Please write a MATLAB program which is able to read in s2p files (S-parameters), and fit the parameters of the small signal model.All the parameters such as Cgd, Cgs...etc, have their equation shown in the paper, please write a MATLAB program and make a slide of how to apply it.If you need s2p files to try your program, please let me know! Thanks!
3440 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 11, NOVEMBER 2005 A New Small-Signal Modeling Approach Applied to GaN Devices Anwar Jarndal, Student Member, IEEE, and Günter Kompa, Member, IEEE Abstract—A new small-signal modeling approach applied to GaN-based devices is presented. In this approach, a new method for extracting the parasitic elements of the GaN device is devel- oped. This method is based on two steps, which are: 1) using cold -parameter measurements, high-quality starting values for the extrinsic parameters that would place the extraction close to the global minimum of the objective function for the distributed equivalent circuit model are generated and 2) the optimal model parameter values are searched through optimization using the starting values already obtained. The bias-dependent intrinsic pa- rameter extraction procedure is improved for optimal extraction. The validity of the developed modeling approach and the pro- posed small-signal model is verified by comparing the simulated wide-band small-signal -parameter, over a wide bias range, with measured data of a 0.5- m GaN high electron-mobility transistor with a 2 50 m gatewidth. Index Terms—Computer-aided analysis, GaN high electron-mo- bility transistor (HEMT), parameter extraction, semiconductor device modeling. I. INTRODUCTION THE GaN high electron-mobility transistor (HEMT) issupposed to be an excellent candidate for high power applications, where both the high frequency response and high breakdown voltage for this device make it ideally suited for high power application. GaN amplifier design requires accurate large-signal model (LSM) for the GaN HEMT. This accurate model should simulate the breakdown, forward conduction, and frequency dispersion effects. In bottom-up modeling technique, a multibias small-signal measurement is carried out over a range of bias points, and LSM is then determined from small-signal model (SSM) derived at each of these bias points. Therefore, the accuracy of the constructed LSM depends on the accuracy of bias-dependent SSM, which should reflect the electrical and physical characteristics of the device. Accurate determination for the intrinsic bias-dependent circuit of GaN HEMT SSM re- quires an efficient extraction method for the parasitic elements of the device. Due to high contact resistance of GaN device, the standard circuit model extraction method [1]–[4] cannot be applied directly [5]. Chigaeva et al. [6] showed that the series elements of the equivalent circuit model for GaN HEMT could be extracted from cold -parameter measurement at high Manuscript received April 5, 2005; revised July 1, 2005. This work was supported by the German Ministry of Education and Research under Contract 01BU385 and by the Top Amplifier Research Group European Team under Contract 507893. The authors are with the Fachgebiet Hochfrequenztechnik, University of Kassel, Kassel D-34121, Germany (e-mail:
[email protected]). Digital Object Identifier 10.1109/TMTT.2005.857332 Fig. 1. 22-element distributed model for active GaN HEMT. gate-forward voltage. However, the extracted feedback induc- tance has unreliable value. Therefore, a special extraction method should be developed to extract the parasitic elements of GaN device. In [7], a new reliable parasitic elements extraction method, applied for GaN HEMT, was developed. This method uses only a cold -parameter measurement for accurate deter- mination of the parasitic elements. The main advantage of this method is that it gives reliable values for the parasitic elements of the device without need for additional measurements or sepa- rate test pattern. In this paper, the whole procedure for accurate small-signal modeling of the active device will be discussed. In the second part of this paper, the proposed equivalent circuit model for GaN HEMT is described. The technique developed in this work for model parameter extraction is then discussed in the third and fourth parts. Validity of the proposed small-signal modeling procedure will be discussed in the fifth part. Finally, the conclusion will be presented in the last part. II. GENERAL DISTRIBUTED SMALL-SIGNAL EQUIVALENT-CIRCUIT MODEL Since the knowledge of distributed effects is important to identify the device parasitic elements for further minimization, a 22-element distributed model shown in Fig. 1 is used as SSM for GaN HEMT. This model is general and applicable for large gate periphery devices. The main advantages of this model are as follows. • It accounts for all expected parasitic elements of the de- vice. • It reflects the physics of the device over a wide bias and frequency range. Therefore, this model may be suitable for scalable LSM con- struction. 0018-9480/$20.00 © 2005 IEEE JARNDAL AND KOMPA: NEW SMALL-SIGNAL MODELING APPROACH APPLIED TO GaN DEVICES 3441 Fig. 2. Gate–drain and gate–source capacitances estimation from different measured data ranges for a 0.5 �m GaN HEMT with a 2� 50 �m gatewidth. In this model, , , and account for the interelec- trode and crossover capacitances (due to air–bridge source con- nections) between gate, source, and drain. While , , and account for parasitic elements due to the pad connec- tions, measurement equipment, probes, and probe tip-to-device contact transitions. III. EXTRINSIC PARAMETER EXTRACTION Many of the SSM parameters in Fig. 1 are difficult if not impossible to determine directly from measurements. There- fore, these parameters are determined through an optimization algorithm. The efficiency of this algorithm depends on the quality of starting values and the number of optimization vari- ables. Under cold pinchoff condition, the equivalent circuit in Fig. 1 can be simplified by excluding some elements, thereby reducing the number of unknowns. For further minimization of the number of optimization variables, only the extrinsic elements of the SSM will be optimized, while the intrinsic elements are determined from the deembedded -parameters. Furthermore, under this bias condition, the reactive elements of the SSM are strongly correlated. Therefore, the starting values estimation should be carried out in a way that takes this correlation into account. In addition, the -parameter measure- ments must cover the frequency range where this correlation is more obvious. The results of starting values estimation for the gate–source (gate–drain) capacitances, shown in Fig. 2, support our suggestion. These results show that the distribution of the total gate–drain (gate–source) capacitance converges using a measured data above 60 GHz for the analyzed 2 50 m device. Furthermore, the estimated capacitances from data lower than 60 GHz attain values that may not be physically justifiable. This is because the inductive effects have been found to become in- fluential only above this frequency range. The required mea- surements frequency range for reliable starting values genera- tion reduces significantly for larger devices, e.g., up to 20 GHz for an 8 125 m device. The proposed technique for starting values generation is based on searching for the optimal distri- bution of the total capacitances. This is achieved by scanning the outer capacitance values within the specified ranges. For each scanned value, the interelectrode capacitances are assigned suitable values and then deembedded from the measured -pa- rameter. The rest of the model parameters are then estimated from the stripped -parameters. The whole estimated parame- ters are then used to simulate the device -parameters, which are then compared with the measured ones. Using this system- atic searching procedure, high-quality measurement-correlated starting values for the SSM parameters can be found [8]. The closeness of the starting values to the real values simplifies the next step of parameters optimization since the risk of a local minimum is minimized. A. Generation of Starting Value of SSM Parameters The starting values generation procedure is described by the flowchart in Fig. 3. As shown in this flowchart, the starting values of the extrinsic capacitances and inductances are gener- ated from pinchoff measurements, while those of extrinsic re- sistances are generated from forward measurements. The whole starting values generating procedure can be summarized as fol- lows. Step 1) Let and V. In this case, the equivalent circuit in Fig. 1 of the active device can be used for this cold pinchoff device if the drain current source and the output channel conductance are excluded. Moreover, at low frequencies (below 5 GHz), this circuit reduces to a capacitive network shown in Fig. 4 and the -parameters of this equiv- alent circuit can be written as (1) (2) (3) where (4) (5) (6) The total capacitances for gate–source, gate–drain, and drain–source branches are determined from the low frequency range of pinchoff -parameter mea- surements, which are converted to -parameter. Step 2) The next step is searching for the optimal distribu- tion of the total capacitances, which gives the min- imum error between the measured and simulated 3442 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 11, NOVEMBER 2005 Fig. 3. Flowchart of the model parameter starting value generation algorithm. Fig. 4. Cold pinchoff equivalent circuit for the GaN HEMT at low frequency. Fig. 5. T-network representation of a cold pinchoff FET equivalent circuit. -parameters. This is achieved by scanning , , and values within the specified ranges. and are scanned from 0 to while is scanned from 0 to . During the scan- ning process, is assumed to be equal to [8] (7) The gate–drain interelectrode capacitance is assumed to be twice the pad capacitance value (8) For symmetrical gate–source and gate–drain spacing, the depletion region will be uniform under pinchoff, so that (9) The value of is calculated using (10) With the GaN device under analysis, is a sig- nificant part of the total drain–source capacitance. Therefore, it is found that the assumption (11) minimizes the error between the simulated and measured -parameters. For medium and high frequency range, the intrinsic transistor of the pin- choff model is represented in T-network as shown in Fig. 5 where the interelectrode capacitances ( , , and ) have been absorbed in the intrinsic capacitances ( , , and ). The JARNDAL AND KOMPA: NEW SMALL-SIGNAL MODELING APPROACH APPLIED TO GaN DEVICES 3443 Fig. 6. Inductance estimation from the cold pinched-off strippedZ-parameters for a 0.5-�m GaN HEMT with a 2 � 50 �m gatewidth. values for , , and are deembedded from -parameter and then converted to -param- eter. This stripped -parameter can be written as (12) (13) (14) where (15) (16) (17) , , and represent correction terms related to the intrinsic parameters of the model. Ignoring the correction terms and multiplying the -parameters by and then taking the imaginary parts gives (18) (19) (20) Hence, the values of , , and can be ex- tracted from the slope of versus curve as shown in Fig. 6. The estimated values of in- ductances described above and the interelectrode capacitances ( , , and ) are deem- bedded. However, the incomplete deembedding of the outer capacitances and the inductances intro- duce nonlinear frequency dependence in the real part of deembedded -parameters. By multiplying Fig. 7. Resistance estimation from the cold forward strippedZ-parameters for a 0.5-�m GaN HEMT with a 2 � 50 �m gatewidth. the deembedded -parameter by , this effect is reduced [8].