Polymeric Materials for Electronics Packaging and ... - ACS Publications

Chapter 15

Conduction Transients in Polyimides Herbert J. Neuhaus and Stephen D. Senturia

Downloaded by MICHIGAN STATE UNIV on February 18, 2015 | http://pubs.acs.org Publication Date: September 5, 1989 | doi: 10.1021/bk-1989-0407.ch015

Microsystems Technology Laboratories, Massachusetts Institute of Technology, Cambridge, MA 02139

Space charge effects in electrical measurements of polymeric insulators have received considerable attention (1-7). In polyimide (PI) the formation of space-charge at the electrode under bias has been cited as a factor contributing to a space-charge modified Schottky barrier at the metal-PI contact (8), and mobile ionic impurities have been shown to give rise to measurement-history effects (9). Control of insulator space-charge is critical to reproducibility of electrical response measurements. In this paper, reproducible, history-free PI conduction transients are reported. At temperatures above 200°C the transients observed in PI films with Al cathodes have a characteristic peak, the time of which is a function of temperature, voltage, and ionic impurity concentration. Transient currents of this form have not been previously reported in PI films. No peak is observed when A u cathodes are used. A simple model has been formulated which explicitly couples the space-charge due to ionic polarization and electronic conduction (10). Ion and electron transport are modeled as hopping mechanisms. Numerical techniques are employed to compute the current-time transient response to a constant applied bias which is compared to data from PI samples containing controlled ion content. PI, like many other insulating polymers, exhibits a complex transient response to an applied D C bias. The shape of the current-time transient varies with temperature. Figure 1 shows the PI transient current at several temperatures in A l PI-A1 parallel plate capacitors fabricated on Si substrates. The experimental method has been reported previously ( U ) . The BTDA - MPD A / O D A PI (DuPont Pyralin PI-2555) contains 1 ppm Na by weight in the cured film (12), and the film thickness is 3.3 microns. The measurements are made in in dry N , and the PI films are dried before measurement by heat-treatment at 150°C for 30 min. The bias (100V) is applied directly to the lower A l electrode, and the upper electrode and guard ring are held at ground potential. The current from the upper electrode is measured with a pico-ammeter. Any surface currents are shunted around the pico-ammeter via the guard ring. 2

0097-6156/89/0407-0176$06.00/0 c 1989 American Chemical Society

In Polymeric Materials for Electronics Packaging and Interconnection; Lupinski, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

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Conduction Transients in Polyimides


1E-5

1E-6

1E-7

1E-8U

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1E-10b-

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100 1000 log T i m e (sec)

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Figure 1. Transient currents in A1-PI-A1 structure at various temperatures. The 3.3 micron film is a B T D A - MPD A / O D A PI, and is subjected to 100V. A1-PI-A1 structure is used. Between each transient, the sample is discharged at 370°C for 10,000 sec. (Reproduced with permission from Ref. 10. Copyright 1989 M.I.T.)



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History-effect problems are worsened at elevated temperatures. Wash-out of the transient structure occurs if the sample is not fully discharged between measurements. At a given temperature, discharge proceeds more slowly than charging. For this reason, the sample is heated to 370°C to discharge for 10,000 sec before each transient is recorded. This procedure results in stable and repeat able transient data. At temperatures above 200°C the history-free transient has a characteristic peak, the time of which is a function of temperature, voltage, and ion concentration. No such PI transients have been previously reported. Near 200°C, the current is nearly constant for more than two hours before turning up to the peak. The voltage dependence of the transient current in the as-received (1 ppm Na) material is shown in Figure 2 for voltages between 10 and 100V. Controlled introduction of Na has been used to prepare PI films containing 30 ppm Na. The method of Na-doping has been reported earlier (12). Figure 3 shows the voltage dependence of the transient current in the 30 ppm Na films. A direct comparison of the effect of Na is made in Figure 4 for the 10 and 100V data. The peak time is shorter for higher voltages and longer for higher Na levels. The current increases with voltage and Na concentration. The charge under the current-time curves has been calculated by numerical integration and compared to the amount of charge due to Na ions. In Figure 4 the time at which the charge transported equals the Na charge is indicated by the arrows. At long times the total charge transported is much greater than the Na charge. The transients in Al-PI-Au samples (Au upper electrode) are compared to A1-PI-A1 data in Figure 5. The transient current in A1-PI-A1 samples is polarity independent. In Al-PI-Au sample the transient peak is observed only for A l cathode polarity, but the peak current is smaller than in the A1-PI-A1 case. For the Au-cathode polarity no peak is observed within 10,000 sec, however, the current is not monotonically decreasing. Model The data show that true steady state conduction is established only on a time scale of days or longer, even at elevated temperatures. Therefore, examination of steady currents is a formidable task. A quantitative model of the transient response in PI would permit useful data collection on a shorter time scale. The salient features of a model for the metal-PI-metal system are reviewed here. An exhaustive treatment has been given elsewhere (10). Electrical conduction is modeled as a two carrier system: positive mobile ions which are blocked at the electrodes, and electrons which may be injected or ejected at A l PI contacts. The Al-PI contacts are represented as ideal ohmic contacts. This means (1) none of the applied voltage is dropped at the contact, and (2) an accumulation of injected electrons forms in the PI near the contacts. Such a contact corresponds to the insulator work-function being greater than that of the contacting metal. Since the work-function of A l (4.3 eV) is smaller than that of Au (5.1 eV), one expects the Al-PI contact to be a better electron injector than the Au-PI contact. The behavior of such a system is easy to predict in the absence of mobile ions. Ohmic contacts and a high resistivity bulk give rise to a bulk-controlled or space-charge limited currents (Li). A complete analysis of the space-charge limited transient current in insulating crystals has been given (14). The analysis in polymers is modified by the presence of mobile ionic impurities in two ways. First, in thermal equilibrium the bulk ion and electron concentrations must be



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Figure 2. Variation of transient with voltage in as-received (1 ppm Na) films with A l electrodes. Temperature is 300°C. (Reproduced with permission from Ref. 10. Copyright 1989 M.I.T.)



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Figure 3. Variation of transient with voltage in films doped with 30 ppm Na and A l electrodes. Temperature is 300°C. (Reproduced with permission from Ref. 10. Copyright 1989 M.I.T.)



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Figure 4. Comparison of voltage dependence in 1 ppm and 30 ppm films. Temperature is 300°C. The time at which the charge transported equals the Na charge is indicated by the arrows. (Reproduced with permission from Ref. 10. Copyright 1989 M.I.T.)



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300°C AI-PI-AI

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cathode

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Figure 5. Comparison of transient currents in A1-PI-A1 and Al-PI-Au samples. Current is polarity independent in A1-PI-A1 samples. Two polarities are shown for Al-PI-Au samples. A u is upper (air side) electrode. Voltage is 100V and temperature is 300°C. (Reproduced with permission from Ref. 10. Copyright 1989 M.I.T.)



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equal to ensure bulk neutrality. Second, the mobile ions drift under bias toward the cathode and modify the space-charge field in the PI. The result is a twocarrier, single-injection, ion-modified space-charge limited transient. In the usual space-charge limited theory, electrons are injected into the insulator conduction band, and some of these electrons are immobilized in localized defect states. We have considered an alternate mechanism more appropriate to the polymer structure. Contact charge transfer studies in Polyethylene Terephthalate (PET) and other polymers (15-16) suggest that the electronic states accessible from metal contacts are localized molecular-ion states located deep in the forbidden energy gap. Charge transport is by hopping between localized states. Carrier transport in the PI is calculated using a hopping formalism due to Iwamoto (17-18). The hopping formalism reduces to ordinary drift and diffusion in the limit of hopping length goes to zero. Electrons and ions move through two distinct sets of sites or wells, each with a characteristic potential height and hopping length. The potential barrier between wells is modified by the electric field near the wells. We have considered only one species of ion and have assumed the total number of ions is fixed. The extensions to more general cases, such as more than one species or a temperature dependent ion concentration, are obvious. We have neglected the thermal or electron-hole pair contribution to conductivity. The electric field in the film is calculated from the Poisson equation along with the constraint placed on the integral of the field by the fixed applied voltage. For each of a series of time steps, the carrier fluxes are calculated from the electric field and carrier concentrations. The time evolution of the system is calculated using fourth order Runge-Kutta integration of the carrier flux equations. Finite differences are used for spatial functions. The external current is given by the sum of injection and displacement currents. Comparison of Calculated and Experimental Transients The calculated current-time transient for A1-PI-A1 are shown in Figure 6. The solid curve shows the behavior of the system if the ionic impurities are present but immobile. This corresponds to the space-charge limited transient in an insulating crystal with slow trapping (14). The behavior at short time is related to electron diffusion near the contacts, while the long time behavior is related to the propagation of the electronic space charge front across the film. Figure 7 shows the time-evolution of the total space-charge distribution. Initially, the insulator is neutral except near the contacts. As electrons are injected the net space-charge becomes increasingly negative. The steady-state distribution has the characteristic x " dependence. The dashed curve in Figure 6 includes the effect of mobile ions. The initial current is greater due to the ionic contribution, but the steady current is not affected. A comparison of Figs. 7 and 8 shows the differences in space charge distribution due to mobile ions migrating to the cathode. With the simplified model described above, we may expect to reproduce only the gross features of the transient. Numerical agreement will require a more realistic model. As an example, Figure 9 compares the voltage dependence of both experimental and calculated transient currents. The shape of the model and experimental curves differ, but the variation with applied bias in both sets is similar. 1/2




184

Time 0 Time 1 T i m e 10 T i m e 100 T i m e 1000 T i m e 10000

-0.5 •

2.5E-5

5E-5 position

7.5E-5

•

*

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Figure 7. Calculated space-charge distributions at various times with fixed ions. Normalized times correspond to the time axis of Figure 1. (Reproduced with permission from Ref. 10. Copyright 1989 M.I.T.)



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2.5E-5

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1E-4

Figure 8. Calculated space-charge distributions at various times with mobile ions. (Reproduced with permission from Ref. 10. Copyright 1989 M.I.T.)


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1

300°C

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.

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. i)

100V Downloaded by MICHIGAN STATE UNIV on February 18, 2015 | http://pubs.acs.org Publication Date: September 5, 1989 | doi: 10.1021/bk-1989-0407.ch015

1E-6

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1E-8U 10 1E-9U

CALCULATED 1E-5

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50 10

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EXPERIMENTAL 1E-10 0.1

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Figure 9. Comparison of transients at various voltages. The conditions are: 3.3 micron thick, lppm Na by weight, 300°C, 50 electronic and 20 ionic wells. Each transient starts with uniform ion and electron distributions, except near the contacts.


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Discussion


PI Degradation. Because the transient measurements reported above are made at elevated temperatures, possible degradation of the PI must be considered. However, since the transient data are repeatable, we infer that the PI has not been significantly degraded during the bias-temperature exposure. Electrode Metal. The fabrication sequence used for A1-PI-A1 samples results in different histories for the upper and lower A l electrodes ( Π ) . In particular, the lower electrode is exposed to the PI cure cycle while the upper electrode is evap orated directly on to cured PI. However, the polarity independence of the tran sient current in the A1-PI-A1 samples indicates that the two A l electrodes are electrically equivalent. The Au-PI-Al samples are no longer symmetric. The observed behavior is consistent with electron injection at the Al-PI contact but not at the Au-PI con tact. The increase in work function in A u over A l implies a less effective elec tron injector. When the A l is biased negatively, a peaked space-charge limited transient is observed, and when the A u is biased negatively, the transient has no peak. Model. The comparison of theory and experiment in Figure 9 indicates that the simplified model can be used to calculate transients which agree with experiment in gross trends. The model permits quantitative analysis of bulk and contact space-charge effects in PI transient current measurements. In particular, this model is sufficient to calculate measurement-history effects due to mobile ions and bulk electronic space-charge (9). The relaxation of space-charge upon re moval of the bias is intrinsically slower than its accumulation. Thus, the sample history is stored in the space-charge distributions. These results will be demon strated in a future publication. To improve the agreement between model and experiment, several enhancements to the model are possible. This model can be extended to include less idealized injecting Al-PI contacts, and Au-PI contacts can be simulated as blocking contacts. Also, a more detailed picture of the distribution of electronic states can be employed. Implications. These results have an important implication concerning the use of Fourier analysis of D C transients in polymeric materials to extract the frequency-dependence of the dielectric response (12). In order for the principle of superposition to apply the electric field inside the material being measured must be time- and space-invariant. This critical condition may not be met in polymers which contain mobile ionic impurities or injected electrons. Experi mentally, we can fix only the average of the electric field. Moreover, our calcu lations demonstrate that the bulk field is not constant in either time or space. Thus, the technique of extracting the dielectric response from the Fourier com ponents of the transient response is fundamentally flawed because the contribu tion due to the formation of ionic and electronic space-charge to the apparent frequency-dependent dielectric response can not generally be separated from the dipole contribution. Similarly, the application of isochronal analysis to transient data (20) assumes that the time dependence of the transient response is independent of the parameter being varied. For example, plotting current at a particular time against temperature yields useful data only if the transient proceeds at a rate independent of temperature. However, the example of Figure 1 and transients calculated from the model have features which would appear as peaks in an iso chronal plot, yet are intrinsic to the conduction mechanism.


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Conclusions History-free, reproducible, transient currents are reported in as-received and Na doped PI films between 150 and 330°C. From a calculation of the total charge transported, purely ionic mechanisms can be ruled out, and an electronic con duction mechanism must be invoked. The electronic conduction is, however, modulated by the presence mobile ionic impurities. The current and total charge transported vary in proportion to the amount of Na ions in the film. Thus an ion/electron interaction in PI is postulated. When the cathode is A l a peak is observed in the transient, but not when the cathode is A u . This observation is consistent with a space-charge limited transient due to electron injection from the smaller work-function A l electrode. Ionic polarization and electron injection under bias result in a timedependent, non-uniform electric field within the films. If complete discharge of the space-charge is not permitted between measurements, apparently nonreproducible transient behavior results from the space-charge field. Reproduci bility is restored by high temperature discharge before each measurement. A simple quantitative model for the metal-PI-metal system has been presented. The model was used to calculate space-charge modified conduction transients in PI. The calculated transients model the gross trends observed in experimental data. The effect of mobile ions is to change the shape of the current transient, but the steady current is not strongly dependent on ionic con centration. It has been shown that a detailed analysis of the formation of spacecharge during electrical measurements is critical to the understanding of tran sient phenomena in insulating polymers.

This work was supported in part by Ε. I. DuPont de Nemours & Co. Sample fabrication was carried out in the Microsystems Technology Laboratories and in the Microelectronics Laboratory of the Center for Materials Science and Engineering, which is supported in part by the National Science Foundation under Contract DMR-84-18718. The assistance of Melissa Frank in searching the literature is gratefully acknowledged. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9.

Lengyel, G . J. App. Phys. 1966, 37, 807. Lilly, Α.; McDowell, J. J. App. Phys. 1968, 39, 141. Wintle, H . J. App. Phys. 1971, 42, 4724. Miyairi, K ; Ieda, M . Elec. Eng. Japan 1976, 96, 14. K o , Α.; Hirsch, J. Solid State Commun. 1981, 39, 215. Lewis, T.J. IEEE Trans. Elec. Insul. 1984, EI-19. 210. Ieda, M . Int. Conf. Props. and App. Diel. Mat., 1986, p. 17. Sessler, G.; Hahn, B.; Yoon, D . J. App. Phys. 1986, 60, 318. Neuhaus, H.; Feit, Z.; Smith, F.; Senturia, S. In Recent Advances in Polyimide Science and Technology; Weber, W.; Gupta, M . , Eds.; Soc. of Plastic Eng.: Poughkeepsie, N Y , 1987; p 362. 10. Neuhaus, H . Ph.D. Thesis, Mass. Inst. Tech., Cambridge, Mass, 1989. 11. Smith, F.; Neuhaus, H.; Senturia, S.; Feit, Z.; Day, D.; Lewis, T.J. J. Elec. Mat. 1987, 16, 93. 12. Neuhaus, H.; Day, D.; Senturia, S. J. Elec. Mat. 1985, 14, 379.



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13. Lampert and Mark, Current Injection in Solids, Academic Press, New York (1970). 14. Many, Α.; Rakavy, G . Phys. Review 1962, 126, 1980. 15. Fabish, T.; Duke, C. A n . Rep.: Conf. Elec. Ins. Diel. Phenom, 1977, p. 175. 16. Duke, C. Mat._Sçi. 1984, Vol. X, 341. 17. Iwamoto, M . ; Hino, T. Elec. Eng. Japan 1980, 100, No. 2, 9. Translated from Denki Gakkai Ronbushi 1980, 100A, 213. 18. Iwamoto, M . ; Hino, T. Elec. Eng. Japan 1980, 100, No. 3, 9. Translated from Denki Gakkai Ronbushi 1980, 100A, 299. 19. Mopsik, F. IEEE Trans. on Elec. Ins. 1985, EI-20, 957. 20. Das-Gupta, D.; Brockley, R. A n . Rep.: Conf. Elec. Ins. Diel. Phenom. 1977, p. 197. RECEIVED

February 23, 1989


Polymeric Materials for Electronics Packaging and ... - ACS Publications

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