How dielectric Tg affects substrate performance
11/01/2000
Transitions in polymer mechanical and dielectric properties accompany glass transition, a second-order phase change.
BY LI VOON NG, HERBERT J. FICK AND MINH BUI
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When choosing a dielectric material, there are various factors an electronic packaging designer should consider. Dielectric dissipation and partial discharge of a material during operation are among the important criteria. This article focuses on dielectric dissipation as a performance criterion, introducing some fundamentals of dielectric dissipation and polymer glass transition. In doing so, this article attempts to bridge the chemical and electrical disciplines and to offer some explanations as to why a material glass transition temperature (Tg) should be considered for high-temperature operation.
Neat resin formulations are chosen to demonstrate the effect of polymer Tg. Addition of filler should generally increase modulus and permittivity, but should not change the transition temperature. Similarly, any ionic contaminant from substrate fabrication processes, though it increases dielectric dissipation factor, does not affect the transition temperature.
Polymer glass transition is a fundamental thermodynamic phase transition. As a result of this phase transition, physical properties of the polymer - such as bulk modulus and dielectric permittivity - undergo transition in parallel. Transition in physical properties is often used to define glass transition. However, the temperature at which this occurs is strongly dependent on the method, as well as the frequency, of measurement.
The dielectric dissipation factor represents electric power loss under AC condition because of molecular relaxation processes. Glass transition affects molecular relaxation rates and, consequently, dielectric performance.
Polymer Glass Transition
Glass transition is a phase-change property characteristic of amorphous polymer; it depends on the starting materials and the process conditions that produce the polymer. While melting is a first-order transition involving latent heat, glass transition is a thermodynamic second-order transition, not involving latent heat. A first-order transition implies that the first derivatives of Gibbs free energy are discontinuous at the transition temperature. At the glass transition temperature, however, the second, not the first, derivatives of Gibbs free energy are discontinuous.1
The first derivative of Gibbs free energy with respect to pressure, at constant temperature, is the specific volume:1,2
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It is understood that as a material melts, its density (the reciprocal of specific volume) transitions to that of its liquid phase.
At Tg, the specific volume changes continuously with temperature, while the slope jumps from one value to another. This trend is seen in transition of the coefficient of thermal expansion, a second derivative of Gibbs free energy:1,3
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The isothermal compressibility also exhibits discontinuity at Tg:
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A common method used to determine Tg measures transition in specific heat, using differential scanning calorimetry (DSC):3,4
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Specific heat (Cp) represents the amount of heat necessary to increase one degree in temperature of a unit mass material, at constant pressure. It is usually re-ferred to as the heat capacity at constant pressure. The metric unit for Cp is J/g·oC.
 Figure 1. Phasor diagram representing a parallel equivalent circuit model for a real dielectric. |
As a result of glass transition, physical properties of the polymer experience re-versible transition. The transition can be likened to a change from a glass state to a rubbery state to indicate the material resistance to bulk dimensional change. An example is transition in Young's modulus, which can be determined by dynamic mechanical analysis (DMA).3 Modulus characterizes the stress on the material in response to an applied strain (perturbation in dimension) within the linear region (i.e., the region within which perturbation is reversible and stress response is proportional).5,6 Stress has the dimension of force per area, and represents a "potential" for the bulk dimension of a material to change. The metric unit for modulus is N/m2.
 Figure 2. Glass transition temperature from specific heat transition. Figure 3. Young's modulus peaks associated with transitions in modulus. |
Changes in physical properties accompanying glass transition are related to changes in the ease of molecular motion. Transition in rates of ionic and dipolar motion can be seen in dielectric permittivity and dissipation factor.5 This phenomenon has important implications for the reliability of dielectric performance.
Dielectric Permittivity and Dissipation Factor
Ideal Dielectric: When an ideal dielectric is sandwiched between two electrodes, the assembly becomes an ideal capacitor. Under applied DC voltage, ions and dipoles in the dielectric align with the electric field. No steady flow of current occurs. However, under an applied AC voltage, V (t), an AC current, I (t), that is 90° out of phase will result because charge (q) is changing:8
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where (units are in parenthesis):
ω = radian frequency 2Πf (Hz); t = time (seconds); C = capacitance (Farad); Vo = voltage amplitude (Volt); Io = ωCVo = current amplitude (A).
The average power dissipation after a duration t is:
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For an ideal capacitor under AC voltage, it can be shown that the average power dissipation after each half cycle is zero:
Real Dielectric: With a real dielectric, the AC current leads the applied voltage by a phase Θ less than 90°, and some electric power is lost. (Excessive power dissipation can lead to excess dielectric heating and thermal instability).7 Deviation from ideality is represented by a phase factor:
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The dielectric dissipation factor (sometimes called loss tangent) is defined as tan(δ). Note that the dielectric dissipation factor is determined directly from the phase lead (Θ) of the AC current, and does not require a circuit model. Tan(δ) is frequency dependent, representing different modes of molecular relaxation. As frequency approaches zero, and AC voltage becomes DC, tan(δ) goes to infinity.
Parallel Equivalent Circuit
A basic circuit model that often is used to represent a real dielectric is the parallel equivalent circuit model. In this model, a resistor circuit element is connected parallel to a capacitor circuit element. The total current can be determined from a vector (or phasor) combination of the 90° out-of-phase capacitive current and the in-phase resistive ("lossy") current (Figure 1). The component currents are:
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Note that R represents AC insulation resistance at frequency w.
Complex Permittivity
The AC current response of a real dielectric to an applied AC voltage can be characterized by a complex permittivity, Ε*:
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where Co is the equivalent capacitance in vacuo. Ε'r and Ε"r are premittivity and loss-factor relative to permitivity in vacuo:
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It can be shown that, under AC voltage, the above equation results in:
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Permittivity and loss factor can be determined from current measurement in conjunction with a circuit model or molecular model. According to the parallel equivalent circuit model:
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In this model, the resistive component is effectively decoupled from the capacitive component. This is applicable for some select cases. Parallel equivalent circuit is a simple model. It is not adequate in predicting the frequency dependence of the permittivity and loss factor of a real dielectric. Other circuit models have been proposed to describe dielectric behavior, such as simple relaxation process and interfacial polarization.7
Dielectric Relaxation
Introducing a complex permittivity links the nonideality of current response (with associated electric power dissipation) to molecular relaxation. This approach has an analogy in mechanical compliance, which characterizes the strain response to an applied stress within the linear region. Although the cause-and-effect relation is the reverse of that characterized by modulus, compliance is not a direct reciprocal of modulus because they are complex variables.6 Complex permittivity characterizes the motion of ions, dipoles and electrons (resulting in current) in response to an applied potential.7
There are various modes of dielectric relaxation, ranging in time scale and activation energy. Relaxation because of electron conduction, dipole chain rotation, vibration and stretching are rapid processes, observable under high frequency (short time scale). On the other hand, displacement of ions and dipoles (i.e., translational movement) are slower, observable under low frequency (in the order of 10 Hz or lower) and should involve higher activation energy. Thus, dielectric permittivity, loss factor and dissipation factor are functions of frequency.
Sample Preparation
Polymer samples of different Tgs were prepared. The raw materials were formulations of epoxy, curing agent, polymer additive and solvent. Three different formulations (F1, F2 and F3) were prepared. Test samples were dried at 50°C for 30 minutes, then conditioned at 125°C for 90 minutes. The conditioning step was introduced for solvent removal and B-staging. Solvent was removed to trace values determined by equilibrium. Curing was performed in the test chamber (DSC, DMA and DEA) at a ramp rate of 5oC/min to 220°C, and held for 15 minutes. The same sample was cooled to room temperature and then heated at 5oC/min to 250°C to monitor glass transition.
Differential Scanning Calorimetry (DSC)
DSC is a common method used to measure specific heat. As the sample is heated to a specified rate in a furnace, its temperature is monitored and compared with an adjacent reference (usually an empty pan). The amount of heat absorbed or released by the sample is then determined. The specific heat of the sample is determined from the heat flow rate (W/g) at the applied heating rate (°C/s), where KC is a calibration constant:
 Figures 6, 7 and 8. Changes in dielectric dissipation factor with temperature for F1, F2 and F3 at a frequency of 100 kHz, 10 kHz and 1 kHz. |
In this study, DSC was run under a modulated mode.3,9 By applying a sinusoidal (modulated) heating profile in addition to the regular linear profile, modulated DSC (MDSC) separates the total heat flow to the sample (which is recorded by regular DSC) into two components: reversing and non-reversing heat flow. The reversing heat flow represents thermal transitions that are reversible by heating and cooling cycles. Examples of reversing transitions include melting, boiling and glass transition. Conversely, non-reversing heat flow represents thermal transitions that are irreversible, such as heat generation from a chemical reaction or absorption from thermal inertia. Advantages offered by MDSC include separation of overlapping peaks and increased resolution.
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In theory, glass transition occurs at the temperature at which the specific heat jumps to a new value. In practice, however, polydispersity (the presence of molecules ranging in size in a polymer sample) tends to give a broad transition. Moreover, it is difficult to keep the system at thermodynamic equilibrium by applying an infinitely small heating rate. Therefore, glass transition temperature determined from DSC depends slightly on heating rate.
Coating prepared for DEA was collected to about 8 to 12 mg for MDSC analysis. Temperature modulation of 1°C amplitude (±0.5°C) and 40 seconds period was superimposed onto the linear rate of 5°C/min.
Dynamic Mechanical Analysis (DMA)
Young's modulus transition can be monitored by a single cantilever experiment on DMA. A rectangular sheet of sample is clamped on both ends. While one end is held stationary, an oscillatory strain is applied to the other end in a direction perpendicular to the sample plane. This causes an oscillatory stress, lagging by a phase factor δm. The presence of a phase lag is characteristic of most polymers, which are both viscous and elastic (termed viscoelastic). If the material is truly elastic - like an ideal spring -there is no phase lag and no mechanical energy is dissipated. The linear stress response to applied strain is characterized by modulus. Upon glass transition, Young's modulus steps to a lower value, and its tan (δm) peaks accordingly.3,6
DMA sample was prepared by soaking a precut rectangular piece of fiberglass into the resin mixture. Excess liquid was wiped evenly off the surface of the fiberglass using a tongue depressor. This was then dried and conditioned. The fiberglass reinforced resin sample was clamped to a single cantilever. Dimension (length x width x thickness) of the test sample was approximately 17 x 13 x 0.4 mm. Strain oscillation was 50 µm amplitude at 1 Hz frequency. Data sampling rate was 2 seconds/point.
Dielectric Analysis (DEA)
Dielectric analysis was performed using parallel plate mode. Thin resin coating of approximately 0.05 mm was prepared to prevent air voids. After drying and conditioning, no visible air voids were detected. Coating was then stacked between the parallel plates to yield a total thickness of 0.13 mm to 0.3 mm, under a maximum force of 500 N. The test chamber was continuously purged with dry compressed nitrogen during cure and subsequent glass transition test.
Dielectric tan(δ) values at different temperatures and frequencies 1, 10, 100, 1,000, 10,000 and 100,000 Hz were obtained, at a data sampling rate of 5 sec/point.
Results
MDSC results in Figure 2 show that the specific heat transition is broad. The broad response is most likely due to the presence of polydispersity. The glass transition temperature, obtained as the inflection point of specific heat, is 95, 130 and 155°C for formulations F1, F2 and F3, respectively. These combinations of raw materials, upon curing by the same method, are able to produce increasing Tg.
DMA results in Figure 3 also show that the Young's modulus tan (δm) peaks are increasing in this order, signifying the transition in bulk mechanical property accompanying glass transition. Peak temperatures are 135, 165 and 190oC for F1, F2 and F3, respectively.
Figure 4 shows a typical trend of dielectric dissipation factor decreasing dependence on temperature with frequency. Modes of molecular relaxation observed at low frequencies (long time scale) are associated with motions with high activation energy and high dielectric dissipation, such as the displacement of ions and dipole molecules. Motions observed at high frequency, such as dipole chain rotation and vibration, involve low activation energy. Glass transition, with its accompanying change in physical properties, also lowers the polymer network impedance to molecular displacement. In other words, the presence of ions and small dipole molecules (perceived as contaminants) tends to increase the dielectric dissipation factor, especially above Tg.
 Figures 9,10 and 11. Changes in dielectric dissipation factor with temperature for F1, F2 and F3 at a frequency of 100 Hz, 10Hz and 1Hz. |
Figure 5 shows changes in dielectric dissipation factor with temperature. Notice that tan(δ) peak depends strongly on frequency. The onset of tan (δ) is used in some industries to define glass transition , which is not the same as the inherent thermodynamic Tg of the polymer. Above this onset temperature, mobility of ions and small dipole molecules becomes relatively unhindered. Dipole molecules can be traces of retained solvent, low-molecular-weight materials or process contaminants. Such a dielectric that is sandwiched between two electrodes may outgas upon prolonged exposure to high temperature. Outgassing, the release of gas under the electrode, can cause blistering. The value of dielectric dissipation factor at high temperature can be used to predict, empirically, whether a dielectric is sufficiently free of contaminants to withstand prolonged high-temperature exposure.
A dielectric similar to the one depicted in Figure 5 has been prepared to insulate a current-carrying electrode from its ground. (This kind of assembly is generally called insulated metal substrate.) It has repeatedly demonstrated the ability to withstand DC bias-aging at temperatures as high as 200°C up to 2,000 hours.
Differences in Tg among F1, F2 and F3 seem to be reflected in peak positions of tan(δ) at high frequencies (10 and 100 kHz), where large contributions from translational motions (displacements) are absent(Figures 6 through 11). Each of these curves is reproduced by a repeat run; small, but significant, differences are present only above the onset temperature.
Summary
Dielectric materials were prepared to give glass transition temperature ranging from 100 to 150°C, as determined from transition in specific heat using MDSC. As a result of glass transition phase change, Young's modulus and dielectric permittivity showed transition in a consistent trend, as detected by DMA and DEA.
Dielectric dissipation factor, tan(δ), dependence on temperature decreased with frequency. The onset temperature of tan(δ) at 1 to 10 Hz frequencies increased with Tg, which could be attributed to changing relaxation rates and mobility of ions and small dipole molecules. AP
References
- P. C. Hiemenz, Polymer Chemistry: The Basic Concepts, M. Dekker, New York, 1984.
- I. N. Levine, Physical Chemistry, McGraw-Hill, New York, 1976.
- E. A. Turi, ed., Thermal Characterization of Polymeric Materials, 2nd ed., vol. 1, Academic Press, San Diego, 1997.
- R. J. Seyler, ed., Assignment of the Glass Transition, ASTM STP 1249, 1993.
- Y. M. Haddad, Viscoelasticity of Engineering Materials, Chapman & Hall, London, 1995.
- E. J. Donth, Relaxation and Thermodynamics in Polymers, Glass Transition, Akademie Verlag, Berlin, 1992.
- R. Bartnikas and R. M. Eichhorn, eds., Engineering Dielectrics, Vol. IIA: Electrical Properties of Solid Insulating Materials
Note: Adapted from a Pan Pacific Microelectronics Symposium 2000 presentation (SMTA).
LI VOON NG, Ph. D., is application chemical engineer, MINH BUI is laboratory technician and HERBERT J. FICK is application specialist at The Bergquist Company. For more information, contact Li Voon Ng, The Bergquist Company, 18930 West 78th Street, Minneapolis, MN 55317; 952-835-2322; Fax: 952-835-0430: Email: [email protected]
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