Electrostatic MEMS actuators using gray-scale technology 10 страница

Conclusion

This PhD dissertation research has definitively shown that electrostatic MEMS actuators incorporating gray-scale technology have significant advantages over their planar counterparts. In demonstrating that gray-scale is a viable 3-D batch fabrication technique for developing MEMS sensors and actuators, it is my sincere hope that this technology can be leveraged by the MEMS community to develop innovative solutions to many of the technical, economic, and social challenges facing the world today.

APPENDIX A: Matlab Script for Virtual Electrostatic Spring Constants

As discussed in Section 3.3.3, the instability point of a static comb-drive actuator is defined by the perpendicular virtual electrostatic spring (ky-virtual) that is created as the voltage increases and the device deflects. To calculate this instability point, knowledge of both the actuation characteristics (V (x)) and overlap area (A(x)) as a function of displacement is required. However, for variable height profiles these relations are not simple analytical functions. Thus, a Matlab script was created to take any comb-finger height profile (h(x)) and numerically calculate ky-virtual as a function of displacement.

The script first defines all constants and assumptions about the comb actuator design (such as number of fingers and suspension spring constant). A height profile is then input from a text file, where it is assumed that the height profile accounts for fringing fields by scaling the physical height into an “effective” height representing dC/dx. Equation 43 is then evaluated numerically to obtain A(x), while V (x) is calculated numerically using the piecewise constant technique of Equations 36 and 37. Finally, the virtual spring constant ky-virtual(x) as a function of displacement is calculated using Equation 46. The code is shown below with comments in green font.

% Matlab code for calculating the perpendicular virtual electrostatic spring constant as a % function of displacement for arbitrary comb-finger profiles

% Define constants and design assumptions in SI units

step = 1;

stepx = 1e-7;

epsilon = 8.85e-12;

gap = 10e-6;

num_fingers = 200;

k = 5;

max_finger_height = 100e-6;

% Input “effective” height profile from text file - can account for fringing fields

string_input = 'height_profile.txt';

fid = fopen(string_input);

height = fscanf(fid, '%f,[1 inf]);

height = height';

fclose(fid);

% Calculate overlapping area as a function of (x) by integrating over the height profile % Corresponds to A(x) in Equation 43 area(1) = max_finger_height * stepx; for(ii=2:length(x))

increment = x(ii) - x(ii-1); area(ii) = area(ii-1) + height(ii) * increment; end

2 2 % Calculate voltage vs. displacement characteristics for V (x) in Equation 45

% Assumes force is proportional to the given “effective” height profile

Vtemp2 = zeros(length(x),1);

V = zeros(length(x),1);

V2 = zeros(length(x),1);

for(n = 2:length(x));

increment = x(n) - x(n-1);

Vtemp2(n) = increment * gap * K / (epsilon * height(n)) / num_fingers;

V(n) = sqrt(V(n-1)^A2 + Vtemp2(n));

V2(n) = V(n) * V(n); end

% Use A(x) and V (x) in Equation 46 to calculate the virtual electrostatic spring as a

% function of displacement, ky(x)

for(i=1:length(area))

ky(i) = num_fingers * epsilon * area(i) * V2(i) * 2 / gap^A3; end

plot(x,ky)

APPENDIX B: Process Flow for Gray-scale SOI process

The process flow for integrating gray-scale technology within an SOI actuator required significant development. The final process was described qualitatively in Section 3.5 and the details are shown in Table B.1. The gray-scale lithography and DRIE steps were described in more detail elsewhere in this dissertation (see Chapter 2). Slight modifications would be required to adapt this process to devices having different layouts or requiring different etch selectivity.

The wafer saw step is intentionally performed before the wet oxide etch release step to maintain structural integrity during the relatively harsh sawing process. The oxide etch release required significant development as the sequence of etching in buffered oxide etch (BOE) and rinsing in DI water often effected the complete etching between high aspect ratio features. In general, 1-2 rinse steps in DI water (5 min each) helped to ensure complete undercutting of desired structures. The final die rinse process was a combination of multiple soaks in DI, followed by soaks in IPA to avoid stiction problems (due to its low surface tension).

[1] As of 1/14/06 (http://www.analog.com/en/cat/0,2878,764,00.html)

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