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14 ELECTRONICS, VOL. 8, NO.1, MAY 2004. A Robust Approach for the Direct Extraction of HEMT Circuit Elements vs. Bias and Temperature Alina Caddemi, Nicola Donato and Giovanni Crupi 1 Abstract We here present the results of our most recent activity in the implementation of robust and easy-to-perform techniques for the extraction of reliable equivalent circuits for microwave transistors. Our effort also led to the development of a compact software tool written in Agilent VEE language for totally automated measurement and direct model extraction. Its effectiveness has been tested at several bias and temperature points and the modeling results have been compared with those obtained by application of other procedures. This procedure can be adopted for both Schottky-gate devices (MESFET’s, HEMT’s) and insulated gate devices (RF MOSFET’s, CMOS) since no direct polarization of the gate is requested. Keywords – HEMT, MESFET, TEMPERATURE, DIRECT EXTRACTION MODELING . I. IINTRODUCTION Modeling and simulation of solid-state active devices are basic aspects of modern advanced <strong>electronics</strong> and a key point is a rapid and accurate determination of electrical models for CAD of microwave circuits. The target of interest to microwave engineers is the implementation of robust and easy-toperform techniques for the extraction of reliable equivalent circuits of the devices under test, valid over over a wide range of operating conditions. We here present the results of our most recent activity in this field leading to the development of a compact software tool written in HP VEE language for microwave device measurement and direct model extraction. Its effectiveness has been tested at several bias and temperature points and the modeling results have been compared with those obtained by application of other procedures. The structure of the model network is shown in Fig.1. For the direct extraction of the circuit elements, we first derive the extrinsic ones by measuring the scattering parameters in “off” (VGS=0, VDS=0) and “pinched” (VGS
Z 11 = R + R + 0. 5R s g ch ⎡ + j⎢ω ⎢⎣ ELECTRONICS, VOL. 8, NO.1, MAY 2004. ( L + L ) Z ω s g 1 − ωC g ⎤ ⎥ ⎥⎦ (1) 12 = Z 21 = Rs + 0. 5Rch + j Ls (2) 22 = Rd + Rs + Rch + jω( Ls Ld ) (3) Z + The parasitic inductances Ls and Ld can be extracted from imaginary part of (2) and (3). Once Ls is computed, we can extract Lg by considering the imaginary part of (1) at two different frequency values and assuming Lg and Cg constant. The parasitic resistances can be computed by means of the real part of eqs.(1), (2), (3) and the real part of Z11 at the pinch-off condition: [ ] s g R R Z + = 11 Re (4) For the extraction of parasitic capacitances, we need again the [S] parameters at pinch-off conditions and convert them in [Z] parameters. As a first step, we subtract the resistances and inductances previously computed: Z − R − R − jω L + L ( ) 11 s g s g (5) Z ω 12 − Rs − jωLs = Z 21 − Rs − j Ls (6) 22 − Rd − Rs − jω( Ls Ld (7) Z + ) and then transform the results into [Y] parameters: ( C C ) Y + 11 = jω 2 b pg (8) Y ω 12 = Y21 = j Cb (9) ( C + C C ) Y + 22 = jω b pd ds (10) By means of eqs. (8) and (9), we extract the values of Cb (Cb=Cgs=Cgd) and Cpg. From eq. (10), we can compute Cpd by assuming Cpd = Cds / 4 [1]: C pd 1 ⎛ Y22 ⎜ − C 5 ⎝ ω = b ⎞ ⎟ ⎠ (11) Finally, we determine the intrinsic elements from HOT [S] parameters by applying a deembedding procedure of the extracted parasitic elements. By transforming [S] in [Z] parameters, we subtract the gate and drain parasitic series inductances: L j Z ω − 11 g (12) Z ω 22 − j Ld (13) With a conversion to [Y] parameters, we eliminate the effects of the two parasitic parallel capacitances: Y ω 11 − j C pg (14) Y − jωC 22 pd (15) A successive transformation into [Z] parameters allows us to subtract the three resistances and the source inductance, all of them as series elements: Z − R − R − jωL 15 11 s g s (16) Z ω 12 − Rs − jωLs = Z 21 − Rs − j Ls (17) Z ω 22 − Rd − Rs − j Ls (18) Finally, with the last [Y] conversion and using eqs.(19)- (25) we determine the intrinsic elements [4]: m C gs = C gd ( ) Im Y12 = − (19) ω [ Im( Y ) − ] ⎡ 2 11 ωCgd Re ( Y ) ⎢ 11 1+ ω ⎢ Im( Y ) −ωC C ds ⎣ g ds = Re( Y22 ) Im = ( Y ) 22 ω [ ] ⎥ ⎥ 2 − Re( Y11 ) ( Y ) + Im( Y ) 11 11 ωC gd [ ] 2 − ωC 11 gd gd ⎤ ⎦ (20) (21) (22) Ri = (23) 2 Re ( Y21) − ωC gd ωCgs Ri Re( Y21) ⎤ ⎥⎦ 1 ⎡− Im − τ = arcsen⎢ (24) ω ⎣ g m [ ( ) ] ( ) ] ( ) 2 1 1 2 2 2 2 2 2 Im Y21 + ω C gd + Re Y21 1+ R iC gs g = ω III. RESULTS (25) By means of the procedure here described, several pHEMT’s from TRIQUINT foundry (USA) have been modelled. These devices have 250 µm pitch, 0.25 µm gate length and 300 − 600 − 900 µm of gate widths. The on wafer [S] parameter measurements were performed in the 350 MHz - 6 GHz frequency range with a step of 297.5 MHz. In Figs. 2-4, the eight parasitic elements of a 900 µm device vs. frequency are reported. It can be seen that the element values reach a constant level as the frequency increases. L[nH] 0.3 0.2 0.1 0 -0.1 0 1 2 3 4 5 6 Frequency[GHz] Fig.2 Frequency dependence of the parasitic inductances Lg LS Ld
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Page 9 and 10: e significantly reduced or even rem
Page 11 and 12: REFERENCES [1] D.Economou and R.C.A
Page 13 and 14: problem (1)-(3) belongs also to the
Page 15: IV. CONCLUSIONS The test experiment
Page 19 and 20: Ma g Max 0.05 1 65 -180 150 -1 65 0
Page 21 and 22: Input vectors are presented to the
Page 23 and 24: additional measurements of transist
Page 25 and 26: II RF MOSFET NOISE MODEL Circuit-or
Page 27 and 28: It is obvious that the MOSFET noise
Page 29 and 30: (a) (b) Fig.2. Comparison of the st
Page 31 and 32: REFERENCES [1] D.L.Harame et al.,
Page 33 and 34: ductor crystal lattice the majority
Page 37 and 38: elations (16) and (17) given in the
Page 41 and 42: conceived, consists of the followin
Page 45 and 46: c) Fig. 3. Images of test object (m
Page 47 and 48: -minimum voltage in the secondary t
Page 49 and 50: LL L = 3. 9 µ H, C = 5. 6 nF, ρ
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