We have investigated Coplanar Waveguide (CPW) elements on AlN for use in future ... In the early stages of developing a new material system like the AlGaN/GaN system most ... capacitance C [F/m], conductance G [S/m] and resistance R [Ω/m] according to: ... determine the properties of both the line and the adaptor.
Mat. Res. Soc. Symp. Proc. Vol. 693 © 2002 Materials Research Society
Passive components on AlN for application in AlGaN/GaN power amplifiers B. Jacobs1, B.van Straaten1, M. Kramer1, F. Karouta1 P. De Hek2, E. Suijker2, R. Van Dijk2 1 Eindhoven University of Technology, Department of Electrical Engineering, Opto-electronic devices group, PO box 513, NL-5600 MB, Eindhoven, The Netherlands 2 TNO Physics and Electronics Laboratory, 2509 JG, The Hague, The Netherlands ABSTRACT We have investigated Coplanar Waveguide (CPW) elements on AlN for use in future AlGaN/GaN based power amplifiers. This technology becomes crucial if a via-hole technology is not available. Lines, discontinuities, metal-insulator-metal (MIM) capacitors and resistors were measured and modelled. These elements are embedded between two adaptors for RF probing. A technique was developed to de-embed the adaptors from the overall measurement and hence correctly determine the properties of the element itself. Measurements on elements containing multiple ports with right angles can best be carried out using standard calibration techniques followed by carefully reorienting the probes. It is shown that for accurate design of matching networks operating at 10 GHz each element has to be carefully modelled. The method presented in this paper can be a useful contribution tackling some of the problems related to the design of these networks. INTRODUCTION In the early stages of developing a new material system like the AlGaN/GaN system most research efforts are spent on realizing active components like high electron mobility transistors (HEMTs). However, combining these elements requires some sort of matching. The choice of components needed for this matching depends largely on the substrate used and whether a via-hole technology is available or not. In the case of the AlGaN/GaN material system two substrates are commonly used; the relatively cheap sapphire and the much more expensive SiC that has a much higher heat conductivity. In the case of SiC, a via-hole technique can be developed although this is far from trivial. If sapphire is used this technique is not available. The absence of such a technique implicates that microstrip technology cannot be used. In this case one has to resort to CPW technology that is less developed and not so implemented in commercial simulators as microstrip. Therefore, we have chosen to develop our own library of CPW elements. DE-EMBEDDING CPW LINES The general layout of a typical CPW line is illustrated in Figure 1. The structure consists of a line connected to an adaptor on either side. This adaptor is necessary because not every line is suitable for probing. Also, because the elements are on a different substrate than the calibration substrate and the metal geometry around the probe is different, one cannot assume a perfect RF connection between probe and line. The adaptor accounts for all the effects mentioned above.
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Y3 1
2 Y1
adaptor
line
Y2
adaptor
Figure 1: Layout of a CPW line (left); Equivalent circuit of an adaptor (right).
The addition of the two adaptors makes it impossible to determine the characteristics of the line element from an arbitrary number of measurements of structures like the one illustrated in Figure 1. To fully characterize the line one needs additional measurements. These measurements can be in the form of connecting a short or an open instead of one of the two adaptors. The problem with this approach is the difficulty of realizing a perfect open or short at high frequencies (>10 GHz). To bypass these problems we have chosen to follow the approach published by Pantoja [1] and Marks [2]. We model the adaptor by a pi-equivalent circuit shown in the right part of Figure 1. This approach is valid for passive reciprocal twoports. We start off with measuring 2 lines. The first line consists of 2 adaptors in series. We shall denote the measured ABCD parameters of this line by T. A second measurement of a line with a length ldelay of for instance 1000 µm is measured. The ABCD parameters of this line are multiplied by T-1 to give the matrix D. Using these line measurements and notations, one can express the line characteristics, meaning the characteristic impedance Z0 and the propagation constant γ, as a function of the Y3 parameter of the adaptor: Z0-1=Y32(½ T1D11 +½(T0-1)Dl2-½ T1G0)/(G02-1)2 γ=acosh(G0)/ldelay In which G0 is obtained from: G0=½(T0+1)D11-½(T0-1)D22+½D12T2-½D21T1 This indicates that an additional measurement is needed to solve for Y3. The propagation constant however can be determined from these 2 measurements alone. According to classical waveguide theory [3], we can express Z0 as a function of the line inductance L [H/m], capacitance C [F/m], conductance G [S/m] and resistance R [Ω/m] according to: Z0=((R+jωL)/(G+ jωC))0.5 Similarly the propagation constant can be written as: γ=((R+jωL)(G+ jωC))0.5 Assuming that the dielectric losses (G) can be neglected compared to the line capacitance, we can combine these relations to give: Z0=γ/ jωC
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Measuring the difference in capacitance of the two lines at relatively low frequencies (< 1 GHz) and dividing this by ldelay gives the line capacitance. Using the equations for Z0 one can determine the properties of both the line and the adaptor. Figure 2 shows an example of the characteristic impedance as a function of frequency for a CPW line with a signal line width of 45 µm and a signal to ground spacing of 75 µm. Assuming that the propagating mode in the CPW line is a true quasi-TEM mode, analytical solutions for the line properties can be found [4]. Table 1 shows a comparison between the analytical formulas and the measured values. A very good agreement is obtained proving the validity of our approach. Other CPW elements will also have adaptors connected to either side. Once the properties of the adaptors have been determined we can de-embed them from every subsequent element.
Zo (Ohm)
80 75 70 65 60 0
10
20
30
40
Freq (GHz)
Figure 2: Typical result for the characteristic impedance of a CPW line.
Table 1: Comparision between measured values for the line-capacitance(Cexp) and values based on the quasi-TEM approach (Cqtem) for different signal line widths (w) and signal to ground spacings (s).
w [µm] 45 20 100 35 70 50 75 85
s [µm] 75 100 20 20 75 45 45 100
Cexp [pF/m] 99 71 183 138 110 118 132 105
Cqtem [pF/m] 97.4 73.3 179.6 134.8 110.1 116.4 130.7 107.3
ORTHOGONAL STRUCTURES Other CPW elements like Tee’s and crosses present another difficulty. These elements contain right angle bends that require a right angle calibration, see Figure 3. Most calibration substrates contain right angle line elements but mostly these structures cannot be used for accurate calibration. To illustrate this point we have conducted 2 measurements of a CPW bend. One measurement was carried out using a right angle SOLT (short-open-line-through) calibration, for the other measurement we performed a ‘normal’ LRM (line-reflect-match) calibration followed by carefully reorienting the probes to perform the right angle measurement. Figure 3 shows the measured S21 parameter of the bend. In the case of the rightI11.1.3
angle calibration S21 becomes larger than 1, which of course is not valid for a passive structure. Carefully reorienting the probes with the cables seems to be the best option for measuring right-angled structures.
M ag (S 21)
1.1 1.05 SOLT
1
LRM
0.95 0.9 0
10
20
30
40
50
Freq (GHz)
Figure 3: Comparision of the S21 parameter of a right angle bend using a right-angle SOLT calibration and a 'normal' LRM calibration (left); example of a CPW Tee showing the right angles in the devive (right).
CAPACITORS AND RESISTORS To complete the set of CPW passive components we processed NiCr resistors and SiNx MIM (metal-insulator-metal) capacitors. The layouts for these elements, together with a schematic cross-section, are shown in Figure 4.
adaptor
TiAu NiCr SiNx
Au (plated) NiAu taper
capacitor
Figure 4: Schematic cross-sectional view of a resistor and capacitor in series (left); layout for a capacitor to ground. Note the taper between the adaptor and the actual capacitor (right).
Using a NiCr layer thickness of 125nm we obtained a sheet resistance of 17Ω. The MIM capacitance scales with the surface of the top plate giving a capacitance density of 0.2nF/mm2. Both the resistor and capacitor contain 2 tapers that transform the connecting line geometry in the geometry of the NiCr line or the bottom plate of the capacitor. These tapers, which have a length of 100 µm, result in an extra inductance in series with the resistor/capacitor. The equivalent circuit shown in Figure 5 can model both the resistor and capacitor. The first 3 elements on either side model the tapers, although C3 and C4 contain the input capacitance of the resistor/capacitor part as well.
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Figure 5: Equivalent circuit for capacitor/resistor.
The tapers in series with the capacitor constitute a series resonance circuit. The effective capacitance can be approximated by: Ceff=C0/(1-(ω/ωT) 2) Where C0 is the low-frequency capacitance and ωT = 1/(LC0) 0.5 the resonance frequency of the circuit in which L models the inductance of the tapers. This resonance behaviour can clearly be seen in the measurements. Figure 6 shows -Y12/jω (=Ceff) for a series capacitor after the adaptors were de-embedded. For capacitors above 0.3 pF, Ceff significantly differs from C0. This shows that designing a matching network with these elements requires accurate models for both the tapers and the actual capacitor/resistor. 15
Ceff (pF)
10 5 0 -5
0
10
20
30
40
-10 -15
Freq (GHz)
Figure 6: MIM capacitor with a top plate of 75 x 75 µm2 (1.5 pF). The resonance occurs in the X-band.
CONCLUSIONS In this paper we have presented a method to correctly determine the properties of CPW elements needed in matching networks for AlGaN/GaN power amplifiers. To remove the influence of the adaptors needed for probing a de-embedding technique was developed. Using this method we could determine the CPW line properties that show excellent agreement with analytical formulas based on a quasi-TEM model. Elements containing right angles like a bend or a cross must be calibrated using standard through calibrations followed by carefully reorienting the probes. Using right angle calibration structures gives erroneous results. REFERENCES 1. R.R. Pantoja, “Improved Calibration and Measurement of the S-parameters of Microwave ICs”, IEEE Microwave Theory and Techniques, Vol. 37, pp.1675-1680, 1989 I11.1.5
2. R.B. Marks and D.F. Williams, “Characteristic impedance determination using propagation constant measurement”, IEEE Microwave Guided Wave Letters, Vol. 1, pp. 141-143, June 1991. 3. D.M. Pozar, “Microwave Engineering”, 1990 ISBN 0-201-50418-9 4. W. Heinrich, “Quasi-TEM description of MMIC coplanar lines including conductorloss effects”, IEEE transactions on microwave theory and techniques, Vol. 41, no. 1, pp. 45-52.
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