Capacitance and RF-Conductance/Transconductance Look-up Table Based pHEMT Model Ce-Jun Wei1, Yu Zhu, Hong Yin , Oleksiy Klimashov, Cindy Zhang, and Tzung-Yin Lee SKYWORKS SOLUTION INC., 20 SYLVAN ROAD, WOBURN, MA 01801, USA 1 [email protected] ABSTRACT — A capacitance and RF-conductance/RFtransconductance look-up table based large-signal pHEMT model is presented based on an ensemble of bias-dependent small-signal equivalent circuits. The model is capable of accurate simulation of small-signal S-parameters as well as large-signal performance over the data-acquisition bias range. In addition to the dc current sources, the model contains two capacitive current sources and two dynamic RF current sources, which fit RF-DS conductance and transconductance respectively. By introducing the dynamic RF current sources, the problem of path-dependence which occurs in modeling large-size devices and devices with dispersion is resolved. The model is symmetric and swappable between drain and source. The model has also accurate leakage model and can be used for either amplifier or switch applications. The validity of the model is demonstrated by comparing the simulation of DC curves, leakages, and small-signal S-parameters over a wide bias range, by comparison of the measured data. Large-signal power/harmonics simulation shows good comparison to the measured data. Index Terms — look-up table modeling, Emote PHEMT. I. INTRODUCTION For modern communications, design of pHEMT amplifiers and switches with accurate bias-dependent S-parameters and large-signal performances prediction are critical and challenging. Unfortunately, due to complex trapping effects in MESFETs and pHEMTs, it is almost impossible to develop a physics-based model and empirical models and look-up table-based model are widely used. The applicability of empirical models depends on if the equations adequately cover the trapping effects that are normally very tough to do. Look-up table based model or Root model s are considered to be most accurate since it is based on measurement data and it is technology independent. There are a couple of traps when using the look-up table based model. First, the accuracy depends on if the measured data is sufficient to cover all important physical features of the devices. The Root model uses charge-based look-up tables and it has the advantages of good convergence and is very robust. However, due to complex trapping effects, the charges based on integration of 2D-CV functions are not always path-independent. The trans-capacitance near pinchoff may result in unphysical small-signal response. Also the conventional Root model does not take into account the difference both between DC and RF Gm and Gds. Also it is required to be symmetric between drain and source that is important for switch applications and that the conventional look-up table based models do not satisfy. In this paper we present an extended and improved look-up table based model. Instead of a charge-based model, we use capacitance based look-up tables that do not contain transcapacitances. The model contains two RF-currents, one based on RF-Gm current that sets into play when there is gatevoltage swing, and the other RF-Gds based current that comes into play when there is RF-swing of drain-source voltage. The intrinsic model is symmetric between drain and source and they are swappable. Plus with the accurate leakage look-up tables, the model is capable of switch applications. Systematic extraction to extract two RF-IVs and CV functions is described. Following is the validation of the model in terms of fitting of IV, S-parameters in wide range, as well as power/harmonics for typical sizes of devices. The overall model including noise model is illustrated. II. EQUIVALENT CIRCUIT OF THE MODEL The equivalent circuit of intrinsic part of the model is shown in figure 1. Extrinsic model contains, as usual, access resistances Rg, Rs, and Rd and access inductances, Lg, Ls, and Ld and possible some parasitic capacitances, not shown here. In the figure, there are three currents between drain and source, Idc is the dc current, Id_gm is the RF current integrated from RF-Gm. and Id_Gds integrated from RF-Gds. Id_gm Idc Id_Gds Ctrap Rtrap D S Ids_leak Igd_leak Cgd Cds Dgd Cgs Dgs Igs_leak G Figure 1. Equivalent circuit of the intrinsic part of the model Due to large value of CtrapRtrap time constant, that corresponding to trapping effects, the DC current will be Idc and Id_Gm and Id_Gds are shunted by Rtrap. At RF, the current will be Id_Gm and Id_Gds that flow out to circuit via Ctrap and Idc is shorted by the large capacitance Ctrap. The integration path of Irf-Gm starts from far-below pinchoff at any Vds as initial point, at that the Ids is supposed to be zero, the current will be the integration of RF-Gm with respect to Vgs. Id _ Gm = Vg ∫<<Vp Gm _ rf dVgs =fg(Vgs, Vdso) where is Gm _ rf measured bias dependent RF transconductance and the integration assumes Vds is unchanged and it is the DC component. The Vgs is integrated from far below pinchoff to the point of required augument of the function. Similarly, the integration path of Irf-Gds starts from Vds=0 at any Vgs as initial point, at that the Ids is supposed to be zero, the current will be the integration of RFGds with respect to Vds. Id _ Gds = Vd ∫0 Gds _ rf dVds = fp(Vgso, Vds) where the DC-Vgso is a parameter and Gds _ rf is measured bias dependent RF DS-conductance and the integration assumes Vgs is unchanged and is the DC component. It is straightforward to verify that the RF-Gm is exactly the same as measured and the RF-Gds is exactly the same as measured, too. Figure 2 shows these two RF currents and how much difference is between them. The device measured is a 4x75um E-mode pHEMT from Winn-semi. Figure 2. Plot of Id_gm and Id_gds for a device of 4x75um E-mode pHEMT. The charge model is replaced with the capacitance model. The advantage of the capacitance-based model is direct use of measured capacitance look-up tables and there is no transcapacitance involved. The charge equations are replaced with capacitive currents: Icap_gs= Cgs x dVgs/dt and Icap_gd=Cgd x dVgd/dt. Therefore, the model is fully consistent with bias-dependent small-signal models. The leakage look-up table is generated by measuring the gate leakages at Vds=0 and measuring the leakages with the drain open and fitting the drain floating voltages. The model is implemented with a 14 port SSD in ADS, as shown in figure 3. The model also contains a noise model that will not be addressed here. Port G Num =2 G D S Port S Num =3 Tj Port D Num=1 _dgsdt R R44 _dgddt R=1 Ohm _Gc _Dc di si ds _Sc vdsn vgmn SDD14P SDD14P1 I[1,0]=Ig I[2,0]=(_v2)/1e15 I[3,0]=(_v3)/1e15 I[4,0]=-ids*(_v2-_v3) I[4,1]=Cth*(_v4) F[5,0]=-dvgs_dt F[5,1]=vgs/f_nom F[6,0]=-dvgd_dt F[6,1]=vgd/f_nom I[7,0]=Igs_cap+Igd_cap I[8,0]=-Igd_cap I[9,0]=ids-igd I[9,1]=qds I[10,0]=-igs-Idrf I[10,1]=-qds I[11,0]=-ids+Idrf I[12,0]=-Igs_cap I[13,0]=ids*EnNoise I[14,0]=idgn*EnNoise C="Igrf" C="Idrf" C="Igdrf" Cport= Figure 3. Using SDD to build look-up table model. III. MODEL EXTRACTION The model extraction uses a 4x75um E-mode pHEMT from Winn-semi. ICCAP is used for measurements. The measurement range from Vgs=-10V up to 0.8V, Vds from 0V to 6V covers well the linear-saturation region as well as leakage region. The S-parameters measured from Vds=0 to 6V covering active region and Vgs from -10V to 0.3V covering below pinch-off region. The later is important when the device is used for switch or class C and high-power applications. An important extraction step is generating bias-dependent small-signal models with all bias-dependent element values, Cgs, Cgd, Gm, and Gds….ColdFET technique is used to extract the extrinsic element values such as Rg, Rs, and Rd and Lg, Ls, and Ld. After extrinsic elements are extracted, the intrinsic element values can be calculated. This was done with our in-house program. The program also generates a series look-up-table in mdf format that the ADS can read in. It should be pointed out that all look-up-tables generated by measurements are with reference to extrinsic port voltages, Vgse/Vgde, and Vdse. To make the model more robust and faster converge, the lookup-tables were converted in reference to intrinsic port voltages, Vgs/Vgd and Vds. This was done using MATLAB. IV. MODEL VALIDATION It is expected that the model should generate DC-Ids curves as measured. Figure 4 shows indeed the fitting is perfect, where the lines are modeled and the symbols are measured. The Vds changes from 0V to 6V and Vgs changes from 0.3V to 0.8V and the step is 0.05V. It has been also verified that by swapping DS, it generates the same results providing Rd is equal to Rs. In real case, Rs is somewhat smaller than Rd due to the layout, that all source fingers are connected crossover and grounded. It is vital to validate the bias-dependent S-parameter fitting. The model was validated over wide bias range from linear to saturation, from below pinchoff to active region. They all show perfect fitting without any unphysical results. As an example, figure 7 shows the modeled (blue) and measured (red) S-parameters at saturation region, Vds=3V and Vgs varying from 0.2V to 0.65V step 0.05V. 0.07 0.06 IDS.i, A Id_IV 0.05 0.04 0.03 0.02 0.01 2 3 4 5 6 Vd Figure 5. Modeled (lines) and measured (symbols) Ids curves for a 4x75um E-mode pHEMT. Vgs=0.3V to 0.8V step 0.05V and Vds from 0V to 6V. S(4,3) S(2,1) The leakage model is verified by comparing Ids and Ig at and below pinch-off as shown in figure 6. The upper graph shows the Ids as a function of Vgs with Vds varying from 1 to 4V. The lower graph shows corresponding gate leakage current. It is shown that the fitting is excellent. freq (300.0MHz to 10.00GHz) freq (300.0MHz to 10.00GHz) -20 -10 0 10 S(3,4) S(1,2) 1 S(3,3) S(1,1) 0 S(4,4) S(2,2) 0.00 20 -0.4 -0.2 0.0 0.2 0.4 freq (300.0MHz to 10.00GHz) freq (300.0MHz to 10.00GHz) Modeled and measured Ids 0.000025 Figure 7. Modeled (blue lines) and measured (red lines) Sparameters from 0.3 to 10GHz for 4x75um E-mode pHEMT. Vds=3V Vgs=0.2V to 0.65V step 0.05V. 0.000020 0.000015 0.000010 Figure 8 shows another example, the modeled (blue) and measured (red) S-parameters at linear region, Vds=0.5V and Vgs varying from 0.2V to 0.65V step 0.05V. 0.000005 0.000000 -0.000005 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 Vg S(3,3) S(1,1) 2E-2 1E-2 1E-4 freq (300.0MHz to 10.00GHz) freq (300.0MHz to 10.00GHz) 1E-6 1E-10 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 -20 -10 0 10 S(3,4) S(1,2) 1E-8 S(4,3) S(2,1) Modeled and measured Ig S(4,4) S(2,2) (a) 20 -0.4 -0.2 0.0 0.2 0.4 0.5 Vg (b) Figure 6. Modeled (lines) and measured (symbols) Ids leakage (a) and Ig leakage curves (b) for a 4x75um E-mode pHEMT. Vgs=-3V to 0.25V and Vds from 1V to 4V step 1V. freq (300.0MHz to 10.00GHz) freq (300.0MHz to 10.00GHz) Figure 8. Modeled (blue lines) and measured (red lines) Sparameters from 0.3 to 10GHz for 4x75um E-mode pHEMT. Vds=0.5V Vgs=0.2V to 0.65V step 0.05V. The model shows good convergence for a device 4x75um and input power up to 3dBm. Figure 9 shoows the simulated power performance and harmonics with input power sweeping and its comparison with measured data. In harmonic simulation, the real test-set termiinations have been carefully calibrated and the impedancess as function of frequency have been taken into account. The T model predicts very well the output power and 2nd/3rd harm monics. The model shows the small-power gain to be 19.22dB vs measured 19.35dB and the 1dB compression is at Pin=-7.3dBm vs measured -8.5dB, slightly off. The 2nd andd 3rd harmonics as function of input power are in very goodd agreement with measured results. Figure 9. Modeled (lines) and measured (sym mbols) output power, 2nd/3rd harmonics and power gain as function of input power for 4x75um E-mode pHEMT. Vds=3.5V Vgs=0.5V Pin=-20 to 3dBm. VII. CONCLUSION A new lookup-table based model is deveeloped. The model is based on capacitance, RF transconducttance, and RF DS conductance as a function of intrinsic gate and a drain voltages. Two RF currents, one based on RF-Gm annd the other based on RF_Gds, are used to solve the path-deppendence problem due to dispersion. There is no trans-capacitance involved that makes the model perfectly compatible wiith bias-dependent small-signal models. Leakage is incorporated into the model. m Plus the symmetric feature, the model is appliicable to various applications. The model has been implemennted as design kits at Skyworks Solutions, Inc. The new modeel shows exact DC fitting and excellent bias-dependent S-param meter fitting at the wide bias range. Large-signal simulation also shows it is robust. The model extractioon is fast and technologyindependent. The model validation was shown also by the excellent bias-dependent S-parameter fitting f over wide bias range. Large-signal simulation also shows to be robust and the model predicts very well the power and harmonic performances. The model extrraction is fast and technologyindependent. REFER RENCES  D. E. Root, S, Fan, and J. 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