Full Electrothermal Transient Simulation of an X-band GaAs ... · Thermal transients at the active...

Full Electrothermal Transient Simulationof an X-band GaAs MMIC with

Microwave ExcitationC. E. Christoffersen ∗, W. Batty †, S. Luniya ‡ and M. B. Steer ‡

Contact: [email protected]

∗Department of Electrical Engineering, Lakehead Universit y, Thunder Bay, Ontario,

Canada P7B 5E1,† Filtronic Compound Semiconductors Ltd., Newton Aycliffe, UK,

‡ Department of Electrical and Computer Engineering, North C arolina State

University, Raleigh, NC, USA.

Full Electrothermal Transient Simulation of an X-band GaAs MMIC with Microwave Excitation – p.1/23

Motivation

Thermal transients at the active region of transistorscan be as fast as the electrical transients

This effect is most important to evaluate someperformance parameters such as intermodulationdistortion or adjacent-channel distortion

Finite-element modelling (FEM) techniques to analyzethe thermal system are computationally very expensive(≈ 10 hours for a single port)

Several compact thermal modelling approaches havebeen demonstrated in the past (see [2, 3, 4]), but theyapply to simple geometries or specific structures

Thermal nonlinearities → thermal analysis is notindependent of electrical simulation


Objectives

An electrothermal transient simulation of an X-bandMMIC amplifier excited with a 10GHz tone

Full transient behaviour including fast and slowelectrothermal variations is shown.

Envelope-following transient analysis implemented in ageneral-purpose circuit simulator.

Steady-state simulations validated with measurementsin [5]

Compact thermal model [1]


Circuit Simulator — I

Analyses Supported:DCTransient (fixed and adaptive time step)Envelope-following Harmonic Balance

Same device model equations for any analysis type andfor electrical and electrothermal models

Exact derivatives for Jacobian and sensitivitycalculation using automatic differentiation [6]

Devices modelled by a set of basic building blocks →

analysis only depends on building blocks, not specificdevices


Circuit Simulator — II

IndependentCS

+init()

+<<virtual>> eval(out j:double&)

+<<virtual>> paramDeriv(): bool

GenericVCCS

+init()

+<<virtual>> eval()

+<<virtual>> eval_and_deriv()

+<<virtual>> paramDeriv()

+<<inline>> getRow1(): int&


OPUMFPackDI

RType

+newParms()

+paramDeriv(out dg:double*): bool

LinearVCCS

-gain: double

+<<inline>> getGain(): double


+<<inline>> getCol1(): int&

+<<virtual>> paramDeriv(out dg:double*):LinearVCCS

1*:g=getGain()

mna:UMFPackDI

4*:addElement(row1,col1,g)

2*:row1=getRow1()

3*:col1=getCol1()

:OP

run

Actor


Circuit Simulator — III

<<template>>

FADBADGenericVCS

-dparm: double*

+init()

+eval(out f:double&,in v:double*)

+eval_and_deriv(out f:double&,out df:double*, in v:double*)

+paramDeriv(out dg:double*): bool

EV:class

GVCS:class

ncvolt:int

ndparms:int

temp_idx:int

temp_port:bool

BJTBE

+init()

+eval()

+eval_and_deriv()

+paramDeriv(): bool

<<EV:BJTBE_Eval,GVCS:GenericVCCS>>

BJTBE_eval

+<<template>> operator()(out ibe,in v,in dparm, in tvar,in cvar)

+<<template>> setTemp(out tvar,in dparm, in cvar,in temp)

+<<template>> newParms(out cvar,in dparm)

GenericVCCS

+init()

+eval()

+eval_and_deriv()

+paramDeriv()

+getRow1(): int&

+getRow2(): int&


Envelope-Following HB Approach — I

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5

v1 (

V)

Time (s)

1 2

3 4

5

0.005 0.01

0.015 0.02

0 0.2 0.4 0.6 0.8

1 1.2 1.4

v1 (V)

t1 (s)

t2 (s)

v1 (V)

Regular time-domain representation requires 5000samples, bi-dimensional representation only requires 100samples.


Envelope-Following HB Approach — II

A set of differential-algebraic equations

Gu(t) + Cdu(t)

dt+

dQ(u(t))

dt+ I(u(t)) = S(t),

can be converted into a system of partial differentialequations:

Gu + C

(

∂u

∂t1+

∂u

∂t2

)

+∂Q(u)

∂t1+

∂Q(u)

∂t2+ I(u) = S(t1, t2).

In Envelope-Following HB, the t2 time dimension is treatedin the frequency domain.


Thermal Modelling Approach

∆Ti =∑

RTHij(s)Pj(s)

The Thermal Impedance Matrix (RTH) is analyticallycalculated in a thermal simulator [1] for each block inthe structure

RTH(s) is directly used with s = jω for frequencydomain axis (fast variations)

A numerical Laplace inversion technique is used toobtain the unit step response of the thermal system forslow variations (STH)

Slow temperature variations are obtained in theelectrical simulator from the step response:

∆T (tk) = p(tk)ST H(t1) +

k−1X

j=1

p(tj)[ST H(tk−j+1) − ST H(tk−j)]


LMA 411 Layout


Electrical-Thermal Interactions

• Each finger modelledas a separate transistorwith Curtice cubic model• Temperature-dependenttransistor models• Thermal model includesdie, die attach and kovarmount structure, resolvingindividual 0.5 µm gates• non-commensurate volumesfor the die/solder andkovar mount

Tamb

The

rmal

net

wor

k

fingers

HEMT

Resistors


Output Voltage

-0.5-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.5

0 0.01

0.02 0.03

0.04 0.05

0.06 0.07

0.08 0.09

0.1 0.11 0 1e-11 2e-11 3e-11 4e-11 5e-11 6e-11 7e-11 8e-11 9e-11 1e-10

-0.5-0.4-0.3-0.2-0.1

0 0.1 0.2 0.3 0.4 0.5

voltage (V)

time (s)

periodic time (s)

voltage (V)


Power HEMT 1, Finger 1

4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4

0 0.01

0.02 0.03

0.04 0.05

0.06 0.07

0.08 0.09

0.1 0.11 0

1e-11 2e-11

3e-11 4e-11

5e-11 6e-11

7e-11 8e-11

9e-11 1e-10

4.6 4.8

5 5.2 5.4 5.6 5.8

6 6.2 6.4

power (mW)

time (s)

periodic time (s)

power (mW)


Temperature at HEMT 1, Finger 1

39

39.5

40

40.5

41

41.5

42

42.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11

0 1e-11

2e-11 3e-11

4e-11 5e-11

6e-11 7e-11

8e-11 9e-11

1e-10

39

39.5

40

40.5

41

41.5

42

42.5

temperature (C)

time (s)

periodic time (s)

temperature (C)


Zoom

Detail of temperature at HEMT 1, finger 1

42.11 42.115 42.12 42.125 42.13 42.135 42.14 42.145 42.15 42.155 42.16

0.09

0.092

0.094

0.096

0.098

0.1

0 1e-11 2e-11 3e-11 4e-11 5e-11 6e-11 7e-11 8e-11 9e-11 1e-10

42.11 42.115

42.12 42.125

42.13 42.135

42.14 42.145

42.15 42.155

42.16

temperature (C)

time (s)

periodic time (s)

temperature (C)


Power and Temperature

Power and Temperature at HEMT 1, Finger 1, t = 0.1 s

42.125

42.13

42.135

42.14

42.145

42.15

42.155

42.16

0 1e-11 2e-11 3e-11 4e-11 5e-11 6e-11 7e-11 8e-11 9e-11 1e-10

tem

pera

ture

(C

)

time (s)

4.6

4.8

5

5.2

5.4

5.6

5.8

6

6.2

6.4

0 1e-11 2e-11 3e-11 4e-11 5e-11 6e-11 7e-11 8e-11 9e-11 1e-10

pow

er (

mW

)

time (s)



39.5

40

40.5

41

41.5

42

42.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11

0 1e-11

2e-11 3e-11

4e-11 5e-11

6e-11 7e-11

8e-11 9e-11

1e-10

39.5

40

40.5

41

41.5

42

42.5

temperature (C)

time (s)

periodic time (s)

temperature (C)



46 46.5 47 47.5 48 48.5 49 49.5 50 50.5 51

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11

0 1e-11

2e-11 3e-11

4e-11 5e-11

6e-11 7e-11

8e-11 9e-11

1e-10

46 46.5

47 47.5

48 48.5

49 49.5

50 50.5

51

temperature (C)

time (s)

periodic time (s)

temperature (C)


Average Temperature in HEMT 2

Average temperature in a 50µm × 50µm area

39.5 40 40.5 41 41.5 42 42.5 43 43.5 44 44.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11

0 1e-11

2e-11 3e-11

4e-11 5e-11

6e-11 7e-11

8e-11 9e-11

1e-10

39.5 40

40.5 41

41.5 42

42.5 43

43.5 44

44.5

temperature (C)

time (s)

periodic time (s)

temperature (C)


Simulation Data

Thermal pre-computation (2000 samples): 20 hoursNumber of harmonics: 9Electrothermal simulation (0.1 s): 22 min., 17 sElectrothermal simulation (1 ms): 22 s

Thermal: 30 minutes per time point (all 19 ports), 40time points for 6 decades. Each time point → ≈ 10seconds with full series acceleration

Electrothermal: greatly accelerated if variable time stepimplemented (average 2 Newton iterations per timestep)


Conclusions

Full electrothermal transient simulation with a compactthermal model was demonstrated for an X-band MMICamplifier excited by a 10 GHz tone

Computation times are reasonably low and they willimprove in the future

Fast temperature variations at the transistor finger levelobserved but they are very small


Future Work

Improve integration of circuit simulator with thermalsolver

Include nonlinear thermal effects (temperaturedependent thermal conductivity, radiation, convection)in electrothermal simulation.

Implement adaptive time step and arbitrary initialconditions in Envelope-following HB analysis

Implement exact sensitivity analysis for transient andenvelope-following analyses

Test the circuit with more than one tone to investigatethermal contributions to intermodulation products


References[1] W. Batty et al., "Electrothermal CAD of power devices and circuits with fully physical

time-dependent compact thermal modeling of complex nonlinear 3-d systems", IEEETrans. Components & Packag. Technol., vol. 24, no. 4, pp. 566-590, December 2001.

[2] T. Veijola, L. Costa, and M. Valtonen, "An implementation of electrothermal componentmodels in a general purpose circuit simulation programme," THERMINIC ’97, Cannes,France, Sept. 21-23, 1997, pp. 96-100.

[3] A. R. Hefner and D. L. Blackburn, "An experimentally verified IGBT model implementedin the Saber circuit simulator", IEEE Transactions on Power Electronics", Vol. 9, No. 5,September 1994.

[4] V. Szekely, "THERMODEL:A tool for compact dynamic thermal model generation",Microelectron. J., vol. 29, pp. 257-267, 1998.

[5] S. Luniya et al., "Compact Electrothermal Modeling of an X-band MMIC," 2006 IEEE Int.Microwave Symposium, June 2006.

[6] C. Christoffersen, "Implementation of Exact Sensitivities in a Circuit Simulator UsingAutomatic Differentiation", 20th European Conference on Modelling and Simulation, May2006.


Full Electrothermal Transient Simulation of an X-band GaAs ... · Thermal transients at the active...

Documents

Transcript of Full Electrothermal Transient Simulation of an X-band GaAs ... · Thermal transients at the active...