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Comparison of plasma generation behaviors between a single crystal semiconductor bridge (single-SCB) and a polysilicon semiconductor bridge (poly-SCB)
Sensors and Actuators A 115 (2004) 104–108
Comparison of plasma generation behaviors between a single crystal semiconductor bridge (single-SCB) and a polysilicon semiconductor bridge (poly-SCB) Myung-Il Park a,∗ , Hyo-Tae Choo a , Suk-Hwan Yoon b , Chong-Ook Park a a
Department of Material Science and Engineering, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejon 305-701, South Korea b Turbo Pump Group, Korea Aerospace Research Institute, 45 Eoeun-dong, Yuseong-gu, Daejon 305-333, South Korea Received 2 April 2003; received in revised form 23 April 2004; accepted 27 April 2004 Available online 4 June 2004
Abstract A single crystal semiconductor bridge (single-SCB) has been fabricated by a micro-electro-mechanical system (MEMS) technique based on anisotropic wet etching, where an air gap replaces the oxide layer (SiO2 ) used as a thermal insulating barrier in the conventional polycrystalline semiconductor bridge (poly-SCB). Upon flowing current in the single-SCB and the poly-SCB, the single-SCB exhibits a second peak of plasma generation at 500 ns, whereas that of the poly-SCB is founded at 600 ns. The results of an electrical experiment are analyzed through a finite element analysis and a simple discrete-element modeling of the thermal structure. From these investigations, it is clear that more effective heat conduction related to the plasma discharge behaviors is achieved in the single-SCB with a simpler thermal structure. © 2004 Elsevier B.V. All rights reserved. Keywords: Semiconductor bridge; Igniter; Silicon wet etching; Thermal structure
1. Introduction The semiconductor bridge (SCB) device originally conceived by Hollander [1] produces hot plasma when a short and low energy pulse is applied. The plasma from the SCB is a short duration burst with temperatures of around 5000 K, sufficient to ignite explosives [2]. Further, it was found that thermal ignition of pyrotechnic and explosive powders could be achieved with small energy input compared to traditional hot wire devices, while decreasing the firing times by one to two orders of magnitude [3]. This could enhance performance capabilities for automotive air-bag devices and conventional pyrotechnic applications while improving no-fire conditions and electrostatic safety. In this study, a single crystal semiconductor bridge (single-SCB) has been designed and fabricated by a microelectro-mechanical system (MEMS) technique based on anisotropic wet etching, where an air gap replaces the oxide layer (SiO2 ) used as a thermal insulating barrier in the conventional polycrystalline semiconductor bridge (poly-SCB)
∗ Corresponding author. Tel.: +82 42 869 4258; fax: +82 42 869 3310. E-mail address: [email protected] (M.-I. Park).
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.04.038
[4]. The single silicon layer was doped with a concentration of 1020 boron atoms/cm3 , resulting in a 2 -bridge with dimensions of 20 m length × 90 m width × 2 m thickness. In order to elucidate the plasma generation characteristics of two devices, when electrical energy stored in a charged capacitor is applied to the devices, a finite element analysis and a thermal modeling are described in detail.
2. Experimental A single-SCB consists of an “H” shaped thin single crystal silicon membrane, which is directly wet-etched as illustrated in Fig. 1. Two metal lands of aluminum are attached to the membrane. The bridge with dimensions of 20 m length (L) × 90 m width (W)× 2 m thickness (t), is formed from the heavily doped region enclosed by the dashed lines in Fig. 1. The thickness is determined by the depth of the doped single silicon layer, the width is defined by the shape of bridge region, and the length is determined by the space between the aluminum lands. A detailed process step for the fabrication of single-SCB is described in Fig. 2. The thermal oxide layer (SiO2 ) was
M.-I. Park et al. / Sensors and Actuators A 115 (2004) 104–108
used as a diffusion mask in the first photo lithography step, and photoresist development was followed by diffusion of boron impurities (∼1020 cm−3 ) at 1000 ◦ C in a quartz tube containing an inert atmosphere. Once the bridge shape was defined by the diffusion process, the aluminum was sputter-deposited onto the silicon substrate, which provides an electrical contact to SCB. A protection layer (SiO2 ), was deposited on both sides by plasma enhanced chemical vapor deposition (PECVD) without consuming the silicon surface layer [5] and was patterned in the second photolithography step. Anisotropic silicon wet etching was carried out by tetramethyl ammonium hydroxide (TMAH, (CH3 )4 NOH), which begins to slow down for boron-doping levels above approximately 1 × 1019 cm−3 [6]. Finally, the individual die used was mounted with epoxy on a TO5 header pack-
age, where the die pads were electrically attached to the pins of the header using ultrasonically bonded gold wire (0.025 mm). For the evaluation of SCB plasma discharge behaviors, a fast photo diode (Newport Biased Detector, 818-BB-21A) was combined with a firing circuit to record emission of plasma light and electrical features simultaneously from a single-shot discharge of SCB. Both the voltage signals across the SCB and the outputs of the photodiode, were recorded with a multiple channel digital oscilloscope (Agilent, 54845B) at 50 ns intervals during the firing. A capacitor discharge firing circuit (25 F, 25 V) was adopted to force the currents to the SCB with an electrical trigger pulse and off after a predetermined time delay. The firing circuit consists of a driver (Telcom Ltd., High-speed MOSFET Driver) and a timer (Samsung Electronics Ltd., Single Timer KA555/I) which can open a capacitor charged with 25 V dc voltage for 30 s pulse duration.
3. Results and discussion 3.1. Electrical characteristics of SCB devices Fig. 3 shows the voltage transient and output from the photodiode obtained from the two SCB devices when the electric energy is stored (7.8 mJ) into the chips. The solid curve represents the single-SCB while the dotted curve denotes the poly-SCB. The first and the second peak are observed to occur at 200 and 500 ns in the single-SCB, respectively; while they are found at 250 and 600 ns in the poly-SCB, respectively. The data measured in the electrical experiment are less than 10%. It is known that the melting of silicon gives rise to an abrupt increase in the resistance of the bridge, which produces the first voltage peak, and the open circuit created by the bridge melting (especially at the edges) causes the resistance of the bridge to increase instantaneously at the second voltage peak [4]. Once the bridge
Single-SCB Poly-SCB
Electrical voltage(V)
60
800 600
40 Electrical voltage
20
400
0
200 Photodiode voltage
0
250
500
750
1000
Photodiode voltage(mV)
Fig. 1. Schematics of top and cross section view of a single-SCB device.
105
0
1250
Time (ns) Fig. 2. Processing procedure for a single-SCB.
Fig. 3. Comparison of voltage and photo diode output between single-SCB and poly-SCB.
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M.-I. Park et al. / Sensors and Actuators A 115 (2004) 104–108
is vaporized, the current flows through the vapor, producing blue-colored plasma that is detected by the photo-diode. Since the onset of the second voltage peak, as depicted in the higher part of Fig. 3, coincides with the signals from the photodiode as presented in the lower part of Fig. 3 for both cases, it is clear that the single-SCB device generates the plasma discharge faster than the poly-SCB device. The electrical results therefore demonstrate enhancement of the single-SCB in term of plasma formation in comparison with the poly-SCB.
experiment and the vaporization time from the simulation. In the case of the poly-SCB device, some portion of electrical current seems to flow through the oxide layer, which yields slow heating of the bride element. The electrical currents flowing through the oxide layer could be considered as a thermal conduction loss of applied energy, though the amount is not overly large due to the small electrical conductivity of the oxide layer. Conversely, in the single-SCB device, all of the applied currents concentrate in the bridge element without any loss.
3.2. Finite element analysis for SCB devices
3.3. Theoretical modeling for thermal structures of SCB devices
In an effort to understand the results of the electrical experiment as depicted in Fig. 3, computational simulations were performed using a Sysweld package, a commercial finite element code. This package is capable of solving various three-dimensional heating and cooling problems for both transient and steady-state cases as well as considering various phase changes of materials in the course of calculation. It is thus a suitable to examine the plasma generation mechanism of SCB including the phase transition from solid to gas in a non-linear transient state. The results from the finite element analysis are shown in Fig. 4, the inset of which illustrates the structure of two igniters with the same bridge volume. Fig. 4 presents the temperature changes of the heated region in the device as a function of time when electrical energy is applied. Considering the vaporization temperature of silicon Tvapor = 2355 ◦ C, the vaporization time (tvapor ) is 520 ns in the single-SCB and 580 ns in the poly-SCB device, respectively. In addition, it is observed that the rising rate of single-SCB is faster than that of poly-SCB. Outcomes of the simulation agree well with the results presented in Fig. 3. The connection with the structure of the two devices as depicted in the inset of Fig. 4, provides an avenue to explain the relationship between the voltage peak of the electric
This section presents a study of the temperature rise on the bridge region based on the discrete element circuit model [7], to confirm the coincidence of the results between the electrical experiment and computational simulation. In this model, temperature, thermal conductor and thermal mass are equivalent to voltage, the resistor and the capacitor in the electrical circuit, respectively. In order to examine the subsequent model simply, it is assumed that all the power imposed to the system is dissipated in the bridge area and the thermal energy generated is released by only thermal conduction through the solid media. The model is applied to the thermal circuits for two devices as shown in the inset of Fig. 5. Considering the thermal structure of the single-SCB as shown in the upper inset of Fig. 5, the air gap is regarded as only a thermal capacitor because the assumption mentioned above neglects the heat conduction in the gas phase. There is one thermal resistance of the silicon membrane and two heat capacitors of the silicon bridge and air gap, respectively, in the single-SCB thermal circuit. On the other hand, each substrate component includes heat conductance and heat capacitance in the poly-SCB with the polysilicon/oxide/bulk silicon substrate structure as shown in the lower inset of Fig. 5.
Single-SCB P
Temperature (K)
400k
1/R
C
C
T
Poly-SCB
P
200k
0
1/R
1/R
1/R
2
C
C
C
T
4
Time (µs) Fig. 4. Temperature transient of SCB thermal structures based on the computational simulation.
Fig. 5. Step response curves and electric circuits for the discrete-element model of the SCB structures.
M.-I. Park et al. / Sensors and Actuators A 115 (2004) 104–108
Thus, when the heating power (P) is abruptly changed from zero to a constant at time t = 0, the time response of the single-SCB circuit (Ts ) is given by −t P Ts (t) = 1 − exp 1/Rsi τs −t 5 = 4.8 × 10 1 − exp K (1) 0.176 where Rsi represents the thermal resistance of the single silicon membrane. The time constant for the single-SCB (τ s ) is τs = Rsi (Csi + Cair ) = 0.176 s
(2)
where Csi is the thermal capacitance of the single silicon bridge and Cair the air gap, correspondingly. Instead, the equation of time rise (Tp ) for the poly-SCB circuit is as follows: P −t Tp (t) = 1 − exp 1/(Rpoly + Rox + Rsi ) τp −t = 3.9 × 105 1 − exp K (3) 1.29 where Rpoly represents the thermal resistance of the poly silicon membrane and Rox is the thermal resistance of the oxide layer. The time constant (τ p ) for the poly-SCB is then described as Cp + Cox + Csi = 1.29 s (4) τp = 1/(Rp + Rox + Rsi ) where Cp is the thermal capacitance of the poly silicon bridge and Cox is that of the oxide layer. In analyzing (1–4), the final temperature of the single-SCB is 90,000 K higher than that of the poly-SCB and the time constant of the single-SCB is about 10 times as fast as that of the poly-SCB as shown in Fig. 5. It is noted that the value of the final temperature should be understood relatively since we assume thermal modeling without considering phase transitions such as melting and evaporation related to the heat dissipation. For a simple RC time constant, the derivative of the curve at the step time crosses the final value after one time constant, and the curve reaches 63% of its final value after one time constant. It is clear that the more effective heat conduction is achieved in the single-SCB structure in light of the final temperature and the time constant results from the thermal circuit modeling.
4. Conclusions From the electrical experiments comparing single- and poly-SCB fabricated in previous works, it has been demonstrated that the peak of the single-SCB precedes that of the poly-SCB at the time of plasma generation. The results were further assessed with a computational simulation based on finite element analysis and discrete-element modeling of the
107
thermal structures. From the analysis, it was deduced that the rising rate of the temperature of the single-SCB was faster than that of the poly-SCB. The theoretical modeling for the SCB thermal structure showed that more effective heat conduction was achieved in the single-SCB, which has a simpler structure without additional layers. It is therefore clear that the oxide layer added to the silicon bridge in the poly-SCB causes a delay through the thermal conduction during the firing as well as the heat absorption. Consequently, the plasma discharge generation of the single-SCB will occur prior to that of the poly-SCB. Finally, from the aforementioned results and analysis, the structure of the SCB is found to have a significant effect on the discharge behaviors.
Acknowledgements This research was supported by the Dual Use Technology Program.
References [1] L.E. Hollander Jr., Semiconductor explosive igniter, US Patent 3,366,055, 30 January 1969. [2] B.A.M. Tovar, Electrothermal transients in highly doped phosphorous diffused silicon-on-sapphire semiconductor bridge under high current density conditions, Ph. D. dissertation, The University of New Maxico, 1993, p. 11. [3] 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. Apply. Phys. 62 (2) (1987) 1622. [4] K.-N. Lee, M.-I. Park, S.-H. Choi, C.-O. Park, H.S. Uhm, Characteristics of plasma generated by polysilicon semiconductor bridge (SCB), Sens. Actuators A 96 (2002) 252. [5] S.M. Sze, VLSI Technology, McGraw-Hill, 1998 (Chapter 3). [6] G.T.A. Kovacs, Micromachined Transducers Sourcebook, McGrawHill Inc., 1998 (Chapter 2). [7] S.M. Sze, Semiconductor Sensors, Wiley Inc., 1994 (Chapter 7).
Biographies Myung-Il Park received by BS and MS degree in the Department of 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 at KAIST. His research interests are in the area of MEMS using ultrashort pulses laser. Hyo-Tae Choo received the BS degrees in the Department of Materials Science and Engineering from Kyungpook National University in 2000 and MS degree in the Department of Materials Science and Engineering from KAIST in 2002. Currently, he is a member of research staff in the R&D division of Samsung electronics. His research interests include the design and modeling of semiconductor devices. Suk-Hwan Yoon received by BS, MS and PhD degree in the department of Mechanical Engineering from the KAIST in 1996, 1998 and 2004, respectively. Currently, he is a member of research staff in the Turbo Pump Group of Korea Aerospace Research Institute. His research interests are in the area of structural analysis of space launching vehicles.
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Chong-Ook Park received the BS degree in the Department of Metallurgical Engineering from Seoul National University in 1979, and the PhD degree in the Department of Materials Science and Engineering from Ohio State University in 1985, respectively. From 1985 to 1986, he was with University of Pennsylvania as a post doctoral and worked at LG Electronics Central Research Laboratory as the director from 1986 to 1988.
Since 1990, he has been a technical advisor at LG Electronics Corporate Institute of Technology. He joined the Department of Materials Science and Engineering at KAIST as an assistant professor in 1988 and he has been a professor since 1999. His current research fields are solid state devices, especially chemical sensors.
Comparison of plasma generation behaviors between a single crystal semiconductor bridge (single-SCB) and a polysilicon semiconductor bridge (poly-SCB) Myung-Il Park a,∗ , Hyo-Tae Choo a , Suk-Hwan Yoon b , Chong-Ook Park a a
Department of Material Science and Engineering, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejon 305-701, South Korea b Turbo Pump Group, Korea Aerospace Research Institute, 45 Eoeun-dong, Yuseong-gu, Daejon 305-333, South Korea Received 2 April 2003; received in revised form 23 April 2004; accepted 27 April 2004 Available online 4 June 2004
Abstract A single crystal semiconductor bridge (single-SCB) has been fabricated by a micro-electro-mechanical system (MEMS) technique based on anisotropic wet etching, where an air gap replaces the oxide layer (SiO2 ) used as a thermal insulating barrier in the conventional polycrystalline semiconductor bridge (poly-SCB). Upon flowing current in the single-SCB and the poly-SCB, the single-SCB exhibits a second peak of plasma generation at 500 ns, whereas that of the poly-SCB is founded at 600 ns. The results of an electrical experiment are analyzed through a finite element analysis and a simple discrete-element modeling of the thermal structure. From these investigations, it is clear that more effective heat conduction related to the plasma discharge behaviors is achieved in the single-SCB with a simpler thermal structure. © 2004 Elsevier B.V. All rights reserved. Keywords: Semiconductor bridge; Igniter; Silicon wet etching; Thermal structure
1. Introduction The semiconductor bridge (SCB) device originally conceived by Hollander [1] produces hot plasma when a short and low energy pulse is applied. The plasma from the SCB is a short duration burst with temperatures of around 5000 K, sufficient to ignite explosives [2]. Further, it was found that thermal ignition of pyrotechnic and explosive powders could be achieved with small energy input compared to traditional hot wire devices, while decreasing the firing times by one to two orders of magnitude [3]. This could enhance performance capabilities for automotive air-bag devices and conventional pyrotechnic applications while improving no-fire conditions and electrostatic safety. In this study, a single crystal semiconductor bridge (single-SCB) has been designed and fabricated by a microelectro-mechanical system (MEMS) technique based on anisotropic wet etching, where an air gap replaces the oxide layer (SiO2 ) used as a thermal insulating barrier in the conventional polycrystalline semiconductor bridge (poly-SCB)
∗ Corresponding author. Tel.: +82 42 869 4258; fax: +82 42 869 3310. E-mail address: [email protected] (M.-I. Park).
0924-4247/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2004.04.038
[4]. The single silicon layer was doped with a concentration of 1020 boron atoms/cm3 , resulting in a 2 -bridge with dimensions of 20 m length × 90 m width × 2 m thickness. In order to elucidate the plasma generation characteristics of two devices, when electrical energy stored in a charged capacitor is applied to the devices, a finite element analysis and a thermal modeling are described in detail.
2. Experimental A single-SCB consists of an “H” shaped thin single crystal silicon membrane, which is directly wet-etched as illustrated in Fig. 1. Two metal lands of aluminum are attached to the membrane. The bridge with dimensions of 20 m length (L) × 90 m width (W)× 2 m thickness (t), is formed from the heavily doped region enclosed by the dashed lines in Fig. 1. The thickness is determined by the depth of the doped single silicon layer, the width is defined by the shape of bridge region, and the length is determined by the space between the aluminum lands. A detailed process step for the fabrication of single-SCB is described in Fig. 2. The thermal oxide layer (SiO2 ) was
M.-I. Park et al. / Sensors and Actuators A 115 (2004) 104–108
used as a diffusion mask in the first photo lithography step, and photoresist development was followed by diffusion of boron impurities (∼1020 cm−3 ) at 1000 ◦ C in a quartz tube containing an inert atmosphere. Once the bridge shape was defined by the diffusion process, the aluminum was sputter-deposited onto the silicon substrate, which provides an electrical contact to SCB. A protection layer (SiO2 ), was deposited on both sides by plasma enhanced chemical vapor deposition (PECVD) without consuming the silicon surface layer [5] and was patterned in the second photolithography step. Anisotropic silicon wet etching was carried out by tetramethyl ammonium hydroxide (TMAH, (CH3 )4 NOH), which begins to slow down for boron-doping levels above approximately 1 × 1019 cm−3 [6]. Finally, the individual die used was mounted with epoxy on a TO5 header pack-
age, where the die pads were electrically attached to the pins of the header using ultrasonically bonded gold wire (0.025 mm). For the evaluation of SCB plasma discharge behaviors, a fast photo diode (Newport Biased Detector, 818-BB-21A) was combined with a firing circuit to record emission of plasma light and electrical features simultaneously from a single-shot discharge of SCB. Both the voltage signals across the SCB and the outputs of the photodiode, were recorded with a multiple channel digital oscilloscope (Agilent, 54845B) at 50 ns intervals during the firing. A capacitor discharge firing circuit (25 F, 25 V) was adopted to force the currents to the SCB with an electrical trigger pulse and off after a predetermined time delay. The firing circuit consists of a driver (Telcom Ltd., High-speed MOSFET Driver) and a timer (Samsung Electronics Ltd., Single Timer KA555/I) which can open a capacitor charged with 25 V dc voltage for 30 s pulse duration.
3. Results and discussion 3.1. Electrical characteristics of SCB devices Fig. 3 shows the voltage transient and output from the photodiode obtained from the two SCB devices when the electric energy is stored (7.8 mJ) into the chips. The solid curve represents the single-SCB while the dotted curve denotes the poly-SCB. The first and the second peak are observed to occur at 200 and 500 ns in the single-SCB, respectively; while they are found at 250 and 600 ns in the poly-SCB, respectively. The data measured in the electrical experiment are less than 10%. It is known that the melting of silicon gives rise to an abrupt increase in the resistance of the bridge, which produces the first voltage peak, and the open circuit created by the bridge melting (especially at the edges) causes the resistance of the bridge to increase instantaneously at the second voltage peak [4]. Once the bridge
Single-SCB Poly-SCB
Electrical voltage(V)
60
800 600
40 Electrical voltage
20
400
0
200 Photodiode voltage
0
250
500
750
1000
Photodiode voltage(mV)
Fig. 1. Schematics of top and cross section view of a single-SCB device.
105
0
1250
Time (ns) Fig. 2. Processing procedure for a single-SCB.
Fig. 3. Comparison of voltage and photo diode output between single-SCB and poly-SCB.
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M.-I. Park et al. / Sensors and Actuators A 115 (2004) 104–108
is vaporized, the current flows through the vapor, producing blue-colored plasma that is detected by the photo-diode. Since the onset of the second voltage peak, as depicted in the higher part of Fig. 3, coincides with the signals from the photodiode as presented in the lower part of Fig. 3 for both cases, it is clear that the single-SCB device generates the plasma discharge faster than the poly-SCB device. The electrical results therefore demonstrate enhancement of the single-SCB in term of plasma formation in comparison with the poly-SCB.
experiment and the vaporization time from the simulation. In the case of the poly-SCB device, some portion of electrical current seems to flow through the oxide layer, which yields slow heating of the bride element. The electrical currents flowing through the oxide layer could be considered as a thermal conduction loss of applied energy, though the amount is not overly large due to the small electrical conductivity of the oxide layer. Conversely, in the single-SCB device, all of the applied currents concentrate in the bridge element without any loss.
3.2. Finite element analysis for SCB devices
3.3. Theoretical modeling for thermal structures of SCB devices
In an effort to understand the results of the electrical experiment as depicted in Fig. 3, computational simulations were performed using a Sysweld package, a commercial finite element code. This package is capable of solving various three-dimensional heating and cooling problems for both transient and steady-state cases as well as considering various phase changes of materials in the course of calculation. It is thus a suitable to examine the plasma generation mechanism of SCB including the phase transition from solid to gas in a non-linear transient state. The results from the finite element analysis are shown in Fig. 4, the inset of which illustrates the structure of two igniters with the same bridge volume. Fig. 4 presents the temperature changes of the heated region in the device as a function of time when electrical energy is applied. Considering the vaporization temperature of silicon Tvapor = 2355 ◦ C, the vaporization time (tvapor ) is 520 ns in the single-SCB and 580 ns in the poly-SCB device, respectively. In addition, it is observed that the rising rate of single-SCB is faster than that of poly-SCB. Outcomes of the simulation agree well with the results presented in Fig. 3. The connection with the structure of the two devices as depicted in the inset of Fig. 4, provides an avenue to explain the relationship between the voltage peak of the electric
This section presents a study of the temperature rise on the bridge region based on the discrete element circuit model [7], to confirm the coincidence of the results between the electrical experiment and computational simulation. In this model, temperature, thermal conductor and thermal mass are equivalent to voltage, the resistor and the capacitor in the electrical circuit, respectively. In order to examine the subsequent model simply, it is assumed that all the power imposed to the system is dissipated in the bridge area and the thermal energy generated is released by only thermal conduction through the solid media. The model is applied to the thermal circuits for two devices as shown in the inset of Fig. 5. Considering the thermal structure of the single-SCB as shown in the upper inset of Fig. 5, the air gap is regarded as only a thermal capacitor because the assumption mentioned above neglects the heat conduction in the gas phase. There is one thermal resistance of the silicon membrane and two heat capacitors of the silicon bridge and air gap, respectively, in the single-SCB thermal circuit. On the other hand, each substrate component includes heat conductance and heat capacitance in the poly-SCB with the polysilicon/oxide/bulk silicon substrate structure as shown in the lower inset of Fig. 5.
Single-SCB P
Temperature (K)
400k
1/R
C
C
T
Poly-SCB
P
200k
0
1/R
1/R
1/R
2
C
C
C
T
4
Time (µs) Fig. 4. Temperature transient of SCB thermal structures based on the computational simulation.
Fig. 5. Step response curves and electric circuits for the discrete-element model of the SCB structures.
M.-I. Park et al. / Sensors and Actuators A 115 (2004) 104–108
Thus, when the heating power (P) is abruptly changed from zero to a constant at time t = 0, the time response of the single-SCB circuit (Ts ) is given by −t P Ts (t) = 1 − exp 1/Rsi τs −t 5 = 4.8 × 10 1 − exp K (1) 0.176 where Rsi represents the thermal resistance of the single silicon membrane. The time constant for the single-SCB (τ s ) is τs = Rsi (Csi + Cair ) = 0.176 s
(2)
where Csi is the thermal capacitance of the single silicon bridge and Cair the air gap, correspondingly. Instead, the equation of time rise (Tp ) for the poly-SCB circuit is as follows: P −t Tp (t) = 1 − exp 1/(Rpoly + Rox + Rsi ) τp −t = 3.9 × 105 1 − exp K (3) 1.29 where Rpoly represents the thermal resistance of the poly silicon membrane and Rox is the thermal resistance of the oxide layer. The time constant (τ p ) for the poly-SCB is then described as Cp + Cox + Csi = 1.29 s (4) τp = 1/(Rp + Rox + Rsi ) where Cp is the thermal capacitance of the poly silicon bridge and Cox is that of the oxide layer. In analyzing (1–4), the final temperature of the single-SCB is 90,000 K higher than that of the poly-SCB and the time constant of the single-SCB is about 10 times as fast as that of the poly-SCB as shown in Fig. 5. It is noted that the value of the final temperature should be understood relatively since we assume thermal modeling without considering phase transitions such as melting and evaporation related to the heat dissipation. For a simple RC time constant, the derivative of the curve at the step time crosses the final value after one time constant, and the curve reaches 63% of its final value after one time constant. It is clear that the more effective heat conduction is achieved in the single-SCB structure in light of the final temperature and the time constant results from the thermal circuit modeling.
4. Conclusions From the electrical experiments comparing single- and poly-SCB fabricated in previous works, it has been demonstrated that the peak of the single-SCB precedes that of the poly-SCB at the time of plasma generation. The results were further assessed with a computational simulation based on finite element analysis and discrete-element modeling of the
107
thermal structures. From the analysis, it was deduced that the rising rate of the temperature of the single-SCB was faster than that of the poly-SCB. The theoretical modeling for the SCB thermal structure showed that more effective heat conduction was achieved in the single-SCB, which has a simpler structure without additional layers. It is therefore clear that the oxide layer added to the silicon bridge in the poly-SCB causes a delay through the thermal conduction during the firing as well as the heat absorption. Consequently, the plasma discharge generation of the single-SCB will occur prior to that of the poly-SCB. Finally, from the aforementioned results and analysis, the structure of the SCB is found to have a significant effect on the discharge behaviors.
Acknowledgements This research was supported by the Dual Use Technology Program.
References [1] L.E. Hollander Jr., Semiconductor explosive igniter, US Patent 3,366,055, 30 January 1969. [2] B.A.M. Tovar, Electrothermal transients in highly doped phosphorous diffused silicon-on-sapphire semiconductor bridge under high current density conditions, Ph. D. dissertation, The University of New Maxico, 1993, p. 11. [3] 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. Apply. Phys. 62 (2) (1987) 1622. [4] K.-N. Lee, M.-I. Park, S.-H. Choi, C.-O. Park, H.S. Uhm, Characteristics of plasma generated by polysilicon semiconductor bridge (SCB), Sens. Actuators A 96 (2002) 252. [5] S.M. Sze, VLSI Technology, McGraw-Hill, 1998 (Chapter 3). [6] G.T.A. Kovacs, Micromachined Transducers Sourcebook, McGrawHill Inc., 1998 (Chapter 2). [7] S.M. Sze, Semiconductor Sensors, Wiley Inc., 1994 (Chapter 7).
Biographies Myung-Il Park received by BS and MS degree in the Department of 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 at KAIST. His research interests are in the area of MEMS using ultrashort pulses laser. Hyo-Tae Choo received the BS degrees in the Department of Materials Science and Engineering from Kyungpook National University in 2000 and MS degree in the Department of Materials Science and Engineering from KAIST in 2002. Currently, he is a member of research staff in the R&D division of Samsung electronics. His research interests include the design and modeling of semiconductor devices. Suk-Hwan Yoon received by BS, MS and PhD degree in the department of Mechanical Engineering from the KAIST in 1996, 1998 and 2004, respectively. Currently, he is a member of research staff in the Turbo Pump Group of Korea Aerospace Research Institute. His research interests are in the area of structural analysis of space launching vehicles.
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Chong-Ook Park received the BS degree in the Department of Metallurgical Engineering from Seoul National University in 1979, and the PhD degree in the Department of Materials Science and Engineering from Ohio State University in 1985, respectively. From 1985 to 1986, he was with University of Pennsylvania as a post doctoral and worked at LG Electronics Central Research Laboratory as the director from 1986 to 1988.
Since 1990, he has been a technical advisor at LG Electronics Corporate Institute of Technology. He joined the Department of Materials Science and Engineering at KAIST as an assistant professor in 1988 and he has been a professor since 1999. His current research fields are solid state devices, especially chemical sensors.