Overview of Modeling and Simulation TCAD - FLOOPS / FLOODS

Transcription

1 Overview of Modeling and Simulation TCAD - FLOOPS / FLOODS

2 Modeling Overview Strain Effects Thermal Modeling TCAD Modeling Outline FLOOPS / FLOODS Introduction Progress on GaN Devices Prospects for Reliability Simulation

3 Self-consistent Procedure k p self-consistent solution to Poisson and Schrödinger s equation )] ( ) ( [ / ) ( 2 2 z N z N q z V dz d D Si + = " ) ( ) ( )] ( 2 [ 2 z E z z V m P n n = + ) ( ) ( 2 ) ( 2 2 E f z z N D n " n =

4 In and Out-of-Plane Masses (Ge) Biaxial Stress Uniaxial Stress m m m k z m k z k x k y Using k p methods to compute bands k x k y

5 Confinement and Strain Sub-band Shifts Low Vertical Field Uniaxial High Vertical Field Biaxial Si 2 E top E second E top E top E V E second E second E V E V Band splitting due to strain Splitting (increases) / (decreases) under confinement

6 Same Physics for IV, III-V Materials Si Ge GaAs Unstressed 1GPa Biaxial Tension 1GPa Uniaxial Compression

7 Thermal Simulations Use finite element modeling to optimize package design Most important factors in thermal management: heat transfer at the system boundaries and substrate thickness Couple w/ FLOOPS / FLOODS simulations as well

8 Thermal Simulations and IR Imaging T(Junc) of power devices is often significantly hotter than T(stage) Accurate extraction of activation energy requires knowledge of the true channel temperature. We have extensive experience in estimating heat transfer even in complex structures Purchasing a high-resolution IR camera for direct imaging of the device operating temperature. We have collaborated with Nitronex on thermal imaging-a typical example is shown at right for a multi-finger power HEMT. Temp ( C) Y (m) X (m) Temp ( C) Possible Collaborations w/ Samuel Graham, Georgia Tech

9 Modeling Overview Outline Strain Effects Thermal Modeling TCAD Based Approaches TCAD Modeling FLOOPS / FLOODS Introduction Progress on GaN Devices Prospects for Reliability Simulation

10 FLOOPS / FLOODS Object-oriented codes Multi-dimensional P = Process / D = Device 9% code shared Scripting capability for PDE s - Alagator Commercialized - ISE / Synopsis Sentaurus - Process is based on FLOOPS Licensed at over 3 sites world-wide 28 release Manual is online (but needs updating)

11 What is Alagator? Scripting language for PDE s Parsed into an expression tree Assembled using FV / FE techniques Stored in hierarchical parameter data base Models are accessible, easily modified

12 What is Alagator? Operator ddt grad sgrad dot elastic Description Time derivative Spatial derivative Scharfetter / Gummel Discretization Operator Returns the dot product of the gradient of two field electric field in direction of current floq Compute elastic forces - FEM balance Example use of operators for diffusion equation Fick s Second Law of Diffusion ddt(boron) - 9.e-16 * grad(boron) - K * (Boron - Trap) C(x,t) / t = D 2 C(x,t) / x 2

13 Strained PMOS To enhance channel mobility, PMOS strain processing includes embedded SiGe in the source/drain regions and compressive capping layers. FLOOXS predicts strain/stress profiles where the channel stress is ~1 GPa capping layer SiGe compressive SiGe Y Cheng, et al. IEDM 27 Horstmann, et al. IEDM 25 X FLOOXS predicted stress profile [dyne/cm2] (YY component - channel direction)

14 Complex Mobility Models Construction Hole Mobility [cm 2 /Vs] E+14 1E+16 1E+18 1E+2 1E+22 Concentration (cm -3 ) Unifies the description of majority and minority carrier bulk mobilities temperature dependence electron hole scattering screening of ionized impurities by carriers clustering of impurities Majority Minority Surface scattering terms (Vertical Field) Velocity Saturation EffMass changes w/ strain (more later)

15 Piezoresistance Piezoresistivity is the change in electrical resistivity with mechanical stress and involves the relationships between electric field E i, current density J, and mechanical stress σ j kl E = ( " + # ) (Small Change Limit) i ij ijkl kl J j &( ' µ $ $ ( ' µ $ ( ' µ $ $ ( ' µ $ ( ' µ $ $ %( ' µ xx yy zz yz zx xy xx yy zz yz zx xy Mobility Change # &' + $ $ ' + $ ' + = $ $ ' + $ ' + $ " $ %' + xx yy zz yz zx xy / + / + / + / + / + / + xx yy zz yz zx xy Resistivity Change J n, p = # qnµ n, p " n, p # &* $ $ * $ * = $ $ $ $ " $ % * * * & J $ $ J $ % J * * * X Y Z * 44 * 44 Piezoresistance coefficients # &) $ $ ) $ ) $ $ ) $ ) $ * " $ %) 44 xx yy zz yz zx xy () # & 1( ' µ xx $ () = $ ( ' µ xy xy () " $ % ( ' µ zx zx xx # " Stress components ( ' µ 1( ' µ ( ' µ xy yy yz xy yy yz ( ' µ ( ' µ zx yz 1( ' µ zz zx yz zz # & J $ $ J " $ % J X Y Z ()# () ()"

16 Piezoresistance example Silicon beam with an n-type surface Bending induces tensile stress at the surface resulting in a increase in mobility and current. & J X (") # 1+ $%µ ) xx ( + J X () = ( 1+, 11 " xx )J X () ' * µ xx FLOOXS beam bending example

17 Piezoresistance The gradient of the quasi-fermi level gives J n,p vector values for each element J n, p = # qnµ n, p " n, p J Y () J X () () # & 1( ' µ xx = $ () " % ( ' µ xy xy Piezoresistance coefficient matrix can be defined for any orientation using directional cosines Z [1] & J $ % J X Y xx ( ' µ xy 1( ' µ yy xy yy #& J $ "% J X Y ()# () " X [1] ϕ =45 Y [1] X [11]

18 Piezoresistance Piezoresistance coefficients can be set to spatially vary in FLOODS Extracted channel and bulk coefficients different (to do) Piezoresistance coefficients are function of impurity concentration and temperature P(N,T) T Kanda Y., IEEE Trans Electron Devices 1987 FLOODS simulated piezoresistance factor for T=3 K

19 PMOS with L gate =3 nm <11> channel orientation 27 ITRS dimensions Charge strike dist. in drain Strained PMOS Simulations

20 Double-Gate FinFET L gate =18 nm, w si =11 nm Midgap metal gate (typically TiN) Gate-S/D doping underlap to control V t and short channel effects Undoped body FinFET top cross-sectional view nfinfet I-V characteristic

21 AlGaN/GaN HEMT Device Can handle heterostructure bands Gate offsets Field Dependence Energy Band Diagram Sample IV curve

22 Edge Termination Electrode Depletion region contour Oxide n Edge termination is critical for obtaining high breakdown voltage and reduced on-state resistance. Severe electric field crowding around metal contact periphery. High leakage current and breakdown at the highest electric field Potential contour Depletion contour

23 Junction Termination Extension p + Depletion boundary p - JTE layer N V B values are highly sensitive to the charge in the JTE layer. Multiple JTE termination technique (JTE1 + JTE2). Reverse breakdown voltage (V) x1 17 4x1 17 5x1 17 JTE doping concentration (cm -3 )

24 Reliability Simulation Simulate Device in Quasi-Steady State Electrons and Holes equilibrate quickly Similar to assumption in process simulation Generation Events Triggered by Mechanical Stress Current Flow / Electric Field Simultaneous solutions Point Defects / Defect Cluster / Interface Capture Hydrogen TNS, TBP Vanderbilt + UF

25 Example: 3.2µm x 9nm bulk nmosfet Low frequency measured and simulated noise data Graphical depiction of Noise Producing oxide trap locations on mesh for simulating the low frequency noise features. Location 1 has 4 traps, locations 2 and 3.5 traps each.

26 Modeling Integrated Conclusions Fundamental Physics k p feeds TCAD Thermal coupled to TCAD Experimentally Integrated Failure Mechanism Identification feeds M&S Electrical Measurement feeds