.5x2.5
120
120
120
100
100
100
80
80
80
60
60
60
40
40
40
20
20
20
0
0 1
2
3
4
5
6
7
8
9
0
10
1
2
3
2.5x7.5
4
1
5
120
120
100
100
80
80
80
60
60
60
40
40
40
20
20
20
0
0 3
4
4
5
2
3
4
2.5x15
5
6
7
8
9
10
1
2
100
100
80
80
60
60
40
40
20
20
0
0
7
3
2.5x7.5 120
6
8
9
10
0 1
120
5
2.5x7.5
100
2
3
2.5x15
120
1
2
4
5
2.5x15 160 140 120 100 80 60 40
1
2
3
4
5
20 0 1
2
3
4
5
1
2
3
4
5
6
7
8
9
Figure 7: Results from 9 Different Windows (Black Lines are Elastic Modulus in GPa. Grey Lines are Prestress in MPa)
10
Residual Stress [MPa] Wafer Curvature Measurement vs. Bulge Test 250 200 150 100 50 Wafer Curvature
Dia mo nd
Si C arb ide
Bulge Test B+ Si 5
B+ Si 2
0
Figure 8: Results for Residual Stress
Young's Modulus [GPa] Bulk Material vs. Bulge Test
800
600
400
200
E Indentation [GPa]
Dia mo nd
Si C arb ide
E Bulge Test [GPa] B+ Si 5
B+ Si 2
0
Figure 9: Results for the Elastic Modulus
4. DUAL LAYER TESTS Many thin film structures are built out of multiple layers. There is an interest in measuring the bulk mechanical properties of a multilayer thin film structure, as well as identify the mechanical properties of the individual layers. As an initial foray into the testing of multilayer thin films, a dual layer system was created and tested. For a dual layer system, Figure 10, it is possible to develop a simple mechanical model of the mechanics of the system.
Thin film window for bulge testing
Second layer
First layer Substrate
Figure 10: Dual Layer Thin Film Membrane Window.
The material properties of the second layer can be determined by a simple algebraic procedure. It is based on the assumption that the thin film window acts as a membrane under tension (bending effects are neglected). The bulge tester can measure the elastic modulus and prestress in a membrane. For a dual layer membrane the effective total elastic modulus, Eeff, and the effective total prestress, σeff, can be expressed in terms of the elastic moduli of the two individual layers, E1 and E2 , and the prestresses of the two layers, σ1 and σ2 as follows.
Eeff =
E1t1 + E2 t2 t1 + t 2
(6)
σ eff =
σ 1t1 + σ 2t 2 t1 + t 2
(7)
Everything in eqns. (1) and (2) is measured directly, except for the elastic modulus and prestress of layer 2. These two equations can be solved directly to yield the unknown material properties of layer 2.
E2 = Eeff (1 +
t1 t ) − E1 ( 1 ) t2 t2
(8)
σ 2 = σ eff (1 +
t1 t ) − σ1 ( 1 ) t2 t2
(9)
As a preliminary test of the viability of this method, a set of two samples of 1 µm thick B-doped-Si were tested in the bulge tester to measure the elastic properties and prestress. Next a 1 µm layer of Al was evaporation deposited on the Si. The bulk properties of the dual layer structure was them measured in the bulge tester. Combining the single layer data with the bulk dual layer properties in equations (8) and (9) yielded estimated mechanical properties of the Al layer. The average elastic modulus of the Al layer was 70 MPa, which compares well with the bulk nominal value of 68.5 MPa.
5. CONCLUSION Bulge testing as a method to evaluate material properties was revised for this paper. Despite the fact, that the bulge testing technique so far was skipped as a standard film characterization tool, it offers some advantages over competing systems. Especially for the evaluation of very thin films with low stresses, bulge testing promises to be a superior technique. Despite the existence of a theoretical procedure for the determination of Poisson’s ratio, equations were derived that show that the sensitivity of this solution is too high to be useful for experimental analysis. The deformation of films with very high residual stress is dominated by the compensation of this stress and it proved difficult to determine the elastic straining and therefore, the films’ elastic modulus. A critical number that characterizes the suitability of a film concerning the residual stress has experimentally been determined. The bulge tester technique can be extended to dual layer systems and possibly multilayer systems.
ACKNOWLEDGEMENTS This research was supported by VT EPSCoR and equipment donations by IBM and MKS, Inc. Cameron Brooks, Chris Magg, Tim Sullivan and Jason Gill of IBM provided invaluable technical support. The authors would like to acknowledge the visiting graduate students Christoph Brötz, Peter Sonntag and Klaus Schlickenrieder.
REFERENCES 1. J. W. Beams, “Mechanical Properties Of Thin Films Of Gold And Silver,” International Conference on Structure and Properties of Polymer Films, Bolton Landing, NY, 1959. 2. S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill Book Company, New York, NY, 1959. 3. J. J. Vlassak and W. D. Nix, “A new bulge test technique for the determination of Young's modulus and Poisson's ratio of thin films,” J. Mat. Res., 7, No. 12, pp. 3242-3249, 1992. 4. J. Gill, Application of Bulge Testing Techniques in Determining the Mechanical Properties of Thin Films, Masters Thesis, University of Vermont, 1998. 5. W. Sauter, Thin Film Mechanics – Bulging and Stretching, Ph.D. dissertation, Mechanical Engineering Department, University of Vermont, Burlington, VT, October 2000. 6. S. Selby, Standard Mathematical Tables, The Chemical Rubber Co., Cleveland, OH, Nineteenth Edition, 1971. 7. Bronstein and Semendjajew, Taschenbuch der Mathematik, Verlag Harri Deutsch, Frankfurt, Germany, 1956.
