An Improved Gate Charge Model of HEMTs by Direct Formulating the Branch Charges

Transcription

1 Chinese Journal of Electronics Vol.23, No.4, Oct An Improved Gate Charge Model of HEMTs by Direct Formulating the Branch Charges LIU Linsheng (Ericsson (China) Communications Co., Ltd., Chengdu , China) Abstract We present an improved gate charge model for High electron mobility transistors (HEMTs) that is direct formulated from the branch charges. Different charge modeling procedures based on the charge conservation principle have been discussed and the proposed model is more accurate, easier to be implemented into commercial simulators. An improved modeling method on channel length modulation parameter to account for the drain-current kink effect of HEMTs has also been introduced. The nonlinear model is verified by comparing the measurements and simulations using 0.25-µm gate-length GaAs HEMT devices. Key words Large-signal model, Equivalent circuit, Kink effect, High electron mobility transistors (HEMTs). I. Introduction In modern microwave circuits and systems, high electron mobility transistors are good candidates for the realization of Power amplifiers (PAs) in virtue of their high efficiency and high output power [1]. Accordingly, during the Computer-aided design (CAD) of microwave circuits, an accurate nonlinear device model is required to predict the output power, efficiency, harmonics, Intermodulation distortion (IMD), etc. [2] Due to the complexity in heterostructures of HEMTs and the associated physical characteristics, they are most appropriately modeled based on semi-empirical approach with parameters extracted from measurements [3]. The large-signal equation-based HEMT models are usuy justified by their ability to reproduce the current-voltage I-V characteristics of the dominant resistive nonlinearities and the charge-voltage Q-V characteristics of the reactive nonlinearities [4]. As to the gate charge Q-V model, its importance has been emphasized in predicting conventional PA performances [1], especiy for the accurate modeling of input capacitance nonlinearities. Moreover, recent paper [5] discloses the importance of the feedback capacitance Cgd in the output network of the switching-mode high-efficiency Class-E PA with heavily nonlinear properties. For any charge models, the principle of charge conservation must always be obeyed in order to prevent convergence problem during simulations [6], which requires a single gate charge expression to model the local and trans-capacitances simultaneously. There are several popular gate charge models for HEMTs, such as the EEHEMT1 model [7] and the resembled IAF model [8]. However, as representative models, both EEHEMT1 and resembled IAF suffer from the same problem that the gate-source capacitance (Cgs) will continue to expand without a limit, with increasing drain-source voltage (Vds). This will make the model inaccurate and unphysical, which is especiy critical for GaN HEMT that operates at much higher drain-source voltages, but exhibits a nearly independent Cgs value versus Vds in deeply saturation region [9]. Besides, the gate-drain capacitance (Cgd) isalso endangered to become negative at high gate-source voltages (Vgs). Thirdly, the assumption of a constant Cgd value in those models for the purpose of dividing the total charge into gatesource and gate-drain branch is unphysical, and the additional parameter Cgdsat is redundant during large-signal simulations. To solve these problems, we propose an improved HEMT gate charge model direct formulated from the branch charges by satisfying charge conservation law. The proposed charge model is physicy based and easier to be implemented into commercial simulators. Moreover, a simple modeling method to account for the kink effect of the HEMT I-V characteristics is also introduced. The measured and modeled results are presented based on the 0.25-µm gate-length GaAs doubleheterojunction δ-doped phemts. II.GateChargeModelFormulation 1. Conditions for charge conservative modeling It should be noticed that in real HEMT devices there are no separate gate-source and gate-drain charges but only one unified gate charge Qg, which is a function of Vgs and Vgd, or equivalently, Vgs and Vds(Vds = Vgs Vgd) [10]. Fig.1 (a) and(b) show the consistent large-signal and sm-signal HEMT equivalent circuit models consisted of single gate charge source [11]. However, in most CAD simulators, the gate charge is divided into two branches illustrated in Fig.2(a) and (b), so as to enable symmetrical modeling of the bilateral Field Manuscript Received Aug. 2012; Accepted May 2014.

2 674 Chinese Journal of Electronics 2014 effect transistors (FETs), and include the charge delay by utilizing the channel resistances Rgs and Rgd for Gate-source (G- S) and Gate-drain (G-D) branches, respectively. By comparing these two well-known large-signal equivalent circuit topologies and their sm-signal counterparts, the following relations can be obtained: Qg = Qg(Vgs,Vds)=Qg(Vgs,Vgs Vgd) = Qg (Vgs,Vgd) = Qgs(Vgs,Vgd)+Qgd(Vgs,Vgd) (1) C11 = Qg(Vgs,Vds)/ C12 = Qg(Vgs,Vds)/ V ds (2) cgs = Qgs(Vgs,Vgd)/ cm1= Qgs(Vgs,Vgd)/ cgd = Qgd(Vgs,Vgd)/ cm2= Qgd(Vgs,Vgd)/ (3) On the other hand, Fig.2(c) depicts the traditional smsignal HEMT equivalent circuit model which can be found in Ref.[12]. In order to ensure consistency and charge conservation of the conventional large-signal and sm-signal models as shown in Fig.2(a) and(c), the extraction of the gate capacitances Cgs and Cgd in Fig.2(c) should be as follows to eliminate the trans-capacitance elements of cm1 and cm2 in Fig.2(b) [10] : Cgs= Qg (Vgs,Vgd) + Qgd(Vgs,Vgd) = Qgs(Vgs,Vgd) = cgs + cm2 (4) Cgd= Qg (Vgs,Vgd) + Qgd(Vgs,Vgd) = Qgs(Vgs,Vgd) = cgd + cm1 (5) Consequently, the interrelationships of the equivalent circuit models with and without charge partition can be then deduced and established: C11 = Qg(Vgs,Vds)/ = Qg(Vgs,Vgs Vgd)/ = Qg(Vgs,Vgd) + Qg(Vgs,Vgd) (Vgs Vgd) = Cgs + Cgd (6) C12 = Qg(Vgs,Vds) Qg(Vgs,Vgs Vgd) = V ds (Vgs Vgd) = Cgd (7) where Eq.(7) confirms that Cgd is equal to C12 which should be bias-dependent instead of being a constant Cgdsat as in the existing gate charge models shown in Fig.3(a). Furthermore, the parameter Cgdsat for partitioning the gate charge is redundant and unphysical during large-signal simulations, because Qg = Qgs + Qgd = Qg Cgdsat Vgd+ Cgdsat Vgd= Qg, regardless of the Cgdsat value. 2. The improved gate charge model As described in Fig.3(b), the improved modeling methodology will be simplified by avoiding the charge partitioning provided that a suitable charge model expression defined as Qg = Qg(Vgs,Vgd) = Qgs(Vgs,Vgd)+Qgd(Vgs,Vgd)is available, where the gate charge has already been partitioned Fig. 1. (a) Intrinsic HEMT large-signal model without charge partition; (b) Corresponding sm-signal model by omitting the gate currents Fig. 2. (a) Traditional large-signal HEMT model with gate charge been partitioned to Qgs and Qgd; (b) Consistent sm-signal model. (c) Alternative sm-signal HEMT model in conventional topology

3 An Improved Gate Charge Model of HEMTs by Direct Formulating the Branch Charges 675 have been modeled and validated. Fig.4 shows the present equivalent-circuit large-signal HEMT model containing both intrinsic and extrinsic elements. Fig. 3. (a) EEHEMT1 charge model parameter extraction; (b) Improved model parameter extraction procedure into two parts Qgs and Qgd before the parameter extraction procedure. And the proposed HEMT Q-V model satisfying this condition is developed and given below: q «Veff 1,2 =1/2 Vgs+ Vgd± (Vgs Vgd) 2 + δ1 2 (8) q «Vnew=1/2 Veff 1 + vt + (Veff 1 vt) 2 + δ2 2 (9) w = Vnew v1+dc ln[cosh(dk (Vnew De Veff 2))] (10) Qgs = C o1 (w + Cf/Sg ln[cosh(sg w)]) +Cgso Veff 1 (11) Qgd = C o2 (Veff 2 + k ln(cosh(1/k (Veff 2 vt)))) +Cgdo Veff 2 (12) with δ 1,δ 2,vt,v1,Dc,Dk,De,C o1,c o2,sg,cf,cgso,cgdo,k being the fitting parameters. The improved charge-conservative model results in a saturated Cgs value when Vds increases, and a minimum Cgd at high Vgs. Eqs.(8) and (9) are the smoothing functions which have been discussed in Ref.[10]. In addition, any local expressions like Qgs(Vgs) andqgd(vgd) can be added freely to increase modeling accuracy for Qgs and Qgd parts, respectively. To implement the charge formulation into the equivalent circuit model for symmetrical modeling, similar bilateral transition functions used in EEHEMT1 model [4] are introduced, where the added parameter Vas is tuned for asymmetrical devices: ««3 f 1,2 =1/2 1 ± tanh (Vgs Vgd Vas) (13) δ 1 Qgs, gd(vgs,vgd)=qgs (Vgs,Vgd) f 1,2 +Qgd (Vgs,Vgd) f 2,1 (14) 3. Model verification To demonstrate the usefulness of the proposed modeling approach presented here, the 0.25-µm gate-lengths on-wafer GaAs double-heterojunction δ-doped phemts Refs.[13,14] Fig. 4. Proposed complete large-signal equivalent circuit model As a first step, in extracting the extrinsic linear elements, multi-bias sm-signal equivalent circuit model has been firstly determined through the procedure suggested by Dambrine [15]. Then the nonlinear intrinsic large-signal model can be developed by optimizing its performances to the measured results. A GaAs phemt with 2 50µm gate-widths has been used for the gate charge modeling along with the conventional gate forward conduction diode expression. Besides, a normalized least square error function is defined in Eq.(15) to compare the deviations between the simulations and measurements using four different HEMT charge models: v X Cgs,meas Cgs, sim 2 ε total = ε Cgs + ε Cgd = u X t Cgs,meas 2 v X Cgd,meas Cgd,sim 2 + u X. (15) t Cgd,meas 2 As shown in Table 1, both Cgs and Cgd can be modeled more accurately with the new gate charge equations. Here an extra parameter is added to the IAF model to fit different fringe capacitance values for G-S and G-D sides, and the modified statz model is established by incorporating the transition functions in Eq.(13) and a minimum Cgs modeling versus Vgs instead of being decreased to zero. Fig.5 plots the measured and modeled results with the improved gate charge model in the entire intrinsic Vgs Vds planes. Table 1. Comparisons of the error values for different charge models Model name ε Cgs ε Cgd ε total Modified statz 0.12E E E-1 EEHEMT E E E-1 Modified IAF 0.073E E E-1 This work 0.062E E E-1

4 676 Chinese Journal of Electronics 2014 Moreover, for the nonlinear drain-source current (Ids) I-V model in the larges-signal equivalent-circuit shown in Fig.4, the widely-used Angelov HEMT model [3] has been modified by incorporating the kink effect [16] observed in our measured data: Ids= Ipk(1 + tanh(ψ))(1 + λ Vds+ Lsb exp(v dg Vtr)) tanh(αv ds) (16) ψ = p1(vgs Vpk)+p2(Vgs Vpk) 2 +p3(vgs Vpk) 3 (17) λ = λ + λ k (1 + tanh(vst(vds Vdk))) (sec h(ψ k )) 2 (18) ψ k = p1 k (Vgs Vdk)+p2 k (Vgs Vdk) 2 +p3 k (Vgs Vdk) 3 (19) where the modification on channel length modulation parameter (λ) in Eqs.(18) and (19) is to track the strongly bias dependent output conductance in saturation region due to the kink effect, consisting of a sharp increase in the saturated current with respect to drain bias. Otherwise, the discrepancies between measured and modeled results will be much larger (when Vds>3V), as observed in Fig.6. transmitted power gain, Power-added-efficiency (PAE), and output power characteristics of the 2 50µm GaAspHEMT under two different biasing conditions, are simulated and compared with measured data as shown in Fig.7. The input and output terminating impedances were adjusted for maximum PAE performances. It can be seen that the proposed model provides a very good prediction of the power characteristics. Fig. 6. Measured and modeled DC I-V curves for the 2 50µm GaAs phemt. Vgs range from 1.5V to 0V with a step size of 0.1V Fig. 7. Measured (symbols) and modeled (lines) single-tone power sweep results Finy, in order to verify the large-signal accuracy of the proposed model, the output power for the first three harmonics, and two-tone third-order IMD (IM3) versus input power performances with tone spacing of 10MHz are presented in Fig.8(a) and(b), respectively, where very good agreement between simulation and measurement is obtained for the improved large-signal model. Fig. 5. Measured (symbols) and modeled (lines) results over the whole bias range. (a) Cgs; (b) Cgd After obtaining good correspondences between measured and simulated S-parameters from 50MHz to 35GHz at different bias points, on-wafer load-pull power measurements at 7.5GHz have been experimented to validate the nonlinear model. The Fig. 8. Measured (symbols) and simulated (lines) large-signal performances biased at (Vgs,Vds)=( 0.5V,6V).(a) Single-tone power sweep for the first three output harmonics; (b) Two-tone power-sweep for IM3 III. Conclusions An improved nonlinear gate charge Q-V model has been

5 An Improved Gate Charge Model of HEMTs by Direct Formulating the Branch Charges 677 developed for HEMTs. The model formulation is kept compact and straightforward, easy to be implemented into CAD simulators. A detailed analysis is presented to compare different equivalent circuit topologies as well as their charge modeling procedures. Besides, an improved drain current modeling method to account for the frequency-dependent kink effect of HEMTs is proposed, and the well-known Angelov I-V model has been modified to include the kink current modeling of the GaAs phemts. The usefulness and superiority of the developed large-signal model has been successfully validated, where excellent agreement between measurements and simulations is achieved. References [1] J. Staudinger, M. de Baca and R. Vatikus, An examination of several large signal capacitances models to predict GaAs HEMT linear power amplifier performance, IEEE Radio & Wireless Conf. Proc., pp , [2] J.A. Garcia, et al., Characterizing the gate to source nonlinear capacitor role on GaAs FET IMD performance, IEEE Trans. Microwave Theory Tech., Vol.46, pp , [3] I. Angelov, L.Bengtsson and M. Garica, Extensions of the Chalmers nonlinear HEMT and MESFET model, IEEE Trans Microwave Theory Tech., Vol.44, No.10, pp , [4] L.S. Liu, J.G. Ma and G.I. Ng, Electrothermal large-signal model of III-V FETs including frequency dispersion and charge conservation, IEEE Trans. Microw. Theory Tech., Vol.57, No.12, pp , [5] D.K. Choi and S.I. Long, The effect of transistor feedback capacitance in Class-E power amplifier, IEEE Trans. Circ. System, Vol.50, No.12, pp , [6] A. Snider, Charge conservation and the transcapacitance element: An exposition., IEEE Trans. Educ, Vol.38, No.4, pp , [7] F. Kharabi, M.J. Poulton, D. Halchin and D. Green, A classic nonlinear FET model for GaN HEMT Devices, IEEE CSIC Symp. Dig., pp.14 17, [8] R. Osoio, M. Berroth, W. Marsetz, et al., Analytical charge conservative large signal model for MODFETs validated up to MM-wave range, IEEE MTT-S Int. Dig., pp , [9] F. Raay, R. Quay, R. Kiefer, M. Schlechtweg and G. Weimann, Large-signal modeling of AlGaN/GaN HEMT s with Psat> 4 W/mm at 30GHz suitable for broadband power applications, IEEE MTT-S Int. Dig., pp , [10] H. Statz, P. Newman, W. Smith, R. Pucel and H. Haus, GaAs FET device and circuit simulation in SPICE, IEEE Trans. Elect. Devi., Vol.34, No.2, pp , [11] P. Jansen, D. Schreurs, W. D. Raedt, et al., Consistent smsignal and large-signal extraction techniques for heterojunction FET s, IEEE Trans. Microw. Theory Tech., Vol.43, No.1, pp.87 93, [12] C.J. Wei, Y.A. Tkachenko and D. Bartle, An accurate largesignal model of GaAs MESFET which accounts for charge conservation, dispersion, and self-heating, IEEE Trans. Microw. Theory Tech., Vol.46, No.11, pp , [13] L.S. Liu and J.G. Ma, Improved drain-source current model for HEMT s with accurate Gm fitting in regions, IEEE Compound Semiconductor IC Symp. Dig., pp.1 4, [14] L.S. Liu, J.G. Ma, G.I. Ng and Q.J. Zhang, Nonlinear HEMT model direct formulated from the second-order derivative of the I-V/ Q-V characteristics, IEEE MTT-S Int. Microwave Symp. Dig., [15]G.Dambrine,A.Cappy,F.HeliodoreandE.Playez, Anew method for determining the FET sm-signal equivalent circuit, IEEE Trans Microwave Theory Tech., Vol.36, No.7, pp , [16] M.H. Sornerville, A. Ernst and del J.A. Alamo, A physical model for the kink effect in InAlAs/InGaAs HEMT s, IEEE Trans. Electron Device, Vol.47, No.5, pp , LIU Linsheng received the Bachelor s degree and Ph.D. degree in Electronic Engineering from the University of Electronic Science and Technology of China (UESTC), Chengdu, China, in 2005 and 2011, respectively. In 2011, He joined Ericsson (China) Communications Co., Ltd. His research interests include the III-V FET modeling and RF power amplifier design.