034629-1-F A Novel Millimeter-Wave, Low-Loss, Electronically Controlled Phase Shifter for Monolithic, Beam Steering PhasedArray Antenna Application Kamal Sarabandi March 1997 34629-1-F = RL-2470

A NOVEL MILLIMETER-WAVE, LOW-LOSS, ELECTRONICALLY CONTROLLED PHASE SHIFTER FOR MONOLITHIC, BEAM-STEERING PHASED-ARRAY ANTENNA APPLICATION Final Report ONR Code 313 Office of Naval Research 800 North Quincy Street Arlington, VA 22217 Att: Dr. W. Stachnik K. Sarabandi Radiation Laboratory Department of Electrical Engineering and Computer Science The University of Michigan Ann Arbor, MI 48109-2122 Tel: (313) 936-1575 Fax: (313) 747-2106 March 1997

1 Introduction The purpose of this document is to summarize the accomplishments made on the project regarding construction of a millimeter-wave electronically controlled phase shifter funded by OINR under contract N00014-96-1-1120. Our activities in this pilot project can be categorized into two major areas: 1) theoretical analysis, and 2)experimental and development of fabrication methodology. Significant progress has been made in both areas during the very short period of the contract and details of our effort and related results are provided in the following sections. 2 Objective This section provides a short description of the problem at hand and a list of itemized tasks needed for accomplishing the objective of the project. In this effort a new approach for the design of electronically controlled phase shifters appropriate for millimeter and submillimeter wavelengths was investigated. The fundamental concept for achieving phase shift is based on geometric deformation of the cross section of a waveguide structure supporting a traveling wave. Geometric deformation of a waveguide cross section modifies the cutoff frequency of the propagating mode which in turn changes the propagation constant. Therefore, imposing a certain deformation along a finite length of the waveguide will result in the desired phase shift. Micro-machining technology is proposed to construct the waveguide with a flexible membrane wall which can be displaced electronically. The plan was to use silicon wafers (in a specific crystalline orientation) and an anisotropic etchant such as EDP or TMAH to form a trapezoidal groove with the desired dimensions [?]. The groove was to be metallized and its open area will be covered with a thin dielectric membrane. Instead of using silicon wafer to construct the waveguide we used instead a metallic trapezoidal waveguide in this pilot study. The lower surface of the membrane facing the groove must first be metallized in order to form a trapezoidal waveguide as shown in Fig. 1. Electronically controlled displacement of the membrane is accomplished by employing 1

electrostatic forces. In order to move the membrane electrostatically, a very small gap is required which was manufactured using silicon etching technology. Basically, another silicon wafer (conducting) is etched in a similar manner to form a groove with a slightly wider width and much shallower depth than the waveguide groove. This wafer will be placed on top of the other wafer as illustrated in Fig.l. In this configuration a capacitor is formed between the upper silicon wafer and the metallized surface of the membrane. Applying a DC voltage between the two conductors of this capacitor produces an electrostatic force field which pulls the membrane inward. The phase shifter so designed is expected to show an extremely low loss equal to the conductor losses of the waveguide walls. Moreover, since the membrane deflection occurs gradually along the waveguide, the phase shifter does not present any significant mismatch. To demonstrate the feasibility of such phase shifter and characterize its performrance, a prototype phase shifter at W-band was designed and under fabrication. In this frequency range we have an HP vector network analyzer which will be use to measure the S-parameters of the prototype phase shifter directly. The test ports of this network analyzer are rectangular waveguides at W-band frequencies. Since the trapezoidal waveguide made by silicon wafers can't be connected to the waveguide flanges of the test set, it was decided to machine the trapezoidal waveguide out of a block of brass with appropriate flanges to mate the test set and fabricate the membrane assembly using silicon micro-machining. This process will be explained in more detail in Section 4. The following tasks were undertaken: 1 Theoretical analysis of general trapezoidal waveguides to determine the dominant mode, mode bandwidth, cutoff frequency and its relationship to the waveguide geometry and dimensions. The results related to this task are provided in Section 3. 2. Characterization of variation of cutoff frequency as a function of the geometrical (leformlat'ion of the waveguide cross section (memnbranre d-isplacement). Deter

mination of the optimum cross section which produces the maximum change in the cutoff frequency for a given membrane displacement. 3. Verification of the theoretical results by constructing a trapezoidal waveguide. 4. Electro-mechanical design and construction of the membrane including calculation of the membrane displacement as a function of applied DC voltage, membrane thickness, width, and modulus of elasticity. 5. Identification of an appropriate membrane and development of a fabrication process. We used different Du Pont Polyimide Coatings to construct relatively large membranes. 6. Construction of a prototype of a membrane-based phase shifter at 94 GHz and characterization of its performance. We have developed the measurement procedures. 3 Theoretical Analysis 3.1 Trapezoidal Waveguide Analysis As mentioned earlier wet-chemical anisotropic etching creates a trapezoidal groove on a silicon wafer. The small angle of the trapezoid is 54.7~ which is determined by the crystallographic nature of silicon crystals. The wide base of the trapezoid (b) and its altitude (h) are to be determined for the desired cutoff frequency. In this section theoretical analysis for characterization of cutoff frequencies, field distribution of dominant mnode, and variation of cutoff frequency as a function of base deflection is provided. Analytical solution for the cutoff frequency and field distribution of waveguide structures are available for only a few canonical geometries such as rectangular and circular waveguides. For determination of cutoff frequencies and field distribution of different modes of the trapezoidal waveguide we have to resort to a numerical analysis. 3

The finite element method offers an efficient numerical procedure for the calculation of the eigenvalues of a waveguide with arbitrary cross section [1]. This technique is well-known and here only a brief discussion of the method is outlined. For homogeneously-filled waveguides the longitudinal component of the electric (TM case) or magnetic (TE case) field, denoted by b, satisfies the homogeneous lHelmholtz's equation (V2 + K2) = 0 where IKc is the cutoff wavenumber. It is shown that the solution to the Helmholtz's equation minimizes the following functional [2] F() fs V ds (1) fs fS 2ds and the minimum is equal to the smallest eigenvalue A = IK2. To find the minima of the functional the eigenfunction 0 is approximated by a piecewise linear function. In this approximation the cross section of the waveguide is discretized into small triangular elements with unknown values of b at each node of the elements. For the eth element the linear function in terms of the node values (f,) can be represented by [3] 3 O(x, y)=- Nj (x, y)? j=l where NJ(x, y) are the linear basis function given in terms of the element's nodes x - y coordinates. That is 1 e(., y) = (at + bjx + cy), j = 1, 2, 3 al =- X2y3- y2x bl = Y - Y3, 1 = X3 -x (2) where Ae is the area of the triangle given by 1 2A (bl c2 -- b2cl) 2 2 1 and the expressions for a, ce are obtained from (2) by cyclic interchange of the sul)scripts (I -- 2, 2 ->- 3, 3 -3 1). 1

Substituting the piecewise linear function into the functional (1) and searching for the minima by setting - - 0, the following matrix equation is obtained Ad = k1IB where the elements of A and B are given by e,% - 1. (+ Ae and 5- is the Kronecker delta. Since some of the nodes are shared among the adjacent elements, the vector V for the unconnected elements must be related to the vector T for connected elements using a connection matrix C [1]. In this case X = C E and the matrix equation takes the following form A = K B2 (3) where A = CtAC and B = CtBC. Equation (3) is recognized as the generalized eigenvalue problem which can be solved numerically by a standard method [4]. Applying this numerical solution to the trapezoidal or the deformed trapezoidal waveguide the cutoff frequencies and associated propagation constants can be obtained. Figures 2-a and 2-b, respectively, show the discretized cross sections of a trapezoidal and a deformed trapezoidal waveguide with b/h = 2. Since the expected deflection (6) is only a few percent of the base width b, the deformed cross section is simply modeled by changing the altitude of the trapezoid to h + S everywhere except for the corners (see Fig. 2-b). First we investigated the field distributions of the first and second modes of the trapezoidal waveguide. It was found that the first two modes are TE and that the dominant mode field distribution resembles that of the 7-E10 mode of a rectangular waveguide. Figures 3 and 4, respectively, show the field distributions of lie dominant and the second TE mnodes in a trapezoidal waveguide 5

with b/h = 2. Next we considered the variations of the cutoff frequency of the dominant mode as a function of deflection distance 6. Figure 5 shows the normalized cutoff wavelength (Ac/b) as a function of normalized deflection distance (6/b) for three different trapezoidal waveguides with different b/h values 1.5, 2, and 3. It is shown that the cutoff frequency of trapezoidal waveguides increases with decreasing b/h and the rate of change of cutoff wavelength with respect to changes in deflection distance is higher for smaller values of b/h. Noting that b/h = 1.41 corresponds to a triangular cross section and the fact that the electric field strength is rather weak at the corners, the cutoff frequency does not change much by decreasing b/h when b/h < 2. Another important factor in designing a waveguide is the bandwidth of single mode operation. Figure 6 shows the normalized cutoff wavelengths of the first and second modes as a function of normalized deflection distance. It is shown that a single mode operation bandwidth of about 30% can be achieved for a trapezoidal waveguide with b/h = 2. The most important aspect of this analysis is the calculation of phase shift due to deformation of waveguide cross section. Qualitatively Fig. 5 indicates that the cutoff frequency changes considerably with relatively small deflection values. In order to quantify the phase shift property of this device, let us consider the phase difference between two signals one propagating in an undeformed trapezoidal waveguide and the other one propagating in a deformed waveguide with deflection distance 6. The phase difference over a length of one free-space wavelength (Ao) can be obtained from _AO = (Qd - )Ao where Bd"2 =) ( ~_ ) 2 Ao A and superscripts d and u denote deformed and undeformned waveguides respectively. It is obvious that the phase shift is a function of operating wavelength (Ao) and more phase shift can be obtained if the operating frequency is near the cutoff frequency of the tundeformred waveguide. Noting that for b = 0.679Ao the undeformed waveguide is at 1cutoff, I-7i. 7 Sol)ws the paluise shift per Ao lenglth of t le waveiide as a functti0 6i

Material Si3N4 SiO2 Cr Au Polyimide Young's Modulus (E) 146 GPa 60 GPa 248 GPa 80 GPa 8.3 GPa Internal stress o 900 MPa 300 MPa 850 MPa 260 MPa 9 MPa Table 1: Mechanical properties of materials to be used in the design of extremely thin diaphragms. of normalized deflection distance for different values of operating frequencies. It is shown that near cutoff (b = 0.7Ao), a phase shift as high as 44~ per one free-space wavelength of the waveguide length can be achieved for 5% deflection. 3.2 Mechanical Analysis In order to design a diaphragm capable of large deflection using minimal amount of force, the mechanical properties of the diaphragm material must be known. These include the Young's modulus of elasticity, Poisson's ratio, and internal stress of various thin films that are used in making the diaphragm. Table 1 summarizes the Young's modulus and internal stress of materials that are to be used in the design of an optimum diaphragm. For most practical applications the Poisson's ratio can be assumed 0.3 for all materials used here. The expected diaphragm design includes two or more layers of different materials and effective Young's modulus and stress for the composite diaphragm are needed for the mechanical analysis. The Young's modulus and stress of a multi-layered structure can be obtained, respectively, from: ei Eiti Ee t Li t' ~i (Titi Li t? As mentioned earlier. the diaphragm must be designed such that the required deflection occurs with miniimal applied electrostatic force. Thus it is obvious that the diaphragm thickness must be as thin as possible and yet durable. The lower surface of the diaphragm in contact with the waveguide groove must be metallized. The thickness of the metal lavyer is characterized by the conductivity of the metal film. IBecause of its high (1 ( coliIc ivitv and resistantce to corrosion and oxidizat ion. oold will "7lm

be used to metallize the surface of the membrane. Noting that the conductivity of gold is 4.1 x 107 5I/m and a minimum of two skin depth thickness is required to form a metallic surface, at W-band frequencies a minimum of 5000 A gold is needed. Our goal is to design a diaphragm with a thickness thiner than a few microns. In this case the required diaphragm deflections ( 10- 100,m) is much larger than the thickness of the diaphragm. Therefore the membrane theory instead of the plate theory must be used for calculating the deflection. When the diaphragm is very thin, it can be considered to have zero bending stiffness. Simple analytical solutions exist for thin membrane when deflection is relatively small compared to the membrane thickness [7]. It has been shown that the central deflection of a rectangular membrane under a uniform load distribution can be obtained from [7] PW4 -= F3 (1 - 72) (4) where P is the applied pressure, T and w are the membrane thickness and width respectively, y is the Poisson's ratio, and a is a constant function of length to width ratio of the membrane. For a square membrane a:= 0.0151 which almost doubles (0.0312) as the ratio of length to width exceed 2. In our application the deflection is expected to be much larger than the membrane thickness (T) and it should be noted that (4) overestimates the deflection. On the other hand the applied electrostatic force is not uniform and (4) provides an underestimation of deflection in this regard. Although approximate, this formulation gives the order of magnitude of the required voltage. Because of the large deflection and stretching of the diaphragm, the internal stress does not play arn important role in the deflection and therefore is neglected. The required pressure generated by a parallel plate capacitor is given by P -= - (5) 9(d -- 6)2 where d is the capacitor gap before membrane deflection and c is the dielectric constant of the medium (in this case e = co). Substituting (5) into deflection formula (4) -i 166(d- )2ET3 (0(1 -,-)t 8S

This formula relates the applied voltage to the central deflection. 4 Design Parameters and Experimental Results To demonstrate the feasibility of this technology, design of a W-band phase shifter is considered. For this purpose, a trapezoidal groove was machined out of a brass block. The groove dimensions are chosen to be b = 2.40 mm and h = 1.20 mm, (see Fig. 8) which corresponds to a cutoff frequency fc = 85 GHz according to Fig. 5 for b/h = 2. At each end of the brass block, the trapezoidal cross section was tapered to rectangular grooves with dimensions 2.54 mm x 1.25mm to mate the standard WR-10 waveguide. After machining the brass block, the groove was gold-plated for higher conductivity. To check the validity of our numerical results, the cutoff frequency of undeformed trapezoidal waveguide was measured by placing a similar block of goldplated brass (without the groove) over the trapezoidal groove and its S-parameters were measured using an HP vector network analyzer. Figure 9 shows the measured frequency response of the waveguide over the frequency range 75-110 GHz. It is shown that the cutoff frequency is near 85 GHz as predicted. The relatively high return loss near cutoff is caused by the tapered section. Basically the guide wavelength near cutoff is much longer than the length of the tapered section (about 4 mm). Note that this loss is an artifact of rectangular to trapezoidal transition and not the waveguide itself. In fact the insertion of the 4-cm waveguide itself is about 1 dB at 110 GHz. This insertion loss can be further improved by improving the metallic contact between the two pieces making the waveguide. Figure 11 shows the phase of the S12 as a function of frequency where the expected phase variation in a waveguide is observable. With the confidence in our calculation of the design parameters for trapezoidal waveguides, we proceeded with the design of the membrane. This is the process that has taken a lot of time and effort due to the empirical nature of the work. We chose a length of a = 30 mm and a width of b = 4 mmn for the diaphragm to cover the trapezoidal groove. In reality the length of the membrane is 40 mm to cover the ( eltire \(aveguide section, however, the flexible portion is timidted to 30 nmm. 9

A wider width for the membrane is chosen to lower the required voltage for the desired deflection. So far we have tried the construction of a Ium-thick combination of silicon-dioxide (02) and silicon-nitride (Si3N4) covered with a layer of 300 A chromium and a layer of 5000 4 gold. The silicon-nitride layer has a, high tensile stress which is good for planar membranes to avoid rupture [6]. It was soon found out that this membrane would break much sooner before the required maximum deflection 100in is reached. Therefore we decided to chose a different membrane with much lower modulus of elasticity and higher yield strength. It was found that very thin membranes of Dupont polyimide which are very flexible may be fabricated for this application. The proposed diaphragm structure is composed of 2psm polyimide, 0 0 300 ACr, and 5000 AAu. Therefore the effective Young's modulus of the membrane is 25.3 GPa. Assuming a gap of the order of d = 200,um a moderate voltage of about 54 V is required to get, lOOim, deflection. It should be mentioned here that the diaphragm will be pulled down at a deflection of about 6 = 3/5d. The process sequence for the diaphragm fabrication is shown in the Figure 11. It starts with a bare silicon wafer on which about 2500 A of thermal oxide is grown. Our experimental results showed that adhesion of polyimide to SiO2 is not that good 0 and it fails under tensile stress. For this reason 1000 A of aluminum is evaporated on,SiO2 to enhance the adhesion of polyimide to the substrate. Subsequently 2 to 3/inr of polyimide is span on the wafer (Polyimide P12611 Dupont). The thickness of the polyimide is determine by the angular speed of the spinner. The polyimide surface is then roughened by oxygen plasma and a layer of Cr(300 A)/Au(5000 A) is evaporated on top. The oxide on the back side of the wafer is then patterned to define the membrane rim. After many trial we have found that the above process is not, complete yet. Basically the silicon etchant attacks the polyimide through the mnetallized surface. The evaporated gold and chromium is not solid and the etchant reaches the polyimide through the microscopic pores. We are in the process of finding a method to protect the front surface. After protecting the front surface the silicon will )e etched in tetia- InetlivI1 am 1montilnui hydroxide I'M A I (12.) conllceiiltratioI) It0

at 75 C until the membrane is released. A buffered HF dip at the end removes the thin oxide and aluminum from the back side of the diaphragm. 11

References [1] Silvester, P., "A general high-order finite-element waveguide analysis program," IEEE Trans. Microwave Theory Tech., vol. MTT-17, no. 4, April 1969. [2] Dettman, J.W., Mathematical Methods in Physics and Engineering, pp. 149 -169, New York: Dover, 1988. [3] Jin, J., The Finite Element Method in Electromagnetics, New York: John Wiley & Sons, 1993. [4] Wilkinson, J.H., The Algebraic Eigenvalue Problem, New York: Oxford University Press, 1965. [5] Chu, L.J., "Electromagnetic waves in elliptic hollow pipes of metal," J. Appl. Phys., vol. 9, pp. 583-591, Sept. 1938. [6] Wolf, S., and R.N. Tauber, Silicon Processing for the VLSI Era,vol. 1, Lattice Press, 1987. [7] Giovanni, M.D., Flat and Corrugated Diaphragm Design Handbook, pp.211 -216, New York: MARCEL DEKKER.

A narrow gap to allow defection Variable DC bias to control membrane deflection r! I T sl he overall phase hift is linearly roportional to L. Metallized surfaces of \ v an etched groove in a A thin felexible dielectric silicon wafer forming a membrabe. The lower trapezoidal waveguide sumembrabe. The lower surface is metallized. Silicon wafer 1* Electrostatic field pulls the membrane upward. Oxide layer - W o A. i ojo~.-jj^.^gg.o o,~o %.~.;;:%;: \ Metallized dielectric membrane Figure 1: Geometry of the proposed micromachined phase shifter based on a displacement of a waveguide wvall. 13

(a) (b) sAA //,VV V Figure 2: Discretized cross section of an undeformed and deformed trapezoidal waveg 14

E-field distribution...... 0.5 1. \ I 0.4 0.3 I I l 0 Q I 0L 0^ / / / I l l 0.2 / Jr Jr / / / 1 I / / / / I I / / / / I I / / I i / / / / / 0.1 - / I I / J I 0 -0.1 - -- -1 " 0 0.1 0.2 0.3 0.4 0.5 0.6 x-position 0.7 0.8 0.9 1 Figure 3: The field distribution of the dominant mode (TE) in a trapezoidal waveguide with b/h = 2.

E-field distribution 0.5 i! i i iii 0.4, / 0.,, \ "0 I 0.1 I ' 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 x-position Figure 4: The field distribution of the second mode (TE) in a trapezoidal waveguide with b/h = 2. -0.1 -— ' - ^ --- —-------

1.70 f f w w g r * X X * l l * B * xJ I - v -- I 1.60 - - _ 1.50 - 1.40. * * * 'i............... I 1.40.. 0.00 0.01 0.02 0.03 0.04 0.05 6/b Figure 5: The normalized cutoff wavelength (Ac/b) as a function of normalized deflection distance (6/b) for three different trapezoidal waveguides with different b/h values 1.5, 2, and 3. 17

1.60 I... I-T,... I. I. I.... I I......... I......... I......... 1.50 1.40 1.30 1.20 1.10 I -j.. -- -___ _,- -_ _ _ _ __ _ _ _ __,_ -- - - 1.00 L 0.c.........!...... I I I. I I.........I.........I..A...... )0 0.01 0.02 0.03 0.04 0.05 6 Figure 6: The normalized cutoff wavelength (A,/b) as a function of normalized deflection distance (S/b) for the first two modes of a trapezoidal waveguides with b/h = 2 is

60.0 50.0 40.0 30.0. I -. I I I I I I I b=0.70A ------ b=O.75A ----- b=O.8~0X ---- b=0.85A I o I C.VP o o o 7 I I11 -.... . - I - -. — Oi 20.0 10.0 0. 0.00 i - —.. - - - - - - - - m - - - - I - -. --, I.... - - - I I I I I d I. -. I I- -. - —, - 0.01 0.02 0.03 0.04 0.05 6/b Figure 7: Phase shift per unit free-space wavelength length of a trapezoidal waveguide with b/h =2 at different operating frequencies 19

Groove Dimensions 1.20mm 0.7 mm Block of Brass Circular hole diameter 1.7 mm Thread Figure 8: Geometry and dimensions of a trapezoidal waveguide machined out of a brass block designed for operation at W-band frequencies. 20

S1RE REF 0. 0 dB og MAG 10.0 dB, C A S12 REF 0.0 dB L.-~-c -T -—,- --— ~-.. t i i -. ---l --- —- — I --- 1j,- j-.. J. _..,..._ L~ - t —~ -r -- - i —,-~ ~I. -. JA... i 1 og MNG 10.0 dB3/ I M [ S21 REF 0. 0 dB og MFPG 10. 0 dB/ SF22 REF 0. 0 dB 1og MAG 10. 0 dBR - —., -t ---.-. L -- ---- ~ --- t -4 —~-t —~- a --- iJ! I | i iL STOP 109. 999998000 GHz START 75. 000000000 GHz Figure 9: Measured S-parameters of the trapezoidal waveguide over a frequency range 75-110 GHZ. 21

REFA 0. 0 I 100.0 63. G52 1 I- I - 1 C ~jo in -, G4 -- - i i J i CHz i i I L - ---- K I -1 i I I i II I I — —. -- -. --— 4 - I - -.~ T F. -- -- - - - -- -. m I I i I I I i i I I — i- -- - - --- -- i i II I i i II ii i i -— A I I I 11 -—, I -. — A I II ....L. I i I 11 'I-, i 1 I4 II. — -. 7~5. 000000000 GHz S-FOP 105-:,. 999998000 GtH — Figure 10: Measured phase response Of S21 of the trapezoidal waveguide over a frequency range 75-110 GHZ. 22

(a).................. ~ N::...:............:..............:...../.....:.... ':../:...:',.:.,.::,:::,.:::../::::::::: /:../::/:.:../::..:.. /:....:../::::...:..::.:.:..::.;::::.:,.:../::::.:::/....:::.:.:.,.:,:..::,::/.:../:.,.::::/: '.:.:;-..:..-:.::;::::-.:;;: *..:-:~.:-.-::.~::*..:;:.;:..-.::~:;.;::...-.-. (b) (e) (f) (c) 44.......*4 V II I I I I I I: I I I I I I I I I a I I I I 2 I I I I I I --.\\\\\1.,,, A, s -.... a:::.':::.'1 *::::.:.',:, g:.:.:::.:..::,1:,.:...'::,.::,.::1.. - -. -. * - g......... (g) Figure 11: The proposed process sequence for fabrication of a polyimide membrane. 23