EE 245: Introduction to MEMSLecture 8: Surface Micromachining ICTN 9/22/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 66Diffusion ModelingEE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 67Diffusion Modeling (cont.)EE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 68Diffusion Modeling (Predeposition)EE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 69Diffusion Modeling (Limited Source)EE 245: Introduction to MEMSLecture 8: Surface Micromachining ICTN 9/22/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 70Diffusion Modeling (Limited Source)EE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 71Two-Step Diffusion• Two step diffusion procedure:ª Step 1: predeposition (i.e., constant source diffusion)ª Step 2: drive-in diffusion (i.e., limited source diffusion)• For processes where there is both a predeposition and a drive-in diffusion, the final profile type (i.e., complementary error function or Gaussian) is determined by which has the much greater Dt product:(Dt)predep»(Dt)drive-inÖ impurity profile is complementary error function(Dt)drive-in»(Dt)predepÖ impurity profile is Gaussian (which is usually the case)EE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 72Successive Diffusions• For actual processes, the junction/diffusion formation is only one of many high temperature steps, each of which contributes to the final junction profile• Typical overall process:1. Selective doping( Implant → effective (Dt)1= (ΔRp)2/2 (Gaussian)( Drive-in/activation → D2t22. Other high temperature steps( (eg., oxidation, reflow, deposition) → D3t3, D4t4, …( Each has their own Dt product3. Then, to find the final profile, usein the Gaussian distribution expression.()iiitottDDt∑=EE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 73The Diffusion Coefficient(as usual, an Arrhenius relationship)⎟⎠⎞⎜⎝⎛−=kTEDDAoexpEE 245: Introduction to MEMSLecture 8: Surface Micromachining ICTN 9/22/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 74Diffusion Coefficient GraphsSubstitutional & InterstitialcyDiffusersInterstitialDiffusersª Note the much higher diffusion coeffs. than for substitutionalEE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 75Metallurgical Junction Depth, xjxj= point at which diffused impurity profile intersects the background concentration, NBLog[N(x)]NONBx = distance f/ surfacexje.g., p-type Gaussiane.g., n-typeLog[N(x)-NB]NO-NBNBx = distance f/ surfacexjNet impurity conc.n-type regionp-type regionEE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 76Expressions for xj• Assuming a Gaussian dopant profile: (the most common case)• For a complementary error function profile:()BjojNDtxNtxN =⎥⎥⎦⎤⎢⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛−=22exp,⎟⎟⎠⎞⎜⎜⎝⎛=BojNNDtx ln2()BjojNDtxNtxN =⎟⎟⎠⎞⎜⎜⎝⎛=2erfc,⎟⎟⎠⎞⎜⎜⎝⎛=−oBjNNDtx1erfc2→→EE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 77Sheet Resistance• Sheet resistance provides a simple way to determine the resistance of a given conductive trace by merely counting the number of effective squares• Definition:• What if the trace is non-uniform? (e.g., a corner, contains a contact, etc.)EE 245: Introduction to MEMSLecture 8: Surface Micromachining ICTN 9/22/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 78# Squares From Non-Uniform TracesEE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 79Sheet Resistance of a Diffused Junction• For diffused layers:• This expression neglects depletion of carriers near the junction, xj→ thus, this gives a slightly lower value of resistance than actual• Above expression was evaluated by Irvin and is plotted in “Irvin’s curves” on next few slidesª Illuminates the dependence of Rson xj, No(the surface concentration), and NB(the substrate background conc.)() ()11 −−⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡==∫∫jjxoxojsdxxNqdxxxRμσρSheet resistanceEffective resistivityMajority carrier mobilityNet impurity concentration[extrinsic material]EE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 80Irvin’s Curves (for n-type diffusion)Example.Given:NB= 3x1016cm-3No= 1.1x1018cm-3(n-type Gaussian)xj= 2.77 μmCan determine these given known predep. and drive conditionsDetermine the Rs.p-typeEE C245: Introduction to MEMS Design LecM 4 C. Nguyen 8/20/09 81Irvin’s Curves (for p-type diffusion)Example.Given:NB= 3x1016cm-3No= 1.1x1018cm-3(p-type Gaussian)xj= 2.77 μmCan determine these given known predep. and drive conditionsDetermine the Rs.n-typeEE 245: Introduction to MEMSLecture 8: Surface Micromachining ICTN 9/22/09Copyright © 2009 Regents of the University of CaliforniaEE C245: Introduction to MEMS Design LecM 5 C. Nguyen 8/20/09 1EE C245 – ME C218Introduction to MEMS DesignFall 2008Prof. Clark T.-C. NguyenDept. of Electrical Engineering & Computer SciencesUniversity of California at BerkeleyBerkeley, CA 94720Lecture Module 5: Surface MicromachiningEE C245: Introduction to MEMS Design LecM 5 C. Nguyen 8/20/09 2Lecture Outline• Reading: Senturia Chpt. 3, Jaeger Chpt. 11, Handout: “Surface Micromachining for Microelectromechanical Systems”• Lecture Topics:ª Polysilicon surface micromachiningª Stictionª Residual stressª Topography issuesª Nickel metal surface micromachiningª 3D “pop-up” MEMSª Foundry MEMS: the “MUMPS” processª The Sandia SUMMIT processEE C245: Introduction to MEMS Design LecM 5 C. Nguyen 8/20/09 3Silicon SubstratePolysilicon Surface-Micromachining• Uses IC fabrication instrumentation exclusively•Variations: sacrificial layer thickness, fine- vs. large-grained polysilicon, in situvs. POCL3-dopingSilicon SubstrateFree-StandingPolysiliconBeamHydrofluoricAcidReleaseEtchantWafer300 kHz Folded-Beam Micromechanical Resonator NitrideInterconnectPolysiliconSacrificialOxideStructuralPolysilconIsolationOxideEE C245: Introduction to MEMS Design LecM 5 C. Nguyen 8/20/09 4PolysiliconEE 245: Introduction to MEMSLecture 8: Surface Micromachining ICTN 9/22/09Copyright © 2009
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