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Design Considerations for a Solar Micro Power Generator
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 50 (2014) 980 – 987
The International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES14
Design Considerations for a Solar Micro Power Generator Mazhar B. Tayel and Yahya R. Elsayed Electrical Engineering Department, Faculty of Engineering, Alexandria University, Alex. Egypt.
Abstract In this paper, a proposed design for an AC solar micro power generator is introduced. The principle of operation is based on double conversion of incident solar energy to mechanical energy to electrical energy by exciting a Bilayer microcantilever composed of semiconductor and metal to induce electronic stress. The Bilayer microcantilever deflection is used to chop the incident solar energy to produce mechanical oscillation. The produced mechanical oscillation is to be converted to an AC signal using electret-based electrostatic conversion principle. The simulation shows that the obtained electrical AC is in the range from Pico to nano Watt, irrespective of its very low efficiency it is suitable for ultra-low power consuming devices. Ltd. This is an open article under the CC BY-NC-ND license © 2014 2014Elsevier The Authors. Published byaccess Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD). Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) Keywords : Solar energy ; MEMS ; Bilayer microcantilver.
1. Introduction Microelectromencanical systems (MEMS) can participate in the power generation as Micro Power Generators (MPGs). In this study, a proposed design considerations for an AC solar micro power generator (SMPG) is introduced. It is based on Double conversion of solar energy (SE) into electrical energy, through exciting a bilayer microcantilever (BMC) with sunlight to have mechanical oscillation, then convert the mechanical oscillation to AC electrical signal by the electrostatic concept. 2. The Proposed Design 2.1. Model Structure The proposed (SMPG) structure is shown in fig. 1. The fixed and movable plates have optically alligned apertures. The movable plate is suspended by a micro flexure (MF). The BMC is composed of two layers, semiconductor (SC) and metal. Three electret charges are used, one on the BMC tip, the second on the bottom of the movable plate, and the third electret-electrode under the BMC. They are used for electrostatic conversion.
1876-6102 © 2014 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2014.06.117
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(a)
Movable plate
Incident SE
(b)
Fixed plate
MF Reflector B
Reflector A Light chopper
Ps
BMC
x2
x1
Poi
Electrets Movable plate aperture
Electrode
Fixed plate aperture
Fig. 1. (a) The Basic structure of the SMPG; (b) slit shapes in fixed and movable plate
2.2. Principle of operation 2.2.1. Photoinduced stress When the BMC is exposed to the double reflected sunlight, it will absorb the reflected SE. Part of the absorbed SE will be converted to heat causing thermal stress on both the metal and SC layers. Another part of the absorbed SE generates free charge carriers (electron - hole pairs) in the SC layer causing electronic stress [1,2]. Due to different surface stresses on both layers, the BMC will deflect by a certain amount that depends on the incident SE and the BMC structure and materials. Since electronic deflection (due to electronic stress) is much greater than thermal deflection (about four times the thermal deflection) [1]. hence the only considered deflection in this proposed model must be the electronic deflection (Ze), that is given by [1]: ܼ௧ ؆ ൌ Ʉሺ
ఒ
ሻ
ଵ א
ɒ
א
൨
ͳ ʹ
(1)
ܲܨሺݐǡ ܧሻ
where (dא / dP) is the pressure dependence of the SC, K is the quantum efficiency, W is the carrier life time of the SC, P is the total absorbed power,O is the incident wavelength , Og and א are the cut-off wavelength and band gap of the SC respectively, ܨሺݐǡ ܧሻ ൌ ሾݎ௧ ݎ௧ ଶ ሿ൬͵ሾͳ ݎ௧ ሿଶ
ଵ
ିଵ
ݎ௧ ଶ ൨ ൣͳ ݎ௧ ݎ௬ ൧൰
ሺʹሻ
is defined as geometry-material factor, rt =(t1/t2) is the thicknesses ratio, ry =(E1/E2) is the Young’s modulus ratio and suffixes 1, 2 corresponds to layer-1 and layer-2 respectively. 2.2.2. SE chopping During deflection of the BMC, the space between the two electrets decreases and the electrostatic repulsion force will increase. This shifts the movable plate from its initial position, fig. 2-a., to the shifted upward position, leading to closing of apertures, fig. 2-b. The movable plate will be shifted upward by an amount ('x) depending on the strength of the electrostatic repulsion force between the two electrets and the MF spring constant. 2.2.3. Exposure area The upward shift ('x) will decrease the exposure area (As) according to [3]:
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ݔ ݓെ ݓଵ ሺο ݔെ ݔଵ ሻ݄݊݁ݓο ݔ൏ ݔଵ ܣ௦ ሺοݔሻ ൌ ൜ ଶ ଶ ݓଶ ݔଶ െ ݓଶ ሺο ݔെ ݔଵ ሻ݄݊݁ݓο ݔ ݔଵ
ሺ͵ሻ
where w and x are the width and height, suffixes 1 and 2 refer to the large side and small side of the aperture respectively. Equation (3) shows that when the shift is ('x = x1), the exposure area will be decreased to (ܣ௦ ሺݔଵ ሻ ൌ ݓଶ ݔଶ ሻ , and when the shift is ('x = x1 + x2), the exposure area will be decreased to zero (ܣ௦ ሺݔଵ ݔଶ ሻ ൌ Ͳሻ, i.e. no SE incident on the BMC surface, as shown in fig. 3. (a)
(b)
Po
Zbmc
Fig. 2. (a) The BMC at initial position ; (b) The BMC at deflected position. .
$rea (Pm2)
w1x1+w2x2
'x=x1+x2 w1 x1
' 'x=x1 Fig. 3. The change in exposure area due to shift of the movable plate.
'x
The incident SE on the BMC surface at certain shift ('x) is given by: where
ܲሺοݔሻ ൌ ܲ௦ ܰ כ௦ ܲ௦ ൌ ܲ ܣ௦ ሺοݔሻ
ሺͶሻ (5)
where Ns is the number of apertures in the movable plate, Poi is the incident power density per unit area, and (As) is exposure area that passes light from the aperture in the fixed plate to the corresponding aperture in the movable plate as shown in fig. 1-b. Based on the fact that the BMC electronic deflection response time is equal to the charge carrier life time (W) in the SC layer [1], t after one (W) the incident SE will drive the BMC to deflect (Zmax) as represented in fig. 4-a, i.e. it shifts the movable plate by ('x = x1+ x2) as shown in fig. 4-b and fig 4-b. Thus, the exposure area becomes zero , which in turns decreases the incident SE to be zero as shown in fig. 4- d. 2.2.4. Oscillation mechanism During the interval (W - 2W), there is no incident SE on the BMC, hence the BMC will start to relax toward its initial position, which inturn causes the MF to relax [4]:
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If the MF material is selected to relax slower than the BMC, so that after the (0-W) interval the MF will relax by (x2), which means that the BMC surface will be exposed to the small side of the aperture at the end of (W to 2W) as shown in fig. 4-c, thus and the BMC will respond by small deflection corresponding to the small exposure area. In the next interval time (2W to 3W), the movable plate will continue relaxation and exposes the BMC surface by more incident SE through the wide part of the aperture resulting in larger BMC deflection. The relaxation will continue till the repulsion force stops the relaxation of the movable plate (at point (P) where the shift theoretically assumed to be ('x=x1 +0.5 x2 ) , fig. 4-d. When the repulsion force stops the MF relaxation, the exposure area will start to decrease again and the BMC will continue deflection till it decreases the incident SE again to zero at the end of the interval (2W to 3W). Starting from the interval (3W), the BMC will be in the same position as in the interval (W) and the BMC will relax again and the process will be repetitive, i.e. mechanical oscillation is obtained. The mechanical energy that obtained from the mechanical oscillation is converted to electrical energy through the electret-based electrostatic principle. Ze
Zmax
Zmin
(a)
'x x x (b)
F
x 0.5x
F
Time
P(t) (c)
W
W
W
W
W Time
(d)
'x=0
'x=x1+x2
'x=x2
'x=x1 +0.5 x2 'x=x1+ x2
'x=x2
'x=x1+x2
Fig. 4. (a) The BMC deflection; (b) The movable plate shift; (c) The incident exposure power; (d) exposure part of the aperture according to shift.
3. Maximizing the BMC Deflection The BMC deflection can be maximized for a certain incident SE by proper choice of the BMC geometry and material elasticity. This can be done using equation (2), and illustrated by fig (5-a) that shows the (F) factor variation with respect to the thicknesses ratio for different values of Young’s modulus ratio.
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Mazhar B. Tayel and Yahya R. Elsayed / Energy Procedia 50 (2014) 980 – 987 F (a)
0.18
(b)
0.16 0.14
0.075
0.12
Fmax
0.065
0.1
T.O
0.08 0.06 0.04
0.055 0.045
0.02 0
0.085
0.5 0.8 1.1 1.4 1.7 2 2.3 2.6 2.9
rt(opt)
0
ry rt Fig. 5. (a) The BMC deflection as a function of thickness ratio; (b) The T.O versus the Young’s modulus ratio. 1
2
3
4
5
6
7
8
9
10
From fig. 5-a it is seen that the factor (F) has different maximum values corresponding to certain optimum thickness ratios (rt(opt)) that depends on Young’s modulus ratio (ry) value. It is worth to note that the factor F and the value rt(opt) increases as ry decreases. This indicates the need to extract a trade-off factor (T.O) as : ܶǤ ܱ ൌ
ி ሺሻ
(6)
Figure (5-b) shows the value of the T.O. against the young’s modulus ration (ry). From figure (5-b) it is seen that at (ry=0.9), the best solution for maximizing the factor (F) is to select thickness ratio (r t) that achieves (Fmax / rt(opt))=0.074. 4. Selection of SC material Material elasticity and the BMC dimensions are not the only parameters that can maximize the deflection, but also the band gap energy, pressure dependence material and thermal conductivity of the SC layer are to be considered. For a selected SC material that provides maximum deflection for a certain SE power, it should have high thermal conductivity, low band gap energy, high pressure dependence parameter, and high elasticity. Let’s propose a figure of merit (M) for the selected SC as follows: ܯൌכ݃כܧ
ௗሺא ሻ
(7)
ௗ
The figure of merit calculated for some SC is shown in table (1). Table 1. Semiconductor Material Properties [2]. Semiconductor
(ev)
InSb Ge Si GaAs
0.16 0.67 1.12 1.35
d /dP (10-24 cm3) 23.6 11.52 -3.14 -13.67
E (Gpa) 42.79 102.66 130.91 85.5
g (Wm-1 k-1) 36 59 163 55
M 227,214 104,143 59,818 47,617
From Table (1), it is seen that Indium Antimoniode (InSb) has the highest figure of merit (227.214), which means that the (InSb) will give larger deflection than other candidate semiconductor. Also it is worth to note that Silicon and Gallium Arsenide have negative pressure dependence parameter which means that the electronic deflection will be in the opposite direction with respect to the thermal deflection, thus reduces the net BMC deflection [1].
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5. Power Generation 5.1. Modeling the Power Conversion Circuit The BMC deflection over the bottom electret can be modelled as electret-based electrostatic conversion circuit as shown in fig. 6-a. The BMC deflection changes the gap between the BMC and bottom electret resulting in capacitance change as shown in fig. 6-b. The circuit model is shown in fig. 6-c. It consists of variable capacitor C(t) connected in series with the load resistance (R), the voltage source represents the surface voltage of the bottom electret[5]. (a)
L
L
(b)
(c)
Z(x)
C2
de
C1
Fig. 6.(a) Electrostatic power circuit; (b) capacitance variation due to deflection; ( c) modelling the electrostatic conversion circuit model.
From fig. 6-a, the total capacitance of the circuit is the sum of the capacitance in the electret part connected in series with the variable capacitance between the electret and the BMC. The total capacitance normalized to C1 is given by [21]: ሺ௧ሻ భ
where
ൌ
ଵ
(8)
ଵାభ Ȁమ ሺ௧ሻ
ఢ ఢ ௪
ܥଵ ൌ
(9)
ௗ
is the capacitance in the electret part, ߳ is the relative dielectric constant of the electret, L and w are the length and the width of the bottom electret respectively, and the capacitance (C2(t) ) is the capacitance between the BMC and bottom electrode. The capacitance C2(t) above the electret at certain small part (dx) to corresponding a deflection Z(t , x) at a given time (t), fig. 6-b. is given by :
ܥଶ ሺݐሻ ൌ οܥଶ ሺݐǡ ݔሻ ݀ ݔൌ
where ܼሺݐǡ ݔሻ ൌ
ሺ௧ǡሻ
Then equation (10) yields ܥଶ ሺݐሻ ൌ
ఢ ௪ ሺ௧ǡሻ
ఢ ௪ ௗబ ାሺ௧ǡ௫ሻ
(10)
݀ݔ
(11)
ݔכ
ቂ ሺͳ
ሺ௧ǡሻ ௗబ
(12)
ሻቃ
Substituting by equation (12) into equation (8), the total capacitance is: ܥሺݐሻ ൌ ܥଵ
ೋሺǡಽሻ ሻ బ ೋሺǡಽሻ ሺ௧ǡሻఢ ାௗ ୪୬ ሺଵା ሻ బ
ௗ ୪୬ ሺଵା
(13)
The output current in the load resistance can be calculated from the circuit loop as [5]: ݅ൌ
ௗொమ ௗ௧
ଵ
ொమ
ோ
ሺ௧ሻ
ൌ ሺܸ െ
(14)
ሻ
where Ve is the surface voltage of the electret , Q2 is the charge of the BMC metal layer. The instantaneous harvested power inside load resistance (R) is [5]: ଵ
ொమ
ோ
ሺ௧ሻ
ܲሺݐሻ ൌ ݅ ଶ ܴൌൌ ሺܸ െ
ሻଶ
ሺͳͷሻ
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6. MATLAB Simulation for Power Conversion The MATLAB SIMULINK is used to simulate the expected output power from the SMPG. To simplifying the model simulation, three assumptions are introduced. The first assumption is neglecting the electrostatic force between the electret and the BMC metal layer. The second assumption is that the BMC deflection is triangle signal with peak value (Z(L) =80 Pm) with oscillating frequency ( f=1/2W = 5 KHz ) as shown in fig. 7-a. ((a)) Deflection (m)
(b)
do +0.5Zbmc(t)
C2(t)
Fig. 7. (a) The assumed input BMC deflection signal; (b) Simplified NMC deflection conversion model.
The third assumption is that the BMC acts as parallel plate with respect to the lower electrode with average deflection value, i.e. (Zav=0.5 ZBMC) as shown in fig 7-b. By computing the capacitance C2(t) according to this assumption and substituting into equation (12), the total capacitance becomes: ܥሺݐሻ ൌ ܥଵ
ௗ
(16)
ௗ ାఢ ሺௗబ ାǤହ್ ሺ௧ǡሻሻ
Table 2. values used in the simulation. W (BMC width) 80 (Pm)
L (BMC length) 500 (Pm)
Ve (electret) 1400 volt
do (initial gap) 100 (Pm)
de (electret thickness) 10 (Pm)
The model is represented by the block diagram shown in fig. 8. dQ2/dt
Current
V R Capacitance
0.5 Zbmc
0.5 BMC deflection
ͳ ܵ Zbmc
C(t)
Instantaneous power
Q2 u2
ͳ ݑ
Capacitance calculation
Current R
Average power
Load Resistance Integration period (T) Fig. 8. The Block diagram of the power conversion circuit.
The average output power obtained from the SMPG for one cycle (T=2W) is: ଵ
்
ܲ ൌ ሺݐሻ݀ݐ ்
(17)
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The simulation has been done using the values in table (2) for two values of load resistance (R=200 M and R= 2 G ). The obtained results of the output current and power are shown in table (3), and is plotted in fig 9-a and fig 9-b. Table 3. Simulation results for output current and power. output \ Resistance Peak Current (nA) Average Power (pico Watt)
R= 200M 19.2 7 (b)
(a)
R= 2G 16.8 60
-11
8
x 10
R=200 M(ohm) R=2000M(ohm)
-8
2
x 10
7
R=200 M(ohm) R=2000M(ohm)
1.5
6
Power (W)
Current (A)
1
0.5
0
-0.5
-1
4
3
2
-1.5
-2 1
5
1
2
3
4 Time
Time (S)
5
6 -4
x 10
0 2
3
4
Time (S)
5
6 -4
x 10
Fig. 9. (a) output current.; (b) The average power .
7. Conclusions -
The proposed model introduces a new type of solar energy harvesting techniques using MEMS technology with its known features. The output power of the proposed model is a design dependent. i.e. the output power can be optimized by proper selection of materials and geometry. Arranged arrays of this SMPG can be used to obtain more electrical power, for example, if a structure arrays dimensions of few centimetres are used , the output power expected to be in the range of micro Watt The neglected thermal part of SE can be utilized to produce more power, for example, a pyroelectric material layer can be used instead of metal layer to convert the solar heat energy to electrical energy. MEMS technology provides relatively cheaper technology compared to the convenient PV technology, as well as the facility between the sensors and its own power circuit.
References [1]
Panos G.Datskos “ Micromechanical Uncooled photon Detectors” Oak Ridge National Laboratory , MS-8039
[2]
Zhang Liuqiang, Den Daiwei, Wang Qiang “Optimized Design of High Sensitivity Micromechanical Photon Detectors” International MEMS Conference 2006
[3]
Yahya R. Elsayed , “ Aproposed Solar Micro Power Generator” , thesis ( Msc), Alexandria university , Alexandria Egypt 2014.
[4] David G. Alciatore and Michael B. Histand “Introduction to Mechatronics and Measurement Systems” 4th ed - chapter.4 , McGraw-Hill , New York (2012), ISBN 978-0-07-338023-0. [5] S. Boisseau, G. Despesse and B. Ahmed Seddik, “Electrostatic Conversion for Vibration Energy Harvesting, Small-Scale Energy Harvesting”, Innovative Computing Technology (INTECH), Morocco, 2012.
ScienceDirect Energy Procedia 50 (2014) 980 – 987
The International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES14
Design Considerations for a Solar Micro Power Generator Mazhar B. Tayel and Yahya R. Elsayed Electrical Engineering Department, Faculty of Engineering, Alexandria University, Alex. Egypt.
Abstract In this paper, a proposed design for an AC solar micro power generator is introduced. The principle of operation is based on double conversion of incident solar energy to mechanical energy to electrical energy by exciting a Bilayer microcantilever composed of semiconductor and metal to induce electronic stress. The Bilayer microcantilever deflection is used to chop the incident solar energy to produce mechanical oscillation. The produced mechanical oscillation is to be converted to an AC signal using electret-based electrostatic conversion principle. The simulation shows that the obtained electrical AC is in the range from Pico to nano Watt, irrespective of its very low efficiency it is suitable for ultra-low power consuming devices. Ltd. This is an open article under the CC BY-NC-ND license © 2014 2014Elsevier The Authors. Published byaccess Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD). Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) Keywords : Solar energy ; MEMS ; Bilayer microcantilver.
1. Introduction Microelectromencanical systems (MEMS) can participate in the power generation as Micro Power Generators (MPGs). In this study, a proposed design considerations for an AC solar micro power generator (SMPG) is introduced. It is based on Double conversion of solar energy (SE) into electrical energy, through exciting a bilayer microcantilever (BMC) with sunlight to have mechanical oscillation, then convert the mechanical oscillation to AC electrical signal by the electrostatic concept. 2. The Proposed Design 2.1. Model Structure The proposed (SMPG) structure is shown in fig. 1. The fixed and movable plates have optically alligned apertures. The movable plate is suspended by a micro flexure (MF). The BMC is composed of two layers, semiconductor (SC) and metal. Three electret charges are used, one on the BMC tip, the second on the bottom of the movable plate, and the third electret-electrode under the BMC. They are used for electrostatic conversion.
1876-6102 © 2014 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2014.06.117
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Mazhar B. Tayel and Yahya R. Elsayed / Energy Procedia 50 (2014) 980 – 987
(a)
Movable plate
Incident SE
(b)
Fixed plate
MF Reflector B
Reflector A Light chopper
Ps
BMC
x2
x1
Poi
Electrets Movable plate aperture
Electrode
Fixed plate aperture
Fig. 1. (a) The Basic structure of the SMPG; (b) slit shapes in fixed and movable plate
2.2. Principle of operation 2.2.1. Photoinduced stress When the BMC is exposed to the double reflected sunlight, it will absorb the reflected SE. Part of the absorbed SE will be converted to heat causing thermal stress on both the metal and SC layers. Another part of the absorbed SE generates free charge carriers (electron - hole pairs) in the SC layer causing electronic stress [1,2]. Due to different surface stresses on both layers, the BMC will deflect by a certain amount that depends on the incident SE and the BMC structure and materials. Since electronic deflection (due to electronic stress) is much greater than thermal deflection (about four times the thermal deflection) [1]. hence the only considered deflection in this proposed model must be the electronic deflection (Ze), that is given by [1]: ܼ௧ ؆ ൌ Ʉሺ
ఒ
ሻ
ଵ א
ɒ
א
൨
ͳ ʹ
(1)
ܲܨሺݐǡ ܧሻ
where (dא / dP) is the pressure dependence of the SC, K is the quantum efficiency, W is the carrier life time of the SC, P is the total absorbed power,O is the incident wavelength , Og and א are the cut-off wavelength and band gap of the SC respectively, ܨሺݐǡ ܧሻ ൌ ሾݎ௧ ݎ௧ ଶ ሿ൬͵ሾͳ ݎ௧ ሿଶ
ଵ
ିଵ
ݎ௧ ଶ ൨ ൣͳ ݎ௧ ݎ௬ ൧൰
ሺʹሻ
is defined as geometry-material factor, rt =(t1/t2) is the thicknesses ratio, ry =(E1/E2) is the Young’s modulus ratio and suffixes 1, 2 corresponds to layer-1 and layer-2 respectively. 2.2.2. SE chopping During deflection of the BMC, the space between the two electrets decreases and the electrostatic repulsion force will increase. This shifts the movable plate from its initial position, fig. 2-a., to the shifted upward position, leading to closing of apertures, fig. 2-b. The movable plate will be shifted upward by an amount ('x) depending on the strength of the electrostatic repulsion force between the two electrets and the MF spring constant. 2.2.3. Exposure area The upward shift ('x) will decrease the exposure area (As) according to [3]:
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ݔ ݓെ ݓଵ ሺο ݔെ ݔଵ ሻ݄݊݁ݓο ݔ൏ ݔଵ ܣ௦ ሺοݔሻ ൌ ൜ ଶ ଶ ݓଶ ݔଶ െ ݓଶ ሺο ݔെ ݔଵ ሻ݄݊݁ݓο ݔ ݔଵ
ሺ͵ሻ
where w and x are the width and height, suffixes 1 and 2 refer to the large side and small side of the aperture respectively. Equation (3) shows that when the shift is ('x = x1), the exposure area will be decreased to (ܣ௦ ሺݔଵ ሻ ൌ ݓଶ ݔଶ ሻ , and when the shift is ('x = x1 + x2), the exposure area will be decreased to zero (ܣ௦ ሺݔଵ ݔଶ ሻ ൌ Ͳሻ, i.e. no SE incident on the BMC surface, as shown in fig. 3. (a)
(b)
Po
Zbmc
Fig. 2. (a) The BMC at initial position ; (b) The BMC at deflected position. .
$rea (Pm2)
w1x1+w2x2
'x=x1+x2 w1 x1
' 'x=x1 Fig. 3. The change in exposure area due to shift of the movable plate.
'x
The incident SE on the BMC surface at certain shift ('x) is given by: where
ܲሺοݔሻ ൌ ܲ௦ ܰ כ௦ ܲ௦ ൌ ܲ ܣ௦ ሺοݔሻ
ሺͶሻ (5)
where Ns is the number of apertures in the movable plate, Poi is the incident power density per unit area, and (As) is exposure area that passes light from the aperture in the fixed plate to the corresponding aperture in the movable plate as shown in fig. 1-b. Based on the fact that the BMC electronic deflection response time is equal to the charge carrier life time (W) in the SC layer [1], t after one (W) the incident SE will drive the BMC to deflect (Zmax) as represented in fig. 4-a, i.e. it shifts the movable plate by ('x = x1+ x2) as shown in fig. 4-b and fig 4-b. Thus, the exposure area becomes zero , which in turns decreases the incident SE to be zero as shown in fig. 4- d. 2.2.4. Oscillation mechanism During the interval (W - 2W), there is no incident SE on the BMC, hence the BMC will start to relax toward its initial position, which inturn causes the MF to relax [4]:
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If the MF material is selected to relax slower than the BMC, so that after the (0-W) interval the MF will relax by (x2), which means that the BMC surface will be exposed to the small side of the aperture at the end of (W to 2W) as shown in fig. 4-c, thus and the BMC will respond by small deflection corresponding to the small exposure area. In the next interval time (2W to 3W), the movable plate will continue relaxation and exposes the BMC surface by more incident SE through the wide part of the aperture resulting in larger BMC deflection. The relaxation will continue till the repulsion force stops the relaxation of the movable plate (at point (P) where the shift theoretically assumed to be ('x=x1 +0.5 x2 ) , fig. 4-d. When the repulsion force stops the MF relaxation, the exposure area will start to decrease again and the BMC will continue deflection till it decreases the incident SE again to zero at the end of the interval (2W to 3W). Starting from the interval (3W), the BMC will be in the same position as in the interval (W) and the BMC will relax again and the process will be repetitive, i.e. mechanical oscillation is obtained. The mechanical energy that obtained from the mechanical oscillation is converted to electrical energy through the electret-based electrostatic principle. Ze
Zmax
Zmin
(a)
'x x x (b)
F
x 0.5x
F
Time
P(t) (c)
W
W
W
W
W Time
(d)
'x=0
'x=x1+x2
'x=x2
'x=x1 +0.5 x2 'x=x1+ x2
'x=x2
'x=x1+x2
Fig. 4. (a) The BMC deflection; (b) The movable plate shift; (c) The incident exposure power; (d) exposure part of the aperture according to shift.
3. Maximizing the BMC Deflection The BMC deflection can be maximized for a certain incident SE by proper choice of the BMC geometry and material elasticity. This can be done using equation (2), and illustrated by fig (5-a) that shows the (F) factor variation with respect to the thicknesses ratio for different values of Young’s modulus ratio.
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Mazhar B. Tayel and Yahya R. Elsayed / Energy Procedia 50 (2014) 980 – 987 F (a)
0.18
(b)
0.16 0.14
0.075
0.12
Fmax
0.065
0.1
T.O
0.08 0.06 0.04
0.055 0.045
0.02 0
0.085
0.5 0.8 1.1 1.4 1.7 2 2.3 2.6 2.9
rt(opt)
0
ry rt Fig. 5. (a) The BMC deflection as a function of thickness ratio; (b) The T.O versus the Young’s modulus ratio. 1
2
3
4
5
6
7
8
9
10
From fig. 5-a it is seen that the factor (F) has different maximum values corresponding to certain optimum thickness ratios (rt(opt)) that depends on Young’s modulus ratio (ry) value. It is worth to note that the factor F and the value rt(opt) increases as ry decreases. This indicates the need to extract a trade-off factor (T.O) as : ܶǤ ܱ ൌ
ி ሺሻ
(6)
Figure (5-b) shows the value of the T.O. against the young’s modulus ration (ry). From figure (5-b) it is seen that at (ry=0.9), the best solution for maximizing the factor (F) is to select thickness ratio (r t) that achieves (Fmax / rt(opt))=0.074. 4. Selection of SC material Material elasticity and the BMC dimensions are not the only parameters that can maximize the deflection, but also the band gap energy, pressure dependence material and thermal conductivity of the SC layer are to be considered. For a selected SC material that provides maximum deflection for a certain SE power, it should have high thermal conductivity, low band gap energy, high pressure dependence parameter, and high elasticity. Let’s propose a figure of merit (M) for the selected SC as follows: ܯൌכ݃כܧ
ௗሺא ሻ
(7)
ௗ
The figure of merit calculated for some SC is shown in table (1). Table 1. Semiconductor Material Properties [2]. Semiconductor
(ev)
InSb Ge Si GaAs
0.16 0.67 1.12 1.35
d /dP (10-24 cm3) 23.6 11.52 -3.14 -13.67
E (Gpa) 42.79 102.66 130.91 85.5
g (Wm-1 k-1) 36 59 163 55
M 227,214 104,143 59,818 47,617
From Table (1), it is seen that Indium Antimoniode (InSb) has the highest figure of merit (227.214), which means that the (InSb) will give larger deflection than other candidate semiconductor. Also it is worth to note that Silicon and Gallium Arsenide have negative pressure dependence parameter which means that the electronic deflection will be in the opposite direction with respect to the thermal deflection, thus reduces the net BMC deflection [1].
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5. Power Generation 5.1. Modeling the Power Conversion Circuit The BMC deflection over the bottom electret can be modelled as electret-based electrostatic conversion circuit as shown in fig. 6-a. The BMC deflection changes the gap between the BMC and bottom electret resulting in capacitance change as shown in fig. 6-b. The circuit model is shown in fig. 6-c. It consists of variable capacitor C(t) connected in series with the load resistance (R), the voltage source represents the surface voltage of the bottom electret[5]. (a)
L
L
(b)
(c)
Z(x)
C2
de
C1
Fig. 6.(a) Electrostatic power circuit; (b) capacitance variation due to deflection; ( c) modelling the electrostatic conversion circuit model.
From fig. 6-a, the total capacitance of the circuit is the sum of the capacitance in the electret part connected in series with the variable capacitance between the electret and the BMC. The total capacitance normalized to C1 is given by [21]: ሺ௧ሻ భ
where
ൌ
ଵ
(8)
ଵାభ Ȁమ ሺ௧ሻ
ఢ ఢ ௪
ܥଵ ൌ
(9)
ௗ
is the capacitance in the electret part, ߳ is the relative dielectric constant of the electret, L and w are the length and the width of the bottom electret respectively, and the capacitance (C2(t) ) is the capacitance between the BMC and bottom electrode. The capacitance C2(t) above the electret at certain small part (dx) to corresponding a deflection Z(t , x) at a given time (t), fig. 6-b. is given by :
ܥଶ ሺݐሻ ൌ οܥଶ ሺݐǡ ݔሻ ݀ ݔൌ
where ܼሺݐǡ ݔሻ ൌ
ሺ௧ǡሻ
Then equation (10) yields ܥଶ ሺݐሻ ൌ
ఢ ௪ ሺ௧ǡሻ
ఢ ௪ ௗబ ାሺ௧ǡ௫ሻ
(10)
݀ݔ
(11)
ݔכ
ቂ ሺͳ
ሺ௧ǡሻ ௗబ
(12)
ሻቃ
Substituting by equation (12) into equation (8), the total capacitance is: ܥሺݐሻ ൌ ܥଵ
ೋሺǡಽሻ ሻ బ ೋሺǡಽሻ ሺ௧ǡሻఢ ାௗ ୪୬ ሺଵା ሻ బ
ௗ ୪୬ ሺଵା
(13)
The output current in the load resistance can be calculated from the circuit loop as [5]: ݅ൌ
ௗொమ ௗ௧
ଵ
ொమ
ோ
ሺ௧ሻ
ൌ ሺܸ െ
(14)
ሻ
where Ve is the surface voltage of the electret , Q2 is the charge of the BMC metal layer. The instantaneous harvested power inside load resistance (R) is [5]: ଵ
ொమ
ோ
ሺ௧ሻ
ܲሺݐሻ ൌ ݅ ଶ ܴൌൌ ሺܸ െ
ሻଶ
ሺͳͷሻ
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6. MATLAB Simulation for Power Conversion The MATLAB SIMULINK is used to simulate the expected output power from the SMPG. To simplifying the model simulation, three assumptions are introduced. The first assumption is neglecting the electrostatic force between the electret and the BMC metal layer. The second assumption is that the BMC deflection is triangle signal with peak value (Z(L) =80 Pm) with oscillating frequency ( f=1/2W = 5 KHz ) as shown in fig. 7-a. ((a)) Deflection (m)
(b)
do +0.5Zbmc(t)
C2(t)
Fig. 7. (a) The assumed input BMC deflection signal; (b) Simplified NMC deflection conversion model.
The third assumption is that the BMC acts as parallel plate with respect to the lower electrode with average deflection value, i.e. (Zav=0.5 ZBMC) as shown in fig 7-b. By computing the capacitance C2(t) according to this assumption and substituting into equation (12), the total capacitance becomes: ܥሺݐሻ ൌ ܥଵ
ௗ
(16)
ௗ ାఢ ሺௗబ ାǤହ್ ሺ௧ǡሻሻ
Table 2. values used in the simulation. W (BMC width) 80 (Pm)
L (BMC length) 500 (Pm)
Ve (electret) 1400 volt
do (initial gap) 100 (Pm)
de (electret thickness) 10 (Pm)
The model is represented by the block diagram shown in fig. 8. dQ2/dt
Current
V R Capacitance
0.5 Zbmc
0.5 BMC deflection
ͳ ܵ Zbmc
C(t)
Instantaneous power
Q2 u2
ͳ ݑ
Capacitance calculation
Current R
Average power
Load Resistance Integration period (T) Fig. 8. The Block diagram of the power conversion circuit.
The average output power obtained from the SMPG for one cycle (T=2W) is: ଵ
்
ܲ ൌ ሺݐሻ݀ݐ ்
(17)
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Mazhar B. Tayel and Yahya R. Elsayed / Energy Procedia 50 (2014) 980 – 987
The simulation has been done using the values in table (2) for two values of load resistance (R=200 M and R= 2 G ). The obtained results of the output current and power are shown in table (3), and is plotted in fig 9-a and fig 9-b. Table 3. Simulation results for output current and power. output \ Resistance Peak Current (nA) Average Power (pico Watt)
R= 200M 19.2 7 (b)
(a)
R= 2G 16.8 60
-11
8
x 10
R=200 M(ohm) R=2000M(ohm)
-8
2
x 10
7
R=200 M(ohm) R=2000M(ohm)
1.5
6
Power (W)
Current (A)
1
0.5
0
-0.5
-1
4
3
2
-1.5
-2 1
5
1
2
3
4 Time
Time (S)
5
6 -4
x 10
0 2
3
4
Time (S)
5
6 -4
x 10
Fig. 9. (a) output current.; (b) The average power .
7. Conclusions -
The proposed model introduces a new type of solar energy harvesting techniques using MEMS technology with its known features. The output power of the proposed model is a design dependent. i.e. the output power can be optimized by proper selection of materials and geometry. Arranged arrays of this SMPG can be used to obtain more electrical power, for example, if a structure arrays dimensions of few centimetres are used , the output power expected to be in the range of micro Watt The neglected thermal part of SE can be utilized to produce more power, for example, a pyroelectric material layer can be used instead of metal layer to convert the solar heat energy to electrical energy. MEMS technology provides relatively cheaper technology compared to the convenient PV technology, as well as the facility between the sensors and its own power circuit.
References [1]
Panos G.Datskos “ Micromechanical Uncooled photon Detectors” Oak Ridge National Laboratory , MS-8039
[2]
Zhang Liuqiang, Den Daiwei, Wang Qiang “Optimized Design of High Sensitivity Micromechanical Photon Detectors” International MEMS Conference 2006
[3]
Yahya R. Elsayed , “ Aproposed Solar Micro Power Generator” , thesis ( Msc), Alexandria university , Alexandria Egypt 2014.
[4] David G. Alciatore and Michael B. Histand “Introduction to Mechatronics and Measurement Systems” 4th ed - chapter.4 , McGraw-Hill , New York (2012), ISBN 978-0-07-338023-0. [5] S. Boisseau, G. Despesse and B. Ahmed Seddik, “Electrostatic Conversion for Vibration Energy Harvesting, Small-Scale Energy Harvesting”, Innovative Computing Technology (INTECH), Morocco, 2012.