Optimization of the fabrication of sealed capacitive transducers using surface micromachining

Abstract

Processing issues for the fabrication of capacitive micromachined ultrasonic transducer (cMUT) arrays have been studied using surface micromachining. This work focuses on the critical steps of process fabrication such as membrane formation, sacrificial layer properties and vacuum sealing performance of cavity. We describe a four-mask process for the realization of sealed cMUT. We demonstrate that the use of a sacrificial layer with a columnar structure gives a fast etching rate (29 nm s −1 ) in a buffered hydrofluoric acid solution. The mechanical stress of LPCVD silicon nitride (SiN x ), used as membrane, was evaluated. We compared the vacuum sealing performance of different materials in order to find the best material in terms of lateral deposition inside the cavity. Functional transducers have been obtained. We proposed an electrical test in order to evaluate the vacuum sealing of the cavity based on the collapse voltage determination. Laser interference measurements were used to characterize the dynamic displacement of the membrane.

About the synchronization of MEMs

“…F(v, V ) denotes the electric force acting on the mass when a voltage V is applied and (see [2] for example):…”

“…> λ := proc( 0 , n , e 0 , e n , A) scalar a in the paper according to (3) > 0 * n * A/(2 * e 0 * e n ); > end proc; > α := proc( n , e 0 , e n ) scalar b in the paper according to (4) > ( n * e 0 )/e n ; > end proc; > H := proc(v) function allowing to define the right-hand side of equation according to (2) in the paper > local a, b; > global 0 , e 0 , e n , n ; > a := λ( 0 , n , e 0 , e n , A); > b := α( n , e 0 , e n ); > a/(1 + b * (1 − v)) 2 ; > end proc; > ω 2 1 := proc(V e , v e , m) according to (7) in the paper > local a, b, c, d;…”

“…> Y := proc(y, z) synchronization: average over a period of first equation according to (22) > local a, b, c, a1, a2, a3; > global V e , v e , 0 , e 0 , e n , n , A; > a := H (v)/v; > b := diff (H (v), v); > c := unapply(a − b, v); > a1 := λ( 0 , n , e 0 , e n , A); > a2 := α( n , e 0 , e n ); > a3 := (1/a2 + 1 + v e )/y; > −(a1/( pi * c(v e ) * y 2 * a2 2 )) * I J (z, a3); > end proc; > Z := proc(y, z) synchronization: average over a period of second equation according to (23) > local a, b, c, a1, a2, a3; > global η, V e , v e , 0 , e 0 , e n , n , A; (H (v), v); > c := unapply(a − b, v); > a1 := λ( 0 , n , e 0 , e n , A); > a2 := α( n , e 0 , e n ); > a3 := (1/a2 + 1 + v e )/y; > (η/2) − (a1/(2 * pi * c(v e ) * y 3 * a2 2 )) * I I (z, a3); > end proc; > S := proc() procedure giving the solution y 0 = (y 0 , z 0 ) of equations of synchronization and matrix S = S(y 0 ) = S(y 0 , z 0 ) of synchronization defined by (12) > local sol, a, b, g, g1, g2, g3, g4, g5, g6, c; > global Y, Z , h, G, H, v e , η; > sol := fsolve(Y (y, z), Z (y, z), y, z); > a := eval(y, sol); First component y 0 of y 0 > b := eval(z, sol); Second component z 0 of y 0 > c := G()(v e ) > g := unapply(η * y * cos(z + φ) − (2 * H (v e + y * cos(z + φ), φ)/c), y, z, φ); > g5 := unapply(sin(z + φ) * g(y, z, φ), y, z, φ); > g6 := unapply((1/y) * cos(z + φ) * g(y, z, φ), y, z, φ); > g1 := unapply(D [1](g5)(a, b, φ), φ); > g1 := value(Int(g1(φ), φ = 0..Pi)/(2 * Pi)); > g1 := evalf(%); > g2 := unapply(D [2](g5)(a, b, φ), φ); > g2 := value(Int(g2(φ), φ = 0..Pi)/(2 * Pi)); > g2 := evalf(%); > g3 := unapply(D [1](g6)(a, b, φ), φ); > g3 := value(Int(g3(φ), φ = 0..Pi)/(2 * Pi)); > g3 := evalf(%); > g4 := unapply(D [2](g6)(a, b, φ), φ); > g4 := value(Int(g4(φ), φ = 0..Pi)/(2 * Pi)); > g4 := evalf(%); > Matrix([[g1, g2], [g3, g4]]); Matrix S according to (12) > end proc;…”

Surface micromachined capacitive ultrasonic transducer for underwater imaging

“…This further development has enhanced investigating Capacitive Micromachined Ultrasonic Transducers (CMUTs) (Eccardt et al, 1996;Caliano et al, 2000;Cianci et al, 2004;Belgacem et al, 2004;Liu et al, 2005). Ultrasound (an inaudible acoustic wave, frequency >20 kHz) science is a growing field and has been utilized in many applications that can be identified as either sensing or actuating.…”

“…This paper is organized as follows: the CMUT's equivalent circuit and analysis of its characteristics are described in Section II; the fabrication process and parameters are discussed in Section III; experimental results are reported in Section IV; Section V presents conclusions confirming the utility of the CMUT. Figure 1 presents a typical CMUT cell (Cianci et al, 2004;Belgacem et al, 2004). The membrane is coated with an appropriately sized center top electrode and is suspended above a heavily doped silicon substrate (bottom electrode).…”