Self-heat Modeling of Multi-finger n-MOSFETs for RF-CMOS
ApplicationsHitoshi Aoki and Haruo Kobayashi
Faculty of Science and Technology,
Gunma University
(RMO2D-3)
RFIC –Tampa 1-3 June 2014
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
RFIC –Tampa 1-3 June 2014Slide 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
RFIC –Tampa 1-3 June 2014Slide 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-parametersand static drain current simulations despite accurate model parameter extractions
RFIC –Tampa 1-3 June 2014Slide 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
RFIC –Tampa 1-3 June 2014Slide 5
p-STIn-n+
GATE(1) GATE(2) GATE(n)GATE(n-1)
GATE
STI
GATE(1)GATE(2) GATE(n)GATE(n-1)
Edge Centerp-
STIn-n+
GATE(1) GATE(2) GATE(n)GATE(n--1)
GATE
STI
GATE(1)GATE(2) GATE(n)GATE(n-1)
Edge Center
Hot!Hot!
Research Background (3)• A sub-circuit based self-heat model does not
converge in large circuits
RFIC –Tampa 1-3 June 2014Slide 6
Rises in device temperature
Ambient temperature
2. Operation temperature
3. Main model circuit simulation
1. Temperature terminals are added to the model equivalent circuitas a sub-circuit
Zth :Thermal Impedance
VDS, ID :Drain Voltage and Current
( )0 D DS thT T I V Z= +
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
RFIC –Tampa 1-3 June 2014Slide 7
Purposes of This Work
• To analyze self-heat mechanisms in multi-finger 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
RFIC –Tampa 1-3 June 2014Slide 8
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
RFIC –Tampa 1-3 June 2014Slide 9
Device Simulation of Self-heating Induced Temperature Distribution
Slide 10RFIC –Tampa 1-3 June 2014
• Simulated with a 2-D device simulator (PISCES-2HB)• A slow pulsed DC source was used for better convergence
Dependence of ΔT on the number of fins
RFIC –Tampa 1-3 June 2014Slide 11
• 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
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
RFIC –Tampa 1-3 June 2014Slide 12
Temperature Dependence on Resistance
RFIC –Tampa 1-3 June 2014
( ) ( ), , ,ds ds dev iso ds th ds ds ds dev devI V T I V R V I V T T⎡ ⎤= ⋅ ⋅ +⎣ ⎦
The DC and Isothermal current is written as
ds ds thT I V RΔ = ⋅ ⋅ΔT is defined as
thLRS
ρ=
Rth can be written as an electrical resistance equation by
( ) ( )th dev devLR T T T TS
ρ+ Δ = + Δ
Temperature dependence is given by
(1)
(2)
(3)
(4)
Thermal Resistance
RFIC –Tampa 1-3 June 2014
Since ρ is linearly proportional to the rise in temperature, we have
( ) ( )dev devT T T c Tρ ρ+Δ = + ⋅Δ (5)
By plugging eq. (5) into eq. (4), we obtain
( ) ( )0 0th dev th dev thLR T T R c T R TS
+ Δ = + ⋅ ⋅ ⋅Δ (6)Now we define Kth as
( ) 0th dev thLK c T RS
= ⋅ ⋅ (7)Rth can be simply represented as
0th th thR R K T= + ⋅Δ (8)
Thermal Impedance
RFIC –Tampa 1-3 June 2014
For AC analysis, thermal capacitance, Cth, should be included in parallel with Rth, which is written as
1th
thth th
RZj C Rω
=+ ⋅ ⋅ ⋅
Now eq. (2) becomes
ds ds thT I V ZΔ = ⋅ ⋅
(9)
(10)
Fin-number Dependence on Rth
RFIC –Tampa 1-3 June 2014
NFth thR A NF R= ⋅ +
Rth is proportional to the number of fins, NF, of n-MOSFETs. Rth is a linear function as
Zth is replaced with
1
NFNF thth NF
th th
RZj C Rω
=+ ⋅ ⋅ ⋅
(11)
(12)
Drain Current with Self-heating
RFIC –Tampa 1-3 June 2014
Temperature dependence of effective mobility is referred as
( )( )eff eff devdev
TT TT
μ μ=
Effective mobility with self-heating can be( )
1.0eff
eff dev
dev
T T TT
μμ + Δ =
Δ+
Finally, a drain current with self-heating of a multi-finger n-MOSFET is written as
_1.0
dsds th
NF
dev
II TT
=Δ+
(13)
(15)
(14)
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
RFIC –Tampa 1-3 June 2014Slide 18
BSIM6 Model as a Modeling Vehicle
• 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
RFIC –Tampa 1-3 June 2014
BSIM6 model
‘Cold’ DC Measurement (1)• AC conductance method* with a Network
Analyzer (‘Cold’ DC measurement) is developed
RFIC –Tampa 1-3 June 2014
dev
d d d
d d d T
dI I ITdV T V V
∂ ∂∂= ⋅ +∂ ∂ ∂
*R. H. Tu. et.al, IEEE EDL, vol. 16, Feb. 1995.
Can be neglected at high frequencies
‘Cold’ DC Measurement (2)
RFIC –Tampa 1-3 June 2014
S22
Frequency
S22 - Vd
Gds - Vd
Id - Vd
Id-Vd Measurement
RFIC –Tampa 1-3 June 2014
0
50
100
150
200
250
300
350
400
0.0 0.5 1.0 1.5 2.0
I d(A
/m)
Vd (V)
Drain current characteristics of 64-fin n-MOSFET
Static DC
‘Cold’ DC
PISCES-2HBSimulation
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
RFIC –Tampa 1-3 June 2014
DC Drain Current Characterization of 16-fin n-MOSFET
RFIC –Tampa 1-3 June 2014
0
5
10
15
20
25
30
0 0.5 1 1.5 2
MeasuredProposed ModelBSIM6
Vd [V]
Id [mA]
DC Drain Current Characterization of 64-fin n-MOSFET
RFIC –Tampa 1-3 June 2014
0
10
20
30
40
50
60
70
80
0 0.5 1 1.5 2
MeasuredProposed ModelBSIM6
Vd [V]
Id [mA]
DC Drain Current Characterization of 128-fin n-MOSFET
RFIC –Tampa 1-3 June 2014
0
20
40
60
80
100
120
0 0.5 1 1.5 2
MeasuredProposed ModelBSIM6
Vd [V]
Id [mA]
S21 Characterization of 16-fin n-MOSFET
RFIC –Tampa 1-3 June 2014
-5-4-3-2-10123456789
10
0 5 10 15
Measured
Proposed Model
BSIM6
Frequency [GHz]
S21 [dB]
S21 Characterization of 64-fin n-MOSFET
RFIC –Tampa 1-3 June 2014
0
2
4
6
8
10
12
14
16
18
20
0 2 4 6 8 10 12 14 16
MeasuredProposed ModelBSIM6
Frequency [GHz]
S21 [dB]
S21 Characterization of 128-fin n-MOSFET
RFIC –Tampa 1-3 June 2014
02468
1012141618202224
0 5 10 15
MeasuredProposed ModelBSIM6
Frequency [GHz]
S21 [dB]
S11 Characterization of 128-fin n-MOSFET
RFIC –Tampa 1-3 June 2014
Measurement
Proposed Model
Simulation Speed Comparison of n-MOSFETs Ring Oscillators
RFIC –Tampa 1-3 June 2014
# of Stages 17 35 71 143
BSIM6 simulation time [sec]
0.32 2.93 4.81 9.92
Proposed Model simulation time [sec]
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
RFIC –Tampa 1-3 June 2014Slide 32
Slide 33
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
RFIC –Tampa 1-3 June 2014
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
RFIC –Tampa 1-3 June 2014
APPENDIX
RFIC –Tampa 1-3 June 2014
Verilog-A Source Implementations
RFIC –Tampa 1-3 June 2014
Tdev = idt((Ids * Tem0 / Tdev * vds - (Tdev - Tem0) / (RTH + (Tdev - Tem0)*KTH * RTH)) +Tem0;
• Time dependent heating implementation
• Small-signal AC simulations
if ((COSELFHEAT == 1)&&analysis("ac")) beginfreq = 1.0 / (2.0 * `PI * $realtime());cdrain = Ids / (1.0-2.0*`PI*freq*RTH*CTH);
end