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Characteristics of semiconductor bridge (SCB) plasma generated in a micro-electro-mechanical system (MEMS)
Physics Letters A 305 (2002) 413–418 www.elsevier.com/locate/pla
Characteristics of semiconductor bridge (SCB) plasma generated in a micro-electro-mechanical system (MEMS) Jong-Uk Kim a,∗ , Chong-Ook Park b , Myung-Il Park b , Sun-Hwan Kim c , Jung-Bok Lee c a Korea Electrotechnology Research Institute, Center for Advanced Accelerators, 28-1 Seongju-dong, Changwon 641-120, South Korea b Department of Materials Science and Engineering, KAIST, 373-1 Kusong-dong, Yusong, Taejon 305-701, South Korea c Hanwha Coporation, R&D Center, 50 Kojan-dong, Namdong-Gu, Inchon, South Korea
Received 17 October 2002; received in revised form 23 October 2002; accepted 28 October 2002 Communicated by F. Porcelli
Abstract Plasma ignition method has been applied in various fields particularly to the rocket propulsion, pyrotechnics, explosives, and to the automotive air-bag system. Ignition method for those applications should be safe and also operate reliably in hostile environments such as; electromagnetic noise, drift voltage, electrostatic background and so on. In the present Letter, a semiconductor bridge (SCB) plasma ignition device was fabricated and its plasma characteristics including the propagation speed of the plasma, plasma size, and plasma temperature were investigated with the aid of the visualization of micro scale plasma (i.e., 350 µm), which generated from a micro-electro-mechanical poly-silicon semiconductor bridge (SCB). 2002 Elsevier Science B.V. All rights reserved.
1. Introduction The micro-scale semiconductor bridge (SCB) produces hot plasma when applied by relatively a short and low electrical energy pulse (i.e., 10 mJ). The idea of the SCB plasma is originally conceived by Hollander [1] and developed further by Benson et al. [2] and Tovar [3] to apply it to pyrotechnic or secondary explosive devices [1]. In such devices, the duration of the plasma discharge is less than few µs and the plasma temperature is known to be around 4200–
* Corresponding author.
E-mail address: [email protected] (J.-U. Kim).
5500 K [2,3], which is sufficient to ignite explosive materials such as pyrotechnics, propellants, and primary or secondary explosive powders. Furthermore, the SCB ignition device consumes relatively small energy input compared to traditional hot-wire devices with decreasing the firing times by one or two orders of magnitude [2]. Therefore, it may enhance performance capabilities for automotive air-bag devices and conventional pyrotechnic applications with improving no-fire conditions and electrostatic safety. In the current Letter, the characteristics of the SCB plasma, which originated from the micro-scale polysilicon semiconductor bridge (poly-SCB) [4], have been investigated by measuring the output voltage characteristics of the discharging plasma and also,
0375-9601/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 ( 0 2 ) 0 1 4 9 8 - 6
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J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
by visualizing the plasma emission with respect to time to understand the flow characteristics of the SCB plasma. In this Letter, the SCB plasma temperature has been also estimated by measuring the propagation speed of the plasma and the results were compared with the previous experiments [2], in which the size of the SCB is similar to the present Letter.
2. Experimental—design and operation of the SCB plasma Since the detailed process for the fabrication of single-SCB is well described in our earlier work [4], we will just briefly refer to the structure of the SCB here. A single-SCB is consisted of a “H” shaped thin single crystal silicon membrane that is directly wetetched as depicted in Fig. 1 and two metal lands of aluminum are attached on a membrane. The bridge, 20 µm long (L) by 90 µm wide (W) by 2 µm thick (t), is formed from the heavily boron-doped region enclosed by the dashed lines in Fig. 1. The thickness is determined by the depth of the boron-doped single silicon layer and the width is defined by the shape of bridge region, and the length is determined by the space between the aluminum lands. The electrical resistance obtained between the gaps is approximately ≈ 1 . The fabricated SCB plasma ignition device is presented in Fig. 2. As seen in Fig. 2(b), the SCB micro-scale plasma chip is located in the center
Fig. 1. Schematic of the boron-doped polysilicon semiconductor bridge (SCB). The size of the bridge is 20 µm in length (L), 90 µm in width (W), and 2 µm in thickness (t), respectively.
(i.e., dotted circle) and solid insulation material (i.e., ceramic) was used to provide the electrical insulation between the SCB and the main housing of the ignition unit. A schematic diagram of the experimental arrangement for generation of micro-scale SCB plasma is shown in Fig. 3. The plasma source is generated by the rapid discharge of ≈ 8 mJ of electrical energy into a polysilicon substrate located between two aluminum electrodes that are apart approximately 20 µm. The energy is stored in a 25 µF capacitor, charged to a maximum of 25 V. The SCB plasma ignition unit is operated with a capacitor firing circuit (25 µF, 25 V) to switch the current on with an electrical trigger pulse and off after a predetermined time delay. The firing circuit is consisted of a power driver (Telcom Ltd., Highspeed MOSFET Driver) and a timer (Samsung Elec-
(a)
(b)
Fig. 2. An example of the manufactured SCB plasma-firing device. (a) Side view, (b) top view.
Fig. 3. Schematic diagram of the SCB plasma discharge experimental setup.
J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
tronics Ltd., Single Timer KA555/I), which generates a rectangular electronic pulse of 30 µs pulse duration. And this firing circuit functions to open a capacitor that charged with 25 V DC voltage. Once the SCB plasma discharge is initiated with breakdown of the electrical energy between two aluminum electrodes, then the subsequent ablation and ionization of material from the surface of boron-doped polysilicon sustains the main plasma discharge. The resulting plasma rapidly expands into room air and the temporal evolution of the emission from the SCB plasma is then obtained by a commercially available Kodak DC 260 1536 × 1024 digital CCD camera (whose resolution is 7.5 µm × 7.5 µm), triggered by a delay generator at desirable times. It should be noted that since the SCB is designed to be used in the automotive air-bag system the SCB is disposal after use. Therefore, the SCB is broken after electric discharge. For the evaluation of SCB plasma discharge behaviors, the voltage characteristics across the SCB were recorded with a multiple channel digital oscilloscope (Agilent, 54845B) at 50 ns intervals during the firing. Since the size of the SCB is very small (i.e., 2 µm × 20 µm × 90 µm) the emission from the SCB is very weak (i.e., ≈ 8 mJ discharge), therefore, a magnifying optical system was employed in front of the CCD detector and the resultant image is magnified approximately ≈ 70 times. The obtained images are then transferred to computer hard disk for further analysis.
3. Results and discussions The discharging voltage characteristic through the SCB plasma is measured with time, which is presented in Fig. 4. The duration of the SCB plasma for discharge energy of 8 mJ is less than few µs and the measured peak current and the voltage are approximately 30 A and 55 V, respectively. Interestingly, however, there were two peaks observed in the SCB discharge at t ≈ 250 ns (i.e., denoted as (a) in Fig. 4), and t ≈ 600 ns (i.e., denoted as (b) in Fig. 4), respectively. Those two peaks are mainly attributed to the phase transitions of the SCB from solid to liquid or hot temperature vapor for the former peak, and from liquid or vapor phase to hot temperature plasma for the latter peak, respectively.
415
Fig. 4. Voltage characteristics of the SCB plasma.
Temporal evolution of the typical SCB plasma is shown in Fig. 5. The spatial resolution of the plasma is well indicated in the figure with a white bar at t ≈ 50 ns. Here, z and r are the vertical and horizontal directions from the surface of the SCB unit, respectively. Since only one image can be obtained per every plasma shot the present image in Fig. 5 is the ensemble averaged with 5 subsequent images at specific time. As shown in Fig. 5, it shows the SCB plasma emission at the beginning of the plasma discharge (i.e., when triggered the SCB unit at t ≈ 50 ns) and the plasma shape seems to be uneven revealing the sizes of approximately 180 and 150 µm in the horizontal (r) and vertical (z) directions, respectively. The reason for relatively longer size in horizontal direction than vertical at t ≈ 50 ns is attributed to the SCB structure, which is imposed to discharge the voltage between the aluminum electrodes in horizontal (r) direction. As time increased further, the vertical size of the plasma increased. It can be clearly seen that with the increase of the time the whole part of the SCB plasma expands further and the plasma emission intensity correspondingly increases until t ≈ 600 ns. Also, it should be noted that in the SCB plasma, two components, a bright core and its blur ambient surrounding it, could be found in Fig. 5. Li et al. [5], found that the bright core part is mainly consisted of hot temperature plasma with atoms, ions and electrons in it, while the blur ambient part is consisted of more like a vaporous plume. The change of the emission intensities of the SCB plasma/plume images in Fig. 5 is plotted in Fig. 6 as a function of time. The symbols are the mea-
416
J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
Fig. 5. Typical images of the SCB plasma with respect to time.
sured mean intensity averaged with 5 consequent images, and the line is the best polynomial fit to the data. As seen in Fig. 6, the mean intensity increased continuously from the beginning of its discharge and reached
to peak intensity of the emission at t ≈ 600 ns. When the delay is more than 600 ns, the intensity of the emission decreased rapidly. This is in excellent agreement with the electric discharge characteristic curve
J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
Fig. 6. Mean intensity of the SCB plasma emission with respect to time.
Fig. 7. Radial (r) and axial (z) plasma size with respect to time.
observed in Fig. 4. The decrease in emission intensity is attributed to the energy (or heat) transfer from the hot plasma core to ambient air, which has relatively cooled temperature encircling the plasma. Temporal evolutions of the SCB plasma are plotted in Fig. 7. Here, the symbols (i.e., rectangle and circle represent the fully expanded horizontal and vertical size of the plasma) are measurements and the solid and dashed lines are best fits to the data. Generally, as time increased the size of the plasma increased correspondingly in both directions. Specifically, for t 100 ns the horizontal size of the plasma expanded faster, while for 100 t 700 ns the vertical size of the plasma expanded faster than the horizontal size. When t ≈ 600 ns, the plasma seemed to be
417
developed fully and after that it decreased. Again, this is believed to be due to the plasma quenching by thermal diffusion of relatively cooled ambient gas into the hot plasma as the pressure of the plasma decreases when the plasma discharge terminates [6]. The plasma expansion speeds for both the vertical (z) and horizontal (r) directions with respect to time were calculated as the time derivative of the curve fits to the data points in Fig. 7, and it is presented in Fig. 8. The highest expansion speeds for both directions were found when the discharge is initiated and their approximate values were ≈ 1.15 × 105 and ≈ 0.55 × 105 cm/s for the vertical and horizontal directions, respectively. By the time t ≈ 300 ns the plasma expansion speeds were dramatically reduced and they finally came to stop at t ≈ 600 ns. When the delay time is greater than 600 ns, both the plasma expansion speeds have negative values. This means that at this time of delay, the direction of the motion is reversed, retreating upstream towards the SCB due to a pressure decrease in the SCB plasma as the discharge terminates [6]. Previously, Benson et al. [2], measured the SCB plasma temperature (Te ) by optical emission spectroscopy using a very much similar scheme of the SCB device studied here. In order to estimate the plasma temperature, they employed an optical multichannel analyzer (OMA) and obtained the SCB emission spectra. They found the SCB plasma is mainly consisted of Si+ , Si, and neutral Al. Their best estimates of the SCB plasma temperature from the spectral line analy-
Fig. 8. Propagation speed of the SCB plasma with respect to time.
418
J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
sis were ranged from 4200 K to 5500 K. In order to estimate the SCB plasma temperature (Te ) investigated here, we used shock speed expression of Vs ≈ [γ Z ∗ kTe /Mi ]1/2 assuming that the pressure of the SCB plasma is greater than the background pressure [7]. Here, γ is the specific heat ratio of order of unity and Z ∗ , k, Mi are ionization level of SCB plasma, Boltzmann constant, and mass of the ionized gas, respectively. The SCB, which is mainly consisted of silicon (Si), has very small size (i.e., 2 µm × 20 µm × 90 µm) and the mass within the volume can be calculated as ≈ 8.4 × 10−9 g. This amount of mass corresponds to approximately ≈ 1.8 × 1014 Si-atoms in the SCB. Considering the physical properties of Si the energy required for evaporation of this amount of Siatoms can be calculated as approximately ≈ 0.13 mJ. From the curve of the energy dissipated in the SCB, which we have reported earlier [4], the electrical energy applied to the SCB continuously after its evaporation can be estimated as ≈ 0.7 mJ. This amount of energy is presumably thought to be consumed to heat and ionize the evaporated Si-gases and finally to produce Si-plasma in the SCB. Considering the total number of the Si-atoms in the SCB (i.e., ≈ 1.8 × 1014) the average energy applied to the individual Si-atom in the SCB can be calculated as ≈ 6.45 eV. This amount of energy corresponds to approximately 80% of the first ionization level of Si-atom (i.e., first ionization energy of Si-atom is 8.151 eV), therefore, it is reasonable to assume that the ionization level of the SCB plasma is roughly ≈ 0.8. Applying this value with the mass of the Si-atom to the shock speed expression noted earlier, the peak plasma temperature can be estimated as ≈ 5600 (K) and this value is in good agreement with the previous measurement reported by Benson et al (i.e., 4200–5500 K) [2].
4. Conclusions In conclusion, very small size plasma, which was produced from a microchip-size semiconductor bridge
(SCB) designed to be used in a plasma ignition method such as rocket propulsion or automotive air-bag system, was obtained and its fluid characteristics including the plasma size, plasma expansion speed and temperature were investigated. It indicated that as time increased, the size of the plasma increased correspondingly, showing fully developed plasma around t ≈ 600 ns after the plasma discharge. As time increased further, the size of the plasma decreased. This is attributed to the plasma quenching by thermal diffusion of relatively cooled ambient gas into the hot plasma as the pressure of the plasma decreases when the plasma discharge terminates [6]. The highest plasma expansion speed was measured as ≈ 1.15 × 105 cm/s at early time in the SCB plasma discharge. Also, the corresponding peak plasma temperature was calculated as a value of ≈ 5600 K, and it shows a good agreement with the previous results [2]. However, further studies are required for the careful understanding of the microchip plasma, especially axial and radial distribution of the electron number density and plasma temperature, more detail.
References [1] L.E. Hollander Jr., Semiconductor explosive igniter, US Patent 3 366 055, issued January 30, 1969. [2] D.A. Benson, M.E. Larsen, A.M. Renfund, W.M. Trott, R.W. Bickes Jr., J. Appl. Phys. 62 (1987) 1622. [3] B.A.M. Tovar, Electrothermal transients in highly doped phosphorous diffused silicon-on-sapphire semiconductor bridge under high current density conditions, PhD dissertation, University of New Mexico, 1993. [4] K.-N. Lee, M.-I. Park, S.-H. Choi, C.-O. Park, H.S. Uhm, Sens. Actuators A 96 (2002) 252. [5] P. Li, D. Lim, J. Mazumder, J. Appl. Phys. 92 (2002) 666. [6] J.U. Kim, N.T. Clemens, P. Varghese, Appl. Phys. Lett. 80 (2002) 368. [7] T.R. Clark, H.M. Milchberg, Phys. Rev. Lett. 78 (1997) 2373.
Characteristics of semiconductor bridge (SCB) plasma generated in a micro-electro-mechanical system (MEMS) Jong-Uk Kim a,∗ , Chong-Ook Park b , Myung-Il Park b , Sun-Hwan Kim c , Jung-Bok Lee c a Korea Electrotechnology Research Institute, Center for Advanced Accelerators, 28-1 Seongju-dong, Changwon 641-120, South Korea b Department of Materials Science and Engineering, KAIST, 373-1 Kusong-dong, Yusong, Taejon 305-701, South Korea c Hanwha Coporation, R&D Center, 50 Kojan-dong, Namdong-Gu, Inchon, South Korea
Received 17 October 2002; received in revised form 23 October 2002; accepted 28 October 2002 Communicated by F. Porcelli
Abstract Plasma ignition method has been applied in various fields particularly to the rocket propulsion, pyrotechnics, explosives, and to the automotive air-bag system. Ignition method for those applications should be safe and also operate reliably in hostile environments such as; electromagnetic noise, drift voltage, electrostatic background and so on. In the present Letter, a semiconductor bridge (SCB) plasma ignition device was fabricated and its plasma characteristics including the propagation speed of the plasma, plasma size, and plasma temperature were investigated with the aid of the visualization of micro scale plasma (i.e., 350 µm), which generated from a micro-electro-mechanical poly-silicon semiconductor bridge (SCB). 2002 Elsevier Science B.V. All rights reserved.
1. Introduction The micro-scale semiconductor bridge (SCB) produces hot plasma when applied by relatively a short and low electrical energy pulse (i.e., 10 mJ). The idea of the SCB plasma is originally conceived by Hollander [1] and developed further by Benson et al. [2] and Tovar [3] to apply it to pyrotechnic or secondary explosive devices [1]. In such devices, the duration of the plasma discharge is less than few µs and the plasma temperature is known to be around 4200–
* Corresponding author.
E-mail address: [email protected] (J.-U. Kim).
5500 K [2,3], which is sufficient to ignite explosive materials such as pyrotechnics, propellants, and primary or secondary explosive powders. Furthermore, the SCB ignition device consumes relatively small energy input compared to traditional hot-wire devices with decreasing the firing times by one or two orders of magnitude [2]. Therefore, it may enhance performance capabilities for automotive air-bag devices and conventional pyrotechnic applications with improving no-fire conditions and electrostatic safety. In the current Letter, the characteristics of the SCB plasma, which originated from the micro-scale polysilicon semiconductor bridge (poly-SCB) [4], have been investigated by measuring the output voltage characteristics of the discharging plasma and also,
0375-9601/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 ( 0 2 ) 0 1 4 9 8 - 6
414
J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
by visualizing the plasma emission with respect to time to understand the flow characteristics of the SCB plasma. In this Letter, the SCB plasma temperature has been also estimated by measuring the propagation speed of the plasma and the results were compared with the previous experiments [2], in which the size of the SCB is similar to the present Letter.
2. Experimental—design and operation of the SCB plasma Since the detailed process for the fabrication of single-SCB is well described in our earlier work [4], we will just briefly refer to the structure of the SCB here. A single-SCB is consisted of a “H” shaped thin single crystal silicon membrane that is directly wetetched as depicted in Fig. 1 and two metal lands of aluminum are attached on a membrane. The bridge, 20 µm long (L) by 90 µm wide (W) by 2 µm thick (t), is formed from the heavily boron-doped region enclosed by the dashed lines in Fig. 1. The thickness is determined by the depth of the boron-doped single silicon layer and the width is defined by the shape of bridge region, and the length is determined by the space between the aluminum lands. The electrical resistance obtained between the gaps is approximately ≈ 1 . The fabricated SCB plasma ignition device is presented in Fig. 2. As seen in Fig. 2(b), the SCB micro-scale plasma chip is located in the center
Fig. 1. Schematic of the boron-doped polysilicon semiconductor bridge (SCB). The size of the bridge is 20 µm in length (L), 90 µm in width (W), and 2 µm in thickness (t), respectively.
(i.e., dotted circle) and solid insulation material (i.e., ceramic) was used to provide the electrical insulation between the SCB and the main housing of the ignition unit. A schematic diagram of the experimental arrangement for generation of micro-scale SCB plasma is shown in Fig. 3. The plasma source is generated by the rapid discharge of ≈ 8 mJ of electrical energy into a polysilicon substrate located between two aluminum electrodes that are apart approximately 20 µm. The energy is stored in a 25 µF capacitor, charged to a maximum of 25 V. The SCB plasma ignition unit is operated with a capacitor firing circuit (25 µF, 25 V) to switch the current on with an electrical trigger pulse and off after a predetermined time delay. The firing circuit is consisted of a power driver (Telcom Ltd., Highspeed MOSFET Driver) and a timer (Samsung Elec-
(a)
(b)
Fig. 2. An example of the manufactured SCB plasma-firing device. (a) Side view, (b) top view.
Fig. 3. Schematic diagram of the SCB plasma discharge experimental setup.
J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
tronics Ltd., Single Timer KA555/I), which generates a rectangular electronic pulse of 30 µs pulse duration. And this firing circuit functions to open a capacitor that charged with 25 V DC voltage. Once the SCB plasma discharge is initiated with breakdown of the electrical energy between two aluminum electrodes, then the subsequent ablation and ionization of material from the surface of boron-doped polysilicon sustains the main plasma discharge. The resulting plasma rapidly expands into room air and the temporal evolution of the emission from the SCB plasma is then obtained by a commercially available Kodak DC 260 1536 × 1024 digital CCD camera (whose resolution is 7.5 µm × 7.5 µm), triggered by a delay generator at desirable times. It should be noted that since the SCB is designed to be used in the automotive air-bag system the SCB is disposal after use. Therefore, the SCB is broken after electric discharge. For the evaluation of SCB plasma discharge behaviors, the voltage characteristics across the SCB were recorded with a multiple channel digital oscilloscope (Agilent, 54845B) at 50 ns intervals during the firing. Since the size of the SCB is very small (i.e., 2 µm × 20 µm × 90 µm) the emission from the SCB is very weak (i.e., ≈ 8 mJ discharge), therefore, a magnifying optical system was employed in front of the CCD detector and the resultant image is magnified approximately ≈ 70 times. The obtained images are then transferred to computer hard disk for further analysis.
3. Results and discussions The discharging voltage characteristic through the SCB plasma is measured with time, which is presented in Fig. 4. The duration of the SCB plasma for discharge energy of 8 mJ is less than few µs and the measured peak current and the voltage are approximately 30 A and 55 V, respectively. Interestingly, however, there were two peaks observed in the SCB discharge at t ≈ 250 ns (i.e., denoted as (a) in Fig. 4), and t ≈ 600 ns (i.e., denoted as (b) in Fig. 4), respectively. Those two peaks are mainly attributed to the phase transitions of the SCB from solid to liquid or hot temperature vapor for the former peak, and from liquid or vapor phase to hot temperature plasma for the latter peak, respectively.
415
Fig. 4. Voltage characteristics of the SCB plasma.
Temporal evolution of the typical SCB plasma is shown in Fig. 5. The spatial resolution of the plasma is well indicated in the figure with a white bar at t ≈ 50 ns. Here, z and r are the vertical and horizontal directions from the surface of the SCB unit, respectively. Since only one image can be obtained per every plasma shot the present image in Fig. 5 is the ensemble averaged with 5 subsequent images at specific time. As shown in Fig. 5, it shows the SCB plasma emission at the beginning of the plasma discharge (i.e., when triggered the SCB unit at t ≈ 50 ns) and the plasma shape seems to be uneven revealing the sizes of approximately 180 and 150 µm in the horizontal (r) and vertical (z) directions, respectively. The reason for relatively longer size in horizontal direction than vertical at t ≈ 50 ns is attributed to the SCB structure, which is imposed to discharge the voltage between the aluminum electrodes in horizontal (r) direction. As time increased further, the vertical size of the plasma increased. It can be clearly seen that with the increase of the time the whole part of the SCB plasma expands further and the plasma emission intensity correspondingly increases until t ≈ 600 ns. Also, it should be noted that in the SCB plasma, two components, a bright core and its blur ambient surrounding it, could be found in Fig. 5. Li et al. [5], found that the bright core part is mainly consisted of hot temperature plasma with atoms, ions and electrons in it, while the blur ambient part is consisted of more like a vaporous plume. The change of the emission intensities of the SCB plasma/plume images in Fig. 5 is plotted in Fig. 6 as a function of time. The symbols are the mea-
416
J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
Fig. 5. Typical images of the SCB plasma with respect to time.
sured mean intensity averaged with 5 consequent images, and the line is the best polynomial fit to the data. As seen in Fig. 6, the mean intensity increased continuously from the beginning of its discharge and reached
to peak intensity of the emission at t ≈ 600 ns. When the delay is more than 600 ns, the intensity of the emission decreased rapidly. This is in excellent agreement with the electric discharge characteristic curve
J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
Fig. 6. Mean intensity of the SCB plasma emission with respect to time.
Fig. 7. Radial (r) and axial (z) plasma size with respect to time.
observed in Fig. 4. The decrease in emission intensity is attributed to the energy (or heat) transfer from the hot plasma core to ambient air, which has relatively cooled temperature encircling the plasma. Temporal evolutions of the SCB plasma are plotted in Fig. 7. Here, the symbols (i.e., rectangle and circle represent the fully expanded horizontal and vertical size of the plasma) are measurements and the solid and dashed lines are best fits to the data. Generally, as time increased the size of the plasma increased correspondingly in both directions. Specifically, for t 100 ns the horizontal size of the plasma expanded faster, while for 100 t 700 ns the vertical size of the plasma expanded faster than the horizontal size. When t ≈ 600 ns, the plasma seemed to be
417
developed fully and after that it decreased. Again, this is believed to be due to the plasma quenching by thermal diffusion of relatively cooled ambient gas into the hot plasma as the pressure of the plasma decreases when the plasma discharge terminates [6]. The plasma expansion speeds for both the vertical (z) and horizontal (r) directions with respect to time were calculated as the time derivative of the curve fits to the data points in Fig. 7, and it is presented in Fig. 8. The highest expansion speeds for both directions were found when the discharge is initiated and their approximate values were ≈ 1.15 × 105 and ≈ 0.55 × 105 cm/s for the vertical and horizontal directions, respectively. By the time t ≈ 300 ns the plasma expansion speeds were dramatically reduced and they finally came to stop at t ≈ 600 ns. When the delay time is greater than 600 ns, both the plasma expansion speeds have negative values. This means that at this time of delay, the direction of the motion is reversed, retreating upstream towards the SCB due to a pressure decrease in the SCB plasma as the discharge terminates [6]. Previously, Benson et al. [2], measured the SCB plasma temperature (Te ) by optical emission spectroscopy using a very much similar scheme of the SCB device studied here. In order to estimate the plasma temperature, they employed an optical multichannel analyzer (OMA) and obtained the SCB emission spectra. They found the SCB plasma is mainly consisted of Si+ , Si, and neutral Al. Their best estimates of the SCB plasma temperature from the spectral line analy-
Fig. 8. Propagation speed of the SCB plasma with respect to time.
418
J.-U. Kim et al. / Physics Letters A 305 (2002) 413–418
sis were ranged from 4200 K to 5500 K. In order to estimate the SCB plasma temperature (Te ) investigated here, we used shock speed expression of Vs ≈ [γ Z ∗ kTe /Mi ]1/2 assuming that the pressure of the SCB plasma is greater than the background pressure [7]. Here, γ is the specific heat ratio of order of unity and Z ∗ , k, Mi are ionization level of SCB plasma, Boltzmann constant, and mass of the ionized gas, respectively. The SCB, which is mainly consisted of silicon (Si), has very small size (i.e., 2 µm × 20 µm × 90 µm) and the mass within the volume can be calculated as ≈ 8.4 × 10−9 g. This amount of mass corresponds to approximately ≈ 1.8 × 1014 Si-atoms in the SCB. Considering the physical properties of Si the energy required for evaporation of this amount of Siatoms can be calculated as approximately ≈ 0.13 mJ. From the curve of the energy dissipated in the SCB, which we have reported earlier [4], the electrical energy applied to the SCB continuously after its evaporation can be estimated as ≈ 0.7 mJ. This amount of energy is presumably thought to be consumed to heat and ionize the evaporated Si-gases and finally to produce Si-plasma in the SCB. Considering the total number of the Si-atoms in the SCB (i.e., ≈ 1.8 × 1014) the average energy applied to the individual Si-atom in the SCB can be calculated as ≈ 6.45 eV. This amount of energy corresponds to approximately 80% of the first ionization level of Si-atom (i.e., first ionization energy of Si-atom is 8.151 eV), therefore, it is reasonable to assume that the ionization level of the SCB plasma is roughly ≈ 0.8. Applying this value with the mass of the Si-atom to the shock speed expression noted earlier, the peak plasma temperature can be estimated as ≈ 5600 (K) and this value is in good agreement with the previous measurement reported by Benson et al (i.e., 4200–5500 K) [2].
4. Conclusions In conclusion, very small size plasma, which was produced from a microchip-size semiconductor bridge
(SCB) designed to be used in a plasma ignition method such as rocket propulsion or automotive air-bag system, was obtained and its fluid characteristics including the plasma size, plasma expansion speed and temperature were investigated. It indicated that as time increased, the size of the plasma increased correspondingly, showing fully developed plasma around t ≈ 600 ns after the plasma discharge. As time increased further, the size of the plasma decreased. This is attributed to the plasma quenching by thermal diffusion of relatively cooled ambient gas into the hot plasma as the pressure of the plasma decreases when the plasma discharge terminates [6]. The highest plasma expansion speed was measured as ≈ 1.15 × 105 cm/s at early time in the SCB plasma discharge. Also, the corresponding peak plasma temperature was calculated as a value of ≈ 5600 K, and it shows a good agreement with the previous results [2]. However, further studies are required for the careful understanding of the microchip plasma, especially axial and radial distribution of the electron number density and plasma temperature, more detail.
References [1] L.E. Hollander Jr., Semiconductor explosive igniter, US Patent 3 366 055, issued January 30, 1969. [2] D.A. Benson, M.E. Larsen, A.M. Renfund, W.M. Trott, R.W. Bickes Jr., J. Appl. Phys. 62 (1987) 1622. [3] B.A.M. Tovar, Electrothermal transients in highly doped phosphorous diffused silicon-on-sapphire semiconductor bridge under high current density conditions, PhD dissertation, University of New Mexico, 1993. [4] K.-N. Lee, M.-I. Park, S.-H. Choi, C.-O. Park, H.S. Uhm, Sens. Actuators A 96 (2002) 252. [5] P. Li, D. Lim, J. Mazumder, J. Appl. Phys. 92 (2002) 666. [6] J.U. Kim, N.T. Clemens, P. Varghese, Appl. Phys. Lett. 80 (2002) 368. [7] T.R. Clark, H.M. Milchberg, Phys. Rev. Lett. 78 (1997) 2373.