Self-heat Modeling of Multi-finger n-mosfets for RF-CMOS Applications Hitoshi Aoki and Haruo Kobayashi Faculty of Science and Technology, Gunma University (RMO2D-3)
Outline Research Background Purposes of This Work Investigation of Self-heating in a Multi-finger n-mosfet with a 2-D Device Simulator Model Derivations Measurements and Model Verifications Summary and Future Research Slide 2
Outline Research Background Purposes of This Work Investigation of Self-heating in a Multi-finger n-mosfet with a 2-D Device Simulator Model Derivations Measurements and Model Verifications Summary and Future Research Slide 3
Research Background (1) A multi-finger structure is popularly used in MOSFETs for various RF-CMOS circuits including power amplifiers, mixers, and oscillators There is an inconsistency between S-parameters and static drain current simulations despite accurate model parameter extractions Slide 4
Research Background (2) In bulk MOSFETs for the multi-finger structure, self-heating effect (SHE) may occur especially if shallow trench isolation (STI) technology is adopted GATE(1) GATE(2) GATE(n-1) GATE(n--1) GATE(n) Edge p - Center n + n - STI Hot! STI GATE Hot! GATE(1) GATE(2) GATE(n-1) GATE(n) Slide 5
Research Background (3) A sub-circuit based self-heat model does not converge in large circuits 1. Temperature terminals are added to the model equivalent circuit as a sub-circuit Z th V DS, I D :Thermal Impedance :Drain Voltage and Current 2. Operation temperature T = T + I V Z ( ) 0 D DS th Rises in device temperature 3. Main model circuit simulation Ambient temperature Slide 6
Outline Research Background Purposes of This Work Investigation of Self-heating in a Multi-finger n-mosfet with a 2-D Device Simulator Model Derivations Measurements and Model Verifications Summary and Future Research Slide 7
Purposes of This Work To analyze self-heat mechanisms in multifinger n-channel MOSFETs To develop a general self-heat model without using thermal sub-circuits To analyze and modeling fin-number dependencies of thermal resistance with DC and S-parameter measurements and simulations Slide 8
Outline Research Background Purposes of This Work Investigation of Self-heating in a Multifinger n-mosfet with a 2-D Device Simulator Model Derivations Measurements and Model Verifications Summary and Future Research Slide 9
Device Simulation of Self-heating Induced Temperature Distribution Simulated with a 2-D device simulator (PISCES-2HB) A slow pulsed DC source was used for better convergence Slide 10
Dependence of ΔT on the number of fins The gate width of each fin is 20 μm Simulated ΔT is obtained at the center fin Measurement was made by using DC source/monitor Slide 11
Outline Research Background Purposes of This Work Investigation of Self-heating in a Multi-finger n-mosfet with a 2-D Device Simulator Model Derivations Measurements and Model Verifications Summary and Future Research Slide 12
Temperature Dependence on Resistance The DC and Isothermal current is written as I ( V, T ) = I V, R V I ( V, T ) + T ds ds dev iso ds th ds ds ds dev dev ΔT is defined as Δ T = I V R ds ds th ( +Δ ) = ρ ( +Δ ) Rth Tdev T Tdev T S (2) (1) R th can be written as an electrical resistance equation by L Rth = ρ (3) S Temperature dependence is given by L (4)
Thermal Resistance Since ρ is linearly proportional to the rise in temperature, we have ρ T +Δ T = ρ T + c Δ T (5) ( ) ( ) dev dev By plugging eq. (5) into eq. (4), we obtain L Rth ( Tdev +Δ T) = Rth 0 + c ( Tdev ) Rth0 Δ T (6) S Now we define K th as L Kth = c ( Tdev ) R (7) th0 S R th can be simply represented as R = R + K Δ T (8) th th0 th
Thermal Impedance For AC analysis, thermal capacitance, C th, should be included in parallel with R th, which is written as Z th Rth = 1 + j ω C R Now eq. (2) becomes th th (9) Δ T = Ids Vds Zth (10)
Fin-number Dependence on R th R th is proportional to the number of fins, NF, of n- MOSFETs. R th is a linear function as R = A NF + R NF th th Z th is replaced with Z NF th NF Rth = 1 + j ω C R th NF th (11) (12)
Drain Current with Self-heating Temperature dependence of effective mobility is referred as T μeff ( T) = μeff ( Tdev ) T dev Effective mobility with self-heating can be μ ( T T) eff μ eff dev +Δ = 1.0 + Δ T T dev Finally, a drain current with self-heating of a multifinger n-mosfet is written as I ds _ th Ids = ΔT 1.0 + NF T dev (13) (14) (15)
Outline Research Background Purposes of This Work Investigation of Self-heating in a Multi-finger n-mosfet with a 2-D Device Simulator Model Derivations Measurements and Model Verifications Summary and Future Research Slide 18
BSIM6 Model as a Modeling Vehicle BSIM6 model is continuous in all operation regions has accurate derivatives to predict harmonic distortion is satisfied both Gummel symmetry and AC symmetry has better physical capacitance behavior supports Verilog-A code which is supplied by the authors
Cold DC Measurement (1) AC conductance method * with a Network Analyzer ( Cold DC measurement) is developed di I T I = + dv T V V d d d d d d T Can be neglected at high frequencies dev *R. H. Tu. et.al, IEEE EDL, vol. 16, Feb. 1995.
Cold DC Measurement (2) S 22 -V d S 22 G ds -V d Frequency I d -V d
I d -V d Measurement 400 Drain current characteristics of 64-fin n-mosfet I d (A/m) 350 300 250 200 150 100 50 0 0.0 0.5 1.0 1.5 2.0 V d (V) Cold DC PISCES-2HB Simulation Static DC
Model Parameter Extractions 1. Input process parameters for BSIM6 2. DC I-V measurement 3. Measurements of S-parameters and de-embedded parasitic components, which are used for Cold DC calculations and AC parameter extractions 4. Extractions of DC parameters including BSIM6 and SHE parameters 5. AC parameter (L, C, and R) extractions 6. Model verifications with small circuit modules
DC Drain Current Characterization of 16-fin n-mosfet I d [ma] 30 25 20 Measured Proposed Model BSIM6 15 10 5 0 0 0.5 1 1.5 2 V d [V]
DC Drain Current Characterization of 64-fin n-mosfet I d [ma] 80 70 60 Measured Proposed Model BSIM6 50 40 30 20 10 0 0 0.5 1 1.5 2 V d [V]
DC Drain Current Characterization of 128-fin n-mosfet I d [ma] 120 100 Measured Proposed Model BSIM6 80 60 40 20 0 0 0.5 1 1.5 2 V d [V]
S 21 Characterization of 16-fin n- MOSFET S 21 [db] 10 9 8 7 6 5 4 3 2 1 0-1 -2-3 -4-5 Measured Proposed Model BSIM6 0 5 10 15 Frequency [GHz]
S 21 Characterization of 64-fin n- MOSFET S 21 [db] 20 18 16 14 Measured Proposed Model BSIM6 12 10 8 6 4 2 0 0 2 4 6 8 10 12 14 16 Frequency [GHz]
S 21 Characterization of 128-fin n- MOSFET S 21 [db] 24 22 20 18 16 14 12 10 8 6 4 2 0 Measured Proposed Model BSIM6 0 5 10 15 Frequency [GHz]
S 11 Characterization of 128-fin n- MOSFET Measurement Proposed Model
Simulation Speed Comparison of n-mosfets Ring Oscillators # of Stages 17 35 71 143 BSIM6 simulation time [sec] Proposed Model simulation time [sec] 0.32 2.93 4.81 9.92 0.34 2.96 4.91 10.86 HSPICE was used for the simulations on Windows PC (Pentium i5) Each stage consists of a 128-fin n-mosfet
Outline Research Background Purposes of This Work Investigation of Self-heating in a Multi-finger n-mosfet with a 2-D Device Simulator Model Derivations Measurements and Model Verifications Summary and Future Research Slide 32
Summary SHE has been verified with a 2-D device simulator The proposed model was implemented into BSIM6 model with the Verilog-A language The proposed model has been verified with DC and small-signal S-parameter measurements The self-heat model can be applied to other MOSFET models Slide 33
Future Research Since the Verilog-A code itself is not so fast for circuit simulation, the proposed model will be converted to a C code model for practical use Thermal capacitance measurement and the extraction will be developed for more gate fins of multi-finger MOSFETs A temperature-dependent method for circuit simulations will be considered
APPENDIX
Verilog-A Source Implementations Time dependent heating implementation Tdev = idt((ids * Tem0 / Tdev * vds - (Tdev - Tem0) / (RTH + (Tdev - Tem0)*KTH * RTH)) +Tem0; Small-signal AC simulations if ((COSELFHEAT == 1)&&analysis("ac")) begin freq = 1.0 / (2.0 * `PI * $realtime()); cdrain = Ids / (1.0-2.0*`PI*freq*RTH*CTH); end