- Email: [email protected]
Investigation of surface PiN diodes for a novel reconfigurable antenna
Solid State Electronics 139 (2018) 48–53
Contents lists available at ScienceDirect
Solid State Electronics journal homepage: www.elsevier.com/locate/sse
Review
Investigation of surface PiN diodes for a novel reconfigurable antenna a,⁎
a
a
b
a
a
Han Su , Huiyong Hu , Heming Zhang , Bin Wang , Haiyan Kang , Yu Wang , Minru Hao a b
MARK a
Wide Bandgap Semiconductor Technology Disciplines State Key Laboratory, School of Microelectronics, Xidian University, Xi’an 710071, China School of Advanced Materials and Nanotechnology, Xidian University, Xi’an 710071, China
A R T I C L E I N F O
A B S T R A C T
The review of this paper was arranged by Dr. Y. Kuk
In this paper, investigations of surface PiN diodes developed for a reconfigurable plasma antenna have been described. To increase carrier concentration within the surface PiN diodes as much as possible, parameters of the plasma region have been extensively discussed. According to these studies, it has been found that the average carrier concentration within the ‘i’ region has been achieved the level of 1018 cm−3 at forward bias of 2 V. The carrier concentration becomes larger when the length and width of the ‘i’ region are reduced. Furthermore, a novel frequency reconfigurable antenna based on SPiN diodes is presented at Ku-band. The resonance frequencies at 13.71 GHz, 15.17 GHz, and 17.81 GHz have been easily achieved by turning on or off different sections of the antenna. The radiation efficiencies of the antenna are 79.70%, 80.70%, and 81.70%, respectively. Experimental results shown in this paper confirm the usefulness of the PiN diode’s application within a plasma antenna and other semiconductor fields.
Keywords: Surface PiN diode High carrier concentration Reconfigurable antenna
1. Introduction With the rapid development of communication technology, the traditional antenna, which is made of metal, has been gradually unable to meet the communication requirements. Metals greatly reduce the stealth performance of the antenna. Furthermore, the conventional antenna has a large weight, low flexibility and great bulk. In order to reduce the complexity of an antenna system operating on a desired frequency band, reconfigurable antennas have been developed in the last several years. Many solutions of the reconfigurable antennas have been described in the literature, and it can be divided into two groups: one is that use switches placed on the aperture (PIN diodes, field-effect transistors, or MEMS), another is that use temporarily created switches. For the first group, various predefined conducting regions were reconnected to achieve reconfigurablity, and the operating frequencies were fixed when switches location were determined. For the second group, there are no predefined conducting regions, only well-defined channels consist of PiN diodes. But in most published literature, the reconfigurable antenna contains two parts, one is made of metal, and the other is made of the PiN diodes. Thus, in this paper, a solid state plasma antenna based on surface PiN (SPiN) diodes for the achievement of reconfiguration property has been developed to meet the currentlygrowing communication requirement [1–5]. The SPiN diodes are the basic building blocks plasma channel in which the concentration of carrier should achieve a relatively high level. The high conductivity of silicon is dependent on the number of
⁎
carriers present, and at sufficiently high carrier concentration it can appear metallic to realize the radiation characteristics of the plasma antenna [6–9]. Since the SPiN diodes are not used as a classical switch, their layout is significantly different from the standard semiconductor device. The conventional PiN diode is a vertical device, where the central intrinsic region is stacked between heavily doped P+ and N+ regions. The intrinsic region dimensions are selected based on the offstate isolation, reverse breakdown voltage, and switching speed goals [10]. Our application requires quiet a different structure (surface PiN diode). In this paper, the objective is to derive a relationship between the carrier concentration within the intrinsic region (‘i’ region) and the onstate current, experiments and comparisons are also demonstrated in the next section. According to the results, the carrier concentration is greater than 1018 cm−3 within the ‘i’ region. Furthermore, a novel reconfigurable plasma antenna based on surface PiN diodes is presented in a single system. 2. Structure and analytical model 2.1. Structure of the surface PiN diode Contrary to a conventional PiN diode, the SPiN diode is a lateral device. Similar to the bulk PiN, it requires only two regions: P+ and N + embedded in a highly resistive substrate with metal contacts (Fig. 1). In this device, the carriers (electrons and holes) are confined to the top
Corresponding author at: East Main Building, No. 2 South Taibai Road, Xi’an 710071, Shaanxi, China. E-mail address: [email protected] (H. Su).
http://dx.doi.org/10.1016/j.sse.2017.09.017 Received 13 February 2017; Received in revised form 20 July 2017; Accepted 29 September 2017 Available online 05 October 2017 0038-1101/ © 2017 Elsevier Ltd. All rights reserved.
Solid State Electronics 139 (2018) 48–53
H. Su et al.
Further, np0 = pn0 = ni , and n= p (since high injection prevails). The continuity equations can then be simplified in the steady state (dn/ dt = dp / dt = 0) as follows:
0=
1 ∂Jn p−ni − q ∂x τ
0=−
(3)
1 ∂Jp p−ni − q ∂x τ
(4)
With ambipolar current equation for holes and the equation is further simplified to
d 2p p−ni p−ni = = dx 2 Dτ L2
(5)
where L is referred to as the ambipolar diffusion length, L= ambipolar diffusion coefficient
Fig. 1. Cross section of an SPiN diode, length of the ‘i’ region = W, its depth = D = 80 μm, its width = T.
D=
surface. The thickness of the ‘i’ region is within 2–3 skin depths, and separated from the device body by an oxide layer. It also required, in many applications, that the metal contacts, used for biasing the diode, should be as small as possible. In the ON state, i.e., biased in the forward direction, the PiN diode is characterized by a low resistance of the plasma of injected carriers in the ‘i’ region. Contrarily, it offers a high resistance of the area between the doped regions in the OFF state. The ‘i’ region should be conductive enough that it becomes equivalent to a quasi-metallic layer. The conductivity in the ‘i’ region is approximately proportional to the plasma concentration, the diode dimensions and boundary layers are optimized to trap carriers in well-defined channels approaching high concentration levels exceeding 1018 cm−3.
Dτ , D is
μn μp kT ∗2 q μn + μp
(6)
The general solution to Eq. (5) is
x x p(x) = Asinh ⎛ ⎞ + Bcosh ⎛ ⎞ + ni ⎝L⎠ ⎝L⎠
(7)
where A and B are constants, and it is determined by the boundary conditions. Through a series of derivations and operations, the solution is shown as follows:
p(x) = ni +
(
) ( )
(
) ( )
W W x − 2 / L⎤ μ −μ sinh ⎡ x − 2 /L⎤ ⎫ ⎪ cosh ⎡ τjPiN ⎧ ⎣ ⎦− n p ⎣ ⎦⎪ W W ⎬ μ + μ 2qL ⎨ sinh 2L cosh 2L n p ⎪ ⎪ ⎩ ⎭
(8)
The catenary carrier distribution described by this equation can be drawn, and the carrier concentration of the ‘i’ region can be calculated from the current density.
2.2. Analytical model The on-state current flow in the PiN diode is governed by three current transport mechanisms [11]:
3. Experiments and results
(1) At very low-current levels, the current transport is dominated by the recombination process within the space-charge layer of the P-N junction (referred to as the recombination current). (2) At low-current levels, the current transport is dominated by the diffusion of minority carriers injected into the ‘i’ region (referred to as the diffusion current). (3) At high-current levels, the current transport is dictated by the presence of a high concentration of both holes and electrons in the ‘i’ region (referred to as the high-level injection current).
The SPiN diode process is not complicated, using only 5–6 photomask layers. The design rules are very relaxed, with 1 μm as the smallest feature size. All fabrication steps are compatible with processing on a standard silicon line. The lot processing cycle time is short, and should provide very high yield with low cost. Together with these devices, we have manufactured some SPiN diodes using an SOI substrate, as shown in Fig. 2. Parameters and sizes for the diodes specified are given in Table 1. The bottom silicon layer was made of highly resistive silicon, while the top layer represents fairly low resistivity. For the diode 3, the testing environment of I-V characteristics is presented in Fig. 3. Fig. 4 shows I-V characteristics for simulation and experiment results at forward bias of 2 V, from which it can be seen that the actual forward current can reach 0.03 A. The simulated results slightly above experiment results, because the simulated results were obtained in an ideal situation and uneven doping within the SPiN diode or different testing environment had an important influence on I-V characteristics. The simulated forward current density distribution is also shown in Fig. 5. The relationship between the different lengths of the ‘i’ region is illustrated in Fig. 6, it can be seen that a smaller on-state current is observed when W is increased. Considering the influence of carrier lifetimes and diffusion length, carrier concentration within the ‘i’ region is decreased when W is increased. For the case of μn = 800 cm2 V−1 s−1, μp = 300 cm2 V−1 s−1, τ = 5 μs and L = 132 μm, the carrier concentration obtained by using Eq. (8) is shown in Fig. 7, which is consistent with simulation results. The on-state current of the PiN diode can be expected to increase with increasing the width of the device (T), which is illustrated in Fig. 8. The carrier distribution within the ‘i’ region obtained for the
To derive a more realistic model for the current-voltage characteristics of the PiN diode, we need to gain a better understanding of the plasma distribution within the ‘i’ region. We will carry out the calculations on the basis of the following assumptions [12]:
• Hall’s approximation applies, i.e., the junctions Pi and Ni are ideal (γ1 = γ2 = 1). • The carrier lifetime τ in the ‘i’ region will keep constant. • Quasi-neutrality prevails in the entire ‘i’ region, i.e., n = p. If there is no photo-generation, the continuity equations in the ‘i’ region can be simplified to:
dn 1 ∂Jn n−np0 = − dt q ∂x τn
(1)
dp 1 ∂Jp p−pn0 − =− dt q ∂x τp
(2)
The carrier lifetime τ over the whole of the ‘i’ region is constant. 49
Solid State Electronics 139 (2018) 48–53
H. Su et al.
Fig. 2. A photo of fabricated SPiN diodes using a SOI substrate.
Table 1 Parameters and sizes for the diodes specified. Diode
Number of diodes
W/μm
T/μm
1 2 3 6 9 10 21 30 47
1 1 1 1 1 1 3 5 10
50 20 100 100 100 100 100 100 100
100 100 100 50 20 150 100 100 100
Fig. 4. Comparison of I-V curves.
Fig. 3. The diode 3 was tested at forward bias of 2 V.
same case said above is shown in Fig. 9, indicating that the carrier concentration increases with a reduction in T. Fig. 10 shows the I-V characteristics for the diode strings that have different numbers of PiN diodes. It can be seen that a larger droop in forward current occurs when the number of diodes increased under the same voltage level.
Fig. 5. Current density distribution for the diode 3 at forward bias of 2 V.
be formed with DC control. The plasma antenna functionality depends on the radiating elements’ parameters, such as the shapes, sizes, and electrical parameters. Modifying these parameters will change the radiation characteristics of the plasma antenna. In this section, the objective is to identify the influence of these parameters (sizes, electrical conductivity, and others) on antenna functionality.
4. Design of a Ku-band reconfigurable antenna Shown in Fig. 11 is an assembled dipole antenna structure based on the previous diode 3, which is divided into several parts by bias lines. The antenna comprises 48 SPiN diodes, which are assembled end to end in sequence and are equally divided into two parts by feeding port. The antenna is modeled as a center fed dipole and the plasma channel will 50
Solid State Electronics 139 (2018) 48–53
H. Su et al.
Fig. 6. Measured I-V characteristics at different lengths: W = 20 μm, W = 50 μm, W = 100 μm.
Fig. 9. Comparison of concentration of carriers with T variation.
Fig. 10. Measured I-V characteristics at four types of PiN diodes. Fig. 7. Comparison of concentration of carriers at three different diodes.
This is because the effective length of the antenna is reduced with the increase of the length. Considering the diffusion length and doping concentration, the length of the ‘i’ region is set to be 100 μm.
4.2. The influence of the conductivity of the ‘i’ region The electrical conductivity of the plasma channel is a crucial parameter in the study of the plasma transmission properties, which is of fundamental importance to the design of the plasma antenna. It will affect the antenna gain and efficiency, and the overall antenna efficiency will be determined by the radiation resistance of the antenna and the ohmic loss resistance. Using a highly doped semiconductor material with carriers’ concentration exceeding 1018 cm−3 in the ‘i’ region will lead to high electrical conductivity. Obviously, the electrical conductivity will influence the radiation characteristics of the plasma antenna. Fig. 13 shows the simulated results of return loss and radiation patterns in E-plane. We can clearly see that the resonance frequency and the gain of the plasma antenna increase with the electrical conductivity. Considering the doping concentration and antenna performance, the electrical conductivity of the ‘i’ region is set to be 100,000 S/m. The width and depth of the ‘i’ region, the size and conductivity of the substrate and the isolation layer between the SPiN diodes have also being optimized. According to the above studies, a set of optimum parameters have being obtained: the ‘i’ region length = 100 μm, the ‘i’ region width = 100 μm, the ‘i’ region depth = 80 μm, the ‘i’ region conductivity = 105 S/m, the substrate size = 9.5 ∗ 0.1 mm2, the substrate conductivity = 0.1 S/m. Based on these parameters, the antenna’s reconfigurability was developed in the following section.
Fig. 8. Measured I-V curves at different widths: T = 20 μm, T = 50 μm, T = 100 μm, T = 150 μm.
4.1. The influence of the length of the ‘i’ region The plasma channel will be formed while a carrier concentration of 1018 cm−3 is achieved in the ‘i’ region. Based on published experimental results [10], carrier lifetimes in excess of 5 μs are possible. The carrier’s effective diffusion length is determined by the square root of the product of carrier lifetime and the diffusion constant (estimated at 35 cm2/s in silicon). This leads to an estimate of the length of the ‘i’ region being less than 200 μm. Thus, a set of data is selected to analyze its influence. Besides, the total length of the plasma antenna is kept constant by adjusting the number of diodes in this section. Fig. 12 shows the simulated return loss and radiation patterns in Eplane, from which it can be seen that the resonance frequency and the gain of the plasma antenna increase with the length of the ‘i’ region. 51
Solid State Electronics 139 (2018) 48–53
H. Su et al.
Fig. 11. Structure of the reconfigurable antenna, S = 9.8 mm.
Fig. 12. Simulated return loss and radiation patterns.
Fig. 13. Simulated return loss and radiation patterns.
strongly forward dc bias is applied on the bias lines, different sections of the plasma antenna turned on to achieve different working frequencies. A plasma antenna in three different working states is shown in Table 2. Fig. 14 presents the simulated S11 and radiation patterns in E-plane. We can see that the operating frequencies at 13.71 GHz, 15.17 GHz, and 17.81 GHz are easily achieved in one plasma antenna. Other parameters of the reconfigurable plasma antenna are shown in Table 3. Therefore, a frequency reconfigurable plasma antenna is obtained at Ku-band. These results will provide significant theoretical guidance for related reconfigurable plasma antenna design and fabrication.
Table 2 Three states of the plasma antenna. Structure
A1, A6
A2, A5
A3, A4
State 1 State 2 State 3
ON OFF OFF
ON ON OFF
ON ON ON
4.3. The antenna’s reconfigurability The antenna’s reconfigurability can be demonstrated by turning different sections on or off to change the active length of the dipole. As expected, as more sections are turned on, the resonance frequency shifts to lower values [10]. SPiN diodes are the basic building blocks of the plasma channels, which have been optimized to achieve a relatively high conductivity that is near that of a metal. The plasma antenna was divided into three parts by bias lines (A1, A6, A2, A3, A4, A5). When a
5. Conclusion Taking into account all results obtained, it has been found that the carrier concentration within the ‘i’ region is greater than 1018 cm−3 at forward bias of 2 V and the forward current is approximately equal to 30 mA. Carrier concentration within the diode becomes larger when the 52
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H. Su et al.
Fig. 14. Simulated S11 and radiation patterns. 2010;107(5):053303. [3] Russo P, Primiani VM, Cerri G, Leo RD, Vecchioni E. Experimental characterization of a surfaguide fed plasma antenna. IEEE Trans Anten Propagat 2011;59(2):425–33. [4] Li W, Zeng FH, Zhang T. Simulation of solid state plasma S-PiN diode. Chin J Elect Dev 2014;37(2):177–81. [5] Zhu HL, Liu XH, Cheung SW, Yuk TI. Frequency-reconfigurable antenna using metasurface. IEEE Trans Anten Propagat 2014;62(1):80–5. [6] Afzalian A, Flandre D. Characterization of quantum efficiency, effective lifetime and mobility in thin film ungated SOI lateral PIN photodiodes. Solid-State Electron 2007;51(2):337–42. [7] Kim SH, Lee SH, Jang J. Fabrication and characterization of low-temperature polysilicon lateral p-i-n diode. IEEE Electron Device Lett 2010;31(5):443–5. [8] Tsukuda M, Imaki H, Omura I. Ultrafast lateral 600 V silicon SOI PiN diode with geometric traps for preventing waveform oscillation. Solid-State Electron 2015;104:61–9. [9] Afzalian A, Flandre D. Physical modeling and design of thin-film SOI lateral PIN photodiodes. IEEE Trans Electron Dev 2005;52(6):1116–22. [10] Fathy AE, Rosen A, Owen HS, McGinty F, McGee DJ, Taylor GC, et al. Silicon-based reconfigurable antennas—concepts, analysis, implementation, and feasibility. IEEE Trans Microw Theory Techn 2003;51(6):1650–61. [11] Baliga BJ. Fund Power Semicon Dev 2008:204. [12] Stefan L. Power Semicon 2006:71–3.
Table 3 Other parameters of the plasma antenna. Structure
Relative bandwidth
Radiation efficiency
Gain
State 1 State 2 State 3
13.20% 13.40% 13.90%
79.70% 80.70% 81.70%
1.38 dB 1.45 dB 1.44 dB
length and width of the ‘i’ region are reduced. Therefore, a novel reconfigurable plasma antenna based on SPiN diodes has been designed in this paper. The resonance frequencies at 13.71 GHz, 15.17 GHz, and 17.81 GHz were easily achieved by turning on or off different sections of the antenna. The radiation efficiencies of the antenna are 79.70%, 80.70%, and 81.70%, respectively. Acknowledgments The authors acknowledge support from the National Natural Science Foundation of China (Grant No. 61474085), the Science Research Plan in Shaanxi Province of China (Grant No. 2016GY-085), the Opening Project of Key Laboratory of Microelectronic Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences (Grant No. 90109162905) and the Fundamental Research Funds for the Central Universities (Grant No. 20101166085).
Han Su received the B.Eng. degree in Xi'an Polytechnic University, Xi’an, China, in 2014. He is currently pursuing the Ph.D. degree with the University of Xidian, Xi’an, China. His current research interests include solid state plasma and reconfigurable antenna.
References [1] Bai YY, Xiao SQ, Liu CR, Shuai X, Wang BZ. Design of pattern reconfigurable antennas based on a two-element dipole array model. IEEE Trans Anten Propagat 2013;61(9):4867–71. [2] Kumar R, Bora D. A reconfigurable plasma antenna. J Appl Phys
53
Contents lists available at ScienceDirect
Solid State Electronics journal homepage: www.elsevier.com/locate/sse
Review
Investigation of surface PiN diodes for a novel reconfigurable antenna a,⁎
a
a
b
a
a
Han Su , Huiyong Hu , Heming Zhang , Bin Wang , Haiyan Kang , Yu Wang , Minru Hao a b
MARK a
Wide Bandgap Semiconductor Technology Disciplines State Key Laboratory, School of Microelectronics, Xidian University, Xi’an 710071, China School of Advanced Materials and Nanotechnology, Xidian University, Xi’an 710071, China
A R T I C L E I N F O
A B S T R A C T
The review of this paper was arranged by Dr. Y. Kuk
In this paper, investigations of surface PiN diodes developed for a reconfigurable plasma antenna have been described. To increase carrier concentration within the surface PiN diodes as much as possible, parameters of the plasma region have been extensively discussed. According to these studies, it has been found that the average carrier concentration within the ‘i’ region has been achieved the level of 1018 cm−3 at forward bias of 2 V. The carrier concentration becomes larger when the length and width of the ‘i’ region are reduced. Furthermore, a novel frequency reconfigurable antenna based on SPiN diodes is presented at Ku-band. The resonance frequencies at 13.71 GHz, 15.17 GHz, and 17.81 GHz have been easily achieved by turning on or off different sections of the antenna. The radiation efficiencies of the antenna are 79.70%, 80.70%, and 81.70%, respectively. Experimental results shown in this paper confirm the usefulness of the PiN diode’s application within a plasma antenna and other semiconductor fields.
Keywords: Surface PiN diode High carrier concentration Reconfigurable antenna
1. Introduction With the rapid development of communication technology, the traditional antenna, which is made of metal, has been gradually unable to meet the communication requirements. Metals greatly reduce the stealth performance of the antenna. Furthermore, the conventional antenna has a large weight, low flexibility and great bulk. In order to reduce the complexity of an antenna system operating on a desired frequency band, reconfigurable antennas have been developed in the last several years. Many solutions of the reconfigurable antennas have been described in the literature, and it can be divided into two groups: one is that use switches placed on the aperture (PIN diodes, field-effect transistors, or MEMS), another is that use temporarily created switches. For the first group, various predefined conducting regions were reconnected to achieve reconfigurablity, and the operating frequencies were fixed when switches location were determined. For the second group, there are no predefined conducting regions, only well-defined channels consist of PiN diodes. But in most published literature, the reconfigurable antenna contains two parts, one is made of metal, and the other is made of the PiN diodes. Thus, in this paper, a solid state plasma antenna based on surface PiN (SPiN) diodes for the achievement of reconfiguration property has been developed to meet the currentlygrowing communication requirement [1–5]. The SPiN diodes are the basic building blocks plasma channel in which the concentration of carrier should achieve a relatively high level. The high conductivity of silicon is dependent on the number of
⁎
carriers present, and at sufficiently high carrier concentration it can appear metallic to realize the radiation characteristics of the plasma antenna [6–9]. Since the SPiN diodes are not used as a classical switch, their layout is significantly different from the standard semiconductor device. The conventional PiN diode is a vertical device, where the central intrinsic region is stacked between heavily doped P+ and N+ regions. The intrinsic region dimensions are selected based on the offstate isolation, reverse breakdown voltage, and switching speed goals [10]. Our application requires quiet a different structure (surface PiN diode). In this paper, the objective is to derive a relationship between the carrier concentration within the intrinsic region (‘i’ region) and the onstate current, experiments and comparisons are also demonstrated in the next section. According to the results, the carrier concentration is greater than 1018 cm−3 within the ‘i’ region. Furthermore, a novel reconfigurable plasma antenna based on surface PiN diodes is presented in a single system. 2. Structure and analytical model 2.1. Structure of the surface PiN diode Contrary to a conventional PiN diode, the SPiN diode is a lateral device. Similar to the bulk PiN, it requires only two regions: P+ and N + embedded in a highly resistive substrate with metal contacts (Fig. 1). In this device, the carriers (electrons and holes) are confined to the top
Corresponding author at: East Main Building, No. 2 South Taibai Road, Xi’an 710071, Shaanxi, China. E-mail address: [email protected] (H. Su).
http://dx.doi.org/10.1016/j.sse.2017.09.017 Received 13 February 2017; Received in revised form 20 July 2017; Accepted 29 September 2017 Available online 05 October 2017 0038-1101/ © 2017 Elsevier Ltd. All rights reserved.
Solid State Electronics 139 (2018) 48–53
H. Su et al.
Further, np0 = pn0 = ni , and n= p (since high injection prevails). The continuity equations can then be simplified in the steady state (dn/ dt = dp / dt = 0) as follows:
0=
1 ∂Jn p−ni − q ∂x τ
0=−
(3)
1 ∂Jp p−ni − q ∂x τ
(4)
With ambipolar current equation for holes and the equation is further simplified to
d 2p p−ni p−ni = = dx 2 Dτ L2
(5)
where L is referred to as the ambipolar diffusion length, L= ambipolar diffusion coefficient
Fig. 1. Cross section of an SPiN diode, length of the ‘i’ region = W, its depth = D = 80 μm, its width = T.
D=
surface. The thickness of the ‘i’ region is within 2–3 skin depths, and separated from the device body by an oxide layer. It also required, in many applications, that the metal contacts, used for biasing the diode, should be as small as possible. In the ON state, i.e., biased in the forward direction, the PiN diode is characterized by a low resistance of the plasma of injected carriers in the ‘i’ region. Contrarily, it offers a high resistance of the area between the doped regions in the OFF state. The ‘i’ region should be conductive enough that it becomes equivalent to a quasi-metallic layer. The conductivity in the ‘i’ region is approximately proportional to the plasma concentration, the diode dimensions and boundary layers are optimized to trap carriers in well-defined channels approaching high concentration levels exceeding 1018 cm−3.
Dτ , D is
μn μp kT ∗2 q μn + μp
(6)
The general solution to Eq. (5) is
x x p(x) = Asinh ⎛ ⎞ + Bcosh ⎛ ⎞ + ni ⎝L⎠ ⎝L⎠
(7)
where A and B are constants, and it is determined by the boundary conditions. Through a series of derivations and operations, the solution is shown as follows:
p(x) = ni +
(
) ( )
(
) ( )
W W x − 2 / L⎤ μ −μ sinh ⎡ x − 2 /L⎤ ⎫ ⎪ cosh ⎡ τjPiN ⎧ ⎣ ⎦− n p ⎣ ⎦⎪ W W ⎬ μ + μ 2qL ⎨ sinh 2L cosh 2L n p ⎪ ⎪ ⎩ ⎭
(8)
The catenary carrier distribution described by this equation can be drawn, and the carrier concentration of the ‘i’ region can be calculated from the current density.
2.2. Analytical model The on-state current flow in the PiN diode is governed by three current transport mechanisms [11]:
3. Experiments and results
(1) At very low-current levels, the current transport is dominated by the recombination process within the space-charge layer of the P-N junction (referred to as the recombination current). (2) At low-current levels, the current transport is dominated by the diffusion of minority carriers injected into the ‘i’ region (referred to as the diffusion current). (3) At high-current levels, the current transport is dictated by the presence of a high concentration of both holes and electrons in the ‘i’ region (referred to as the high-level injection current).
The SPiN diode process is not complicated, using only 5–6 photomask layers. The design rules are very relaxed, with 1 μm as the smallest feature size. All fabrication steps are compatible with processing on a standard silicon line. The lot processing cycle time is short, and should provide very high yield with low cost. Together with these devices, we have manufactured some SPiN diodes using an SOI substrate, as shown in Fig. 2. Parameters and sizes for the diodes specified are given in Table 1. The bottom silicon layer was made of highly resistive silicon, while the top layer represents fairly low resistivity. For the diode 3, the testing environment of I-V characteristics is presented in Fig. 3. Fig. 4 shows I-V characteristics for simulation and experiment results at forward bias of 2 V, from which it can be seen that the actual forward current can reach 0.03 A. The simulated results slightly above experiment results, because the simulated results were obtained in an ideal situation and uneven doping within the SPiN diode or different testing environment had an important influence on I-V characteristics. The simulated forward current density distribution is also shown in Fig. 5. The relationship between the different lengths of the ‘i’ region is illustrated in Fig. 6, it can be seen that a smaller on-state current is observed when W is increased. Considering the influence of carrier lifetimes and diffusion length, carrier concentration within the ‘i’ region is decreased when W is increased. For the case of μn = 800 cm2 V−1 s−1, μp = 300 cm2 V−1 s−1, τ = 5 μs and L = 132 μm, the carrier concentration obtained by using Eq. (8) is shown in Fig. 7, which is consistent with simulation results. The on-state current of the PiN diode can be expected to increase with increasing the width of the device (T), which is illustrated in Fig. 8. The carrier distribution within the ‘i’ region obtained for the
To derive a more realistic model for the current-voltage characteristics of the PiN diode, we need to gain a better understanding of the plasma distribution within the ‘i’ region. We will carry out the calculations on the basis of the following assumptions [12]:
• Hall’s approximation applies, i.e., the junctions Pi and Ni are ideal (γ1 = γ2 = 1). • The carrier lifetime τ in the ‘i’ region will keep constant. • Quasi-neutrality prevails in the entire ‘i’ region, i.e., n = p. If there is no photo-generation, the continuity equations in the ‘i’ region can be simplified to:
dn 1 ∂Jn n−np0 = − dt q ∂x τn
(1)
dp 1 ∂Jp p−pn0 − =− dt q ∂x τp
(2)
The carrier lifetime τ over the whole of the ‘i’ region is constant. 49
Solid State Electronics 139 (2018) 48–53
H. Su et al.
Fig. 2. A photo of fabricated SPiN diodes using a SOI substrate.
Table 1 Parameters and sizes for the diodes specified. Diode
Number of diodes
W/μm
T/μm
1 2 3 6 9 10 21 30 47
1 1 1 1 1 1 3 5 10
50 20 100 100 100 100 100 100 100
100 100 100 50 20 150 100 100 100
Fig. 4. Comparison of I-V curves.
Fig. 3. The diode 3 was tested at forward bias of 2 V.
same case said above is shown in Fig. 9, indicating that the carrier concentration increases with a reduction in T. Fig. 10 shows the I-V characteristics for the diode strings that have different numbers of PiN diodes. It can be seen that a larger droop in forward current occurs when the number of diodes increased under the same voltage level.
Fig. 5. Current density distribution for the diode 3 at forward bias of 2 V.
be formed with DC control. The plasma antenna functionality depends on the radiating elements’ parameters, such as the shapes, sizes, and electrical parameters. Modifying these parameters will change the radiation characteristics of the plasma antenna. In this section, the objective is to identify the influence of these parameters (sizes, electrical conductivity, and others) on antenna functionality.
4. Design of a Ku-band reconfigurable antenna Shown in Fig. 11 is an assembled dipole antenna structure based on the previous diode 3, which is divided into several parts by bias lines. The antenna comprises 48 SPiN diodes, which are assembled end to end in sequence and are equally divided into two parts by feeding port. The antenna is modeled as a center fed dipole and the plasma channel will 50
Solid State Electronics 139 (2018) 48–53
H. Su et al.
Fig. 6. Measured I-V characteristics at different lengths: W = 20 μm, W = 50 μm, W = 100 μm.
Fig. 9. Comparison of concentration of carriers with T variation.
Fig. 10. Measured I-V characteristics at four types of PiN diodes. Fig. 7. Comparison of concentration of carriers at three different diodes.
This is because the effective length of the antenna is reduced with the increase of the length. Considering the diffusion length and doping concentration, the length of the ‘i’ region is set to be 100 μm.
4.2. The influence of the conductivity of the ‘i’ region The electrical conductivity of the plasma channel is a crucial parameter in the study of the plasma transmission properties, which is of fundamental importance to the design of the plasma antenna. It will affect the antenna gain and efficiency, and the overall antenna efficiency will be determined by the radiation resistance of the antenna and the ohmic loss resistance. Using a highly doped semiconductor material with carriers’ concentration exceeding 1018 cm−3 in the ‘i’ region will lead to high electrical conductivity. Obviously, the electrical conductivity will influence the radiation characteristics of the plasma antenna. Fig. 13 shows the simulated results of return loss and radiation patterns in E-plane. We can clearly see that the resonance frequency and the gain of the plasma antenna increase with the electrical conductivity. Considering the doping concentration and antenna performance, the electrical conductivity of the ‘i’ region is set to be 100,000 S/m. The width and depth of the ‘i’ region, the size and conductivity of the substrate and the isolation layer between the SPiN diodes have also being optimized. According to the above studies, a set of optimum parameters have being obtained: the ‘i’ region length = 100 μm, the ‘i’ region width = 100 μm, the ‘i’ region depth = 80 μm, the ‘i’ region conductivity = 105 S/m, the substrate size = 9.5 ∗ 0.1 mm2, the substrate conductivity = 0.1 S/m. Based on these parameters, the antenna’s reconfigurability was developed in the following section.
Fig. 8. Measured I-V curves at different widths: T = 20 μm, T = 50 μm, T = 100 μm, T = 150 μm.
4.1. The influence of the length of the ‘i’ region The plasma channel will be formed while a carrier concentration of 1018 cm−3 is achieved in the ‘i’ region. Based on published experimental results [10], carrier lifetimes in excess of 5 μs are possible. The carrier’s effective diffusion length is determined by the square root of the product of carrier lifetime and the diffusion constant (estimated at 35 cm2/s in silicon). This leads to an estimate of the length of the ‘i’ region being less than 200 μm. Thus, a set of data is selected to analyze its influence. Besides, the total length of the plasma antenna is kept constant by adjusting the number of diodes in this section. Fig. 12 shows the simulated return loss and radiation patterns in Eplane, from which it can be seen that the resonance frequency and the gain of the plasma antenna increase with the length of the ‘i’ region. 51
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Fig. 11. Structure of the reconfigurable antenna, S = 9.8 mm.
Fig. 12. Simulated return loss and radiation patterns.
Fig. 13. Simulated return loss and radiation patterns.
strongly forward dc bias is applied on the bias lines, different sections of the plasma antenna turned on to achieve different working frequencies. A plasma antenna in three different working states is shown in Table 2. Fig. 14 presents the simulated S11 and radiation patterns in E-plane. We can see that the operating frequencies at 13.71 GHz, 15.17 GHz, and 17.81 GHz are easily achieved in one plasma antenna. Other parameters of the reconfigurable plasma antenna are shown in Table 3. Therefore, a frequency reconfigurable plasma antenna is obtained at Ku-band. These results will provide significant theoretical guidance for related reconfigurable plasma antenna design and fabrication.
Table 2 Three states of the plasma antenna. Structure
A1, A6
A2, A5
A3, A4
State 1 State 2 State 3
ON OFF OFF
ON ON OFF
ON ON ON
4.3. The antenna’s reconfigurability The antenna’s reconfigurability can be demonstrated by turning different sections on or off to change the active length of the dipole. As expected, as more sections are turned on, the resonance frequency shifts to lower values [10]. SPiN diodes are the basic building blocks of the plasma channels, which have been optimized to achieve a relatively high conductivity that is near that of a metal. The plasma antenna was divided into three parts by bias lines (A1, A6, A2, A3, A4, A5). When a
5. Conclusion Taking into account all results obtained, it has been found that the carrier concentration within the ‘i’ region is greater than 1018 cm−3 at forward bias of 2 V and the forward current is approximately equal to 30 mA. Carrier concentration within the diode becomes larger when the 52
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Fig. 14. Simulated S11 and radiation patterns. 2010;107(5):053303. [3] Russo P, Primiani VM, Cerri G, Leo RD, Vecchioni E. Experimental characterization of a surfaguide fed plasma antenna. IEEE Trans Anten Propagat 2011;59(2):425–33. [4] Li W, Zeng FH, Zhang T. Simulation of solid state plasma S-PiN diode. Chin J Elect Dev 2014;37(2):177–81. [5] Zhu HL, Liu XH, Cheung SW, Yuk TI. Frequency-reconfigurable antenna using metasurface. IEEE Trans Anten Propagat 2014;62(1):80–5. [6] Afzalian A, Flandre D. Characterization of quantum efficiency, effective lifetime and mobility in thin film ungated SOI lateral PIN photodiodes. Solid-State Electron 2007;51(2):337–42. [7] Kim SH, Lee SH, Jang J. Fabrication and characterization of low-temperature polysilicon lateral p-i-n diode. IEEE Electron Device Lett 2010;31(5):443–5. [8] Tsukuda M, Imaki H, Omura I. Ultrafast lateral 600 V silicon SOI PiN diode with geometric traps for preventing waveform oscillation. Solid-State Electron 2015;104:61–9. [9] Afzalian A, Flandre D. Physical modeling and design of thin-film SOI lateral PIN photodiodes. IEEE Trans Electron Dev 2005;52(6):1116–22. [10] Fathy AE, Rosen A, Owen HS, McGinty F, McGee DJ, Taylor GC, et al. Silicon-based reconfigurable antennas—concepts, analysis, implementation, and feasibility. IEEE Trans Microw Theory Techn 2003;51(6):1650–61. [11] Baliga BJ. Fund Power Semicon Dev 2008:204. [12] Stefan L. Power Semicon 2006:71–3.
Table 3 Other parameters of the plasma antenna. Structure
Relative bandwidth
Radiation efficiency
Gain
State 1 State 2 State 3
13.20% 13.40% 13.90%
79.70% 80.70% 81.70%
1.38 dB 1.45 dB 1.44 dB
length and width of the ‘i’ region are reduced. Therefore, a novel reconfigurable plasma antenna based on SPiN diodes has been designed in this paper. The resonance frequencies at 13.71 GHz, 15.17 GHz, and 17.81 GHz were easily achieved by turning on or off different sections of the antenna. The radiation efficiencies of the antenna are 79.70%, 80.70%, and 81.70%, respectively. Acknowledgments The authors acknowledge support from the National Natural Science Foundation of China (Grant No. 61474085), the Science Research Plan in Shaanxi Province of China (Grant No. 2016GY-085), the Opening Project of Key Laboratory of Microelectronic Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences (Grant No. 90109162905) and the Fundamental Research Funds for the Central Universities (Grant No. 20101166085).
Han Su received the B.Eng. degree in Xi'an Polytechnic University, Xi’an, China, in 2014. He is currently pursuing the Ph.D. degree with the University of Xidian, Xi’an, China. His current research interests include solid state plasma and reconfigurable antenna.
References [1] Bai YY, Xiao SQ, Liu CR, Shuai X, Wang BZ. Design of pattern reconfigurable antennas based on a two-element dipole array model. IEEE Trans Anten Propagat 2013;61(9):4867–71. [2] Kumar R, Bora D. A reconfigurable plasma antenna. J Appl Phys
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