Techniques of JFET Gate Capacitance Modeling · Fig. 3. Simpliﬁed C-V macro-model of single-gate JFET (pinch resistor). however, the extracted parameters V j and M j can get quite

Techniques of JFET Gate Capacitance ModelingStanislav Banas, Josef Dobes and Vaclav Panko

Abstract—This paper presents various techniques and prin-ciples of modeling JFET gate capacitance. Various layoutconcepts as well as their gate capacitance measurements andmodeling techniques are presented. Experience with potentialmodeling or measurement challenges is shared. The paper alsodeals with an often-omitted tight interaction between C-V andDC models, necessary for the well-fitting compact model. Goodagreement has been achieved between measured silicon dataand SPICE simulations for all discussed layout variants. Plotsof various layouts and various tests from real production modelsare also presented.

Index Terms—JFET, SPICE model, gate capacitance, pinch-off voltage, p-n junction barrier capacitance.

I. INTRODUCTION

THE Junction Field Effect Transistor (JFET) is a com-ponent used in many applications, as for example low-

noise amplifier, high input impedance amplifier, constantcurrent source, etc. [1]. It can be constructed as 3-terminal(3T) or 4-terminal (4T) component. The more complicated4T JFET contains two independently controlling gates, whichallow two input signals to be applied simultaneously, so itcan be used in signal mixing applications [2].

Development of JFETs especially for high-voltage appli-cations requires considering various aspects, as for exampleoptimization of breakdown voltage with series resistance,ESD robustness, etc. Therefore, various JFET concepts canbe found. Apart from that, the JFET can be found as aparasitic structure in other components as for example inhigh-voltage PMOS, which can be observed in measuredcharacteristics and should be considered in macro-model.

This paper is focused on the modeling of JFET gatecapacitance, which is seemingly only a simple p-n junction,but in reality the measured C-V characteristics can at firstlook quite surprising. Various JFET concepts and measuredgate capacitances including explained physical interpretationof observed phenomena are presented. Modeling techniques(lumped model, behavioral model, etc.) are compared andplots with silicon data vs simulated results are demonstrated.

II. SINGLE-GATE (THREE-TERMINAL) JFET

The example of single-gate JFET cross-section is shown inFig. 1, the related layout is in Fig. 2 and the typical macro-model is in Fig. 3. Such component is often called the pinchresistor and it is often used as a constant current source.

Manuscript received June 30, 2016; revised July 12, 2016. This work wassupported by ON Semiconductor company and by the Grant Agency of theCzech Technical University in Prague, grant No. SGS16/164/OHK3/2T/13.

S. Banas and V. Panko are with the ON Semiconductor, SGC CzechDesign Center, Department of Design Systems Technology, 1.maje 2594,756 61 Roznov pod Radhostem, Czech Republic and Czech TechnicalUniversity in Prague, Faculty of Electrical Engineering, Department ofRadioelectronics, Technicka 2, 166 27, Prague 6 , Czech Republic, e-mail:[email protected].

J. Dobes is with Czech Technical University in Prague, Faculty ofElectrical Engineering, Department of Radioelectronics, Technicka 2, 16627, Prague 6 , Czech Republic., email: [email protected]

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Fig. 1. Cross-section of single-gate JFET (pinch resistor).

Voltage dependent capacitances CGD and CGS are usuallyrepresented by the compact diode SPICE models with thevoltage dependent p-n junction barrier capacitance describedby the equation [3], [4]

C =Cj0(

1− VVj

)MjAREA (1)

where Cj0 is the zero-bias junction capacitance per unit area,Vj is junction built-in potential, Mj is grading coefficient, andAREA is the area of pn junction (representing the half ofJFET gate area).

These compact diode SPICE models can be either part ofcustomized lumped macro-model or integrated in the JFETmodel as for example in R3 model [5].

It is apparent, that low doped substrate and high dopedP+ gate are connected in our three-terminal JFET, so thequestion is, how to measure and evaluate model parametersof CGD and CGS for the equation 1. The equation assumes aphysical p-n junction with depletion area spreading with theapplied p-n junction voltage, not two parallel p-n junctionsaffecting each other.

One of possible solutions is to measure the gate andsubstrate p-n junctions separately and implement two paralleldiodes in the model instead of one. However, such solutiondoes not correctly represent the real situation, where theJFET channel can be pinched off by a few volts. The separatemeasurements in artificial structures do not cover this case.

It is more correct to measure the real situation of gate andsubstrate connected in a real JFET device. In such a case,

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Fig. 2. Layout of single-gate JFET (pinch resistor).

Proceedings of the World Congress on Engineering and Computer Science 2016 Vol II WCECS 2016, October 19-21, 2016, San Francisco, USA

ISBN: 978-988-14048-2-4 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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Fig. 3. Simplified C-V macro-model of single-gate JFET (pinch resistor).

however, the extracted parameters Vj and Mj can get quite farfrom their expected physical values, which especially occursat low temperatures. In compact models the parameter Vj hasthe integrated temperature dependency [3]

VJ(T ) = VJ(Tnom)

(T

Tnom

)+ 2Vtln

(ni(Tnom)

ni(T )

)(2)

where T is simulation temperature, Tnom is nominal ref-erence temperature at which the values of basic modelparameters were extracted, Vt is the thermal voltage and ni

is the intrinsic carrier concentration of used material, in ourcase silicon, with its own temperature dependency [3]

ni(T ) = ni(Tnom)

(T

Tnom

)Xti

exp

(q

2k(EG(Tnom)

Tnom− EG(T)

T)

)(3)

where Xti is intrinsic carrier concentration temperature ex-ponent used in SPICE as a tunable temperature parameter,typically set to the value 1.5, and EG is the gap width withits own temperature dependency described in [6].

Therefore, if the extracted VJ value gets too far from itsexpected physical value, it can become too low at very lowtemperatures, and making V /Vj too dominant, in extremecase even larger than 1, which could cause negative capac-itance. The extracted parameters should thus be carefullyverified in the full temperature range. If the verification failsand obtaining precise voltage dependent capacitance withthe integrated model equation 1 becomes impossible, thealternative solution of behavioral voltage dependent capacitormodel can be used.

0.0E+0

5.0E-12

1.0E-11

1.5E-11

2.0E-11

2.5E-11

3.0E-11

3.5E-11

4.0E-11

4.5E-11

-30 -25 -20 -15 -10 -5 0

CG

D(F

)

VGD (V)

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Fig. 4. CGD-V characteristic of single-gate JFET with full depletion atVGD = −15 V.

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SubSourceDrain��

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Fig. 5. Cross-section of high-voltage dual-gate 4T JFET.

In any case it is necessary to measure the gate capacitancein the real three-terminal structures containing drain, sourceand gate terminals, and not (as is often practised) in largetwo-terminal customized p-n junction structures. If the JFETis too small and gate capacitance value is under testermeasurement limit (sometimes called measurement noisefloor), more JFETs in parallel can be used instead. Correctmeasurement of gate-drain capacitance CGD is with floatingsource, correct measurement of gate-source capacitance CGS

is with floating drain.Let us for simplicity only talk about measurement of

gate-drain capacitance CGD in the following text. In sucha case the measured gate-drain capacitance CGD is equal tothe sum of two parallel capacitances: gate-drain capacitance(direct p-n junction) and gate-source capacitance in serieswith the source-drain resistance, which is basically a JFETrepresented by its DC model. When the gate-drain voltageVGD voltage across the p-n junction reaches the JFET pinch-off voltage, the JFET body becomes fully depleted, and thementioned second parallel path containing gate-source capac-itance CGS is disconnected. This appears as a steep drop ofcapacitance in measured C-V characteristic, as demonstratedin Fig. 4. Measurement of the gate capacitance with shorteddrain and source does not show this effect. The same effectwas observed also in gate capacitances of MESFET/pHEMTor microwave varactors [7].

III. DUAL-GATE (FOUR-TERMINAL) JFET

An example of dual-gate JFET cross-section is shown inFig. 5, the related layout is in Fig. 6 and the typical macro-model is in Fig. 7. This component is designed for high-voltage applications, therefore it has a circular or oval shapewith the high voltage pad in the center, as illustrated in Fig. 6.This configuration ensures that the high voltage applied to

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Fig. 6. Layout of high-voltage dual-gate 4T JFET.



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Fig. 7. Simplified C-V macro-model of dual-gate 4T JFET.

the drain appears only in vertical direction in the center ofthe oval where the high breakdown voltage is ensured bylow concentration of carriers in the substrate. Sufficient driftlength or other techniques (e.g. double RESURF [8]) makesure that this high voltage does not appear in the device’sperimeter and the device can operate at such high voltages[9]. Examples of the dual-gate JFET applications can befound in [10].

In the case of dual-gate JFET there are two effective gates(gate and substrate) represented by two p-n junctions, sothere are four voltage dependent capacitors in the macro-model, as depicted in Fig. 7. Therefore, four C-V testsmust be measured: Gate-drain capacitance CGD with floatingsource, substrate-drain capacitance CSUBD with floatingsource, gate-source capacitance CGS with floating drain andsubstrate-source capacitance CSUBS with floating drain. Theprinciple is analogous with that described in previous sectionfor single gate JFET, but in this case the measurement ofgate capacitances has substrate voltage as a parameter andthe measurement of substrate capacitances has gate voltageas a parameter.

The measured characteristics as well as the simulatedcurves are presented in Fig. 8 and Fig. 9. Fig. 8 showsgate-drain capacitance CGD measured for various substratevoltages. It is apparent, that the substrate voltage is affectingthe pinch-off voltage VGD, because the pinch-off voltage ofdual-gate JFET is affected by depletion areas of both gates.The more dominant gate is the one with higher concentrationof carriers, because the diffusion of minor carriers to theJFET body is higher in this case. This can be demonstrated

0.E+00

5.E-13

1.E-12

2.E-12

2.E-12

3.E-12

3.E-12

4.E-12

4.E-12

-25 -20 -15 -10 -5 0

CG

D (F

)

VGD (V)

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Fig. 8. CGD-V characteristic of high-voltage dual-gate JFET withparametrized VSUB = -20, -22, -24, -26, -28 V.

0.E+00

2.E-12

4.E-12

6.E-12

8.E-12

1.E-11

1.E-11

1.E-11

-40 -30 -20 -10 0

CS

UB

D (F

)

VSUBD (V)

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Fig. 9. CSUBD-V characteristic of high-voltage dual-gate JFET withparametrized VG = -12, -14, -16, -18, -20 V.

by the comparison of Fig. 8 and Fig. 9, where the same stepof second parameter has different impacts: the gate charge isapparently more concentrated and therefore the gate voltageVG in Fig. 9 has a higher impact on the pinch-off voltagethan the substrate voltage VSUB does in Fig. 8.

As mentioned in previous section, a well-fitting DC model(especially for pinch-off voltage) is a necessity for the correctprecise low-signal capacitance model. For the dual-gate JFETit is even more challenging, because the pinch-off voltageis determined by a combination of both gate voltages VG

and VSUB and each of them has a different impact. Variousbehavioral DC models of dual-gate JFET are published forexample in [2] or in [9].

The next challenge for the dual-gate JFET gate capacitancemodeling is the device with a non-uniform JFET channel.Fig. 5 shows a JFET with gate covering only a smaller partof JFET channel. In such a case the gate-drain capacitanceis in reality a p-n junction capacitance in series with a very-high-voltage Nwell (VHVNW) layer not covered by the gate.Ideal modeling solution would be the macro-model of dual-gate JFET in series with single gate JFET and the gate-drain capacitance would rather be the capacitance betweengate and internal node between the two mentioned JFETs.Such a solution directly corresponds with the layout, but itis overly complicated, difficult for the parameter extraction(how can these two segments be measured separately?) andpredisposed to convergence issues.

Another possible modeling solution is using the standardbarrier capacitance of equation 1, but unfortunately with ahigh probability of the extracted parameters far from theirphysical values and thus the temperature model failing, asexplained in section A. So the verification in full temperature

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Fig. 10. Cross-section of high-voltage dual-gate 4T JFET with parasiticsurfact channel.



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range is again necessary.The last proposed modeling solution is using the cus-

tomized behavioral voltage dependent capacitance. It is pre-ferred to model the capacitance with a charge controlledmodel as recommended in [11].

IV. DUAL-GATE (FOUR-TERMINAL) JFET WITHPARASITIC SURFACE CHANNEL

A high-voltage JFET does not necessarily have to havenon-uniform channel. Fig. 10 demonstrates JFET describedin previous section, in this case with the additional buried-layer gate covering almost whole the JFET channel. How-ever, this construction has another challenge, consisting inthe parasitic JFET channel between silicon surface and buriedgate.

In such case the gate-drain capacitance is predominantlylocated in the parasitic JFET channel between the surface andburied layer, while the majority of current flows via the mainchannel under buried layer. Measurement of such gate-draincapacitance with substrate voltage as a parameter and floatingsource is shown in Fig. 11. Unlike in the previous tests, inthis case the gate was grounded while the drain voltage beingswept on. Therefore, −VDG instead of VGD is on X-axis.This information is important only for correct understandingof parameter VSUB . Measured is the gate-drain capacitanceCGD like in previous tests.

At low gate-drain voltages the measured capacitance iscomposed of the surface gate-drain capacitance, the mainchannel gate-drain capacitance and the gate-source capaci-tance in series with JFET. At about VGD = 15V the parasiticsurface channel becomes depleted and the surface gate-drain capacitance becomes disconnected. Because it was thedominant one, the measured capacitance significantly dropsdown. In the range of gate-drain voltage between about 15Vand 20V the main channel gate-drain capacitance and thegate-source capacitance in series with JFET are significant.And finally at VGD > 20V the main JFET channel getsfully pinched, with the pinch-off voltage affected by theapplied substrate voltage, as detailed Fig. 12. This effectwas explained in previous section. In other words, thesubstrate voltage affects only the second capacitance dropat VGD > 20V , while the rest of the C-V curve is substrate-voltage independent.

0.0E+00

2.0E-11

4.0E-11

6.0E-11

8.0E-11

1.0E-10

1.2E-10

1.4E-10

1.6E-10

-40 -30 -20 -10 0

CG

D (F

)

-VDG (V)

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Fig. 11. CGD-V characteristic of high-voltage dual-gate JFET withparasitic surface channel and parametrized VSUB = 0, -5, -10 V affectingthe pinching of main JFET channel.

0.0E+00

1.0E-11

2.0E-11

3.0E-11

4.0E-11

5.0E-11

6.0E-11

7.0E-11

-27 -22 -17 -12

CG

D (F

)

-VDG (V)

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Fig. 12. CGD-V characteristic of high-voltage dual-gate JFET withparasitic surface channel and parametrized VSUB = 0, -5, -10 V, focusedto disconnection of ”source path” due to pinched main JFET channel.

The modeling of the second capacitance drop is coverednaturally by the combination of precise DC model of dual-gate JFET [2], [9] and four related voltage dependent capac-itances (compact diode SPICE models). The modeling of thefirst dominant capacitance drop can be done by two possiblemethods.

The first one was demonstrated in [9]. The gate-drainsurface channel capacitor is modeled by a behavioral voltage-dependent capacitor using equation 1 multiplied with themultiplication factor Cmult

Cmult =

(√(VGD + Vpoff)

2+ Vst + 0.5−

√(VGD + Vpoff − 0.5)

2+ Vst

)(4)

where VGD = −VDG is the gate-to-drain voltage, Vpoff isthe gate capacitance pinch-off voltage and Vst controls thesteepness of the gate capacitance drop.The approximate behavior of (4) is

for VGD ≤ −Vpoff : Cmult = 0for VGD ∈ (−Vpoff ,−Vpoff + 0.5): Cmult ∈ (0, 1)for VGD ≥ −Vpoff + 0.5: Cmult = 1.

The voltage-dependent gate-drain capacitance is then definedas

CGD = CmultCj0(

1− VGD

Vj

)MjAREA (5)

This solution, however, brings a risk of convergence errorsin transient analysis, as mentioned in [11], where the charge-controlled model is recommended. Another possible solutionis to implement the surface parasitic JFET channel in themacro-model as a JFET DC model and put it in series withthe substrate gate-drain capacitor. The disadvantage of thisis the increase of model complexity. However, it is close tothe natural layout, which is usually a good solution.

V. PARASITIC JFET IN OTHER COMPONENTS

As mentioned earlier, the JFET device, especially for highside applications, can be constructed in different ways whichshould be taken into account during model development. Pre-vious sections demonstrated only some examples of possibleJFET types.



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P substrate

NW

NBL

PW NW

NBL

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Fig. 13. Cross-section of high-voltage PMOS with parasitic drain JFET(p-type). N-body shorted to P-source represents JFET gate (n-type).

In Fig. 13 the cross-section of another component, inthis case high voltage PMOS, is shown, where the drain-source capacitance is affected by the parasitic JFET createdby the P-substrate channel and two N buried layers (NBL)representing JFET gate. This PMOS has its bulk shorted withthe source, so the measured output drain-source capacitancefor negative VDS might be expected to be the simple barriercapacitance with voltage dependency described by the equa-tion 1. But the data shows a similar capacitance drop as inFig. 4, which is caused by the pinching of the mentionedparasitic JFET. In this case the drain-source capacitancemust be modeled, similarly as the surface parasitic channeldescribed in previous section, either by behavioral voltagedependent capacitance or by the implementation of parasiticJFET in the lumped macro-model.

Similar parasitic JFETs can appear also in other compo-nent types, as for example bipolar transistors, diodes, etc. Soa careful measurement using the right measurement setup andconsidering this phenomena in the final model are necessaryto obtain an accurate model representing the real electricalbehavior of the device.

VI. CONCLUSION

JFET gate capacitance is often considered to be just asimple p-n junction. Its measurement and careful modeling istherefore often underestimated. This capacitance is howeverusually affected by the pinching JFET effect, which mustbe taken into account. It was demonstrated, that JFET canappear also as a parasitic component in other electricalcomponents and must be also considered in the macro-model.Various examples were presented and for each of them var-ious techniques and principles of modeling gate capacitancewere proposed. Some plots with measured silicon data andsimulated models were demonstrated.

ACKNOWLEDGMENT

The authors would like to thank to Jan Mıchal for hiscorrection of English and contribution after careful readingof the manuscript.

REFERENCES

[1] G. Cesura and F. Svelto, “Junction field effect transistors circuits,”Wiley Encyclopedia of Electrical and Electronics Engineering.

[2] W. Wu, S. Banerjee, and K. Joardar, “A four-terminal JFET compactmodel for high-voltage power applications,” in International Confer-ence on Microelectronic Test Structures. IEEE, 2015, pp. 37–41.

[3] G. Massobrio and P. Antognetti, Semiconductor device modeling withSPICE, 2nd ed. New York: McGraw-Hill, 1993.

[4] A. Vladimirescu, The SPICE book. John Wiley & Sons, Inc., 1994.

[5] C. C. McAndrew, “Integrated resistor modeling,” in Compact Mod-eling: Principles, Techniques and Applications. Springer, 2010, pp.271–297.

[6] H. S. Nalwa, Silicon-Based Material and Devices, Two-Volume Set:Materials and Processing, Properties and Devices. Academic Press,2001, vol. 1.

[7] J. Dobes and L. Pospisil, “Enhancing the accuracy of microwave ele-ment models by artificial neural networks,” Radioengineering, vol. 13,pp. 7–12, 2004.

[8] A. W. Ludikhuize, “A review of RESURF technology,” in Proceedingsof The 12th International Symposium on Power Semiconductor Devicesand ICs, 2000, pp. 11–18.

[9] S. Banas, V. Panko, J. Dobes, P. Hanys, and J. Divın, “Comprehensivebehavioral model of dual-gate high voltage jfet and pinch resistor,”Solid-State Electronics, vol. 123, pp. 133–142, 2016.

[10] D. A. Masliah and A. G. Bracale, “Electronic circuits including aMOSFET and a dual-gate JFET,” Nov. 3 2014, US Patent App.14/531,754.

[11] C. C. McAndrew, G. J. Coram, K. K. Gullapalli, J. R. Jones, L. W.Nagel, A. S. Roy, J. Roychowdhury, A. J. Scholten, G. D. Smit,X. Wang et al., “Best practices for compact modeling in Verilog-A,”IEEE Journal of the Electron Devices Society, vol. 3, no. 5, pp. 383–396, 2015.



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Techniques of JFET Gate Capacitance Modeling · Fig. 3. Simpliﬁed C-V macro-model of single-gate JFET (pinch resistor). however, the extracted parameters V j and M j can get quite