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CRITICALLY DAMPED SILICON MICRODEFLECTORS

IP.com Disclosure Number: IPCOM000025385D
Original Publication Date: 1985-Feb-28
Included in the Prior Art Database: 2004-Apr-04
Document File: 6 page(s) / 184K

Publishing Venue

Xerox Disclosure Journal

Abstract

In the design of a silicon microdeflector, for use for example as a facet tracker or print bar, one of the major requirements is that the microdeflector be fast enough to return to the undeflected state in time to be ready for the next deflection. However, when the voltage is removed from a deflected beam such as a microdeflector (a microdeflector can be considered as a cantilever beam), the beam behaves like a damped free spring-mass vibratory system. As a consequence, the beam will return to its undeflected state over a time interval and with or without oscillations as determined by the damping properties, i.e., the damping factor (Q), of the system. Under critical damping condition (0 = K), the beam will return to its equilibrium position in the shortest possible time and without oscillations. This proposal describes how a microdeflector with a given config-uration can be critically damped by adjusting the width of the microdeflector finger or fingers and the viscosity of the ambient gas in which the microdeflector operates.

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Page 1 of 6

XEROX DISCLOSURE JOURNAL

CRITICALLY DAMPED SILICON MICRODEFLECTORS Kwok-leung Yip

Proposed Classification
U.S. CI. 350/356

Int. CI. G02f 1/03

FIG I

Volume 10 Number 1 January/February 1985 25

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Page 2 of 6

CRITICALLY DAMPED SILICON MICRODEFLECTORS (Cont'd)

F/G 2

EFFECT OF DEFLECTOR WIDTH ON DAMPED VIBRATIONS

- 1.004 I I I 1 I I

0 .05 .I0 .I5 .20 25 .30 .35 40

T (SEC.) ,t IO-~

F/G 3

EFFECT OF AMBIENT

0 .05 .I0 .I5 .20 .25 .30 .35 40

T ISEC.) w 10'~

    XEROX DISCLOSURE JOURNAL Volume 10 Number 1 January/February 1985

26

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Page 3 of 6

CRITICALLY DAMPED SILICON MICRODEFLECTORS (Cont'd)

In the design of a silicon microdeflector, for use for example as a facet tracker or print bar, one of the major requirements is that the microdeflector be fast enough to return to the undeflected state in time to be ready for the next deflection. However, when the voltage is removed from a deflected beam such as a microdeflector (a microdeflector can be considered as a cantilever beam), the beam behaves like a damped free spring-mass vibratory system. As a consequence, the beam will return to its undeflected state over a time interval and with or without oscillations as determined by the damping properties, i.e., the damping factor (Q), of the system. Under critical damping condition (0 = K), the beam will return to its equilibrium position in the shortest possible time and without oscillations. This proposal describes how a microdeflector with a given config- uration can be critically damped by adjusting the width of the microdeflector finger or fingers and the viscosity of the ambient gas in which the microdeflector operates.

Referring to Figure 1, a microdeflector 5 is there shown having a flexible finger 6 supported in cantilever fashion on a base 7. A portion of base 7 below the unsupported end 8 of finger 6 is removed to provide a well 9 accommodating deflection or bending of finger 6. The mechanical damping factor (Q) of microdeflector 5 is expressed by:

Where Y = Young's modulus of microdeflector finger 6,

P = the mass density of the microdeflector finger 6,

1 = the length of finger 6,

b = the width of finger 6,

tl = the thickness of finger 6,

d = the distance between finger 6 and base 7 (i.e. the depth of the we11 9), and

p = the viscosity of the ambient gas.

The dimensions of microdeflector finger 6 (P, tl, and d) are primarily determined by the operating requirements imposed on the microdeflector; namely, the deflec- tion angle (Q), the resonant frequency (fn), and the drive voltage (V), as follows:

    XEROX DISCLOSURE JOURNAL Volume 10 Number 1 January/February 1985 27

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Page 4 of 6

CRITICALLY DAMPED SILICON MICRODEFLECTORS (Cont'd)

where

6 = the deflection at the tip 8 of the finger 6, and

fd= the permittivity constant in vacuum,

where,

Vt is the threshold voltage at which the microdefl...