Magnetic Force and Thermal Expansion as Failure Mechanisms of Electrothermal MEMS Actuators Under Electrostatic Discharge Testing

[+] Author and Article Information
Jonathan D. Weiss

 Sandia National Laboratories, P.O. Box 5800, Mail Stop 1081, Albuquerque, NM 87185-1081jdweiss@sandia.gov

J. Appl. Mech 74(5), 996-1005 (Jan 31, 2007) (10 pages) doi:10.1115/1.2723813 History: Received October 06, 2005; Revised January 31, 2007

Like microelectronic circuits, microelectromechanical systems (MEMS) devices are susceptible to damage by electrostatic discharge (ESD). At Sandia National Laboratories, polysilicon electrothermal MEMS actuators have been subjected to ESD pulses to examine that susceptibility. Failures, in the form of cracks at points of high stress concentration, occurred that could not be explained by thermal degradation of the polysilicon caused by excessive heating, or by excessive displacement of the legs of the actuator of the same nature that occur in normal operation. One hypothesis presented in this paper is that the internal magnetic forces between the legs of the actuator, resulting from the ESD-associated high current pulses, might produce vibrations of amplitude sufficient to produce these cracks. However, a dynamic analysis based on simple beam theory indicated that such cracks are unlikely to occur, except under rather extreme conditions. On the other hand, these same current pulses also cause resistive heating of the legs and, therefore, thermally induced compression that can lead to buckling. Buckling stresses, particularly when augmented by magnetic forces, can readily explain failure. Both the magnetic and thermal analyses were performed using the human body model and the machine model of ESD. A justification for ignoring shuttle motion and eddy currents induced in the substrate during the ESD pulse is presented, as well.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Scanning electron micrograph showing a plan view the electrothermal actuator

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Figure 2

Line drawing of Fig. 1 and a cross section of its polysilicon legs. The time-dependent current, I(t), is assumed to be equally divided between the legs. All dimensions are in microns.

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Figure 6

Time-dependent stress at the two ends of a leg for an initial capacitor voltage of 6500V (human body model). This curve scales with the square of the initial capacitor voltage.

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Figure 3

Circuits used to implement the human body model (top) and the machine model (bottom) of ESD

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Figure 4

Typical current wave forms for the human body model and the machine model (from Ref. 9)

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Figure 5

Magnetic force per unit length per current squared versus position along a leg

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Figure 7

Time-dependent stress at the two ends of a leg for an initial capacitor voltage of 6500V (machine model). This curve scales with the square of the initial capacitor voltage.

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Figure 8

(a) Maximum stress achieved at x=0 versus the number of modes included in the calculation, for both HBM and MM; (b) the product of integrals, TmSm used to calculate the stress in Fig. 8 for the HBM versus mode number. Similarly for Sm alone and a simplified calculation of Sm (Simp.(Sm)) illustrating the basic dependence of Sm on mode number; and (c) time integral, Tm, versus mode number for HBM and MM. Also, the asymptotic behavior of Tm versus mode number (1∕(m+1∕2)2).

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Figure 9

Integral of the linear thermal expansion coefficient from 300K to some elevated temperature T

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Figure 10

Maximum achievable temperature of the thermal actuator during ESD testing versus initial voltage on the capacitor

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Figure 11

Amplification factor, X(Uc) versus U0 for constant compression, where Pc=P0, and for values of q that would produce flexural stress at the end points of 7/40 and 1/40 the nominal stress of silicon, according to simple beam theory and Pc=0. For all q>0, Pc<P0. U0,c=(L∕2)√(P0,c∕EI).

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Figure 12

Pc versus P0 for the two values of q in Fig. 1

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Figure 13

(a) Geometry of eddy current discussion; and (b) Eddy current versus vertical and horizontal distances from the filament



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