Revisiting the Charge Concept in HBT/BJT Models

Transcription

1 evisiting the Charge Concept in HBT/BJT Moels Zoltan Huska an Ehrenfrie Seebacher austriamicrosystems AG 23r Bipolar Arbeitkeis BipAK Meeting at STM Crolles, France, 5 October 2

2 Outline recalling the junction epletion approimation the al charge-al junction voltage relation introuction of the available charge concept overview of the various charge applications correcting the temperature epenence of rbi suggesting alternative MNA charge for moel optimiation summary 2 2 austriamicrosystems

3 Built in an al voltages The metallurgical junction is in, the oping concentrations in < an > are of opposite kins. The electron an hole currents in the structure can be written as [] I n q A E D n ln n E n + T I p q A E D p ln p p Besies the familiar notations A E is the junction area an T is the thermal voltage. When both currents are ero the electric fiel can be epresse e.g. from the left equation yieling the built in voltage B nsie p nsie ln ln nn E T n > psie T n sie p An applie forwar voltage a > yiels the al voltage across the junction E + T B a The al voltage is always non-negative 3 2 austriamicrosystems

4 4 2 austriamicrosystems Space charge an junction bias is maintaine by the potential ifference over the space charge sustaine by the ionie impurity centers. Applying Gauss theorem within [- <ξ < ] where an stan for the left an right sie bounaries of the space charge layer The sign is etermine by the sequence of the oping types Integrating the negative fiel by part, the al voltage reas electric fiel charge balance E > < sgn if if ξ ξ ξ r r N q E 2 ln sgn sgn i T r T B r a B n N N

5 5 2 austriamicrosystems Junction charge increment Since charge balance unconitionally eists its variation shall also be ero The two terms are the charge increments of equal magnitues on the left an right sies respectively. The HS charge is Multiplying with the sign sgn an the area A E sgn sgn + E E A A sgn E j A

6 6 2 austriamicrosystems Junction voltage increment The variation of the al voltage reas ecogniing the junction capacitance: Making use of the charge balance variation j j C r r sgn sgn j r E r r A + + sgn sgn This epression manifests that a larger - increasing the with of the epletion layer - implies a larger HS charge. The rate of increase is C j.

7 Capacitance an actual charge The semi-empirical capacitance function generally applie in all HBT/BJT evice moels reas C j C j T v v an v are the built-in voltages at arbitrary an nominal temperatures. In transistor moeling the base charge contribution is measure by the charge increment from the actual base-sie epletion layer position to its new position in the base. The actually store charge is elimite by the metallurgical junction where C j Inf or. This store actual charge reas jact The actual charge resies in [ j ] when the base is on the HS v jnom C j u u jnom C j T v v a 7 2 austriamicrosystems

8 Application of junction charges in HBT/BJT moels Description of the Moll-oss-Gummel charges in AC linke HBT/BJT moels Moeling the conuctivity moulation of the internal base resistance Energy storing elements for circuit simulators ecent moels apply one single epression for all It will be shown that these specific applications benefit from eicate iniviual charge formulations 8 2 austriamicrosystems

9 Moll-oss-Gummel charges in AC linke approaches The following correcte MG charge has been erive in [2] Γ JT J Ji pt _ low p vji vji T + m ji E + Φ JT jenom ~ Γ jcnom Formerly it was J an only Φ JT has taken care of the escription of the bias an temperature epenence. The latter is the normalie applie charge at the effect of the applie voltage Φ JT jnom a C v u u jnom This is reference to the ero bias actual charge at the same temperature, use for all purposes in present moel variants v 9 2 austriamicrosystems Φ ET JT + m C C w w jact ~ Γ vji vji CT jnom vji jact v

10 Base resistance in Hicum/2 The quiescent part of the store minority charge in the npn base reas Cb Cb ~ Eb, Cb are the base-sie q AE p q AE N quiescent epletion bounaries Eb The conuctivity moulation is controlle by the al minority charge between the actual epletion layer bounaries r i Eb rbi ~ ~ ~ + je + jc The al AC junction relate charges are reference to the quiescent epletion bounaries at ero bias an nominal temperature v nom v ~ j jact jact nom jnom ~ v 2 austriamicrosystems + TC of the current rbi formulation [3] is eficient f not use in present moels

11 Base resistance in Hicum/2: interpretation vbe> quiescent minority charge vbc< poly-mono interface Eb T Cb T Eb vbe,t Cb vbc,t ~ ~ je T>T jc > < actual minority charge epi-b interface E je jc C Eisting formulation efines as a fraction of the low bias MG charge with an incorrect temperature epenence. Suggeste solution in figure regars constant, attributing all bias an temperature epenence to the junction relate al charges 2 austriamicrosystems

12 Charges as energy storing elements for MNA Circuit simulators are using the Moifie Noal Analysis MNA for solving the nonlinear network equations. Nonlinear energy storing elements require numerical integration for the solution of the unknown currents an voltages v i v charge basis i t v t t capacitance basis C v t v t t C v It has been shown by Calahan [4] that an increase stability can be achieve by using charges flues instea of capacitances inuctors in the numerical integration schemes Use of capacitances may violate charge conservation law 2 2 austriamicrosystems i t

13 Charges vs. capacitances in MNA Cv conservation error v - v 2 - v C v v v v v C v v Cv v v v v using capacitances the charge ifference between timesteps evelops along the charge graients. A close voltage loop reveals a conservation error selection of charges as sytem variables inherently gurantees charge conservation It oes not help that the problem eists only at nonlinear charges since it is eactly the case at transistor moeling 3 2 austriamicrosystems

14 Charges as energy storing elements for MNA, cont. Present moels integrate the Cv function from ero to the actual bias for computing the MNA charge ~ jmna v C j v u T u C j T v ~ jmna v v jact v v This is the same charge epression that the one generally use for all purposes in recent moels ~ jmna jnom ~ Φ JT jact v v w v w 4 2 austriamicrosystems

15 Moifie charges as energy storing elements for MNA The first term of the present normalie MNA charge Φ JT is voltage inepenent hence it has effect neither on the gra v Jacobian elements at AC analysis nor on the integration schemes for T. The preferre alternative is ~ jmna jact This form requires half the computational effort than the original. The cost of computation reuces by the time spent on approimately evaluating two eponential functions. Hicum/2 calls the t operator more than times a computational cycle for nonlinear charges 5 2 austriamicrosystems jnom v v v

16 Summary of efinitions - actual position: present location of the base-sie epletion bounary at a given temperature an bias - actual charge: charge store in the interval from the actual position to the metallurgical junction - applie charge: charge increment from the ero bias position to the applie bias position at the same temperature - al charge: charge increment from the ero bias, nominal temperature position to the applie bias, applie temperature position 6 2 austriamicrosystems

17 7 2 austriamicrosystems Overview MNA Base resistance AC linke MG Propose Current moels Charge use in Formulas are normalie to jnom v v v v v v v v v v v v v v v v v v v v

18 Summary junction capacitance efine as the erivative of the electrostatic charge w.r.t. the al voltage moeling applications of the junction charges pinpointe present conuctivity moulation of rbi shown to be eficient actual, applie an al charge concepts introuce spee optimiation with reuce computational effort an improve rbi temperature epenence suggeste by using eicate charge forms 8 2 austriamicrosystems

19 eferences [] Joseph inmayer an Charles Y. Wrigley, Funamentals of Semiconuctor Devices, D. an Nostran Co. Inc., 965 [2] Z. Huska, D. Celi an E. Seebacher, A Novel ow-bias Charge Concept for HBT/BJT Moels Incluing Heterobangap an Temperature Effects -- Part I: Theory, IEEE Trans. Electron Dev., submitte [3] [4] D. A. Calahan, Numerical Consierations for Implementation of a Nonlinear Transient Circuit Analysis Program," IEEE Trans. Circuit Theory, CT-8, January 97, pp austriamicrosystems

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