18 www.DownloadPaper.ir S. Diaham et al.: Dielectric Breakdown of Polyimide Films: Area, Thickness and Temperature Dependence Dielectric Breakdown of Polyimide Films: Area, Thickness and Temperature Dependence S. Diaham, S. Zelmat, M.-L. Locatelli, S. Dinculescu, M. Decup and T. Lebey Université de Toulouse; UPS, INPT; LAPLACE (Laboratoire Plasma et Conversion d'Energie); 118 route de Narbonne, F-31062 Toulouse cedex 9, France. CNRS; LAPLACE; F-31062 Toulouse, France. ABSTRACT Changes in the dielectric breakdown field of polyimide (PI) films have been studied from 25 to 400 °C under dc ramps. Both the area (from 0.0707 to 19.635 mm2) and thickness (from 1.4 to 6.7 µm) dependences of the dielectric breakdown field have been carried out using the Weibull distribution function. The 63%-breakdown field value (i.e. the g-scale parameter) of PI shows a decrease with increasing area, thickness and temperature but always remains above 2 MV/cm. The -scale parameter of the distribution shows a typical decrease with increasing area, however, it exhibits an increase with increasing thickness. This ‘curious’ behavior is discussed on the basis of the percolation theory. No temperature-dependence is clearly observed. Moreover, physical interpretations are carried out using the pre-breakdown current analysis. Index Terms — Polyimide (PI), dielectric breakdown, dielectric strength, area, thickness, temperature, Weibull distribution. 1 INTRODUCTION THE development of electronic devices operating under high temperatures (200-400 °C) involves the use of appropriate thin dielectric materials to achieve the electrical insulation of the components [1–3]. Polyimide (PI) materials are often used for the surface insulation of power electronic devices due to their excellent intrinsic properties such as thermal stability (weight losses <1% at 500 °C), high dielectric breakdown field (EBR>2 MV/cm), relatively low losses, also at higher temperatures (tan <10-2) and thermo-mechanical matching with components [4, 5]. They also appear as potential candidates for high temperature power electronic device insulation. A study of their electrical properties and particularly of their dielectric breakdown field across a high temperature range has to be performed. The dielectric breakdown of PI has already received much attention since their development for electrical insulation and their intensive use in industrial applications [6, 7]; however, for temperatures ranging above 200 °C few has been investigated and in any case never exceeds 250-300 °C [8, 9]. Hence, for higher operating temperatures, an extended study appeared as necessary. Moreover, the impact of other parameters usually affecting the breakdown field of polymers such as geometrical parameters (thickness and area) has to be investigated too. The study of their influence is of primary importance since this allows predicting the dielectric breakdown field for wider Manuscript received on 14 October 2008, in final form 24 June 2009. geometries. Several studies have reported the area or thickness dependence of the dielectric breakdown field of PI [10, 11]. Nevertheless, among the large range of values found in the literature, usually between 1 and 5 MV/cm, it appears as relatively difficult to establish laws where the influence of each parameter is clearly identified when combined to another one. In a previous study [12], the changes in the electrical conductivity of PI up to 400 °C were carried out. In the present study, the measurements of the dielectric breakdown field across the same temperature range have been performed. It corresponds to the highest temperature range of investigation reported up to now for these materials. In addition, the close dielectric breakdown dependence existing between the area and the thickness combined to the temperature is presented. Finally, a particular analysis is done both to the scale and shape Weibull parameters versus the experimental parameters. 2 THEORETICAL PART 2.1 TEMPERATURE DEPENDENCE OF THE DIELECTRIC BREAKDOWN OF POLYMERS Several studies have already carried out the relationships between the high electric field conduction and the breakdown processes in polymers [13–15]. Theories on the breakdown mechanisms are usually divided into three categories: electronic, thermal and mechanical processes. However, the measured dielectric breakdown field could sometimes be influenced by secondary effects such as field 1070-9878/10/$25.00 © 2010 IEEE Authorizedlicensduselimtedto:IEXplore.dDownlaeonMay13,20at1:529UTCfromIEXplore. nsRetricoaply. www.DownloadPaper.ir IEEE Transactions on Dielectrics and Electrical Insulation Vol. 17, No. 1; February 2010 distortion due to space charge, temperature increase due to local heating and thickness deformation due to Maxwell stress [15, 16]. The temperature dependence of the dc dielectric breakdown field (EBR) of polymers usually shows a decreasing behavior with increasing temperature. However, this decrease appears as non-linear displaying different slopes in the EBR thermal dependence, as shown in Figure 1. Dielectric breakdown field EBR (II) low critical temperature (T<TC1) and is roughly not depending of the temperature despite in some cases below room temperature, a slight increase can be observed [16]. The second one is the thermal breakdown process appearing for an intermediate temperature range (TC1<T<TC2). It is initiated by the steady state or impulse thermal processes. Finally, above a high critical temperature (T>TC2), an electromechanical mechanism is preferred due to deformations and softening of polymers induced by the electrostatic forces between the test electrodes. (III) (I) 2.2 STATE OF THE ART OF THE DIELECTRIC BREAKDOWN FIELD OF POLYIMIDES Few papers present a combined study (thickness, electrode area and temperature) of the dielectric breakdown field of PI. Table 1 shows a review of the dielectric breakdown field values of PI found in the literature, varying with different experimental parameters [8–11, 17– 25]. A wide range of EBR values has been reported up to now, usually between 1 and 5 MV/cm, but the influence of the different parameters is not clearly identified when combined to another one particularly if extrapolation laws are under concerns. Last, a statistical approach of the dielectric breakdown phenomenon is not always used to provide accurate and comparable results. It, nevertheless, constitutes the state of the art regarding the thickness, area and temperature dependence of the dielectric breakdown field of PI. Typical experimental curve TC1 TC2 19 Temperature (I): T<TC1; Electronic avalanche breakdown (II): TC1<T<TC2; Thermal and electro-thermal breakdown (III): T>TC2; Electromechanical breakdown Figure 1. Typical temperature dependence of the dielectric breakdown field of polymers and the failure processes related (after [15]). Three breakdown processes are usually cited. The first one is the electronic avalanche breakdown which is a pure electronic breakdown. This phenomenon occurs below a Table 1. State of the art of the dielectric breakdown field of PI varying with different experimental parameters. Thickness (µm) Electrode area Temperature (°C) Voltage form EBR (MV/cm) Atmosphere Ref. 0.017 – 0.021 0.1 – 0.5 mm2 -243 – 27 dc ~ 0.01 vacuum [17] 30 – 170 ac (10 Hz – 3 kHz) 2–4 vacuum [18] 20 – 250 dc: 200 V/s 1.2 – 3 SF6, N2 and dry air [9] -100 – 200 dc 1.9 – 5 vacuum [10] 0.12 – 0.4 0.4 – 1.6 2 5 × 5 mm 2 0.15 – 0.4 cm 0.8 – 2 13 – 125 Ø 5 mm 25 ac (50 Hz): 500 V/s DC: 500 V/s 3.1 – 4 5 – 5.2 transformer oil / dibutyl phthalate (DBP) [19] 13 – 175 Ø 5 mm 25 ac: 500 V/s 0.8 – 3.75 transformer oil / DBP [20] 25 Ø 0.2 mm 90 dc: 30 V/s 4.7 – 5.2 silicone oil [21] -196 ac: 500 V/s 1.8 – 3.4 liquid N2 [22] 25 dc: 200 V/s 2 – 3.5 air [11] 26 – 78 -196 – 300 dc: 0.5 – 10 kV/s 0.9 – 4.9 liquid N2, silicone oil [8] 125 23 – 160 dc: 5 kV/s 1.5 – 2 125 90 Pulse: 200 V, 5 ns 3 125 100 – 140 Step: 2 kV for 1 min 1.8 – 2.2 25 25 – 75 Ø: diameter. Authorizedlicensduselimtedto:IEXplore.dDownlaeonMay13,20at1:529UTCfromIEXplore. nsRetricoaply. Ø 1.25 – 5 cm [23] silicone oil [24] [25] www.DownloadPaper.ir S. Diaham et al.: Dielectric Breakdown of Polyimide Films: Area, Thickness and Temperature Dependence 20 3 EXPERIMENTAL 3.1 POLYIMIDE FILM PREPARATION The PI studied here is compound of a biphenyl tetracarboxilic dianhydride and a p–phenylene diamine (BPDA/PDA), as shown in Figure 2. O performed between 25 and 400 °C (± 1 °C checked with a thermocouple on the sample surface) thanks to a regulated Signatone heating chuck in an air-closed cell (i.e. homemade closed cell with a transparent glass upper face for no fresh air exchange with the environment). The heating rise rate was of 5 °C.min-1. A thermalization of the samples during 10 minutes at the studied temperature was achieved before the breakdown measurements. Figure 3 shows a schematic representation of the experimental set-up. Voltage control O N U O N HV probe * GPIB IEEE 488 DC voltage source U(t)=(U0/t0).t U0 VBR n -1 Probe station Faraday cage Air-closed cell K-type thermocouple Heating chuck -1 +5 °C.min t Heating system (25-400 °C) Temperature control HV Voltage source Top electrode U(t) PI film Substrate Lower electrode Figure 3. Schematic representation of the experimental set-up. Pre-breakdown current-voltage characteristics have been measured using a source meter Keithley 2410 (0–1100 V) owning an internal ammeter. Figure 4 shows a typical result of the measurement of the pre-breakdown current for a linear applied voltage rising. 0 10 UBR 496 -1 10 -2 Authorizedlicensduselimtedto:IEXplore.dDownlaeonMay13,20at1:529UTCfromIEXplore. nsRetricoaply. T RS 232 -3 I (A) 397 dE = 200 kV .cm −1 .s −1 dt 10 3.2 MEASUREMENT SET-UP Dielectric breakdown field measurements have been performed using a dc voltage ramp supplied by a 3.5 kV FUG voltage source connected to the sample through a probe station using HV insulated needles fixed to precision xyz-micropositioners S725 from Microworld. Prior to the measurements, the needles have been disposed on the top of the electrodes with a high precision using a microscope. The equivalent dc electric field rising was controlled using a software program and was set to 200 kV.cm-1.s-1. The breakdown field was identified when the voltage source switched into current source supplying a shortcircuit current (ISC) set to 20 mA. The maximum voltage supplied was also recorded using a voltmeter connected to the source via a HV probe and was considered as the breakdown voltage. Measurements followed the D149-97a ASTM norm related to the breakdown of solid dielectric materials [27]. High temperature measurements have been -1 dE/dt=200 kV.cm .s Figure 2. Chemical structure of the BPDA/PDA polyimide [4]. PI films have been obtained from a polyamic acid (PAA) precursor dissolved in N-methyl-2-pyrrolidone (NMP) solvent. PI coatings have been obtained by dispensing subsequently an adhesion promoter and the PAA solution on golden stainless steel substrates (16 cm2), followed by a spin-coating at 4000 rpm during 30 seconds and a progressive soft-bake up to 175 °C for 3 minutes on a hot plate in air. For higher film thicknesses, multilayer coatings have been realized using the same process. The coatings have been finally cured at 400 °C for 1 h in an oven under nitrogen atmosphere in order to drive off the NMP solvent and to complete the imidization chemical reaction of the films. Three film thicknesses of 1.4, 3.6 and 6.7 µm have been used and measured thanks to a KLA Tencor profilometer (accuracy +/- 1 nm). Circular metal-insulator-metal (MIM) capacitor structures have been achieved by the thermal evaporation under vacuum of a gold metallization (150 nm) onto the PI film surface followed by the design of circular electrodes using a photolithographic process, as already presented elsewhere [26]. Five different diameters have been used from 0.3 to 5 mm corresponding respectively to areas from 0.0707 to 19.635 mm2. t t0 O 10 ISC=20 mA 298 -4 10 U (V) * 198 -5 10 99 -6 10 -7 10 0 5 10 15 20 25 0 30 Time (sec) Figure 4. Example of the pre-breakdown current measurement versus time for an applied DC voltage ramp. 3.3 SAMPLE POPULATION Due to the stochastic nature of the dielectric breakdown, measurements have been performed on 30-60 samples for each of the parameters under study (electrode area, film thickness and temperature). During measurements, the www.DownloadPaper.ir IEEE Transactions on Dielectrics and Electrical Insulation Vol. 17, No. 1; February 2010 breakdown craters have rarely been observed near the electrode edge (due to their neat circular design using microelectronic photolithographic masks, and also to the small film thicknesses). In almost all cases, the final location of the irreversible breakdown is near the center of the structure. A self-healing phenomenon has sometimes been observed only within the largest area tested electrodes (diameters Ø = 2.5 and 5 mm). In this case, few healedcraters (~1 to 3) scattered within the metallization before the irreversible breakdown were observed, as seen in Figure 5a. The self-healing craters within the metallization (in a poor quantity compared to other works [9]) are here preferably related to a local extrinsic contamination during the coating process. SEM images from Figures 5b to 5d show a typical selfhealing crater at different scales. A central puncture can be observed in the crater. It corresponds to the breakdown channel through the PI film caused by the arcing (cf. Figure 5b). All around this path, an extended dark carbonized region (region 3 in Figure 5c) with PI peelings at surface film is observed up to the metalized edge of the crater. This appears as a consequence of a local heating. The main breakdown channel is around 30 m in diameter. It lets appear the lower electrode of the MIM structure below the PI film (cf. Figure 5d). Figure 5e shows the profilometer scan across the self-healing crater of Figure 5b. It is possible to observe in the regions 4 and 5 the location of the main breakdown channel through the PI bulk. It is also possible to observe two sharp peaks at the edge of the crater that correspond to a roll of melted gold (see also in Figure 5b in region 2). The melting temperature of gold (Tm= 1064 °C) shows the very high local temperature involved during the breakdown process. The huge diameter of the crater (~300 m), ten times wider than the main breakdown channel, is certainly due to the release of the electrostatic energy stored in the MIM capacitance strongly associated with thermo-mechanical constraints involved by the local heating around an extrinsic defect. failure F( )=63.2%, is the shape parameter. A high – value is related to a low scattering of the data. The location (or threshold) parameter has been set to zero. (a) Irreversible breakdown craters Self-healing craters 2 mm 4 1 (1) where UBR is the breakdown voltage and d is the film thickness. Experimental data have been statistically analysed using the Weibull distribution law [28]: F ( x) = 1 − e ⎛ x −γ ⎞ −⎜ ⎟ ⎝ α ⎠ β (2) where F(x) is the cumulative probability of failure, is the scale parameter (V/cm) corresponding to a probability of Authorizedlicensduselimtedto:IEXplore.dDownlaeonMay13,20at1:529UTCfromIEXplore. nsRetricoaply. 3 (c) 4 3 (d) 3 4 2,8 (e) 2 2,1 2 Height (μm) U BR d (b) 2 3.4 STATISTICAL ANALYSIS Dielectric breakdown field under homogeneous conditions has been calculated using the following relation: E BR = 21 crater width 1,4 1 1 0,7 3 3 4 0,0 -0,7 5 -1,4 0 100 200 Width (μm) 300 400 Figure 5. Breakdown craters observed within the test electrodes (a). SEM images of a self-healing crater (b, c, d). Profilometer scan across a breakdown crater for a 1.4 m-thick PI film (e). 1: edge of the safe gold electrode around the crater; 2: roll of melted gold around the crater; 3: carbonized PI film surface; 4: diameter of the main breakdown channel; 5: depth of the main breakdown channel corresponding also to the PI thickness. www.DownloadPaper.ir S. Diaham et al.: Dielectric Breakdown of Polyimide Films: Area, Thickness and Temperature Dependence The experimental data have been ranking using the median rank approximation given by [29, 30]: F (i, n) = i − 0.3 n + 0.4 (3) ⎡ ⎛ 1 ⎞⎤ ⎟⎟⎥ = β [log 10 ( x) − log 10 (α )] log 10 ⎢log e ⎜⎜ ⎝ 1 − F ( x) ⎠⎦ ⎣ 0 10 2 where i and n are the rank of a failed sample and the total number of tested samples, respectively. For plotting the Weibull distribution law, the transformation of equation (2) into equation (4) has been realized: the material bulk leading to the failure of the insulating layer. This behaviour has already been reported in organic materials such as polypropylene [32, 33], aramid paper, polyester mylar and Kapton-H films [11], but also in liquids [34, 35] and gases [36]. Last, it may be seen that the temperature has an effect on the Weibull parameter values that will be discussed in section IV.3. j (A/cm ) 22 (4) The Weibull parameters have been extracted considering a confidence interval of 90 %. Both the maximum likelihood and least square fit methods have been also applied leading to similar – and –parameter values [31]. 10 -4 10 T=25 °C -6 10 3,0 3,5 4,0 4,5 5,0 5,5 6,0 E (MV/cm) -1 10 (b) Ø 0.3 mm Ø 0.5 mm Ø 1 mm Ø 2.5 mm Ø 5 mm 2 j (A/cm ) 3.5 PRE-BREAKDOWN CURRENT-VOLTAGE CHARACTERISTICS Figure 6 shows an example of the conduction current density in PI films versus the applied electric field at 25 and 300 °C for different electrode diameters. A good superimposition of the current densities is observed for all the electrode areas investigated. PI films may therefore be considered of homogeneous quality whatever the investigated area. Hence, it is also acceptable to assume that the breakdown current mechanisms are mainly related to the material bulk and not to edge effects. -2 (a) Ø 0.3 mm Ø 0.5 mm Ø 1 mm Ø 2.5 mm Ø 5 mm -3 10 T=300 °C -5 10 2,00 2,25 2,50 2,75 3,00 3,25 3,50 E (MV/cm) 4 RESULTS AND DISCUSSION Figure 6. Pre-breakdown conduction current density in PI films versus applied electric field in the high field region for different electrode diameters at 25 °C (a) and 300 °C (b). (Film thickness d=1.4 µm). 4.1 ELECTRODE AREA EFFECT ON THE WEIBULL PARAMETERS Figure 7 shows the cumulative probability of failure in PI films both at room temperature and 300 °C versus the dielectric breakdown field for the different electrode diameters. The values of the dielectric breakdown field ranged from 0.6 to 7 MV/cm depending on the temperature and the electrode area. These orders of magnitude are in agreement with those reported in [9] and [10] for equivalent PI film thickness ranges. For each temperature, it is possible to observe that the cumulative probability curve shifts slightly towards lower breakdown fields with increasing the electrode diameter. The scale parameter (F=63.2 %) decreases also with increasing the electrode diameter. In the same way, the shape parameter (i.e. the slope of the fitting straight line) decreases with increasing the electrode diameter. These two simultaneous observations deal typically with an increase in the result scattering. They usually are characteristic of an increase in the probability to find defects or impurities in For the lowest breakdown fields (F(x)<10 %), it appears that PI displays a deviating behaviour of the distribution of the breakdown field values. Indeed, another slope of the cumulative probability of failure with a lower value can be distinguished. Trying to fit a non-zero location parameter to the experimental data, a value close to the lowest dielectric breakdown field for each electrode area has been found. For the study of polymers, a natural location parameter could be the dielectric breakdown field of air (i.e. the minimum Paschen breakdown voltage ~300 V) due to the presence of vacuoles in the film. However, the thickness range investigated here is lower than the minimum vacuole diameter allowing the occurrence of partial discharges (~8 µm) and none of this kind of defects has been observed even by microscopy. Otherwise, there is no obvious physical or technological reason to take into account a nonzero location parameter. It appears more realistic to consider that there is another Weibull distribution law for low electric fields (not investigated here) [14], more Authorizedlicensduselimtedto:IEXplore.dDownlaeonMay13,20at1:529UTCfromIEXplore. nsRetricoaply. www.DownloadPaper.ir Vol. 17, No. 1; February 2010 pronounced with increasing the electrode area. A similar discussion has been reported by Laihonen et al. on polypropylene films [33]. The presence of two Weibull distribution laws across distinct field ranges could be due to two failure mechanisms of different nature. The first one occurring at low fields and more influent for large electrode areas could be related to the presence of macroscopic impurities in the MIM structure, while the second one appearing across the high field range could be explained by a thermal and/or electromechanical origin. 1 F (%) log10[loge(1/1-F)] T=25 °C 5 4 3 2 63.2 25 °C 200 °C 300 °C 340 °C 400 °C 1 0,01 27.1 (a) 0,1 1 10 100 2 Electrode area (mm ) 9.5 -1 Ø 0.3 mm Ø 0.5 mm Ø 1 mm Ø 2.5 mm Ø 5 mm -2 0,1 0.95 25°C 200°C 300°C 340°C 400°C 10 (a) 1 10 β EBR (MV/cm) 1 F (%) T=300 °C log10[loge(1/1-F)] 7 6 95.7 0 23 where kA and mA are empirical area coefficients. kA represents the extrapolated dielectric breakdown field for an area of 1 m2. α (MV/cm) IEEE Transactions on Dielectrics and Electrical Insulation 95.7 0 (b) 63.2 1 0,01 27.1 0,1 1 10 100 2 -1 Electrode area (mm ) 9.5 Ø 0.3 mm Ø 0.5 mm Ø 1 mm Ø 2.5 mm Ø 5 mm -2 0,1 Figure 8. Changes in the scale (a) and shape (b) parameters versus the electrode area and for different temperatures (film thickness d=1.4 µm). Solid lines represent the best fits given by equation (6). 0.95 (b) 1 Transformation of equation (5) into equation (6) allows obtaining kA and mA fitting linearly data in Figure 8a: 10 EBR (MV/cm) Figure 7. Cumulative probability of failure in PI films versus the dielectric breakdown field at 25 °C (a) and 300 °C (b) and for different electrode diameters (film thickness d=1.4 µm). Solid lines represent the best fits given by equation (4) considering a confidence interval of 90%. Figure 8 shows the changes in the scale and shape parameters versus the electrode area for different temperatures. Both the – and –parameters present a linear decrease in a bi-logarithmic plot with increasing the electrode area. Assuming that the weak points present in the material leading to a breakdown are randomly and uniformly scattered, it is known that the scale parameters used to decrease with increasing the electrode area following the area extrapolation law given by [31, 34, 36]: α ( A) = k A A 1 − mA Authorizedlicensduselimtedto:IEXplore.dDownlaeonMay13,20at1:529UTCfromIEXplore. nsRetricoaply. (5) log 10 (α ) = log 10 ( k A ) − 1 log 10 ( A) mA (6) Table 2 lists the changes in kA and mA versus temperature. These parameters allow extrapolating the – parameter whatever the electrode area. It also appears that the dielectric breakdown field of PI remains high (above 1 MV/cm) even for large areas and high temperatures. Table 2. Evolution of the kA and mA coefficients from equation (6) versus temperature for a PI film thickness of 1.4 µm. Temperature (°C) kA (MV/cm) mA 25 2.33 18.64 200 2.02 20.92 300 1.88 24.06 340 400 1.14 0.61 15.05 9.87 www.DownloadPaper.ir S. Diaham et al.: Dielectric Breakdown of Polyimide Films: Area, Thickness and Temperature Dependence The decrease in with increasing the electrode area (cf. Figure 8b) shows also the widening of the Weibull distribution law related to a higher dispersion of the breakdown measurements for large electrodes. The slopes of the area extrapolation law for the –parameter range between 0.18 and 0.32. 4.2 THICKNESS EFFECT ON THE WEIBULL PARAMETERS The influence of the thickness on the Weibull parameters has also been investigated. The impact of the PI film thickness has only been studied for the lowest electrode area (diameter Ø = 0.3 mm) to avoid the occurrence of two Weibull distribution laws. It is also assumed that the breakdown is intrinsic. Figure 9 shows the cumulative probability of failure in PI versus the dielectric breakdown field for the different thicknesses investigated. As expected, a unique Weibull distribution law is observed. 1 (8) 5 4 3 2 300 °C 400 °C 1 95.7 0 1 log 10 (d ) md Values of md in the range from 0.16 to 0.25 have been obtained between 300 and 400 °C. This result is in good agreement with typical values found in the literature for polymers and for such a little variation of the thickness. Usually, the md coefficient tends towards 0.5 for higher changes in the thickness [38]. F (%) T=300 °C 1 2 3 4 5 6 7 8 Thickness (µm) 63.2 Figure 10. Changes in the scale parameter versus the PI film thickness (electrode Ø 0.3 mm). Solid lines represent the best fits given by equation (8). 27.1 9.5 -1 0.95 1.4 µm 3.6 µm 6.7 µm -2 1 10 EBR (MV/cm) Figure 9. Cumulative probability of failure of PI versus the dielectric breakdown field for different film thicknesses (T=300 °C; electrode Ø 0.3 mm). As for the electrode area dependence, the –parameter shifts towards lower field when the film thickness increases. However, unlike the area case, the slope of the Weibull distribution law (i.e. the –parameter) increases with increasing the film thickness. The first observation leads to show that the dielectric breakdown field is affected by the thickness increase due to the increase in the probability to find defects or impurities in the bulk of the insulating layer leading to the failure. Such a behavior has already been observed in PI films [8, 10, 19, 20]. Reporting the –parameter values in a plot versus the PI film thickness (cf. Figure 10), it seems that the scale parameter obeys to the following thickness extrapolation law [36, 37]: α (d ) = k d d − m d (7) where kd and md are empirical thickness coefficients. Transformation of equation (7) into equation (8) allows obtaining kd and md fitting linearly data in Figure 10: Authorizedlicensduselimtedto:IEXplore.dDownlaeonMay13,20at1:529UTCfromIEXplore. nsRetricoaply. The second observation was unexpected. Indeed, the shape parameter shows an increase with increasing PI thickness (cf. Figure 11). It could be a priori supposed that when the probability to find defects into the bulk increases, an increase in the scattering of the breakdown and a decrease in the shape parameter value ought to be observed. This atypical behavior has already been discussed in the literature for thin oxides and seems to be related to percolation theories [39–41]. 2 10 β log10[loge(1/1-F)] log 10 (α ) = log 10 ( k d ) − α (MV/cm) 24 1 10 300 °C 320 °C 340 °C 360 °C 380 °C 400 °C 0 10 1 2 3 4 5 6 7 8 Thickness (µm) Figure 11. Changes in the shape parameter versus the PI film thickness (electrode Ø 0.3 mm). It has been shown that the shape parameter decreases as a result of scaling-down of oxide thickness. The reduction of the shape parameter with decreasing oxide thickness has been attributed to the decrease in the critical defect www.DownloadPaper.ir Vol. 17, No. 1; February 2010 4.3 TEMPERATURE EFFECT ON THE WEIBULL PARAMETERS As presented in section 2.1, the typical change in the dielectric breakdown field of polymers usually decreases with increasing temperature even if, in some cases below room temperature, a slight increase can be observed [15, 16]. This decrease is usually due to thermal and/or electromechanical processes. In PI materials, the widest and highest temperature region of investigation found in the literature up to now has been reported by Nagao et al in PMDA/ODA from -196 to 300 °C using a dc electric field rising rate of 200 kV.cm-1.s-1 [8]. These authors observed a slight increase in the dielectric breakdown field from -196 to 25 °C, before measuring an exponential decrease up to 300 °C. A higher temperature range of investigation has been studied here (up to 400 °C) as long as the dielectric breakdown field remained high (≥2 MV/cm) even above 300 °C. This high temperature range was also motivated by both theoretical and application interests. The observed behavior corresponds exclusively to values of EBR measured before the beginning of thermal ageing phenomena that can occur usually at long-term above 300 °C (usually over several hours). So, it can be considered here that ageing phenomena have no time to occur due to the fastness of measurements. Figure 12 shows the changes in the scale parameter versus temperature from 25 to 400 °C and for the different electrode diameters under study. Exponential decreases in the dielectric breakdown field appear with increasing temperature except for electrodes of 0.3 mm in diameter (linear behavior). Even if the dielectric breakdown field decreases with increasing temperature, no dramatic drop has been observed at a critical temperature. This is certainly due to the absence of a glass transition phenomenon across the whole temperature range of investigation, as shown in [42]. The dielectric breakdown field of PI shows also a behavior close to the one of the region II of the Figure 1, just between the two critical temperatures (TC1<T<TC2) and where TC2 often corresponds to the glass transition temperature. So, a thermal origin of the breakdown process is maybe supposed as the most probable failure mechanism. PI films with various electrode areas have shown a dielectric breakdown field from 4.3 to 6 MV/cm and from 1.9 to 3.3 MV/cm, respectively at 25 and 400 °C. For a given electrode diameter of 0.3 mm (as seen in Figure 10), Authorizedlicensduselimtedto:IEXplore.dDownlaeonMay13,20at1:529UTCfromIEXplore. nsRetricoaply. 25 the dielectric breakdown field shows a slight decrease when the film thickness increases with values of the –parameter from 3.7 to 2.9 MV/cm and from 3.3 to 2.3 MV/cm, respectively at 300 and 400 °C. 7 6 α (MV/cm) 5 4 3 Ø 0.3 mm Ø 0.5 mm Ø 1 mm Ø 2.5 mm Ø 5 mm 2 1 0 0 50 100 150 200 250 300 350 400 Temperature (°C) Figure 12. Changes in the scale parameter versus temperature for different electrode diameters (film thickness d=1.4 µm). Figure 13 shows the high temperature dependence of the –parameter versus geometrical changes. Contrary to the – parameter, the –parameter is independent with increasing temperature. 2 10 Ø 0.3 mm Ø 0.5 mm Ø 1 mm β density required to form a breakdown path. It is evident that such a behavior may have a physical origin that cannot be resolved experimentally with the statistical accuracy even with large experimental data, as seen in Figure 9. However, the values obtained here from 8 to 30 are of the same order and show the same tendency than those reported by Laihonen et al on polypropylene films across the similar thickness range [33]. Up to now, no clear interpretation has been proposed for explaining such an increase. On-going works have recently started in order to explain this behavior. Ø 2.5 mm Ø 5 mm 1 10 (a) 0 10 300 320 340 360 380 400 Temperature (°C) 2 10 β IEEE Transactions on Dielectrics and Electrical Insulation 1 10 1.4 µm 3.6 µm 6.7 µm (b) 0 10 300 320 340 360 380 400 Temperature (°C) Figure 13. Changes in the shape parameter versus temperature for different (a) electrode diameters (film thickness d=1.4 µm) and (b) PI thicknesses (electrode diameter Ø = 0.3 mm). 26 www.DownloadPaper.ir S. Diaham et al.: Dielectric Breakdown of Polyimide Films: Area, Thickness and Temperature Dependence The only changes are induced by the geometrical parameters of the MIM structures with a main effect caused by the surface (see Figure 8b). It seems that the Weibull shape parameter, characterizing the density of defects (intrinsic or extrinsic) in the PI film, does not appear as a thermal activated parameter. So, the density of defects leading to the breakdown process should remain constant up to 400 °C. 5 CONCLUSION The dielectric breakdown field of polyimide (PI) thin films has been studied across the temperature range from 25 to 400 °C under dc conditions. This is the highest temperature range ever investigated up to now for this material. This study has mainly been motivated by both theoretical and application interests. Moreover, both the area and thickness dependences of the dielectric breakdown field have been carried out using the Weibull statistical model of failure. In summary, it appears that both the – and –parameters decrease with increasing electrode area following the area extrapolation law. This behavior translates naturally an increase in the result scattering and is characteristic of an increase in the probability to find defects or impurities underneath the electrode leading to a failure. Regarding the thickness changes at a given electrode area, only the –parameter shows a decrease with increasing PI thickness. The –parameter has presented an unexpected increase with increasing the thickness. Although this behavior has been often reported in the literature and can find some explanation thanks to percolation theories, this point of the study is still unclear. The effect of the temperature is characterised by a decrease in the dielectric breakdown field of PI with increasing temperature whatever the film thickness or the electrode area. 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Lai, “On the Weibull Shape Factor of Intrinsic Breakdown of Dielectric Films and Its Accurate Experimental Determination—Part II: Experimental Results and the Effects of Stress Conditions”, IEEE Trans. Electron Devices, Vol. 49, pp. 2141-2150, 2002. [42] S. Diaham, M. L. Locatelli, and T. Lebey, “High Temperature Dielectric Behavior of Al/Polyimide/Al Capacitor Structures”, IEEE Vonf. Electr. Insul. Dielectr. Phenomena (CEIDP), pp. 97-100, 2006. Sombel Diaham was born in Montauban, France, in 1982. He received the M.Sc. and Ph.D. degrees in electrical engineering, respectively in 2005 and 2007, both from the Paul Sabatier University of Toulouse, France. In 2005, he joined the LAPLACE laboratory in Toulouse where he has been since 2008 an Associate-Professor. His current research fields focus on the study of dielectric materials for the insulating environment (passivation and encapsulation) of high temperature and/or high voltage wide band gap semiconductor power devices (SiC, GaN and Diamond). His fields of interest cover from both the study of the physical properties of insulating materials and their reliability in high temperature, up to the study of their impact on the electrical characteristics of the devices. He is co-author of 6 communications in international scientific reviews and 8 papers in international conferences. View publication stats Authorizedlicensduselimtedto:IEXplore.dDownlaeonMay13,20at1:529UTCfromIEXplore. nsRetricoaply. 27 Samir Zelmat was born in Sidi Bel Abbes, Algeria in 1978. He received the Engineer degree in electrical engineering from Djilali Liabes University, Sidi Bel Abbes, Algeria in 2000, the M’Res degree and the Ph.D. degree in electrical engineering, respectively in 2002 and 2006 from Paul Sabatier University, Toulouse, France. From 2002 to 2007, he worked as an Assistant Professor at Paul Sabatier University, and the University of Poitiers, France. He currently works at LAPLACE Laboratory in Toulouse as a Research Associate Fellow. His research interests include dielectric materials and high temperature power electronic packaging. Marie-Laure Locatelli was born in Nantua, France, in 1965. She received the engineering degree in electrical engineering in 1988 and the Ph.D. degree in integrated electron devices in 1993 from the INSA of Lyon (France). As a Research Associate of the National Center of Scientific Research (CNRS) since 1993, she had been working at CEGELY Laboratory in Lyon for 8 years, on the study of silicon power device high temperature limitations, and on the study of new SiC power devices. Since 2001, she has been working at the LAPLACE laboratory in Toulouse. She studies dielectric materials suitable for the insulating environment of high temperature and/or high voltage wide band gap semiconductor dies (SiC, GaN and Diamond). She is co-author of 43 communications in international scientific reviews, and 50 papers in international conferences. Sorin Dinculescu was born in 1971 and obtained his electrical engineer degree in 1996 from the "Politehnica" University of Bucharest (Romania). He joined the Plasma and Energy Conversion Laboratory at the "Paul Sabatier" University of Toulouse in 1999 as a Research Engineer. His main fields of interest are in power electronics, from both an active devices point of view and their dielectric environnement. He is particularly dealing with different high power and/or high voltage characterisation and diagnostic setups and methods. Michaël Decup was born at Albi, France in 1982. He received the M.Sc degree in electrical engineering from Paul Sabatier Toulouse France University in 2007. At present, he is working at the Plasma and Energy Conversion Laboratory in order to obtain the Ph.D. degree in electrical engineering. He belongs to the Dielectric Materials and Energy Conversion team. His main research interest is to analyze the impact of fabrication and assembly technologies on the dielectric properties of ceramic substrates used in power electronic applications. Thierry Lebey (M’98) received the M.Sc. degree in solid state physics in 1984, his Ph.D. in electrical engineering in 1989, both from University Paul Sabatier in Toulouse. Since 1990, he is engaged with the French National Scientific Research Center (CNRS) where he is now Senior Research Scientist. He is the author of more than 60 journal and 100 conference papers and holds 8 international patents.