An Angelov Large Signal Model and its Parameter Extraction Strategy for GaAs HEMT

Transcription

1 TSINGHUA UNIVERSITY An Angelov Large Signal Model and its Parameter Extraction Strategy for GaAs HEMT Yan Wang Wenyuan Zhang Tsinghua University

2 Outline Motivation Large Signal Model Parameter Extraction Strategy Model verification Conclusion 2

3 Outline Motivation Large Signal Model Parameter Extraction Strategy Model verification Conclusion 3

4 Motivation Device modeling is to find a suitable equivalent description of the transistor and accurate models play an important role in the success of IC design. A good model accurate within a certain frequency range as simple as possible The parameters in the model should be easily extracted The model should be able to reflect the temperature effect The parameters should have clear physical meaning scalable The model should have good convergence The model should ensure high-order derivative of the expression, especially for the large signal model in order to accurately predict harmonic components. A good model is a good trade off 4

5 Outline Motivation Large Signal Model Parameter Extraction Strategy Model verification Conclusion 5

6 Large Signal Model the number of papers on the research of transistor modeling You can find from the published papers that the number 6of transistor modeling show a significant growing trend

7 Large Signal Model numbers of research papers on different types of transistor modeling HEMT Modeling had an obvious down times, but in recent years, with the advantages of high electron mobility, high linearity and low noise, It has become a hot spot in the 7 research of modeling. The modeling work in this talk will also aim at GaAs HEMT.

8 Large Signal Model Statistics of research papers on HEMT large signal nonlinear modeling Transistors will exhibit obvious nonlinear effects when working under large signal conditions. We can see that the number of articles related to nonlinear large signal accounts for nearly half, and the proportion increases year by year 8

9 Large Signal Model For RF and microwave applications, transistors often work in large signal states. The nonlinear behavior of transistors is more important. As early as eighty in the last century, the large signal empirical model of microwave devices was established. Over the past thirty years, there have been many excellent large signal models, such as: Curtice Model Tajima Model Materka Model Statz Model TOM Model Angelov Model EEHEMT1 business Model 9

10 Large Signal Model Curtice Model: In 1980, Walter R. Curtice first proposed an FET large signal empirical model and simulated it through Spice, which include the drain current Ids gate capacitance Cgs and parasitic parameters, but the model does not take into account the principle of charge conservation. Statz Model: In1987. A large signal transistor model is put forward by Statz, and considering the conservation of charge, a two dimensional capacitance model is established. The gate charge and drain charge are unified as gate charge, which is determined by gate voltage and drain voltage. The precision of the model is further improved. These two models are proposed for MESFET, None of the models can10be directly applied to HEMT Device

11 Large Signal Model Angelov model In 1992, Sweden professor ( in Chalmers)Angelov put forward a new large signal model, based on the empirical formula of the exponential function and the current-voltage relationship is a hyperbolic tangent function. This form is more applicable to large signal modeling of MESFET and HEMT. From the first HEMT model to present,the most widely used models are Curtice and Angelov Model and EEHEMT1 business model. Many later scholars are based on these three models to consider the improvement of thermal effect, frequency migration effect and charge conservation. 11

12 Large Signal Model Tajima Model In 1981, Tajima proposed the model applied to the frequency domain, based on the model GaAs FET. A large signal model is established for DC characteristics of the device and was successfully applied to the design of the oscillator. Materka model In 1983, Materka proposed a simple large signal model based on DC characteristics. Four measuring parameters can be applied to any size in theory. And it is convenient to be extended to computer aided analysis and design.

13 Large Signal Model Later works have made many improvements to the previous models, such as 1990, Mccamant put forward TOM1 model, Statz model has been changed, and Ids are varied as outside voltage. Considering the negative DC conductance characteristic, the proposed model can guarantee high precision in the larger bias range. In the business model, in 1993, Agilent established the model EEHEMT1, which has a wide range of applications, but it is represented by a piecewise function. The input output characteristics of different current output stages are in different modes.

14 Large Signal Model In 1997, Dr. C.Wei of Alpha proposed a charge conservation model including the self heating effect and frequency migration effect. This model can predict the current voltage relations, charge voltage relations and S parameters of different frequencies, more accurately.

15 Large Signal Model To sum up : the small signal equivalent circuit model of HEMT has been developed relatively mature. How to establish a precise nonlinear model to improve the nonlinear performance of RF / microwave power circuits has always been a key and difficult point, especially the high order derivative is need to be guaranteed. the input and output characteristics of HEMT are different under different temperature environments. Self heating effect should be considered. the relatively complex extraction method is generally used, the difference of the research mainly focus in the extraction of the embedded technology, the parasitic parameters, and the simpleness of the extraction strategy. 15

16 Large Signal Model Why Angelov model is chosen in this work? Accurate for HEMT Simple although the extraction is a little bit complicated High order continuous and derivative can be used for harmonic analysis in the nonlinear performance of RF / microwave circuits Charge conservation is considered and the convergence can be ensured. 16

17 Large Signal Model Structure and band diagram of typical GaAs HEMT Due to the wide band gap, the conduction band bends a lot in order to supply 17 enough electron, which leads to strong quantum effect.

18 Large Signal Model Traditional small signal equivalent circuit model 18

19 Large Signal Model A schematic diagram of large signal equivalent model 19

20 Large Signal Model Angelov model The Angelov model uses an exponential function, and the relationship between the current and the voltage is reflected by the hyperbolic tangent function. The current and capacitance of the Angelov model is as following Proposed large signal equivalent circuit model 20

21 Large Signal Model I I ( e I I ( e gd j 6 P tanh( V V ) P V Kbdge e P tanh( V V ) g gd jg 6 Pbdg tanh( Vgd Vbdgd ) Pg Vjg 10 Kbdge e ) I I (1 tanh ) tanh( V )(1 V ) d pk0 ds ds 2 (1 tanh ) P ( V V ) P ( V V ) P( V V ) r gs j P tanh( V V ) g gs jg bdg gs bdgs g jg 10 ) s P P(1 B / cosh ( BV )) 2 1m Cgs Cgspi Cgs0(1 tanh 1)(1 tanh 2) Cgd Cgdpi Cgd 0(1 tanh 3)(1 tanh 4) P P V 2 P20 P21Vds gs 3 P30 P31Vds 4 P40 PV 41 gd 1m gs pks 2 gs pks 3 gs pks ds 21

22 Outline Motivation Large Signal Model Parameter Extraction Strategy Model verification Conclusion 22

23 Parameter Extraction Strategy Extract Rg, Rd, Rs, Lg, Ld, Ls under cold FET condition (Ig=0, Id=0) using the flat range for Rg, Rd, Rs at low frequency band using the flat range for Lg, Ld, Ls at high frequency band Cold FET Extraction 1. Extract Rg, Rd, Rs from cold FET at low frequency 2. Extract Lg, Ld, Ls from cold FET at high frequency G Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld D Cgd Igs Id Cds S Rgs Rs Ls Cgs Cold FET Cold FET Equivalent Circuit Model G Lg Rg Rd Ld Rs Ls D S

24 Parameter Extraction Strategy Extract Ij, Pg, Vjg from Ig-Vgs at forward Vgs at zero Vds where Igs Igd Ig/2 P tanh( V V ) 6 P tanh( V V ) P V gs j bdg g gs jg bdg gs bdgs g jg I I ( e 10 K e e ) G Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld D Cgd Igs Id Cds Rgs Cgs Rs Ls I V Extraction 3. Extract Ij, Pg, Vjg from Ig Vgs at forward Vgs S I gs I e j Vgs>0 P tanh( V V ) g gs jg linear range saturation range ln I PV PV ln I gs g gs g jg j I, P, V j g jg Pg gs, sat, for / I I e j 4. Extract Kbdg, Pbdg, Vbdgs, Vbdgd from Ig Vgs at reverse Vgs 5. Extract Ipk0, Vpks, P1 from Id Vgs 6. Optimize P2, P3 from Id Vds 7. Extract λ from Id Vds 8. Optimize B1, B2, αr, αs from Id Vds

25 Parameter Extraction Strategy Extract Kbdg, Pbdg, Vbdgs, Vbdgd from Ig-Vgs at reverse Vgs introduce 0 k 1 assume Igs=kIg, Ids=(1-k)Ig scan k to achieve the smallest error P tanh( V V ) 6 P tanh( V V ) PV gs j bdg g gs jg bdg gs bdgs g jg I I ( e 10 K e e ) linear range ln I P V P V gs bdg gs bdg bdgs 6 ln(10 Kbdg I j ) Vgs<0 6 Pbdg tanh( Vgs Vbdgs ) Igs 10 Kbdg I je saturation range 6 Pbdg bdg gs, sat, re /10 j K I I e Kbdg, Pbdg, Vbdgs G Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld D Cgd Igs Id Cds I gd V bdgd in the same way as left Rgs Cgs Rs Ls I V Extraction 3. Extract Ij, Pg, Vjg from Ig Vgs at forward Vgs 4. Extract Kbdg, Pbdg, Vbdgs, Vbdgd from Ig Vgs at reverse Vgs 5. Extract Ipk0, Vpks, P1 from Id Vgs 6. Optimize P2, P3 from Id Vds 7. Extract λ from Id Vds 8. Optimize B1, B2, αr, αs from Id Vds S

26 Parameter Extraction Strategy Extract Ipk0, Vpks, P1 from Id-Vgs Ipk0, Vpks, P1 are found to be Id, Vgs, gm/id for maximum gm I I (1 tanh ) tanh( V )(1 V ) d pk0 ds ds 2 3 G P ( V V ) 1m gs pks 2 gs Vpks 3 gs Vpks P ( V ) PV ( ) Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld D Cgd Igs Id Cds Rgs Cgs Rs Ls I V Extraction 3. Extract Ij, Pg, Vjg from Ig Vgs at forward Vgs 4. Extract Kbdg, Pbdg, Vbdgs, Vbdgd from Ig Vgs at reverse Vgs S I I (1 tanh ) d pk0 P ( ) 1 Vgs Vpks 5. Extract Ipk0, Vpks, P1 from Id Vgs I g PI (1 tanh ) PI (1 tanh ) g g d 2 m 1 pk0 1 d Vgs 2 d 2 2 m2 P 2 1 Ipk0 Vgs m2 I 2 tanh (1 tanh ) 0 tanh 0 6. Optimize P2, P3 from Id Vds 7. Extract λ from Id Vds 8. Optimize B1, B2, αr, αs from Id Vds

27 Parameter Extraction Strategy Optimize P2, P3 with targets of Id, gm, gm2, gm3 versus Vgs Extract λ from Id-Vds λ is the slope at the saturation range Optimize B1, B2, αr, αs with targets of Id, Id versus Vds G Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld D Cgd Igs Id Cds Rgs Cgs Rs Ls I V Extraction 3. Extract Ij, Pg, Vjg from Ig Vgs at forward Vgs 4. Extract Kbdg, Pbdg, Vbdgs, Vbdgd from Ig Vgs at reverse Vgs 5. Extract Ipk0, Vpks, P1 from Id Vgs 6. Optimize P2, P3 from Id Vds 7. Extract λ from Id Vds 8. Optimize B1, B2, αr, αs from Id Vds S

28 Parameter Extraction Strategy Extract Cgspi, Cgs0 from Cgs Vgs at zero Vds and Cgs Vds at zero Vgs G Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld D Cgd Igs Id Cds Cgs Cgspi Cgs0(1 tanh 1)(1 tanh 2) (at zero V ) C C (1 tanh( P P V ))(1 tanh P ) ds P Rgs Cgs gspi gs gs 20 ( C, C 2 C ) gspi gspi gs0 PV gs C min{min C ( V ), min C ( V ) } gspi gs gs V 0 gs ds V 0 C max C ( V ) min C ( V ) ds gs0 gs gs V 0 gs gs V 0 ds gs ds Rs P PVds (at zero ) P V d s 20 Ls S C V Extraction 9. Extract Cgspi, Cgs0 from Cgs Vgs at zero Vds and Cgs Vds at zero Vgs 10. Extract Cgdpi, Cgd0 from Cgd Vgs at zero Vds and Cgd Vds at zero Vgs 11. Extract Cds from Cds Vgs at zero Vds and low Vgs 12. Extract P10, P11 from Cgs Vgs at zero Vds 13. Extract P40, P41 from Cgd Vgs at zero Vds 14. Extract P20, P21 from Cgs Vds at zero Vgs 15. Extract P30, P31 from Cgd Vds at zero Vgs 16. Optimize Rgs, Rgd from Rgs,eq and Rgd,eq frequency

29 Parameter Extraction Strategy Extract Cgdpi, Cgd0 from Cgd Vgs at zero Vds and Cgd Vds at zero Vgs at a fixed 3 P30 PV 31 frequency (at zero ) Cgd Cgdpi Cgd 0(1 tanh 3)(1 tanh 4) (at zero V ) C C (1 tanh P )(1 tanh( P P V )) ds gdpi gd gs ( C, C 2 C ) G V d s gdpi gdpi gd 0 C min{min C ( V ), min C ( V ) } gdpi gd gs V 0 gd ds V 0 C max C ( V ) min C ( V ) ds gs0 gd gs V 0 gd gs V 0 ds Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld D Cgd Igs Id Cds ds P 30 Rgs Cgs 4 P40 P41Vgd (at zero V ) P ds gs ds Rs P Ls V gs S C V Extraction 9. Extract Cgspi, Cgs0 from Cgs Vgs at zero Vds and Cgs Vds at zero Vgs 10. Extract Cgdpi, Cgd0 from Cgd Vgs at zero Vds and Cgd Vds at zero Vgs 11. Extract Cds from Cds Vgs at zero Vds and low Vgs 12. Extract P10, P11 from Cgs Vgs at zero Vds 13. Extract P40, P41 from Cgd Vgs at zero Vds 14. Extract P20, P21 from Cgs Vds at zero Vgs 15. Extract P30, P31 from Cgd Vds at zero Vgs 16. Optimize Rgs, Rgd from Rgs,eq and Rgd,eq frequency

30 Parameter Extraction Strategy G Extract Cds Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld D Cgd Igs Id Cds Rgs from Cds-Vgs at zero Vds using the flat range for Cds at small Vgs Cgs Rs Ls S C V Extraction 9. Extract Cgspi, Cgs0 from Cgs Vgs at zero Vds and Cgs Vds at zero Vgs 10. Extract Cgdpi, Cgd0 from Cgd Vgs at zero Vds and Cgd Vds at zero Vgs 11. Extract Cds from Cds Vgs at zero Vds and low Vgs 12. Extract P10, P11 from Cgs Vgs at zero Vds 13. Extract P40, P41 from Cgd Vgs at zero Vds 14. Extract P20, P21 from Cgs Vds at zero Vgs 15. Extract P30, P31 from Cgd Vds at zero Vgs 16. Optimize Rgs, Rgd from Rgs,eq and Rgd,eq frequency

31 Parameter Extraction Strategy Extract P10, P11 from Cgs-Vgs at zero Vds linear regression: 1 tanh (( Cgs Cgspi ) / Cgs0 1) P11Vgs P10 Extract P20, P21 from Cgs-Vds at zero Vgs linear regression: 1 tanh Cgs C gspi 1 C (1 tanh P ) gs0 10 Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld G D Cgd Igs Id Cds S Rgs Rs Ls Cgs P V P 21 ds 20 C V Extraction 9. Extract Cgspi, Cgs0 from Cgs Vgs at zero Vds and Cgs Vds at zero Vgs 10. Extract Cgdpi, Cgd0 from Cgd Vgs at zero Vds and Cgd Vds at zero Vgs 11. Extract Cds from Cds Vgs at zero Vds and low Vgs 12. Extract P10, P11 from Cgs Vgs at zero Vds 13. Extract P40, P41 from Cgd Vgs at zero Vds 14. Extract P20, P21 from Cgs Vds at zero Vgs 15. Extract P30, P31 from Cgd Vds at zero Vgs 16. Optimize Rgs, Rgd from Rgs,eq and Rgd,eq frequency

32 Parameter Extraction Strategy Extract P40, P41 from Cgd-Vgs at zero Vds linear regression: 1 tanh (( C C ) / C 1) P V P Extract P30, P31 from Cgd-Vds at zero Vgs linear regression: Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld G D Cgd Igs Id Cds S Rgs Rs Ls Cgs gd gdpi gd 0 41 gs 40 1 tanh Cgd C gdpi 1 Cgd 0(1 tanh( P40 P41Vds )) P V P 31 ds 30 C V Extraction 9. Extract Cgspi, Cgs0 from Cgs Vgs at zero Vds and Cgs Vds at zero Vgs 10. Extract Cgdpi, Cgd0 from Cgd Vgs at zero Vds and Cgd Vds at zero Vgs 11. Extract Cds from Cds Vgs at zero Vds and low Vgs 12. Extract P10, P11 from Cgs Vgs at zero Vds 13. Extract P40, P41 from Cgd Vgs at zero Vds 14. Extract P20, P21 from Cgs Vds at zero Vgs 15. Extract P30, P31 from Cgd Vds at zero Vgs 16. Optimize Rgs, Rgd from Rgs,eq and Rgd,eq frequency

33 Parameter Extraction Strategy Equivalent Circuit Model Igd Lg Rg Rgd Rd Ld G D Cgd Igs Id Cds S Rgs Rs Ls Cgs Optimize Rgs, Rgd with targets: R Y Y 1 gs, eq Re(( 11 12) ) R Y 1 gd, eq Re(( 12) ) versus frequency C V Extraction 9. Extract Cgspi, Cgs0 from Cgs Vgs at zero Vds and Cgs Vds at zero Vgs 10. Extract Cgdpi, Cgd0 from Cgd Vgs at zero Vds and Cgd Vds at zero Vgs 11. Extract Cds from Cds Vgs at zero Vds and low Vgs 12. Extract P10, P11 from Cgs Vgs at zero Vds 13. Extract P40, P41 from Cgd Vgs at zero Vds 14. Extract P20, P21 from Cgs Vds at zero Vgs 15. Extract P30, P31 from Cgd Vds at zero Vgs 16. Optimize Rgs, Rgd from Rgs,eq and Rgd,eq frequency

34 Outline Motivation Large Signal Model Parameter Extraction Strategy Model verification Conclusion 34

35 Model verification HEMTs of six different sizes (finger number finger width = 2 20μm, 4 20μm, 6 20μm, 8 20μm, 4 15μm, 4 25μm) are fabricated in 70nm GaAs technology and measured in extensive ways to evaluate the proposed model along with its parameter extraction. S-parameters are measured up to 67GHz. Large signal performances including power gain and power added efficiency (PAE) are also evaluated35 by measurements at 30GHz.

36 Model verification Measured and modeled RF small signal characteristics 36

37 Model verification 37

38 Model verification Measured and modeled RF large signal characteristics: (a) output power, (b) power gain, (c) PAE versus input power at 30GHz 38

39 Outline Motivation Large Signal Model Parameter Extraction Strategy Model verification Conclusion 39

40 Conclusion An Angelov large signal model and its parameter extraction strategy for GaAs HEMT are established. The model is composed of a unified equivalent circuit model and a set of analytical formulas. All the key parameters are taken directly from measurements step by step. The above work is validated by extensive measurements with good accuracy and can contributes to GaAs HEMT millimeter-wave circuit and system design. Heat effect modeling is our next emphasis. 40

41 Thanks for your attention! 41