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Characteristics of plasma generated by polysilicon semiconductor bridge (SCB)
Sensors and Actuators A 96 (2002) 252±257
Characteristics of plasma generated by polysilicon semiconductor bridge (SCB) Kye-Nam Leea, Myung-Il Parka, Sung-Ho Choia, Chong-Ook Parka,*, Han S. Uhmb a
Department of Material Science and Engineering, KAIST, Solid State Devices Laboratory, 373-1 Kuseong-Dong, Yuseong-ku, Taejon 305-701, South Korea b Department of Molecular Science and Technology, Ajou University, San 5 Wonchon-Dong, Paldal-Gu, Suwon 442-749, South Korea Received 14 December 2000; accepted 1 November 2001
Abstract In an effort to elucidate the plasma generation mechanism of the semiconductor bridge (SCB), currents were forced to ¯ow through a polysilicon bridge with a resistance of 1 O, while the voltage drop was measured to obtain the in situ power dissipation through the bridge. The energy stored in a 25 mF capacitor was used to activate the plasma. The typical behavior of two peaks in the voltage±time curve was observed. It is inferred from the photodiode signal that the second peak in the voltage curve results from the plasma generation of the bridge material. The breakdown voltage of the electrical discharge at high pressure proved that the SCB is an effective plasma generator. The experimental data for the no-®re condition, directly related to the safety of the explosive system, is compared with the analytical results from a theoretical model. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Plasma; Semiconductor bridge; No-®re condition; Igniter
1. Introduction The plasma generated from the semiconductor bridge (SCB) is sometimes used to ignite the explosives, where the heavily doped polysilicon in contact with powder gets melt and evaporated to form a high pressure of plasma upon introduction of large currents through SCB [1]. Because the typical value of the bridge resistance is about 1 O, the bridge is ohmic-heated through the electrical current. The SCB may melt down and eventually evaporate if enough electrical energy is deposited into the bridge within a limited time. Once the bridge material is vaporized, the applied electric voltage breaks down the vaporized silicon gas, generating silicon plasmas called the late-time discharge [1]. This plasma will eventually ignite the explosive materials. The SCB works within a few microseconds compared with the milliseconds response of a conventional hot-wire unit. It also functions at a few millijoules of energy, which is one-tenth of the input energy of a conventional hot-wire unit [2]. The plasma generation mechanism of the SCB was investigated in this article by comparing the measured energy from the SCB with the theoretically calculated energy of the * Corresponding author. Tel.: 82-42-869-4218; fax: 82-42-869-3310. E-mail address: [email protected] (C.-O. Park).
mass of the bridge. The breakdown voltage for the electrical discharge is described in terms of the ionization properties of the gas and the gas pressure. In addition, a theoretical model for the no-®re condition, which is directly related to the safety of the explosive system, is developed and compared with experimental data. 2. Experiment of plasma generation and no-fire condition A typical SCB device is schematically illustrated in Fig. 1. The bridge is formed from the heavily doped H-shaped region enclosed by the dashed lines in the ®gure. The thickness of the bridge is determined by that of the polysilicon ®lm deposited onto the silicon dioxide (SiO2) layer. The insulating layer of SiO2 enables the heat to concentrate on the bridge when the SCB device is functioning. The bridge width, W is decided from the shape of the doped region. The aluminum lands determine the length, L of the bridge and provide the means for electrical contact with the underlying polysilicon layer. A conventional CMOS process was used to fabricate SCB chips as shown in Fig. 2. A silicon dioxide layer, about 2 mm thick, was formed on the silicon substrate by means of
0924-4247/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 ( 0 1 ) 0 0 8 3 6 - 6
K.-N. Lee et al. / Sensors and Actuators A 96 (2002) 252±257
Fig. 1. Schematic view of a typical SCB.
thermal oxidation. For n-type devices, phosphorous was diffused into polysilicon to give a heavy doping concentration of 1020/cm3 using a phosphorous oxy-chloride (POCl3) source. In the case of a p-type device, boron was implanted into exposed regions of the wafer by a high current ion implantor. Once the bridge shape had been de®ned, the sputtered aluminum was deposited on polysilicon, which provides an electrical contact with the SCB. In order to make a 1 O bridge with dimensions of 20 mm length 90 mm width 2 mm thickness, the polysilicon layer was doped with a concentration of 1020 phosphorous atoms/cm3. The devices were packaged into TO5 cans with 1 ml (0.025 mm) gold wire of ball bonding joining the aluminum lands to the package pins. For the evaluation of SCB discharge behaviors, a fast photodiode (FPD) was combined with a ®ring circuit to record the emission of plasma light and electrical features simultaneously from a single-shot discharge of the bridges.
Fig. 2. Processing procedure for SCB fabrication.
253
For the simultaneous measurement of the voltage across the SCB and the output signals of the photodiode, a fast digital oscilloscope was used. A capacitor discharge ®ring set was selected in the electrical test. It consists of a capacitor (25 mF), a fast switch circuit and dc power supply. The fast switch circuit includes a driver (Telcom Ltd., high-speed MOSFET Driver) and a timer (Samsung Electronics Ltd., Single Timer KA555/I) that functions to open a capacitor charged with dc voltage during a period of 30 ms. The light emitted from the device was measured using a photodiode (Newport Biased Detector, 818-B8-21A). To perform a no-®re current test, a direct current is passed through the SCB for 5 min. It is loaded with ZPP powder, 60 mg. The ``up and down'' or Bruceton technique [3] was selected for obtaining the explosive data. This means choosing an initial voltage, h0, and a succession of higher voltages, h1, h2, h3 above h0 together with a succession of lower voltages h 1, h 2, h 3, . . .. If the ®rst specimen explodes, the second specimen will be tested at h 1, otherwise the second specimen will be tested at h1. In general, any specimen will be tested at the level immediately below or immediately above the level of the previous test according to whether or not there was an explosion in the previous test. 3. Experimental results and discussions 3.1. Plasma generation mechanism from SCB We measured the resistances of SCB by a four-point probe method during the manufacturing process. But, in the test the resistance of SCB includes those of wires and pads, which are negligible in our case compared with that of SCB. The voltage and current measured across the SCB during the test are shown in Fig. 3, where the letters V, I, P, and E represent the voltage, current, electrical power, and the
Fig. 3. Electrical characteristics of SCB. The letters V, I, P, and E represent the voltage, current, electrical power, and the energy deposited on the bridge, respectively.
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energy deposited on the bridge, respectively. Two peaks in the voltage±time curve occur at 250 ns (®rst peak) and 600 ns (second peak), with the current reaching its maximum at the second peak. The power dissipated in the device is calculated from the measured current and voltage. The energy dissipated in the SCB can be obtained by integrating the power with respect to time and is superimposed in Fig. 3. The mass of silicon in the bridge is calculated to be 8:4 10 9 g for a SCB device with dimensions of 90 mm wide, 20 mm long and 2 mm thick. The liquefaction energy and vaporization energy of the mass can be theoretically calculated to be 0.0248 and 0.1052 mJ, respectively by making use of the thermodynamic data of the silicon, such as speci®c heat, density (2.33 g/cm3) and atomic weight (28.086 g/mol). Assuming that there is no heat loss through the substrate during this short operation time, these energies correspond to the energy accumulated, up to 400 and 550 ns in Fig. 3 for the melting and vaporization, respectively. Therefore, it may be concluded that the ®rst peak results from the melting of the bridge, and that the vaporization is complete before the second peak appears. Benson et al. [1] have ascertained through high-speed framing camera images of the bridges that the ®rst peak in Fig. 3 corresponds to the initial silicon heating prior to the onset of silicon vaporization at the second peak. According to their experiment, once the bridge is vaporized, the current ¯ows through the vapor producing heated plasma (5000 K). It is obvious that the silicon bridge undergoes phase changes or transitions. It seems that the melting gives rise to an abrupt increase in the resistance of the bridge, which produces the ®rst voltage peak. The open circuit created by the bridge melting (especially at the edges) causes the resistance of bridge to increase instantaneously. The resistance remains relatively low after the ®rst peak because the vapor produced by the phase changes of the silicon bridge is utilized as a current path. Since the SCB devices produce a blue-colored discharge when ®red, the photodiode is used to con®rm the generation of plasma discharge at the second peak. The second peak of voltage measured from the SCB coincides with the output from the photodiode as shown in Fig. 4. Therefore, it is concluded that the second peak results from the plasma generated by the SCB. 3.2. Breakdown voltage of SCB plasma An applied electrical voltage breaks down the vaporized silicon gas, after the bridge melts down and evaporates. The electrical discharge resulting from this breakdown of the vaporized silicon gas is called the late-time discharge [1]. Assuming that the anode±cathode distance is d, the breakdown voltage, Vb across the gap distance is given by [4]: Vb
gpd ; lnhpd=ln 1 1=g
(1)
Fig. 4. Correlation between voltage and photodiode output.
where p is the pressure and g the secondary electron emission from the cathode. The coef®cients g and h are characteristic values, which are somewhat proportional to the ionization energy and the ionization cross-section, respectively [5]. For a high pressure (1 atm) regime characterized by hpd @ 1;
(2)
the breakdown voltage is mostly decided by the coef®cients g and h. The ionization energy of silicon is 8.15 eV, which is far less than that of air, which is about 15 eV. Therefore, the value of the coef®cient g of silicon is far less than that of air. We also believe that the ionization cross-section characterized by h may be relatively large compared to the air molecules, due to the large atomic size of the vaporized silicon atoms. Therefore, the breakdown voltage of the silicon gas is considerably less than that of air. For example, the breakdown voltage for the late-time discharge of silicon gas is less than 50 V, which is far less than the discharge voltage (about 300 V) of air for a similar geometrical con®guration. 3.3. Hot-spot melting model for no-fire condition The SCB has been investigated in connection with application to plasma generation for the ignition of explosives. One of the most important issues in this application is the no®re condition under which the SCB never ignites the explosive. We therefore develop a theoretical model for the no-®re condition, which is directly related to the safety of the explosive system. The no-®re condition is the condition under which the bridge may not melt down for a given electrical current. In order to ®nd out the critical steady-state current, below which the bridge is ensured not to melt down, we develop a theoretical model called the hot-spot melting model. The bridge loses its heat mostly by heat conduction through the polysilicon on which it is mounted and the aluminum pad adjacent to it. The heat loss through the
K.-N. Lee et al. / Sensors and Actuators A 96 (2002) 252±257
explosive may not be important, due to its low heat conductivity. For simplicity in the subsequent analysis, we assume that the bridge is a hot spot and the heat from the bridge is semi-spherically ¯owing away through the substrate. The temperature T in the polysilicon must satisfy 1 d 2 d r T r 0; (3) r2 dr dr for a steady-state case [6]. The symbol r in Eq. (3) represents the radial distance from the center of the spherical coordinate system. A solution to the differential Eq. (3) is given by: r2
dT C constant: dr
(4)
For time being, we assume that the hot spot (or the bridge) has the melting temperature Tm and that radius of the hot spot is r0. Integrating Eq. (4) over the radial coordinate r, the temperature T in the polysilicon is expressed as: 1 1 T r Tm C : (5) r0 r We note that the temperature T at r 1 is the ambient room temperature Tr. This property relates the integral constant C in Eq. (4) to the melting temperature Tm by: C r0 Tr
Tm :
(6)
The heat ¯ux density J is along the radial direction and is de®ned by J Jr er, where er is the unit vector along the radial direction. The radial component of the heat ¯ux density is expressed as: Jr
K
d T r; dr
(7)
where K is the thermal conductivity (cal/cm/s/8). The total heat ¯ux per unit time passing through the semi-spherical surface of radius r is given by: dQ 2pr2 Jr dt
2pr2 K
d T r dr
2pKr0 Tm
255
for no-melting, below which the bridge will not melt. Assuming that the bridge area U is de®ned by U pr20, the critical current, Ic for no-melting is expressed as: p 1=2 8:4 pK 1=4 Tm Tr U 1=4 ; (11) Ic bU R which is proportional to one-fourth power of the bridge area. The coef®cient b is proportional to the square root of the thermal conductivity K and inversely proportional to the square root of the bridge resistance R. In reality, the bridge can be of any shape but circular. However, for simplicity, we assume a circular shape of the bridge. Since heat is lost by conduction through the substrate in contact with the bridge, the shape of the bridge may not be very important in determining the no-®re condition. In order to check the validity of the hot-spot melting model, we compare the theoretical results obtained from Eq. (11) with the experimental data of the critical current for the no-®re condition in Fig. 5. The closed rectangular dots in Fig. 5 represent the experimental data for the critical current and the solid curve is obtained from Eq. (11) for the coef®cient b 2:25, which is determined by the leastsquare ®tting of the theoretical curve with experimental data. Note that the bridge is mounted on a substrate consisting mostly of polysilicon and aluminum. The substrate can also be made of silicon oxide and aluminum oxide crystals. In this context, it is very dif®cult to predict the thermal conductivity K. Nor is it easy to maintain a constant value of the bridge resistance R for different bridge areas. Therefore, we compare the overall trend of the no-®re condition of experimental data with theoretical results in terms of the bridge area. It is obvious from Fig. 5 that the experimental data agree reasonably well with the theoretical result, predicting one-fourth power dependence of the critical current on the bridge area. Assuming that the bridge
Tr ; (8)
where Q is the heat deposited at the bridge. Eqs. (4) and (6) have been used in obtaining Eq. (8). Assuming that the bridge resistance is R, the heat deposited into the bridge per unit time is given by: dQ 1 RI 2 ; dt 4:2
(9)
where I represents the steady-state electrical current. Eliminating dQ/dt from Eqs. (8) and (9), we can obtain the critical current Ic: r K Ic 8:4p r0 Tm Tr ; R
(10)
Fig. 5. No-fire current with various bridge areas. The closed rectangular dots represent the experimental data for the critical current and the solid curve is obtained from Eq. (11) for the coefficient b 2:25, which is determined by the least-square fitting of the theoretical curve with experimental data.
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resistance is R 1 O and the melting temperature is T m 1410 8C (the melting temperature of silicon crystal) and the room temperature of T r 20 8C, we ®nd that the coef®cient b 2:25 corresponds to the thermal conductivity K 0:024 cal/cm/s/8, which equals approximately the thermal conductivity of the quartz. We believe that the thermal conductivity K 0:024 cal/cm/s/8 is a reasonable value for the polysilicon substrate mixed with aluminum land of the experiment. However, we point out that the one-fourth power dependence of the critical current on the bridge area in Eq. (11) agrees remarkably well with previous experimental data [1] obtained from a bridge area considerably larger than those in our experiment. The reason for this is that the conductivity K for large bridge area is mostly determined by the bridge and substrate materials rather than anything else, including the aluminum land. Several points are noteworthy from Eq. (11). First, the critical current Ic for no bridge melting increases as the thermal conductivity K increases. Increasing the critical current improves the safety of the explosive ignition system. Therefore, safety can be considerably improved by selecting a substrate material that has a high thermal conductivity value. For example, sapphire has a thermal conductivity of K 0:08 cal/cm/s/8, which is about four times higher than the conductivity used in Fig. 5. The critical current can be increased to twice the value in Fig. 5 if sapphire is used as a substrate, which is in contact with the bridge. Second, the lower the bridge resistance R, the greater is the critical current Ic. Reduction of the bridge resistance can also improve the safety of the ignition system. It may be possible to enhance safety by changing the impurity ratio, thereby reducing the resistance. Third, the higher the melting temperature of the bridge, the safer is the ignition system. It is also possible to improve safety by selecting a bridge material that has a high melting temperature. Finally, we note from Eq. (11) that the critical current Ic increases with an increasing value of the bridge area. However, safety enhancement by bridge size is not a very effective means, due to an insensitive dependence of critical current on the area. However, we remind the reader that an excessive increase of the critical current Ic for safety may burden the late-time discharge for explosive ignition. 4. Conclusions In order to understand the physical phenomena occurring at two peaks in voltage±time measurement, the energy and the accumulation of power dissipated from the bridge during the supply of electrical energy were compared with the theoretical energy for melting and vaporization of polysilicon, calculated from the thermodynamic quantities. The ®rst peak was found to come from the melting of the bridge and the vaporization was found to end before the second peak appears. The second peak results from the plasma generation of the silicon vapor, as con®rmed by photodiode analysis. The SCB is an effective plasma generator because the
breakdown voltage of silicon gas is less than that of ambient air. This is easily seen by comparing the ionization potential and gas temperature of silicon gas with those of ambient air. The hot-spot melting model is introduced to describe the critical no-®re current. It is obvious from the model that the experimental data agree reasonably well with the theoretical result, predicting one-fourth power dependence of the critical current on the bridge area. Acknowledgements This research was supported in part by the Dual Use Technology Program of Ministry of National Defense. References [1] D.A. Benson, M.E. Larsen, A.M. Renlund, W.M. Trott, R.W. Bickes Jr., Semiconductor bridge: a plasma generator for the ignition of explosive, J. Appl. Phys. 62 (1987) 1622. [2] B.A.M. Tonor PhD dissertation, University of Maxico (1993) 12. [3] W.J. Dixon, A.M. Mood, A method for obtaining and analyzing sensitivity data, J. Am. Stat. Assoc. 110 (1948) 121. [4] H.S. Uhm, E.H. Choi, G. Cho, Breakdown properties of high-pressure electrical discharge, Phys. Plasmas 7 (2000) 2744. [5] H.S. Uhm, Properties of plasma generated by electrical breakdown in flames, Phys. Plasmas 6 (1999) 4366. [6] C. Kittel, H. Kroemer, Thermal Physics, Freeman, New York, 1995 (Chapter 15).
Biographies Kye-Nam Lee received the BS and MS degrees in physics from Kyunghee University, Seoul, South Korea in 1986 and 1988, respectively and PhD degree in materials science and engineering from Korea Advanced Institute of Science and Technology (KAIST), Tagejon, South Korea in 2001. Currently, he is a member of research staff in the R&D division of Hynix Company, Ichon, Kunggido, South Korea. His research interests include the design and fabrication of MRAM devices. Myung-Il Park received the BS and MS degree in materials science and engineering from the Korea Advanced Institute of Science and Technology (KAIST) in 1999 and 2001, respectively and is currently pursuing the PhD degree in materials science and engineering at KAIST. His research interests are in the area of semiconductor devices and bio-mems. Sung-Ho Choi received the MS degree in materials science and engineering from the Korea Advanced Institute of Science and Technology (KAIST) in 1998 and is currently pursuing the PhD degree in materials science and engineering at KAIST. His research interests are in the field of chemical sensors and solid-state devices such as a semiconductor bridge and a luminescent device. Chong-Ook Park received the BS degree in the metallurgical engineering from the Seoul National University, Korea, and the PhD degree in the materials science and engineering from the Ohio State University, in 1979, 1985, respectively. From 1985 to 1986, he was with University of Pennsylvania as a Post doc. and worked at LG Central Research Lab. as the director from 1986 to 1988. Since 1990, he has been a technical advisor at LG Corporate Institute of Technology. He joined the department of materials science and engineering at the Korea Advanced Institute of Science and Technology as an assistant professor in 1988 and he has been
K.-N. Lee et al. / Sensors and Actuators A 96 (2002) 252±257 a professor since 1999. His current research fields are solid state devices, especially thin and thick film devices. Han S. Uhm received the BS degree from Seoul National University, Seoul, Korea, and the MS and PhD degrees from the University of Maryland, College Park, in 1969, 1973 and 1976, respectively.
257
He was a Research Associate from 1976 to 1978 at the University of Maryland. He was a research associated from 1978 to 1998 at the Naval Surface Warfare Center. He joined the A-Jou University, Suwon, Korea, as a Professor in 1997. He is an expert concerning charged particle beans characterized by intense self electric and magnetic fields. Dr. Uhm is a member of the American Physical Society.
Characteristics of plasma generated by polysilicon semiconductor bridge (SCB) Kye-Nam Leea, Myung-Il Parka, Sung-Ho Choia, Chong-Ook Parka,*, Han S. Uhmb a
Department of Material Science and Engineering, KAIST, Solid State Devices Laboratory, 373-1 Kuseong-Dong, Yuseong-ku, Taejon 305-701, South Korea b Department of Molecular Science and Technology, Ajou University, San 5 Wonchon-Dong, Paldal-Gu, Suwon 442-749, South Korea Received 14 December 2000; accepted 1 November 2001
Abstract In an effort to elucidate the plasma generation mechanism of the semiconductor bridge (SCB), currents were forced to ¯ow through a polysilicon bridge with a resistance of 1 O, while the voltage drop was measured to obtain the in situ power dissipation through the bridge. The energy stored in a 25 mF capacitor was used to activate the plasma. The typical behavior of two peaks in the voltage±time curve was observed. It is inferred from the photodiode signal that the second peak in the voltage curve results from the plasma generation of the bridge material. The breakdown voltage of the electrical discharge at high pressure proved that the SCB is an effective plasma generator. The experimental data for the no-®re condition, directly related to the safety of the explosive system, is compared with the analytical results from a theoretical model. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Plasma; Semiconductor bridge; No-®re condition; Igniter
1. Introduction The plasma generated from the semiconductor bridge (SCB) is sometimes used to ignite the explosives, where the heavily doped polysilicon in contact with powder gets melt and evaporated to form a high pressure of plasma upon introduction of large currents through SCB [1]. Because the typical value of the bridge resistance is about 1 O, the bridge is ohmic-heated through the electrical current. The SCB may melt down and eventually evaporate if enough electrical energy is deposited into the bridge within a limited time. Once the bridge material is vaporized, the applied electric voltage breaks down the vaporized silicon gas, generating silicon plasmas called the late-time discharge [1]. This plasma will eventually ignite the explosive materials. The SCB works within a few microseconds compared with the milliseconds response of a conventional hot-wire unit. It also functions at a few millijoules of energy, which is one-tenth of the input energy of a conventional hot-wire unit [2]. The plasma generation mechanism of the SCB was investigated in this article by comparing the measured energy from the SCB with the theoretically calculated energy of the * Corresponding author. Tel.: 82-42-869-4218; fax: 82-42-869-3310. E-mail address: [email protected] (C.-O. Park).
mass of the bridge. The breakdown voltage for the electrical discharge is described in terms of the ionization properties of the gas and the gas pressure. In addition, a theoretical model for the no-®re condition, which is directly related to the safety of the explosive system, is developed and compared with experimental data. 2. Experiment of plasma generation and no-fire condition A typical SCB device is schematically illustrated in Fig. 1. The bridge is formed from the heavily doped H-shaped region enclosed by the dashed lines in the ®gure. The thickness of the bridge is determined by that of the polysilicon ®lm deposited onto the silicon dioxide (SiO2) layer. The insulating layer of SiO2 enables the heat to concentrate on the bridge when the SCB device is functioning. The bridge width, W is decided from the shape of the doped region. The aluminum lands determine the length, L of the bridge and provide the means for electrical contact with the underlying polysilicon layer. A conventional CMOS process was used to fabricate SCB chips as shown in Fig. 2. A silicon dioxide layer, about 2 mm thick, was formed on the silicon substrate by means of
0924-4247/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 ( 0 1 ) 0 0 8 3 6 - 6
K.-N. Lee et al. / Sensors and Actuators A 96 (2002) 252±257
Fig. 1. Schematic view of a typical SCB.
thermal oxidation. For n-type devices, phosphorous was diffused into polysilicon to give a heavy doping concentration of 1020/cm3 using a phosphorous oxy-chloride (POCl3) source. In the case of a p-type device, boron was implanted into exposed regions of the wafer by a high current ion implantor. Once the bridge shape had been de®ned, the sputtered aluminum was deposited on polysilicon, which provides an electrical contact with the SCB. In order to make a 1 O bridge with dimensions of 20 mm length 90 mm width 2 mm thickness, the polysilicon layer was doped with a concentration of 1020 phosphorous atoms/cm3. The devices were packaged into TO5 cans with 1 ml (0.025 mm) gold wire of ball bonding joining the aluminum lands to the package pins. For the evaluation of SCB discharge behaviors, a fast photodiode (FPD) was combined with a ®ring circuit to record the emission of plasma light and electrical features simultaneously from a single-shot discharge of the bridges.
Fig. 2. Processing procedure for SCB fabrication.
253
For the simultaneous measurement of the voltage across the SCB and the output signals of the photodiode, a fast digital oscilloscope was used. A capacitor discharge ®ring set was selected in the electrical test. It consists of a capacitor (25 mF), a fast switch circuit and dc power supply. The fast switch circuit includes a driver (Telcom Ltd., high-speed MOSFET Driver) and a timer (Samsung Electronics Ltd., Single Timer KA555/I) that functions to open a capacitor charged with dc voltage during a period of 30 ms. The light emitted from the device was measured using a photodiode (Newport Biased Detector, 818-B8-21A). To perform a no-®re current test, a direct current is passed through the SCB for 5 min. It is loaded with ZPP powder, 60 mg. The ``up and down'' or Bruceton technique [3] was selected for obtaining the explosive data. This means choosing an initial voltage, h0, and a succession of higher voltages, h1, h2, h3 above h0 together with a succession of lower voltages h 1, h 2, h 3, . . .. If the ®rst specimen explodes, the second specimen will be tested at h 1, otherwise the second specimen will be tested at h1. In general, any specimen will be tested at the level immediately below or immediately above the level of the previous test according to whether or not there was an explosion in the previous test. 3. Experimental results and discussions 3.1. Plasma generation mechanism from SCB We measured the resistances of SCB by a four-point probe method during the manufacturing process. But, in the test the resistance of SCB includes those of wires and pads, which are negligible in our case compared with that of SCB. The voltage and current measured across the SCB during the test are shown in Fig. 3, where the letters V, I, P, and E represent the voltage, current, electrical power, and the
Fig. 3. Electrical characteristics of SCB. The letters V, I, P, and E represent the voltage, current, electrical power, and the energy deposited on the bridge, respectively.
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energy deposited on the bridge, respectively. Two peaks in the voltage±time curve occur at 250 ns (®rst peak) and 600 ns (second peak), with the current reaching its maximum at the second peak. The power dissipated in the device is calculated from the measured current and voltage. The energy dissipated in the SCB can be obtained by integrating the power with respect to time and is superimposed in Fig. 3. The mass of silicon in the bridge is calculated to be 8:4 10 9 g for a SCB device with dimensions of 90 mm wide, 20 mm long and 2 mm thick. The liquefaction energy and vaporization energy of the mass can be theoretically calculated to be 0.0248 and 0.1052 mJ, respectively by making use of the thermodynamic data of the silicon, such as speci®c heat, density (2.33 g/cm3) and atomic weight (28.086 g/mol). Assuming that there is no heat loss through the substrate during this short operation time, these energies correspond to the energy accumulated, up to 400 and 550 ns in Fig. 3 for the melting and vaporization, respectively. Therefore, it may be concluded that the ®rst peak results from the melting of the bridge, and that the vaporization is complete before the second peak appears. Benson et al. [1] have ascertained through high-speed framing camera images of the bridges that the ®rst peak in Fig. 3 corresponds to the initial silicon heating prior to the onset of silicon vaporization at the second peak. According to their experiment, once the bridge is vaporized, the current ¯ows through the vapor producing heated plasma (5000 K). It is obvious that the silicon bridge undergoes phase changes or transitions. It seems that the melting gives rise to an abrupt increase in the resistance of the bridge, which produces the ®rst voltage peak. The open circuit created by the bridge melting (especially at the edges) causes the resistance of bridge to increase instantaneously. The resistance remains relatively low after the ®rst peak because the vapor produced by the phase changes of the silicon bridge is utilized as a current path. Since the SCB devices produce a blue-colored discharge when ®red, the photodiode is used to con®rm the generation of plasma discharge at the second peak. The second peak of voltage measured from the SCB coincides with the output from the photodiode as shown in Fig. 4. Therefore, it is concluded that the second peak results from the plasma generated by the SCB. 3.2. Breakdown voltage of SCB plasma An applied electrical voltage breaks down the vaporized silicon gas, after the bridge melts down and evaporates. The electrical discharge resulting from this breakdown of the vaporized silicon gas is called the late-time discharge [1]. Assuming that the anode±cathode distance is d, the breakdown voltage, Vb across the gap distance is given by [4]: Vb
gpd ; lnhpd=ln 1 1=g
(1)
Fig. 4. Correlation between voltage and photodiode output.
where p is the pressure and g the secondary electron emission from the cathode. The coef®cients g and h are characteristic values, which are somewhat proportional to the ionization energy and the ionization cross-section, respectively [5]. For a high pressure (1 atm) regime characterized by hpd @ 1;
(2)
the breakdown voltage is mostly decided by the coef®cients g and h. The ionization energy of silicon is 8.15 eV, which is far less than that of air, which is about 15 eV. Therefore, the value of the coef®cient g of silicon is far less than that of air. We also believe that the ionization cross-section characterized by h may be relatively large compared to the air molecules, due to the large atomic size of the vaporized silicon atoms. Therefore, the breakdown voltage of the silicon gas is considerably less than that of air. For example, the breakdown voltage for the late-time discharge of silicon gas is less than 50 V, which is far less than the discharge voltage (about 300 V) of air for a similar geometrical con®guration. 3.3. Hot-spot melting model for no-fire condition The SCB has been investigated in connection with application to plasma generation for the ignition of explosives. One of the most important issues in this application is the no®re condition under which the SCB never ignites the explosive. We therefore develop a theoretical model for the no-®re condition, which is directly related to the safety of the explosive system. The no-®re condition is the condition under which the bridge may not melt down for a given electrical current. In order to ®nd out the critical steady-state current, below which the bridge is ensured not to melt down, we develop a theoretical model called the hot-spot melting model. The bridge loses its heat mostly by heat conduction through the polysilicon on which it is mounted and the aluminum pad adjacent to it. The heat loss through the
K.-N. Lee et al. / Sensors and Actuators A 96 (2002) 252±257
explosive may not be important, due to its low heat conductivity. For simplicity in the subsequent analysis, we assume that the bridge is a hot spot and the heat from the bridge is semi-spherically ¯owing away through the substrate. The temperature T in the polysilicon must satisfy 1 d 2 d r T r 0; (3) r2 dr dr for a steady-state case [6]. The symbol r in Eq. (3) represents the radial distance from the center of the spherical coordinate system. A solution to the differential Eq. (3) is given by: r2
dT C constant: dr
(4)
For time being, we assume that the hot spot (or the bridge) has the melting temperature Tm and that radius of the hot spot is r0. Integrating Eq. (4) over the radial coordinate r, the temperature T in the polysilicon is expressed as: 1 1 T r Tm C : (5) r0 r We note that the temperature T at r 1 is the ambient room temperature Tr. This property relates the integral constant C in Eq. (4) to the melting temperature Tm by: C r0 Tr
Tm :
(6)
The heat ¯ux density J is along the radial direction and is de®ned by J Jr er, where er is the unit vector along the radial direction. The radial component of the heat ¯ux density is expressed as: Jr
K
d T r; dr
(7)
where K is the thermal conductivity (cal/cm/s/8). The total heat ¯ux per unit time passing through the semi-spherical surface of radius r is given by: dQ 2pr2 Jr dt
2pr2 K
d T r dr
2pKr0 Tm
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for no-melting, below which the bridge will not melt. Assuming that the bridge area U is de®ned by U pr20, the critical current, Ic for no-melting is expressed as: p 1=2 8:4 pK 1=4 Tm Tr U 1=4 ; (11) Ic bU R which is proportional to one-fourth power of the bridge area. The coef®cient b is proportional to the square root of the thermal conductivity K and inversely proportional to the square root of the bridge resistance R. In reality, the bridge can be of any shape but circular. However, for simplicity, we assume a circular shape of the bridge. Since heat is lost by conduction through the substrate in contact with the bridge, the shape of the bridge may not be very important in determining the no-®re condition. In order to check the validity of the hot-spot melting model, we compare the theoretical results obtained from Eq. (11) with the experimental data of the critical current for the no-®re condition in Fig. 5. The closed rectangular dots in Fig. 5 represent the experimental data for the critical current and the solid curve is obtained from Eq. (11) for the coef®cient b 2:25, which is determined by the leastsquare ®tting of the theoretical curve with experimental data. Note that the bridge is mounted on a substrate consisting mostly of polysilicon and aluminum. The substrate can also be made of silicon oxide and aluminum oxide crystals. In this context, it is very dif®cult to predict the thermal conductivity K. Nor is it easy to maintain a constant value of the bridge resistance R for different bridge areas. Therefore, we compare the overall trend of the no-®re condition of experimental data with theoretical results in terms of the bridge area. It is obvious from Fig. 5 that the experimental data agree reasonably well with the theoretical result, predicting one-fourth power dependence of the critical current on the bridge area. Assuming that the bridge
Tr ; (8)
where Q is the heat deposited at the bridge. Eqs. (4) and (6) have been used in obtaining Eq. (8). Assuming that the bridge resistance is R, the heat deposited into the bridge per unit time is given by: dQ 1 RI 2 ; dt 4:2
(9)
where I represents the steady-state electrical current. Eliminating dQ/dt from Eqs. (8) and (9), we can obtain the critical current Ic: r K Ic 8:4p r0 Tm Tr ; R
(10)
Fig. 5. No-fire current with various bridge areas. The closed rectangular dots represent the experimental data for the critical current and the solid curve is obtained from Eq. (11) for the coefficient b 2:25, which is determined by the least-square fitting of the theoretical curve with experimental data.
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resistance is R 1 O and the melting temperature is T m 1410 8C (the melting temperature of silicon crystal) and the room temperature of T r 20 8C, we ®nd that the coef®cient b 2:25 corresponds to the thermal conductivity K 0:024 cal/cm/s/8, which equals approximately the thermal conductivity of the quartz. We believe that the thermal conductivity K 0:024 cal/cm/s/8 is a reasonable value for the polysilicon substrate mixed with aluminum land of the experiment. However, we point out that the one-fourth power dependence of the critical current on the bridge area in Eq. (11) agrees remarkably well with previous experimental data [1] obtained from a bridge area considerably larger than those in our experiment. The reason for this is that the conductivity K for large bridge area is mostly determined by the bridge and substrate materials rather than anything else, including the aluminum land. Several points are noteworthy from Eq. (11). First, the critical current Ic for no bridge melting increases as the thermal conductivity K increases. Increasing the critical current improves the safety of the explosive ignition system. Therefore, safety can be considerably improved by selecting a substrate material that has a high thermal conductivity value. For example, sapphire has a thermal conductivity of K 0:08 cal/cm/s/8, which is about four times higher than the conductivity used in Fig. 5. The critical current can be increased to twice the value in Fig. 5 if sapphire is used as a substrate, which is in contact with the bridge. Second, the lower the bridge resistance R, the greater is the critical current Ic. Reduction of the bridge resistance can also improve the safety of the ignition system. It may be possible to enhance safety by changing the impurity ratio, thereby reducing the resistance. Third, the higher the melting temperature of the bridge, the safer is the ignition system. It is also possible to improve safety by selecting a bridge material that has a high melting temperature. Finally, we note from Eq. (11) that the critical current Ic increases with an increasing value of the bridge area. However, safety enhancement by bridge size is not a very effective means, due to an insensitive dependence of critical current on the area. However, we remind the reader that an excessive increase of the critical current Ic for safety may burden the late-time discharge for explosive ignition. 4. Conclusions In order to understand the physical phenomena occurring at two peaks in voltage±time measurement, the energy and the accumulation of power dissipated from the bridge during the supply of electrical energy were compared with the theoretical energy for melting and vaporization of polysilicon, calculated from the thermodynamic quantities. The ®rst peak was found to come from the melting of the bridge and the vaporization was found to end before the second peak appears. The second peak results from the plasma generation of the silicon vapor, as con®rmed by photodiode analysis. The SCB is an effective plasma generator because the
breakdown voltage of silicon gas is less than that of ambient air. This is easily seen by comparing the ionization potential and gas temperature of silicon gas with those of ambient air. The hot-spot melting model is introduced to describe the critical no-®re current. It is obvious from the model that the experimental data agree reasonably well with the theoretical result, predicting one-fourth power dependence of the critical current on the bridge area. Acknowledgements This research was supported in part by the Dual Use Technology Program of Ministry of National Defense. References [1] D.A. Benson, M.E. Larsen, A.M. Renlund, W.M. Trott, R.W. Bickes Jr., Semiconductor bridge: a plasma generator for the ignition of explosive, J. Appl. Phys. 62 (1987) 1622. [2] B.A.M. Tonor PhD dissertation, University of Maxico (1993) 12. [3] W.J. Dixon, A.M. Mood, A method for obtaining and analyzing sensitivity data, J. Am. Stat. Assoc. 110 (1948) 121. [4] H.S. Uhm, E.H. Choi, G. Cho, Breakdown properties of high-pressure electrical discharge, Phys. Plasmas 7 (2000) 2744. [5] H.S. Uhm, Properties of plasma generated by electrical breakdown in flames, Phys. Plasmas 6 (1999) 4366. [6] C. Kittel, H. Kroemer, Thermal Physics, Freeman, New York, 1995 (Chapter 15).
Biographies Kye-Nam Lee received the BS and MS degrees in physics from Kyunghee University, Seoul, South Korea in 1986 and 1988, respectively and PhD degree in materials science and engineering from Korea Advanced Institute of Science and Technology (KAIST), Tagejon, South Korea in 2001. Currently, he is a member of research staff in the R&D division of Hynix Company, Ichon, Kunggido, South Korea. His research interests include the design and fabrication of MRAM devices. Myung-Il Park received the BS and MS degree in materials science and engineering from the Korea Advanced Institute of Science and Technology (KAIST) in 1999 and 2001, respectively and is currently pursuing the PhD degree in materials science and engineering at KAIST. His research interests are in the area of semiconductor devices and bio-mems. Sung-Ho Choi received the MS degree in materials science and engineering from the Korea Advanced Institute of Science and Technology (KAIST) in 1998 and is currently pursuing the PhD degree in materials science and engineering at KAIST. His research interests are in the field of chemical sensors and solid-state devices such as a semiconductor bridge and a luminescent device. Chong-Ook Park received the BS degree in the metallurgical engineering from the Seoul National University, Korea, and the PhD degree in the materials science and engineering from the Ohio State University, in 1979, 1985, respectively. From 1985 to 1986, he was with University of Pennsylvania as a Post doc. and worked at LG Central Research Lab. as the director from 1986 to 1988. Since 1990, he has been a technical advisor at LG Corporate Institute of Technology. He joined the department of materials science and engineering at the Korea Advanced Institute of Science and Technology as an assistant professor in 1988 and he has been
K.-N. Lee et al. / Sensors and Actuators A 96 (2002) 252±257 a professor since 1999. His current research fields are solid state devices, especially thin and thick film devices. Han S. Uhm received the BS degree from Seoul National University, Seoul, Korea, and the MS and PhD degrees from the University of Maryland, College Park, in 1969, 1973 and 1976, respectively.
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He was a Research Associate from 1976 to 1978 at the University of Maryland. He was a research associated from 1978 to 1998 at the Naval Surface Warfare Center. He joined the A-Jou University, Suwon, Korea, as a Professor in 1997. He is an expert concerning charged particle beans characterized by intense self electric and magnetic fields. Dr. Uhm is a member of the American Physical Society.