A one-dimensional model is presented which describes the release-etch behavior of sacrificial oxides in aqueous HF. Starting from first principles and an empirical rate law, release etch kinetics are derived for primitive geometries. The behavior of complex three-dimensional structures is described by joining the solutions of constituent primitives and applying appropriate boundary conditions.The two fitting parameters, k{sub 1} and k{sub 2}, are determined from the simplest structure and describe the more complex structures well. Experimental validation of the model is presented with data for all of the geometries and four types of sacrificial oxides

Eaton, W. P.

Jarecki, R. L.

Smith, J. H.

UNT Digital Library

I a A C(X), Cfr) C(6) c* A, h., t proportionality constant. constant of integration. concentration of HF at position x, r. concentration of HF at etch front. bulk concentration of HF. width. heipht of sac. oxide for neometrv N. Prediction of Release-Etch Times for Surface-Micromachined Structures c YN * J*m e., - William P. Eaton*+, Robert L. Jarecki**, and James H. Smith* **Sub-0.35 ,urn Processes Department, Mail Stop 1077 i; 1! ' 1  ~ I.-:{ ; Lv 6 - L7 ,, I? :&- -; -$ 0 8 ~ 0  - J  w;, *Intelligent Micromachines Department, Mail Stop 1080 Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185, USA /%4Y Q 8 lp~? angle determined by number of etch ports. geometrical constant for etching regime N. flux of HF to  etch front. SUMMARY A one-dimensional model is presented which describes the release-etch behavior of sacrificial oxides in aqueous HF. Starting from first principles and an empirical rate law, release etch kinetics are derived for primitive geome- tries. The behavior of complex three-dimensional struc- tures is described by joining the solutions of constituent primitives and applying appropriate boundary conditions. The two fitting parameters, kl and k2, are determined from the simplest structure and describe the more com- plex structures well. Experimental validation of the model is presented with data fo f the geometries and four types of sacrificial oxid 7 c MOTIVATION A common desire in surface-micromachining is to re- duce the release-etch time. Unfortunately, linear etch rates do not apply to large lateral etch distances, since diffusion limitations are encountered. Hence, a more so- phisticated method of determining etch times is required. Release-etch modeling for surface-micromachining was first examined in detail by Monk et d.[l-71. They exam- ined effects of etchant concentration, etchant pH, etchant additives, and etch channel height and width effects on etching behavior. Liu et d.[8] and Tai et al.[9] added an empirical formulation of the etch kinetics. Like Monk et al., they used rectangular etch channels exclusively (Figure 2a). In this paper, the above work is extended by adding more geometric complexity to the available mod- els. The range of structures is shown in Figure 2 and 3. THEORY Modeling of release etching in this work is based upon finding relationships among flux, concentration, and etch rate. Details of the model have been reported previ- ously[lO], and the method of solution is briefly discussed here. The basic equations of the model are given in Table 2, and the conventions are illustrated in Figure 1. The reader is referred to Table 1 for definitions of variables. The oxide etch rate, 6, is presumed to be directly pro- portional to the flux of HF to the etch front, JHF (Equation 2). The proportionality constant is inferred from the net reaction of HF with SiOz (Equation 1). The flux is determined an empirical rate law, et d[8] and Tai et d,[9], this is a k,, k2 L IMW,, +Present address: Reliability Physics Departmedt, Sandia National Laboratories, Albuquerque, NM 87185- 1081, USA, w.p.eaton@ieee.org first and second order rate constants. length of etch port. molecular weinht of SO,. - Table 1. List of variables. N geometries: P=port, B=bu b ble, C=concen tric circles, PP=port- tc+port, PB=port-to-bu bble, B W=bu bble-to-wedge, PB W=port- n 4v /?$;oz r, x S t number of etch ports for PBW geometry. decreasing angle in wedge regime. mass density of SO2. radial and linear coordinates. hole-to-hole or 2x hole-to-wall spacing. etch time. position of etch front. radius above which wedge solution is valid. diffusivitv of HF in water. 4" D for the kinetics of the reaction, since it describes etch be- havior over a wide range of concentrations. Both convective components and the instantaneous rate of change of the concentration are presumed to be small, so that Fick's second law is written as Equation 4. The concentration is Co at x = 0 or ro, so that solving Equation 4 yields Equations 5 and 6 for linear and polar Table 2. Theoretical foundations of release-etch model. Details are given in reference (IO] 6HF+Si02 K= H2SiF,+2H20 (1) DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spe- cific commercial product, process, or service by trade name, trademark, manufac- turer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thenof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. . I I Portions of this document may be illegible in electronic image products. hags are produced from the best available original document. DISCLAIMER 1 1 ! I . .  0 HF solution 0 S(t> Figure 1: Conventions for coordinates and concentrations of releasketch model. After references REFS symmetry, respectively. In many cases solving etch front position as a function of time, ‘d(t), provides more insight than the etch rate, dd/dt, and therefore requires an integration. In all cases except for the rectangular etch port, numerical integra- tions must be used, and can be performed with commer- cial mathematical software, such as Mathematicam, Ma- plem, MathCADTM, or others. Furthermore, it is gener- ally easier to solve for t(s) instead of S(), where the inte- gration takes the form d6 5 a(k1C+bC2) ’ t(6) = J.6 (7) where x i s  is 0, r,, S,, or R,, depending on the geometry in question. Primitive Geometries The three primitives considered are the rectangular etch port, bubble, and concentric circles. Completed test structures are shown in Figure 2. The relevant solutions to all of the concentrations and etch times are given in Table 3. The rectangular etch port (Figure 2a) is the simplest of all geometries and consists of a rectangular box that is open at one end to HF. The bubble geometry Table 3. Solutions for primitives. The general form for !tch times is given by Equation 7. - port  J(k,6+ D)2 + 4k26C0 D - (k, + 24C0)6- D 2k26 CP(4 = bubble , concentric circles d(k$ln($)-D) 2 -4k261n($)CoD -k16ln(t)D+D CB (4 = 2k261n($) (Figure 2b) is a circular or semicircular anchored at its edges and etched from a ter. The concentric circles geometry cular structure that is anchored at its center and etched from its edges. Complex Geometries Complex geometries are broken up into their primitive constituents. Fabricated test structures of all of the primitive geometries are shown in Figure 3. Additional total mass flux boundary conditions are required to join primitive solutions. For example, the boundary condition for the port-to-port structure (Figure 3a), which is two rectangular etch ports joined end to end, is In this case the flux is said to change discontinuously when the etch proceeds into the second port. However, the other solutions can be easily forced to change con- tinuously. The port-to-bubble geometry (Figure 3b) is a rectan- gular etch port joined to a semicircular region. As the etch proceeds into the bubble regime, the etch front is an ever-expanding semicircle until all of the sacrificial oxide is consumed. The bubble-to-wedge geometry (Figure 3c) is particu- larly useful, since it describes the etching of surface mi- cromachined structures &om a square array of etch holes. This is the configuration used for many devices, such as accelerometers and comb drives. The etch front starts out with a circular shape until it meets a wall or a neighbor- ing etch front. Then the etch front is broken into four wedge-shaped regions. Because of the symmetry of the problem, only one wedge needs to  be examined. An angle, OB,  is constructed which accounts for the decreasing etch front area as the etch progresses. It starts a t  ~ / 2  and diminishes to zero. The port-to-bubble-to-wedge (Figure 3c) geometry describes the etching of a large, regular-polygonal area from its edges. This type of structure has been used to make diaphragms for surface-micromachined pressure sensors and flow sensors. Because of the symmetry of the structure, only one etch port needs to  be tracked through the releaseetch. First the rectangular etch port is etched. then as the etch proceeds underneath the diaphragm, a “bubble” forms. Once all of the adjoining etch fronts col- lide the etch proceeds into the wedge regime with angle RESULTS The etch structures of Figure 2 and 3 were made by depositing and patterning 1 p m  thick sacrificial oxides, followed by depositing and patterning 0.8 pm of low stress silicon nitride. Four types of sacrificial oxide were used: undoped LPCVD oxide, 2.6 wt% boro-silicate glass (BSG), 2.4 wt% phospho-silicate glass, and 4.8 wt%/3.7 wt% boro-phospho-silicate glass (BPSG). S ix  inch silicon substrates h etch structures were diced into individual die. The dice were placed in individual baskets for the etch studi t time zero, the etch tank was filled with ~ P B W  4 I I 2.6% BSG 2.4% PSG 4.813.7 BPSG able 4. Solutions for complex structures. Etch times axe given in general by Equation 7. port-to-port L ,  dPPhPP CPP(4 = cP(4iG+Gpp 9 Y P P = d p h p  C O P P ( 4  = 2k2cosZ-Ypp[~[k l ( s+Ypp)+D~ +4k2C0D(6+Ypp) +(kl -2k2Co)S+k1Ypp +D I .  2k2@+ Y P P Y  port-to-bubble 4.5’10” 7.0’104 1.1-lo4 4.6’10-3 4.5’10“ 1 .7’10-2 .~ port-to-bubble-to-wedge - h 49 wt% HF, thereby immersing the dice. ice were then was quenched in deionized water. The quenched etch front positions were measured optically. For all of the different oxides, the etch kinetics, kl and k2 were determined from the simplest structures, the rec- tangular etch ports, using a nonlinear least-squares fit. These coefficients were then applied to the more complex ical and experimental curves are shown d coefficients kl and k2 are given in of 1.6.10-5 [cm2/sec] was used for the diffusivity of HF in water. Of all of the different oxides, the undoped LPVCD oxide results had the worst fit to theory. This was due in part to the fact that the etch front shapes of the undoped oxide films were notch-shaped for the rectangular etch removed from the tank at regular intervals v nd the etch ports. This no ch- h e evpve d ‘n ,t e cours of the etch, making &a&&&$% e -f oca %%hhch& ion f i p W T h e  shape was presumed to be due to unrelieved stresses in the sidewalls of the films, causing the edges to etch faster than the bulk. The other oxides had flat etch fronts and fit -the theoretical m o d e l . . w  . Table 5, Etch kinetics for all four oxides used in PaPer. ACKNOWLEDGEMENTS Special thanks go to the staff and operators of Sandia National Laboratories’ Microelectronics Development Laboratory, without whom the test structures could not have been made. Sandia is a multiprogram laboratory operated by San- dia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract un- der contract DEAC0494AL85000. REFERENCES [l] D. J. Monk, Controved Structure Release for Silicon Surfice Micromachhing Ph.D. Thesis, University of California at  Ber- keley, 1993. [2] D. J. Monk, D. S. Soan, and R. T. Howe, “Sacrificial layer SiO, wet etching for micromachining applications”, Digest of Technical Papem: Transducers 92., pp. 647-650 (1991). [3] D. J. Monk, D. S. Soan, and R. T. Howe, “A di f i -  sion/chemical reaction model for HF etching of LPCVD phos- phosilicate glass sacrificial layers”, Technical Digest: IEE% Solid State Sensor and Actuator Workshop, pp. 46-49 (1992). [4] D.J. Monk, D. S. Soane, and R.T. Howe, “Determination of the etching kinetics for the hydrofluoric acid/silicon dioxide system,” J. ECS 140(8), pp. 2339-2346(Aug. 1993). [5] D. J. Monk, D. S. Soane, and R.T. Howe, “A review of the chemical reaction mechanism and kinetics for hydrofluoric acid etching of silicon dioxide for surface micromachining appli- cations,” Thin Solid Fihs ,  232(1), pp.1-12(10 Sept. 1993). [6] D. J. Monk, D. S. Soane, and R. T. Howe, “Hydrofluoric - _ -  acid etching of silicon dioxide sacrificial layers, part I. Experi- mental observations,” J. ECS 141(1), pp. 264269 (Jan. 1994). [7] D. J. Monk, D. S. Soane, and R. T. Howe, “Hydrofluoric acid etching of silicon dioxide sacrificial layers, part II. Model- ing,” J. ECS, 141(1), pp. 270-274 (Jan. 1994). [8] J. Liu, Y.-C. Tai, J. Lee, K.-C. Pong, Y. Zohar, and C.-H. Ho, ‘‘h situ monitoring and universal modeling of sacrificial PSG etching using hydrofluoric acid”, Proceedings of Mcro EIectro MechmicaZSptems, EEe pp. 71-76 (February 1993). [9] Y.-C. Tai and C.-M. Ho, “Silicon Micromachining and Its Applications”, Proc. SPE, Vol 2448, pp. 141-151 (Mar. 1995). [lo] W. P. Eaton, R. L. Jarecki, and J. H. Smith, ‘‘Release etch modeling for complex surface-micromachined structures”, Proc. SPB, Vol 2879, pp. 80-93 (Oct. 1996). ble-to-wedge. (d) port-to-bubble-to-wedge. 300 6001- 250 iz A p200 .- -0 5 150 100 50 0 800 1600 2400 (4 Etch time [sec] Etch time [sec] ....h... -+- - e  - -.-@.-. port bubble conc. port-to- port-to- circles port bubble g07 Etch time [sec] -I+ --v- bubble-to- port-to- bubble- wedge to-wedge Etch time [sec] Figure #. Etch distance (pm] vs etch timelsec] for four different sacrificial oxides and d geometries. (a) undoped LPCVD oxide. (b) 2.6% BSG. (c) 2.4% PSG. (d) 4.8/3.7 BPSG. I 

Prediction of release-etch times for surface-micromachined structures

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Prediction of release-etch times for surface-micromachined structures

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