Evaluation of single-transistor extrac- tion methods for ... · Evaluation of single-transistor extraction methods for HBT series resistances Evaluation of single-transistor extrac-

Evaluation of single-transistor extraction methods for HBT series resistances

Evaluation of single-transistor extrac-

tion methods for HBT series resistancesT. Nardmann1), J. Krause1), S. Lehmann1)

1)Chair for Electron Devices and Integr. Circuits, Univ. of Technol. Dresden, Germany

[email protected], [email protected]

http://www.iee.et.tu-dresden.de/iee/eb/eb_homee.html

© TN, JK 1


HICUM Workshop, Dresden, September 2010

OUTLINE

1 Preliminary Considerations

2 Base Resistance

3 Emitter Resistance

4 Collector Resistance

5 Conclusion

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• HICUM elements RB = RBx + RBi, RE and RCx

• Measured Data from FHG InP DHBTs and SiGe HBTs

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• Extraction from terminal data necessary for single-transistor pro-
cesses or when no test structures are available

• Focus on single-transistor methods that do not require additional measurement efforts

• Many methods may be available that produce slightly different results; test against model or simulation data can be used to evaluate suitability

• Methods need to be evaluated for each technology or process

• Exact description of methods beyond the scope of this talk

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2 Base Resistance extraction
2.1 Preliminary considerations
• Base Resistance influences most figures of merit (FoMs) and many further extraction steps

• Geometry dependence well researched; can be estimated based on materials, process and layout

• Many methods available in literature. Evaluated here:

- Ning and Tang 1984 [1]

- Modified Circle Impedance (Nakadei1991) [2]

- Gobert et al. 1997 [3]

- McAndrew 2006 [4]

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2 Base Resistance extraction 2.2 Ning and Tang

• Based on real vs. ideal base cur-rent; ideal value from model

• From ratio of ideal to actual base current, equation for resistance is developed:mBE VT⋅IC

---------------------⎝ ⎠⎛ ⎞ IB 0,

IB---------⎝ ⎠

⎛ ⎞ln rErE rBi rBx+ +( )

Bf-------------------------------------+= •

• Authors claim rBi/Bf = const.

• Intercept with y-axis is rE+rBi/Bf, slope is (rE+rBx)

• Assumptions (small Irec, only R-influence on IB) may not apply

InP result: rBx = 1141 Ω, rE= -11 Ω

SiGe result: rBx = 18 Ω, rE= -0.11 Ω

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2 Base Resistance extraction 2.3 Circle Impedance

h11corr1

y11 y12+--------------------- 1

gBE jωCBE+-------------------------------- 1

gB------+= = •

Im h11corr( ) 12gBE------------⎝ ⎠

⎛ ⎞ 2Re h11corr( ) 1

gB----- 1

2 gBE( )-----------------+–⎝ ⎠

⎛ ⎞ 2–±= •

• Intercept of semicircle with x-axis (interpolation for f -> ∞) cor-responds to RB

• Fit performed on y2 R2 x x0–( )2–= to avoid imaginary values

• Results questionable; some val-ues of Re(h11corr) negative

• Inconclusive or even inapplica-ble for modern transistors

Evaluation of circle shape

SiGe result: rBx = 11 Ω

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2 Base Resistance extraction 2.4 Gobert

• AC-based extraction

• According to publication, calcula-tion of rBi at all bias points not possible

• Asymptote of Re(Z11-Z12) for large currents should give rBx

• Values are in the correct range for both transistors

• Fit function used: Zp2IB----- p2+=

InP result: rBx = 13.4 Ω

SiGe result: rBx = 9.6 Ω


2 Base Resistance extraction
2.5 McAndrew 2006
• DC method

• Based on difference quotient to determine conductances

• rB and rE calculated; both show strong variation in low bias range

• rE

1 Gπ⁄

Bf 1Bf( )log∂IB( )log∂

---------------------+⎝ ⎠⎛ ⎞ Go

Gr------–

-------------------------------------------------------

rBVBE VB'E'–

IB rB 1 Bf+( )⋅ ⋅--------------------------------------

=

=

• Results for RE similarly erratic, with larger value range

InP result: rBx = 0.1 Ω, rE= 6.6 Ω

SiGe result: rBx = 0.2 Ω, rE= 4.1 Ω

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3 Emitter Resistance extraction
• Many methods exist

• Large influence on DC characteristics due to negative feedback

• Often simple geometry dependence

• When multiple devices available, extraction can be verified via scaling rules

• Methods evaluated

- gmi method [5]

- Open-Collector method [6]

- Gobert 1997 [3]

- Huszka 2009 [7]

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3 Emitter Resistance extraction 3.2 gmi

• Uses relationship between gm, gmi and rE

• gm taken from Re(y21), gmi from model1gm------ 1

gmi-------- rE 1 1

βf----+⎝ ⎠

⎛ ⎞ rBβf-----+ += •

• for large βf, 1/βf fractions can be neglected; for InP, several % error can be introduced

• extended version taking into account current dependence of mcf exists and has been used

InP result: rE= 8.6 Ω

SiGe results: rE= 2.0 Ω

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3 Emitter Resistance extraction 3.3 Open-collector

• Follows formulation of Gabl and Reisch

• Calculation of VCE for IC = 0 based on physical knowledge

VCE rEIE2VT

1μn c,

λ μp c,⋅------------------+

--------------------------- 1 IE IoS⁄+( )ln+= •

• Since some necessary values unknown, preliminary investiga-tion with nonlinear fit

VCE x1IE x2 1 IE x3⁄+( )ln+= •

SiGe result: rE= 2.6 Ω



3.4 Gobert
• Extraction from AC measure-ment

• Original publication uses IB; however, IC should be used

• Extrapolation of Re(Z12) towards infinite current

• For infinite currents, internal resistances tend to zero

• Extracts values in proper range for both technologies



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3.5 Huszka
• Based on gmi method

• Reformulation to eliminate need for linear regression

rEIm h̃11e( )

Im h̃21e( )---------------------- Re 1

h̃21e----------⎝ ⎠

⎛ ⎞ VTIB------⋅–= •

• Extraction point for RE chosen as that with lowest derivative w.r.t. VBE

• Good results for both technolo-gies



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4 Collecter Resistance extraction
• Very few methods available in literature

• Extraction usually performed via test structures; even then not trivial

• Calculation from geometry often difficult, many ways of contact-ing the collector exist

• Impact on DC characteristics usually small

• incorrect value impacts AC time constants

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4 Collecter Resistance extraction
4.2 Gobert
• Similar to RE extraction

• Interpolation of Re(Z22-Z12) towards infinite current

• Results are uncertain

- For InP, region may be right, but geometry scaling is not satisfactory

- For SiGe, value is most likely too large

InP result: rCx= 26.5 Ω

SiGe result: rCx= 26.5 Ω

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5 Conclusion
Result overviewTechnology InP SiGe modelMethod rBi rBx rCx rE rBi rBx rCx rE rBi rBx rCx rENing and Tang n/a 1142 - -12 - 18.6 - -0.1 n/a 102 - 0.54Circle Impedance n/a 45 - - n/a 10 - - n/a 13.5 - -gmi - - - 8.6 - - - 2.0 - - - 0.13Open collector - - - 3 - - - 2.6 - - - -McAndrew n/a 0.15 - 6.5 n/a 0.15 - 4.2 n/a -1 - -0.5Gobert - 12.3 25.8 3.3 - 19.2 25.8 1.5 - 5.6 25.7 1.00Huszka - - - 3.3 - - - 4 - - - 1.41model values - - - - - - - - 3.67 9.32 1.88 1.00
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5 Conclusion
• Base resistance
- no satisfactory method found for RB

• Emitter resistance

- several methods available with comparable results

- exact method chosen may depend on process in question

- Gobert method yields best results wrt. model value

• Collector resistance

- Only one method found, results are insufficient

• For single-transistor extraction, results are not reliable

• Use of test structures for modern processes highly recom-mended

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Brief method failure analysis

• SiGe: model for IRE and IBE necessary - Extraction range for IBE must be chosen high - Often only one component assumed in methods

• InP almost ideal logarithmic to very high voltages - where ΔIB visible: other effects (thermal, current blocking) rele-

vant - in lower region, measurement variation relevant (IB,meas > IB,ideal)

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AcknowledgmentsThis work was financially supported by the European DOTFIVE project. Wafer material was provided by Infineon. The Fraunhofer Institut für an-gewandte Festkörperphysik, Freiburg, is acknowledged for providing InP HBTs

Thank you for your attention

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References[1] T. H. Ning and D. D. Tang, “Method for Determining the Emitter and Base Series Resist-

ances of Bipolar Transistors”, IEEE Transactions on Electron Devices, Vol. 31, No. 4, p. 409-412, 1984

[2] T. Nakadai and K. Hashimoto, “Measuring the Base Resistance of Bipolar Transistors,” IEEE 1991 Bipolar Circuits and Technology Meeting, p. 200-203, 1991

[3] Y. Gobert et al., “A Physical, Yet Simple, Small-Signal Equivalent Circuit for the Hetero-junction Bipolar Transistor,” IEEE Transactions on Microwave Theory and Techniques, Vol. 45, No. 1, p. 149-154, 1997

[4] C. McAndrew, “BJT Base and Emitter Resistance Extraction from DC Data,” IEEE Pro-ceedings of the Bipolar/BiCMOS Circuits and Technology Meeting 2006, p. 1-4, 2007

[5] T. Nardmann, "Evaluierung des Kompaktmodells HICUM für InGaAs/InP Heterobipolar-transistoren," diploma thesis, TU Dresden, 2010

[6] R. Gabl and M. Reisch, “Emitter Series Resistance from Open-Collector Measurements - In-fluence of the Collector Region and the Parasitic pnp Transistor,” IEEE Transactions on Electron devices, Vol. 45, No. 12, 1998

[7] Z. Huszka and E. Seebacher, “Extraction of RE and its temperature dependence from RF measurements”, Working Group Bipolar (AKB) Meeting, 2009

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Additional slides
• Circle impedance method applied to simulation
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Additional slides
• Gobert rBx method applied to simulation
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Additional slides
• Gobert rCx method applied to simulation
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Additional slides
• Gobert rE method applied to simulation
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Additional slides
• Huszka method applied to simulation
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Additional slides
• McAndrew method applied to simulation
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Additional slides
• Ning-Tang method applied to model
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Additional slides
• gmi method applied to simulation
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Additional slides
• rBi/Bf vs. IC for Ning-Tang method (model results)
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Evaluation of single-transistor extrac- tion methods for ... · Evaluation of single-transistor extraction methods for HBT series resistances Evaluation of single-transistor extrac-