1 Introduction

Due to the advance of CMOS VLSI technology, the power consumption of electronic devices has been reduced considerably. The low-power technology enables the development of such applications as wireless sensor networks (Rabaey et al. 2000) or personal health monitoring (Tashiro et al. 2000), where remote or independent power supply is critical for building more compact or longer-lifetime systems. In particular, energy scavenging from ambient natural sources, such as vibration (Roundy et al. 2002), radioisotope (Lal et al. 2005) and ambient heat (Douseki et al. 2003), is attracting much recent interest as a self-sustainable power source for these applications. Among various approaches, electrostatic vibration-to-electricity conversion using the micro-electromechanical systems (MEMS) technology is chosen in this study due to its compatibility to IC processes and the ubiquity of the energy source in nature.

The output power of a vibration driven energy converter is closely related to the nature of the vibration source, which must be known in order to design the converter and estimate the generated power. The vibration spectra of several household appliances were measured. A typical vibration source has a peak acceleration of about 2.25 m/s2 at about 120 Hz, as shown in Fig. 1. These values are used in the following static and dynamic analysis for the design of the converter.

Fig. 1
figure 1

Typical vibration spectrum of a household appliance

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2 Design

A variable capacitor C v formed by an in-plane gap-closing comb structure is the main component in the energy converter (Roundy et al. 2002; Williams and Yates 1996), as shown in Fig. 2. Figure 3 shows a schematic circuit that can be used to extract the converted energy. The variable capacitor C v is charged by an external voltage source V in through the switch SW1 when C v is at its maximum C max. When C v is charged to V in, SW1 is opened and then the capacitance is changed from C max to C min due to the electrode displacement caused by vibration. In this process, the charge Q on the capacitor remains constant (SW1 and SW2 both open). Therefore, the terminal voltage on the capacitor is increased and the vibration energy is converted to the electrostatic energy stored in the capacitor. When the capacitance reaches C min (V max), SW2 is closed and the charge on C v is transferred to a storage capacitor C stor. SW2 is then opened and C v goes back to C max, completing one conversion cycle. During the period when SW2 is open, the charge on C stor is discharged by the load resistance R L with a time constant τ = R L C stor before it is charged again by C v. In the steady state, the initial and final terminal voltages V L of the discharge process become constant, as shown in Fig. 4.

Fig. 2
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Variable capacitor schematic

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Fig. 3
figure 3

Operation of the electrostatic energy converter

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Fig. 4
figure 4

Output terminal voltage V L in the steady-state charge-discharge cycle

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It can be shown that the steady-state final terminal voltage V sat in the charge-discharge cycle can be expressed as

$$ V_{{{\text{sat}}}} = \frac{{\frac{{C_{{\max }} }} {{C_{{{\text{stor}}}} }}V_{{{\text{in}}}} }} {{{\left( {1 + \frac{{C_{{\min }} }} {{C_{{{\text{stor}}}} }}} \right)} \times \exp (\Delta t/R_{{\text{L}}} C_{{{\text{stor}}}} ) - {\text{ }}1}}{\text{,}} $$
(1)

where Δt = conversion cycle time = 1/2f and f is the vibration frequency. When the voltage ripple of the charge-discharge cycle is small, as will be shown subsequently, the output power can be estimated by

$$ P_{{{\text{out}}}} = \frac{{V^{{\text{2}}}_{{{\text{sat}}}} }} {{R_{{\text{L}}} }}{\text{,}} $$
(2)

which is in general proportional to \( C^{2}_{{\max }} \).

In the comb structure, C max is determined by the minimum finger spacing. In a previous design (Chu et al. 2005), the minimum finger spacing was kept at 0.5 μm to prevent shortage of the uninsulated fingers (Fig. 5a). If a dielectric coating is applied to the side walls of the fingers (Fig. 5b), they become insulated and the minimum spacing can be further reduced to increase C max and P out. In this design, the total capacitance between fingers becomes C dielectric || C air || C dielectric. If a layer of 500-Å-thick silicon nitride is used as the dielectric material due to its process compatibility and high dielectric constant (ε r ∼ 7), C max can be increased by a factor of four compared to the previous design. It is also noted that the dielectric coating barely increases C min. Therefore, the expected increase of output power will not be affected by the change of C min.

Fig. 5
figure 5

Variable capacitor at C max position: a without coating, b with dielectric coating

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2.1 Static analysis

In Eq. 1, R L and C stor can be chosen so that the discharge time constant τ = R L C stor is much larger than the conversion cycle time Δt. The output voltage ripple in the steady state can therefore be neglected. In this case, V sat can be approximated as

$$ V_{{{\text{sat}}}} = \frac{{C_{{{\text{max}}}} V_{{{\text{in}}}} }} {{C_{{{\text{min}}}} {\left( {1 + \frac{{\Delta t}} {{R_{{\text{L}}} C_{{{\text{min}}}} }} + \frac{{\Delta t}} {{R_{{\text{L}}} C_{{{\text{stor}}}} }}} \right)}}} $$
(3)

Usually C min is a small value (in the order of 100 pF). The other circuit components in Eq. 3 can then be chosen so that C stor >> C min and R L C min << Δt. The equation can then be simplified as

$$ V_{{{\text{sat}}}} \approx \frac{{C_{{{\text{max}}}} V_{{{\text{in}}}} }} {{C_{{{\text{min}}}} \frac{{\Delta t}} {{R_{{\text{L}}} C_{{{\text{min}}}} }}}} $$
(4)

The power output becomes

$$ P_{{{\text{out}}}} \approx \frac{{V^{{\text{2}}}_{{{\text{sat}}}} }} {{R_{{\text{L}}} }} \approx {\left( {\frac{{C_{{{\text{max}}}} V_{{{\text{in}}}} }} {{\Delta t}}} \right)}^{{\text{2}}} R_{{\text{L}}} $$
(5)

For a typical low-power sensor node or module, the minimum output power requirement is about 200 μW. In such a module, a power management circuit is needed to convert the high output voltage to lower ones for various sensing and signal processing units. To be compatible with the power management circuit, the maximum output voltage is limited to about 40 V. With these constraints in Eq. 2, the range of R L can be found to be R L ≤ 8 MΩ. Even though a smaller R L can be used, C max must then be increased in order to satisfy the voltage and power requirement (Eqs. 4, 5), which in turn have adverse effects in the dynamic behavior of the converter. Therefore, R L = 8 MΩ and hence C max = 7 nF are used in the following calculation.

The output power P out for various C stor and R L is shown in Fig. 6 for C stor >> C min. It can be seen that the output power does not depend strongly on the storage capacitor C stor when C stor relatively large. Nevertheless, a large C stor will result in long initial charge time when the converter starts to work from a static initial status. Hence, a reasonable C stor of 20 nF is used.

Fig. 6
figure 6

Contour plot of output power for various R L and C stor

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From Eq. 1 and with the values of C stor and R L obtained from above, input voltage V in of 3.3 V, vibration frequency of 120 Hz, and chip area size of 1 cm2, Fig. 7 shows the calculated output saturation voltage and power as a function of the initial finger gap distance for various silicon nitride thickness. The finger thickness, length, and width are 200, 1,200 and 10 μm, respectively (Chu et al. 2005). The dimensions of the fingers are based on the available deep etching process capability. The minimum gap distance is assumed to be 0.1 μm, which is controlled by mechanical stops. It can be seen that with a 500-Å-thick nitride, the initial finger gap has an optimal value of 35 μm for a power output of 200 μW and output voltage of 40 V.

Fig. 7
figure 7

Output saturation voltage and power versus initial finger gap (R L = 8 MΩ, C stor = 20 nF)

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2.2 Dynamic analysis

After the dimensions of the variable capacitor are determined from the static analysis, the dynamics of the micro structure is analyzed so that the desired maximum displacement, and hence C max, can be achieved by the target vibration source. The electro-mechanical dynamics of the converter can be modeled as a spring-damper-mass system with the equation of motion,

$$ m\ifmmode\expandafter\ddot\else\expandafter\"\fi{z} + b_{e} (z) + b_{m} (z,\ifmmode\expandafter\dot\else\expandafter\.\fi{z}) + kz = - m\ifmmode\expandafter\ddot\else\expandafter\"\fi{y}, $$
(6)

where y is the displacement of the device frame caused by vibration, z is the displacement of the shuttle mass m with respect to the device frame, \( b_{m} (z,\ifmmode\expandafter\dot\else\expandafter\.\fi{z}) \) is the mechanical damping force representing energy loss caused by the squeezed film effect, and b e (z) is the electrostatic force acting on the MEMS structure. Notice that the mechanical damping b m is a function of both the displacement z of the shuttle mass and its velocity \( \ifmmode\expandafter\dot\else\expandafter\.\fi{z} \) (Roundy et al. 2002).

A Simulink model was built to simulate the system dynamic behavior based on Fig. 3 and Eq. 6, as shown in Fig. 8. The charge redistribution box calculates the charging and discharging events when C v reaches C max or C min. This process represents the power output. Due to the limited shuttle mass that can be achieved in a MEMS process using only silicon, an external attached mass m is considered in order to increase the displacement of the variable capacitor and the energy conversion efficiency.

Fig. 8
figure 8

Dynamic simulation model

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For various attached mass, Fig. 9 shows the maximum achievable displacement and required spring constant. It can be seen that a mass of 7.2 g is required to achieve the maximum of 34.8 μm according to the static design. The corresponding spring constant, 4.3 kN/m, is used to design the spring structures. With these values, the output voltage simulated by the Simulink model as a function of time is plotted in Fig. 10. The charge-discharge cycles are evident and the saturation voltage V sat is close to the expected value of 40 V. Table 1 summarizes the important device design parameters according to both the static and dynamic analyses.

Fig. 9
figure 9

Maximum displacement and spring constant versus attached mass

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Fig. 10
figure 10

Output voltage versus time

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Table 1 Design parameters of the energy converter
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3 Fabrication

A schematic device layout is shown in Fig. 11. The center hole is used to fix the position of the attached mass. A silicon-on-insulator (SOI) wafer with a 200-μm-thick device layer was used for large capacitance. The oxide layer and the handle wafer are 2 and 500 μm thick, respectively. Figure 12 shows an earlier fabrication process without the dielectric coating. The variable capacitor structure is first defined by deep reactive ion etching (DRIE) (Fig. 12a). After the sacrificial oxide layer is removed using HF solution (Fig. 12b), aluminum is evaporated for electrical contact (Fig. 12c). A steel ball is then attached to the central plate to adjust the resonant frequency to match the vibration source and improve the conversion efficiency (Fig. 12d).

Fig. 11
figure 11

Device layout schematic

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Fig. 12
figure 12

Fabrication process: a define structure by DRIE, b etch oxide by HF solution, c apply Al by thermal evaporation, and d attach external mass

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The fabricated first-generation device is shown in Fig. 13 (Chu et al. 2005). The width of the finger was reduced to 6.8 μm due to the variation in photolithography and RIE processes. The deviation will affect the characteristics of the converter such as the resonant frequency, output power, and output voltage.

Fig. 13
figure 13

Fabricated device: a top view, b cross section of comb fingers, c overview of the converter with attached mass

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4 Measurement

4.1 Mechanical measurement

The displacement of the device without the attached mass was measured using a PROWAVE JZK-1 shaker. The measured response is shown in Fig. 14. Since the mass was not attached, the vibration acceleration was increased to 40 m/s2 for easy observation. The maximum displacement was about 10 μm at 800 Hz, and the quality factor Q=ω 0/Δω was about 10, where ω 0 was the resonant frequency and Δω was the resonant bandwidth shown in Fig. 14. The mass of the center plate was approximately 0.038 g, thus the spring constant can be calculated as \( k = \omega _{0} ^{2} m = 960{\text{ N/m}} \). The measured spring constant is different from the design mainly due to the reduced spring width as shown in Fig. 13.

Fig. 14
figure 14

Frequency response of the device

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4.2 Electrical measurement

The electrical measurement was conducted using an INSTEK-LCR-816 LCR meter and a HP-4192A impedance analyzer. The measured capacitance without vibration was about 500 ∼ 600 pF, while the calculated capacitance C min is about 50 pf. The major contribution of the large capacitance is the parasitic capacitance C par between the center plate and the underneath substrate.

In addition to the parasitic capacitance, there was also a parallel parasitic conductance. The measured conductance varied from die to die with an average resistance of 2.5 kΩ. It is suspected to be caused by the residual particles left in the device after the release process. The presence of the parasitic capacitance and conductance had hindered the measurement of output power. New devices are being fabricated with the underneath substrate removed to prevent residual particles and reduce parasitic capacitance.

5 Conclusion

The design and analysis of a micro vibration-to-electricity converter have been presented. The device was fabricated in a SOI wafer. The reduced feature size of the fabricated device resulted in the decrease of spring constants. Mechanical and electrical measurements of the fabricated device were conducted. Impedance measurements showed an unwanted parasitic conductance which resulted in the failure of output power measurement. Improvement of the fabrication processes is being conducted.