Patent ID: 8367305

Claim:
A method for fabricating a microelectromechanical (MEM) resonator, comprising the steps of: (a) calculating parameters for the MEM resonator for a desired resonant frequency f d , including a sub-width L=λ/2=C m /2f d and an electrode width W=λ/4=C m /4f d where λ is an acoustic wavelength and C m is a material speed for the MEM resonator; (b) calculating an actual resonant frequency f a =C m /2L a =C m /2NG for which the MEM resonator can be fabricated using an actual sub-width L a =NG, with G being a grid size for at least one photolithographic reticle to be used to fabricate the MEM resonator, and with N being calculated from N=C m /2f d G rounded to be an integer number for which the actual resonant frequency f a is nearest to but above the desired resonant frequency f d ; (c) calculating the actual resonant frequency using f a =C m (M,N)/2NG over at least a part of the range of N/2≦M<N, where M is an integer and C m (M,N) accounts for changes in the material speed C m due to an effective electrode width W e =MG which is different from the electrode width W, and selecting the value of M for which a frequency error f e =f d −f a =f d −C m (M,N)/2NG is a minimum; (d) fabricating the MEM resonator using the actual sub-width L a =NG and the effective electrode width W e =MG by: providing a substrate having a plurality of layers deposited thereon, including a lower metallization layer, a piezoelectric layer and an upper metallization layer; photolithographically patterning the upper metallization layer using the at least one photolithographic reticle having the grid size G, thereby forming an upper electrode in each of n actual sub-widths L a =NG where n is an integer, with each upper electrode having the effective electrode width W e =MG; photolithographically patterning the piezoelectric layer using the at least one photolithographic reticle having the grid size G, thereby defining an overall width W o =nL a =nNG for the MEM resonator; and undercutting the MEM resonator with a selective etchant, thereby suspending the MEM resonator on the substrate; increasing the value of N by one; repeating step (c), and selecting the value of M for which the frequency error f e is a minimum; and selecting whichever values of N and M provide the lowest frequency error f e for use in fabricating the MEM resonator in step (d).