Outline. Introduction The Semiconductor Module Demonstration Modeling Advice Model Library Q & A

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1 Semicoductor Module Coyright 2013 COMSOL. COMSOL, COMSOL Multihysics, Cature the Cocet, COMSOL Deskto, ad LiveLik are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the roerty of their resective owers, ad COMSOL AB ad its subsidiaries ad roducts are ot affiliated with, edorsed by, sosored by, or suorted by those trademark owers. For a list of such trademark owers, see htt://

2 Outlie Itroductio The Semicoductor Module Demostratio Modelig Advice Model Library Q & A

3 COMSOL Multihysics 4.4

4 The Semicoductor Module Electrical circuit iterface allows easy coulig of lumed circuits to hysical device models. Secify the circuit maually or imort from a SPICE etlist. Ehaced electrostatics caabilities are available withi the semicoductor iterface ad as a stadalog electrostatics iterface. Heat trasfer i Solids ca be straightforwardly couled to the semicoductor iterface to model o-isothermal devices. Semicoductor iterface imlemets the semicoductor equatios solvig Poisso s equatio ad trasort equatios for the electros ad/or holes.

5 The Semicoductor Iterface The semicoductor iterface solves the Semicoductor equatios: V q N N 1 J t q 1 J t q U U D Numerical methods available: Fiite Volume Method (Scharfetter-Gummel disc.) Best curret coservatio Fiite Elemet Method (Log Formulatio) Solves for the log of the carrier cocetratio Fewer degrees of freedom for the same mesh Fiite Elemet Method (Liear Formulatio) Provided for backwards comatibility (o loger recommeded) A Poisso s Equatio Electro ad Hole Cotiuity Equatios

6 Currets are defied by the drift diffusio equatios: T k T k E J T k T k E J B B v B B c Maxwell Boltzma Carrier Statistics Fermi Dirac Carrier Statistics T T qd N TG k E J T T qd N TG k E J th v B v th c B c,, Solve for : Electros ad holes Majority Carries oly Electros Holes The Semicoductor Iterface

7 Material Library May ew materials added i 4.4 Wide rage of material roerties available New i 4.4 Suort for arbitrary comositios Secify x to defie comositio

8 Icomlete Ioizatio / Bad Ga Narrowig Both comlete ad icomlete ioizatio suorted Stadard Model Arbitrary user defied ioizatio ratios. Arbitrary user defied models for Bad Ga Narrowig

9 MOSFET Demostratio

10 Doig Semicoductor Doig Model Feature: User Defied Defie a costat or fuctioal doig form Imort data ad use iterolatig fuctios Gaussia Doig

11 MOSFET Demostratio (doig setu),,

12 Semicoductor Iterface boudary coditios Metal Cotact Ideal Ohmic (Voltage/Curret/Circuit Termial) Ideal Schottky (Voltage/Curret/Circuit Termial) Thi Isulator Gate (Voltage/Charge/Circuit Termial) Oxide layer assumed thi comared to geometry ot exlicitly modeled. Cotiuity/Heterojuctio Exlicit (domai based) modelig of isulatig regios. Ca be used to model Gates Guard rigs etc. A array of electrostatic boudary coditios icludig, electric otetial, groud, termial, surface charge accumulatio

13 Geeratio ad Recombiatio Summary of the imlemeted recombiatio rocesses for direct (e.g. GaAs) ad idirect (e.g. Si) bad-gas. Recombiatio: User Defied Direct Shockley-Reed-Hall Auger Geeratio: Imact Ioizatio

14 MOSFET Demostratio (boudary coditios)

15 Mobility Models 1. Mobility models are added as sub-features of the Semicoductor Material model 2. A small selectio of mobility models are available as re-defied features: Power-law (Lattice Scatterig) Arora (Imurity+Lattice Scatterig) Fletcher (Carrier-Carrier Scatterig) Lombardi (Surface Mobility) Caughey Thomas (High Field) 3. Mobility models ca be stad aloe or ca start from the outut of aother mobility model (e.g. Fletcher) 4. User defied mobility models ca be mixed freely with i-built models usig the same iut fuctioality 5. The fial mobility model used is selected i the semicoductor material model ode. 6. Cotiuatio settigs allow o-liear mobility models to be gradually itroduced to the equatio system.

16 MOSFET Demostratio (results)

17 Suorted Studies Statioary Studies: For steady state/dc simulatios Trasiet Studies: For time deedet roblems, e.g. tur o trasiets, imact ioizatio, etc. Small Sigal Aalysis, Frequecy Domai: For biased AC devices where a mix of DC ad AC sigals are reset. Curret V AC V DC Voltage

18 Suorted Studies Secific tools available for ost rocessig small sigals.

19 Modelig Advice: Discretizatio Fiite Volume Costat elemets - Caot be differetiated - Secial variables have bee rovided which cover most cases Curret coservatio imlicit i the method. Stabilizatio ot required Fiite Elemet Log Form Liear or Quadratic Elemets - Fully comatible with COMSOL s framework ca use ay variable aywhere i COMSOL. Eergy coservig method, curret coservatio should be checked as art of model validatio (usually OK). Stabilizatio o by default, but ot always required. Some models may solve better if this otio is disabled. Fiite volume variables that ca be differetiated ad used for coulig with other iterfaces: Variables edig with _ost: e.g. semi._ost, semi._ost, semi.v_ost Variables associated with the electric field (E, D, the corresodig orms) All curret variables

20 Modelig Advice: Meshig Resolve the Debye legth:, The fiite volume method uses flux terms at the boudary that deed o the distace to the mesh circumceter. Elemets should be miimally distorted for accurate flux comutatio. Triagular ad structured meshes tyically erform best. I 3D usig a swet mesh with a o-uiform distributio ca hel resolve gates better. Always assess solutios for grid ideedece.

21 Modelig Advice: Solvig The semicoductor equatios are highly oliear this meas the solvers may eed some hel to fid the solutio. Ram u the currets ad voltages i the model from zero. Use the cotiuatio solver set the Reuse solutio for revious ste settig to Auto whe erformig multile swees. Plot the results whilst solvig to get a idea of what the issue is. Use good iitial values the default will work reasoably well for equilibrium situatios (o currets or thermal gradiets), or use the solutio from aother study

22 Modelig Advice: Solvig Use the cotiuity settigs to gradually itroduce equatio terms ito the system for articularly o-liear roblems. Try ramig o the doig, startig from a iitially small value. If the cotiuatio solver does ot work well try the time deedet solver with time deedet arameters. For more detailed advice: Read the Modelig Guidelies chater of the Semicoductor Module users guide

23 Model Library Model Library Examles: Biolar Trasistor Caughey Thomas Mobility Lombardi Surface Mobility MESFET MOSFET MOSFET breakdow MOSFET small sigal MOSFET mobility diode circuit Schottky cotact Heterojuctio (1D) juctio (1D)

24 Model Library: Heterojuctio 1D bechmark to validate the Heterojuctio boudary coditio. The model comares results obtaied with the cotiuous quasi-fermi levels ad the thermioic emissio model. This figure shows the bechmark result for a - GaAs/-Al 0.25 Ga 0.75 As juctio uder forward ad reverse bias usig the thermioic emissio model.

25 Model Library: MOSFET Sequece Sequece of models erformig differet aalyses o a 2D MOSFET Shows may of the imortat features of the semicoductor module

26 Coclusios Semicoductor module is ow aroriate for a rage of simle device simulatios Fuctioality has bee sigificatly exteded i versio 4.4. Lookig ahead Module is curretly beig itesively develoed I the ext year the focus will be o multihysics alicatios