Supplemental Manual for PISCES2H-B - Stanford …fmr/research/docs/HBpisces.pdf · Supplemental Manual for PISCES2H-B Harmonic Balance Module, Circuit Boundary Conditions, and

Supplemental Manual forPISCES2H-B

Harmonic Balance Module,Circuit Boundary Conditions, andOther Improvements

Francis Rotella, Boris Troyanovsky,Wei-Chun Lee, Zhiping Yu, andRobert Dutton

Integrated Circuits LaboratoryStanford UniversityStanford, California 94305

Copyright 1997by The Board of Trustees of Leland StanfordJunior University.

All rights reserved.

PISCES, PISCES-II, PISCES-2ET, PISCES2H-Bare registered trademarks of Stanford University.

. vii

. . .1 . . .1 . . .1

. .3 . . .3 . .3 . . .5 . . .6 . . .7

. . .9 . . .9

Table of Contents

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Harmonic Balance Solver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.2 TBD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Boundary Conditions for Linear Circuit Elements. . . . . . . . . . . . .2.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2 Boundary Condition Equations (DC Analysis) . . . . . . . . . . . . . . . . . . . .2.3 AC Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.4 Transient Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.5 HB Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Improved Modeling for Quantum Mechanical Effects, CompoundMaterials, and Dynamic Traps . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Supplemental Manual for PISCES2H-B

Table of Contents

. . 9. . . 9

. . . 9

. 10 . . 10

. . 10

. . 10

. 10

. 11 . 11 . 11. . 11. . 12

. . 13 . 13. . 13. 14. 15 . 18. 20 . 21 . 22 . 25 . 2627

282930. 31. 32. 39

3.2 Quantum Mechanical Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.2.1 Hansch Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2.2 Van Dort Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3 New Compound Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.3.1 SiGe Hetero-structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3.2 Ternary Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3.3 Quaternary Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.4 Dynamic Trapping Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Improved Numerical Techniques for High Frequency Analysis,Newton Projections, and One Dimensional Simulations . . . . . . . .4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.2 High Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.3 Newton Projections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 One Dimensional Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Users Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5.2 PISCES Card Additions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

CONTACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HBMETH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LOG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MODEL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .SOLVE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .TRAP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.3 The Circuit File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .COMMENT LINES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .NUMERICAL DEVICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .STANDARD ELEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .TRANSMISSION LINE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .DEPENDENT SOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INDEPENDENT SOURCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OPTIONS CARD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

iv Supplemental Manual for PISCES2H-B

Table of Contents

.42. .46. .46

. .47 . .47 . .47 . . 48

. . 48

. .48 . 48

. 48

. . 48

. .48

. . . 51

. 53

. .54 . 55

. 57

. 58

. . .63

ANALYSIS CARDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 NODE NUMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 SCALING FACTORS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.2 Examples Exercising the Improved Numerics . . . . . . . . . . . . . . . . . . . .

6.2.1 Convergence in a Non-Planar Avalanche Photo Diode . . . . . . . . . . . . . .

6.2.2 High Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.3 Applications for the New Physical Models . . . . . . . . . . . . . . . . . . . . . . 6.3.1 C-V Characteristics Using van Dort QM Model . . . . . . . . . . . . . . . . . . . .

6.3.2 AC Analysis of MOSFET Using Hansch QM Model . . . . . . . . . . . . . . . .

6.3.3 Traps in a GaAs Diode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.4 Circuit Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Diode with External Circuit Components and Distributed Contact

Resistance48

6.4.2 Transient Response of a BJT Inverter . . . . . . . . . . . . . . . . . . . . . . . . . .

6.4.3 Gain vs. Bias Condition for a BJT Amplifier . . . . . . . . . . . . . . . . . . . . . .

6.5 Harmonic Balance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.5.1 Large Signal Analysis of AM Demodulator . . . . . . . . . . . . . . . . . . . . . . .

6.5.2 BJT Mixer to Down Covert a 2Mhz Signal to 100KHz . . . . . . . . . . . . . .

6.5.3 Analyzing Gain and Efficiency in a MOS Power Amplifier . . . . . . . . . . .

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Supplemental Manual for PISCES2H-B v

Table of Contents

vi Supplemental Manual for PISCES2H-B

Acknowledgments

t and

search

The authors would like to acknowledge the following industrial partners who have provided inpu

guidance in the development of various parts of this code:

• Hewlett Packard, Santa Rosa, CAHarmonic balance solver development.

• Motorola, Tempe AZHarmonic balance simulation of RF devices.

• Matsushita Electric Industrial Co.Harmonic balance simulation of RF devices.

• Hewlett Packard, Palo Alto, CAQuantum mechanical effects in MOS devices.

The authors would like to acknowledge the continued support of the Semiconductor Re

Corporation through contract #SRC 07-SJ-116.

Supplemental Manual for PISCES2H-B vii

Acknowledgments

viii Supplemental Manual for PISCES2H-B

CHAPTER 1Harmonic Balance Solver

wlett

e the

ISCES.

r to the

ctor

1.1 Introduction

The Harmonic balance solver is an addition to PISCES provided by the EEsof Division of He

Packard. The solver is designed to interface with Stanford’s version PISCES2H-B to provid

numerical capabilities to solve the harmonic balance system of equations generated from P

This section discusses those numerics and procedures, but for a full description please refe

dissertation,Frequency Domain Algorithms for Simulating Large Signal Distortion in Semicondu

Devices, by Boris Troyanovsky.

1.2 TBD

Supplemental Manual for PISCES2H-B 1

Harmonic Balance Solver

2 Supplemental Manual for PISCES2H-B

CHAPTER 2Boundary Conditions forLinear Circuit Elements

circuit

linear

dition

rminal,

at. The

,

2.1 Description

Some simple, yet important circuits consist of only one nonlinear device and a number of linear

components surrounding the device. This chapter discusses a method of including these

components in a device simulation by reducing the surrounding circuit to a set of boundary con

equations. The basics are explained with DC analysis and are then expanded to include AC, te

and harmonic balance analyses.

2.2 Boundary Condition Equations (DC Analysis)

Most device simulators allow external resistances on a contact such that

(2.1)

whereG is the conductance,Vapp is the applied voltage,Vcon is the contact voltage, andI is the current

which is a function of the semiconductor variables for that specific node.

For a linear circuit around a device, the previous equation can be expressed in a matrix form

voltages and currents become vectors andG becomes a matrix. BothG andVapp are constants. Hence

G Vapp Vcon–( ) I Ψ n p, ,( )– 0=


Boundary Conditions for Linear Circuit Elements

ich the

circuit

evice

n that

which

s three

m lay

ng the

ff

the boundary condition on a contact is dependent on the voltages on all circuit nodes to wh

contact is connected.

In order to determine this matrix equation, consider Figure 2.1 where we have a linear

surrounding a numerical device. Substituting ideal current sources for the numerical d

connections, modified nodal analysis (MNA) may be applied to the system with the assumptio

the device currents are unknown:

(2.2)

whereGc is the circuit MNA conductance matrix,Vc is the unknown circuit node voltages,Ic is the

known circuit currents, and is the unknown device terminal currents. is zero for nodes to

the device is not connected. For example, for a three contact numerical device, this vector ha

entries.

Solving this equation yields Equation 2.3 and re-arranging yields Equation 2.4. Within this syste

the boundary conditions for the numerical device as given in Equation 2.1 simply by re-arrangi

equation.

PISCESDevice

Vd2

Vdn

Vd1

Id2

Idn

Id1

Linear Circuit

Vd2

VdnVd1 Id2

IdnId1

Linear Circuit

Figure 2.1 (a) Linear circuit surrounding a numerical device. (b) For the purpose ofinding the boundary conditions, the numerical device is assumed to consist oideal current sources of unknown values.

GcVc I c I d'+=

I d' I d'



ear

cted

d that

o meet

trix can

em is

n is

using

device

(2.3)

(2.4)

Ed can be found by LU decomposingGc and then using backward substitution. Essentially, the lin

circuit is solved for .Ed is then just a subset of that solution for the circuit nodes conne

to the numerical device.

Since Id’ is symbolic, this derivation forces the computation ofGc

-1 which is computationally

inefficient. A better approach is to calculateRd by perturbing the circuit solution for at

the circuit nodes to which the device is connect. This process is represented in Equation 2.5:

(2.5)

Hence, no inverse is needed and a simple LU decomposition of Gc with a few backward substitutions

yields Equation 2.4. To clarify notations, Equation 2.1 and Equation 2.4 are compared to fin

Vd=Vcon, Ed=Vapp, G=Rd-1, andId=I(Ψ, n, p).

The boundary condition equations are loaded into the PISCES matrices to force the solution t

those conditions. When those conditions are met, is determined so that the entire circuit ma

be solved for the values at each circuit node.

2.3 AC Analysis

In AC analysis of the circuit, all nonlinear components are linearized and the resulting syst

solved. A similar approach is followed with circuit boundary conditions. First a DC solutio

computed for the nonlinear device. Upon finding a solution, the PISCES device is linearized

small signal analysis at the frequency of interest. That linearized model replaces the numerical

and a simple circuit solve produces the small signal response.

Vc Gc1– I d'– Gc

1– I c=

Vd Rd I d+ Ed

=

I d' 0=

I d' 0=

r dij i dijd

dvdij∆vdij

∆i dij

-----------= =

I d'



t since

time

ethod

rs and

NA.

tep t

ay be

source

lements.

scribed

2.4 Transient Analysis

Transient analysis presents an additional dimension because of the time discretization, bu

derivatives are linear the boundary conditions are still obtainable. The two methods of

discretization used in device simulations tend to be Backward Euler (BE) and the TR/BDF2 m

of Bank, etc. In the surrounding circuitry, the only two time dependent elements are capacito

inductors. For each, the derivative is locally linearized and the resulting system is solved via M

Referring to Figure 2.2, the voltage across a capacitor is known from the previous solution at sn.

Given the I-V relationship for a capacitor, a Backward Euler approximation for the derivative m

employed. Upon simplification, one notes that the resultant equation is equivalent to a current

and resistor in parallel. Hence, for each time step the capacitors can be reduced to two linear e

As a result, the boundary condition equations can be assembled in the same manner de

previously.

i

v

+

-

In+1 = i(t+Dt)

In = i(t)

Vn+1 = v(t+Dt)

Vn = v(t)

i Ctd

dv=

I n 1+ CVn 1+ Vn–

∆t-------------------------=

I n 1+C∆t-----Vn 1+

C∆t-----Vn–=

IeqGeq

Vn+1

+

-

In+1

Ieq

Geq

Localized linear model:

Figure 2.2 Time discretization of a capacitor using Backward Euler.



atrix

ce, the

od for

iven a

ps.

set of

s. As

ions by

nce, a

ations

oundary

Note thatGeq remains unchanged if the change in time step is constant. As a result, the MNA m

Gc is unchanged as well as the conductance matrix for the boundary condition equations. Hen

only term that needs to be recalculated isEd. For inductors, a similar result is obtained.

In order to have time step control in device simulation, Bank etc. developed a two step meth

using a trapezoidal step (TR) followed by a second order backward difference step (BDF2). G

differential equation as show in Figure 2.3 and a time stephn, a TR step is taken forγhn and is followed

by a BDF2 step of (1-γ)hn. If only one Jacobian is necessary for both time ste

In applying the Bank method to the differential equations for inductors and capacitors yields a

locally linearized model similar to the backward Euler method. Note thatGeq is the same for both the

TR and BDF2 steps given that . Likewise, it is the same ifhn is the same. As a

result, in both these situations, onlyEd needs to be recomputed with each time step.

2.5 HB Analysis

Harmonic balance simulation presents another special case for circuit boundary condition

explained in Chapter 1, harmonic balance is used to solve the semiconductor differential equat

assuming a sinusoidal solution at integer multiples of the fundamental frequency(ies). He

boundary condition equation is required for each frequency. Since the circuit is linear, the equ

are straightforward because no harmonics are generated in the circuit and the set of complex b

condition equations fall into the following three categories.

γ 2 2– 0.586≈=

tn tn+γ tn+1

γhn

hnDIFF. EQ:

tdd

q z t( )( )( ) f t z t( ),( )+ 0=

TR STEP: 2qn γ+ γ hn f n γ++ 2qn γ hn f n–=

BDF2 STEP: 2 γ–( )qn 1+ 1 γ–( )hn f n 1++ γ 1– qn γ+ γ 1– 1 γ–( )2hnqn–=

Figure 2.3 The TR/BDF2 method of Bank etc. for solving a time dependant differentialequation.

γ 2 2– 0.586≈=



similar

on the

trode of

e final

For the DC bias, the equation is determined by the methodology described previously.

(2.6)

For frequencies at which there is a source (i.e. the fundamental(s)) the equation is given in a

format except that it is complex.

(2.7)

Finally, for the harmonics generated by the nonlinear PISCES device, the equation takes

following form. Note that there is no generation term

(2.8)

The harmonic balance module computes the magnitude and phase of the current at each elec

the device for each frequency. That solution is then used in the circuit equations to compute th

circuit solution.

Gd0 Ed0 Vd0–( ) I d0 Ψ0 n0 p0, ,( )– 0=

Yd1 Ed1 Vd1–( ) I d1 Ψ1 n1 p1, ,( )– 0=

Edn

YdnVdn– I dn Ψn nn pn, ,( )– 0=


CHAPTER 3Models for QuantumMechanical Corrections andDynamic Trapping Effects

of the

ffects.

of the

ence of

he gate

ess to

annel

. The

the

or

(either

antum

l

g the

ening.

3.1 Introduction

This chapter describes two features in PISCES 2H-B, which are related to modeling

quantum mechanical effects in silicon MOS devices and analysis of dynamic trapping e

As the feature size of MOSFETs, mainly the gate length, keeps scaled down, the width

surface inversion layer becomes comparable to the gate oxide thickness. The consequ

this dimensionality closeness is that the gate capacitance is no longer determined by t

oxide only. To the first order, one can use an effective (or electrical) gate oxide thickn

model this thickness widening. Another effect of MOS scaling is the raise of the ch

doping in order to minimize the leakage current in the off-state of MOSFET operation

high doping level (typically above cm-3) increases the slope (i.e., steepness) of

surface potential well which is formed when MOS device is in either inversion

accumulation region. This steep potential well leads to the quantization of energy band

conduction or valence band depending on the operation region) due to the qu

mechanical effects in the normal direction to the Si/SiO2 interface. The ground energy leve

in the surface potential well is the lowest state for carriers to occupy, effectively shiftin

edge of the energy band. This effect can be modeled by the bandgap broad

317×10


Models for Quantum Mechanical Corrections and Dynamic Trapping Effects

by the

from

above

rating

wave

device

to the

ction

. The

ethod,

odel,

ormal

ccount

d the

unt of

each

amic

ses can

Furthermore, the carrier spacial density in the surface potential well is now determined

magnitude of the wavefunction, which results in the peak of carrier concentration away

the interface, on contrary to the prediction of classical physics. Even though, the

quantum mechanical (QM) effects can be modeled accurately in principle by incorpo

the SchrÖdinger equation solver in the conventional semiconductor equations, the

nature of particles and the involvement of eigenvalue problem deter this approach in

simulation,especially in the multi-dimensional cases. In stead, an incremental approach

macroscopic solution is much preferred. This approach calls for the introduction of corre

term(s) in the classical semconductor equations to partially include the QM effects

resulted equations still keeps main feature of the original equations and their solution m

but the solution will reflect the effect of QM corrections.

In PISCES 2H-B, there are three models available for QM corrections: the Hansch m

which gives the correct shape of carrier distribution in the channel region along the n

direction to the surface, van Dort model, which applies the bandgap broadening to a

for the QM effects but with a classical carrier distribution (peaking at the surface), an

hybrid model, which combines the above two models hence giving both correct amo

corrections and the shape of carrier distribution. We will first describe the theory for

approach and then give its usage.

Another feature to be described in this chapter is the simulation capability for dyn

trapping effects. By dynamic, it means that both the steady state and transient analy

be conducted.



) for

ier

carrier

met.

ith

of

nction,

m the

hes 0

carrier

n by

In Eq.

3.2 Models for Quantum Mechanical Corrections

3.2.1 Hansch Model

Realizing that quantum mechanical effects call for the repulsive boundary condition (BC

carrier distribution at the Si/SiO2 interface due to the existence of the potential barr

between SiO2 and silicon substrate, the Hansch model imposes a shape function to the

distribution in the direction normal to the interface such that the repulsive BC is

Specifically, it one assumes thatz-axis is along the normal direction to the interface, w

origin at the interface and positive direction towards the substrate, andx-axis is along the

channel, the carrier concentration (take electrons as an example) would take the form

(2.9)

where is the thermal characteristic length and represents how quickly the shape fu

which is the square bracketed part of the above equation, becomes unity away fro

interface ( ). is related to the barrier height between the SiO2 and Si and is different

for electrons from holes. When the barrier height becomes infinitely high, approac

and it means that the carrier concentration is zero at the interface. Otherwise, the

concentration at the interface has a finite value. is the carrier concentratio

applying classical physics, normally the drift-diffusion model. For Boltzmann statistics,

(2.10)

where is the thermal voltage and all other symbols have the conventional meaning.

(2.9) both and are related to the physical parameters as follows:

n x z,( ) nclassic x z,( ) 1 ez z0+( )2 λ2⁄–

–=

λ

z 0= z0z0

nclassic

nclassic nieψ φn–( ) Vt⁄

=

Vtλ z0



and

e for

tween

used

or the

nt

l and

same

ads to

(2.11)

(2.12)

where is the effective mass and is the potential barrier height for carriers, so

are different for electrons from holes, so are and . The following is the tabl

relevant parameters used in the Hansch’s model:

Note that the potential barrier for carriers, , is due to the band edge discontinuity be

SiO2 and Si. In the actual simulation during the calibration process, and are often

as fitting parameters.

The expression, Eq. (2.9), for carriers is used in the Poisson’s equation to solve f

electrostatic potential,ψ. But still further modification needs to be made in the curre

expression in order to meet the zero current bourndary condition at the SiO2/Si interface in

the normal direction for with such a bell shape distribution of carrier in the channe

normal drift current expression both the diffusion and drift components would be in the

direction (not canceled each other as desired). This zero current boundary condition le

the following expressions for carriers:

Table 1. Physical parameters used in Hansch’s model

m* / m0 ΦB (eV) λ (Å) z0 (Å)

electrons 0.916✝ 3.2 12.69 7.165

holes 0.49 3.7 17.35 9.110

✝ Logitudinal effective mass

λ h2

8π2m

*kBT

---------------------------=

z0h

2

2m* ΦB

------------------=

m* ΦB m

*

ΦB λ z0

ΦBλ z0



uantum

the

antum

e the

ersion

in the

he peak

rically,

o the

ck of

aning

on or

rm of

els in

the

(2.13)

The term added to in the square brackets in the above equations is often called the q

potential.

The advantage of Hansch’s model is it gives qualitatively correct carrier profile in

channel. But the drawback is that none of the parameters used to model the qu

corrections, and has any bias dependence, which makes it difficult to reproduc

measured device characteristics at all bias range (i.e., from the accumulation to inv

region). Later on we’ll discuss a way to improve the accuracy of this model.

3.2.2 van Dort Model

This model tries to capture the QM effects using the broadening of the bandgap

substrate surface region. Because both the energy band quantization and the shift of t

in channel carrier profile in the normal direction to the SiO2/Si interface away from the

interface amount to the increase of the effective bandgap in the surface region elect

van Dort model is quite successful in providing close simulation results compared t

measured data (mainly C-V characteristics including threshold voltage). The drawba

this model is that the carrier distribution in the channel still has the classical shape, me

it peaks at the surface of the substrate. The following is the model description.

Assuming a triangular potential well at the substrate surface during either inversi

accumulation region, the eigenfunctions to the Schrödinger equation have analytical fo

so-called Airy function and the eigenvalues which represent the quantized energy lev

the well are function of the slope of the potential well, which in turn is determined

jn qµnn∇ ψkBT

q---------- 1 e

z z0 n,+( )2 λn2⁄

– ln+– kBTµn∇n+=

j p qµpp∇ ψkBT

q---------- 1 e

z z0 p,+( )2 λp2⁄

– ln–– kBTµp∇p–=

ψ

λ z0



nd the

n the

verse

found

ith

lation

ually

trate

5),

s that

been

of

eters

strate

ess [2].

transverse surface electric field. Considering only the ground energy level in the well a

peak shift for the eigenfunction corresponding to the ground level, one can obtai

following relationship between the effective bandgap increase with the surface trans

electric field:

(2.14)

where is the surface transverse field and is a proportionality factor which can be

from the theory [1]. In PISCES, eV, where is a fitting parameter w

value unity or bigger. The effect of the bandgap broadening is included in the simu

through the intrinsic carrier concentration in the following way in order to have a grad

diminishing QM corrections when moving away from the surface towards the subs

contact.

(2.15)

where is a smooth function with form of

(2.16)

and with a characteristic length with typical value of 250Å. In Eq. (2.1

is the intrinsic carrier concentration using the conventional bandgap and i

using the bandgap with correction (i.e., addition) of Eq. (2.14). The van Dort model has

successfully applied to the calibration of 0.18µm CMOS process with gate oxide thickness

around 30Å. With both the polysilicon gate doping concentration and as fitting param

the C-V characteristics from the accumulation to inversion region and with different sub

bias can be simulated accurately. The optimal value of seems 1.7 for the above proc

∆Eg139------β

εSi

4kT----------

1 3⁄

FS2 3⁄

=

FS ββ 4.1

8–×10 κ= κ

ni niconv

1 g z( )–[ ] g z( )niQM

+=

g z( )

g z( ) 2ea2–

1 e2a2–

+

----------------------=

a z σ⁄= σni

convni

QM

κ

κ



orating

hese

ed by

hange

well.

shold

of the

which

ulation

into

and

ere are

ch in

ture of

strate.

of

wn that

.

th the

t from

ted in

shape

of the

ue to

3.2.3 Hybrid QM correction Model

While both Hansch’s model and van Dort model achieve reasonable success in incorp

the QM effects in the classical transport modeling framework, each has its limitations. T

limitations mainly stem from the incompleteness in capturing the physical picture caus

the quantum mechanical effects. For example, while Hansch model accounts for the c

of carrier profile in the channel due to the repulsive boundary condition at the SiO2/Si

interface, it fails to model the quantization of the energy band in the surface potential

So often Hansch’s model does not provide enough correction in predicting the thre

voltage, which is closely related to the bandgap. Also, as mentioned previously, none

paramters in this model has bias (mainly the surface transverse field) dependence,

leads to the failure in predicting the trend of the gate capacitance in the deep accum

region for nMOS structure. On the other hand, van Dort model indeed takes

consideration both the band quantization and shifting of peak in carrier doping profile

hence gives fairly accurate simulated C-V characteritics in the entire bias range. But th

two serious shortcomings with this model. First, the model uses over-simplified approa

lumpping all two effects in the increase of the bandgap, thus preserving the classic pic

the carrier profile, i.e., the peak of the channel carriers is on the surface of the sub

Secondly, model Eq. (2.14) implies the sigularity for when the derivative

channel charge is to be evaluated, which is needed in C-V simulation. It has been sho

the simulated C-V curve shows a spurious spike at the flatband region where

Furthermore, In all two models, in order to match the simulation results more closely wi

measured data, fitting parameters often end up with values which are quite differen

their physically meaningful defaults.

In view of all those shortcomings, a hybrid model has been developed and implemen

PISCES. This model essentially blends the previous two models by incorporating both

function, Eq. (2.9), and bandgap broadening, Eq. (2.14). In doing so, all major aspects

QM effects in MOS structure: band quantization and the bell shape of carrier profile d

FS 0=

FS 0=



ss the

new

inate

ause

vior of

and

, the

range

re the

of the

the

eature

om the

the superposition of eigenfunctions, are taken into consideration in the model. To addre

singularity problem of capacitance calculation intrinsic to van Dort model, Eq. (2.14), a

formula is proposed [3]:

(2.17)

where are two adustable paramters. The purpose of this modification is to elim

the singularity in evaluating the derivative of Eq. (2.14) with respect to (w.r.t.) (bec

of the presence of nonzero ) and at the same time to preserve the asymptotic beha

Eq. (2.14) when . The default values used in PISCES is

.

Applying this hybrid model to a MOS capacitor with the gate oxide thickness of 31Å

simulated C-V characteristics agree with the measured data very well for the entire bias

and there is no glitch in the flatband region as van Dort model often renders. Furthermo

model parameters used in the fitting are either all physical values (for Hansch’s part

model) or close to what theory predicts ( for van Dort’s part of the model while

theoretical value is 1.) And the simulated carrier profile in the channel preserves the f

mandated by the quantum mechanics: the peak of the channel carrier profile is away fr

SiO2/Si interface. This example of simulation is shown in Figure 1.1.

∆Eg139------β

εSi

4kBT-------------

1 3⁄ FS

2

c1eFS

2 c22⁄–

FS4 3⁄

+

------------------------------------------=

c1 c2,FS

c1FS ∞±→ c1 1

7×10=

c2 16×10=

κ 1.3=



3.3 New Compound Materials

3.3.1 SiGe Hetero-structure

3.3.2 Ternary Compounds

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 2.0Vg (volts)

10.0

30.0

50.0

70.0

90.0

Cg

(pF

)

MeasuredSimulated w/ a=2.8E7Hansch w/ optimum params

Figure 1.1 Simulation of C-V characteristics for a MOS capacitor with the gate oxidethickness of 31Å and area of 100-by-100µm2. The hybrid model shows close fit themeasurement data with physically meaningful parameter while Hansch’s model requiresadjustment of physical parameters.



3.3.3 Quaternary Compounds

3.4 Dynamic Trapping Analysis


CHAPTER 4Improved NumericalTechniques for High FrequencyAnalysis, Newton Projections,and One DimensionalSimulations

t three

CES to

o better

uickly

4.1 Introduction

This chapter discusses numerical improvements in PISCES2H-B. The improvements targe

separate areas. First, an improved algorithm for high frequency analysis is incorporated in PIS

improve the robustness of those solutions. Second, improvements in Newton projections lead t

initial guesses and algorithms for curve tracing. A one dimensional mode provides an option to q

analyze a device before a costly two dimensional run is executed.

4.2 High Frequency Analysis

4.3 Newton Projections


Improved Numerical Techniques for High Frequency Analysis, Newton

4.4 One Dimensional Mode


CHAPTER 5Users Manual

ilities. In

ircuit

circuit

lance

ults in

n and

to the

ar to

e the

SCES

5.1 IntroductionNew parameters and new cards were added to the PISCES in order to access the new capab

addition, for circuit boundary conditions, a SPICE like input deck is required to describe the c

configuration. This chapter describes the new PISCES cards and parameters as well as the

description input net list.

5.2 PISCES Card Additions

The improvements from PISCES-2H to PISCES 2H-B involves additions for harmonic ba

simulation, circuit boundary conditions, new models, and improved numerics. Each change res

new parameters in order to invoke the capability. In addition, harmonic balance simulatio

dynamic traps necessitate the addition of two cards.hbmeth (standing for HB method) is used to

define the parameters for the numerics involved in harmonic balance simulation and is similar

method card.trap is used to define profiles for the traps within the device structure and is simil

theprofile card. In addition, a separate file containing a SPICE-like net list is required to describ

circuit surrounding the PISCES device. The format for this file is described after the new PI

parameters and cards are categorized.


Users Manual

the

ing

the

COMMAND CONTACT

A new parameter is introduced for this card to allow the specification of

file containing the netlist of the surrounding circuit of the device be

simulated.

SYNTAX

Contact cktfile = <filename>

NEW PARAMETERS

cktfile

This parameters specifies the input file that contains the net list for

linear circuit surrounding the device.

EXAMPLE

contact cktfile=myckt.ckt


Users Manual

onic

fore

in. A

ctice

his

ery

).

COMMAND HBMETH

This new card specifies numerical limits and methods for the harm

balance module. It is similar in nature to themethod card.

SYNTAX

hbmeth [maxiter = <integer>] [useredpc] [krtol = <real>]

+ [kriter = <integer>] [gmrestart = <integer>]

+ [pkthresh = <real>] [gmrthresh = <real>]

+ [krloosetol = <real> krlooseiter = <integer>]

+ [krconvratio = <real>]

PARAMETERS

maxiter

This parameter specifies the maximum number of Newton iterations be

the HB simulator aborts and steps the voltage sources down to try aga

reasonable value is 30 although a good number is not known in pra

(Default: 30).

useredpc

This logical variable is used to specify the ‘reduced’ pre-conditioner. T

parameter is needed only for two-tone problems with very tightly or v

widely spaced tones and reduces memory dramatically (Default: false


Users Manual

ov)

and

ring

step

ake

ore

be

alue

large

large

d

krtol

This real variable specifies the tolerance for the iterative linear (Kryl

solves during the Newton process. Reasonable values are

(Default: ).

kriter

This integer parameter specifies the maximum number of iterations du

the iterative linear solve before it gives up and just takes the Newton

anyway. A value of 30-50 is reasonable (Default: 40).

gmrestart

This integer parameter is the number of iterations that GMRES will t

before “restarting.” In theory, the higher this number is, the faster and m

robust the linear solve will be. However, an additional vector has to

stored for each GMRES iteration, so its value cannot be too large. A v

of 10 tends to work well (Default: 10).

pkthresh

This real parameter is used to reduce Jacobian memory storage for

problems. Spectral components of less than (pkthresh * DC_value) are

dropped (Default: 0.0).

gmrthresh

This real parameters is used to reduce GMRES memory storage for

problems. GMRES vector entries of less thangmrthresh are dropped

(Default: 0.0).

krloosetol

This real parameter is used jointly with an integer parameterkrlooseiter

to be described next. Ifkrlooseiter GMRES iterations are completed an

1 3–×10

1 4–×10 1 4–×10


Users Manual

.

ter

e

f this

d and

e. In

tion

the GMRES error is belowkrloosetol , then the GMRES iterations are

considered adequate for proceeding with a Newton step (Default: 0.1)

krlooseiter

This integer parameter is used jointly with above real parame

krloosetol . If krlooseiter GMRES iterations are completed and th

GMRES error is belowkrloosetol , then the GMRES iterations are

considered adequate for proceeding with a Newton step (Default: 30).

krconvratio

When the ratio between two successive GMRES reaches the value o

real parameter, GMRES assumes progress toward a solution is stalle

therefore aborts (Default: 1.0).

EXAMPLE

hbmeth krtol=5e-4 kiter=35 ^useredpc

To specify the parameters used in harmonic balance simulation mod

this case, the maximum number of iterations in solving the linear equa

system using Krylov iterative method is 35 (kiter ). The tolerance for

convergence in Krylov iteration is set to (krtol ). And no “reduced”

pre-conditioner is used (^useredpc ).

5 4–×10


Users Manual

the

. It

tage

f the

for

o

th a

le for

fault:

file

at

COMMAND LOG

The following new parameters in this card allow for the storage of

circuit solution which is independent of the device solution.

SYNTAX

log cktfile=<filename> [column.out | spice.out | key.out]

NEW PARAMETERS

cktfile

This parameter specifies the output file name for the circuit solution

contains the voltage at each circuit node, the current through all vol

sources and inductors, and the current flowing into each electrode o

numerical device including any scaling factors. The default format

saved data iscolumn.out (Default: null character string, meaning n

circuit solution will be saved).

column.out

This logic flag forces the output data to be organized column-wise wi

heading describing the data in each column. This data format is suitab

post-processing by many general plotting tools and spreadsheets (De

True).

spice.out

This logic flag forces the data to be saved in a Berkeley SPICE-like raw

format. For those with access to Berkeley’s plotting tools, this form


Users Manual

an

n

s.

mn

in

the

ult:

provides an easily accessible tool to analyze the circuit solution.spice.out

is only available foropckt , acckt , dcckt , or trckt (Default: False).

key.out

This logic flag forces the output data into two files. The first file has

extension of.dat added to thecktfile name and the second has a

extension of.key. The.dat file contains the simulation results in column

The .key contains a mapping of the solution variables to the colu

number in the.dat . This output format allows the user to plot the data

many general plotting tools by excluding the heading information in

data file which can cause problems with some plotting tools (Defa

False).

EXAMPLE

log cktfile=mydata.dat column.out

Save circuit solution in filemydata.dat with column-wise format.

log cktfile=mydata.raw spice.out

Save circuit solution in filemydata.raw with Spice raw file format.

log cktfile=mydata key.out

Save circuit solution in filesmydata.dat and mydata.key as

explained in above parameter description forkey.out .


Users Manual

COMMAND METHOD

The new parameters on themethod card allows for specification of the

new numerical capabilities in PISCES.

SYNTAX

method [New Parameters]

NEW PARAMETERS

EXAMPLES


Users Manual

ical

COMMAND MODEL

Themodel card has additions to specify one of the quantum mechan

model and the parameters that are associated with each.

SYNTAX

model [dort [] [] [] ] [hansch [] [] [] ]

NEW PARAMETERS

EXAMPLES


Users Manual

f

d to

ion.

onic

the

COMMAND SOLVE

Many parameters are added to thesolve card in order to take advantage o

the new capabilities in PISCES. A new set of parameters are provide

invoke the circuit boundary condition and the harmonic balance solut

In addition, solution input/output parameters are provided for the harm

balance results.

SYNTAX

solve [opckt || acckt || dcckt || trckt || acdcckt || hbckt]

+ [hboutfile=<filename> [savestep=<integer>]]

+ [hbinfile=<filename>]

PARAMETERS

opckt

Solves for the operating point on the circuit. (Default: False)

acckt

Solves the small signal ac circuit. This parameter requires a.ac card in the

circuit file.(Default: False)

dcckt

Solves the DC circuit for the values of the swept source(s) specified on

.dc card in the circuit file.(Default: False)


Users Manual

ard

ator.

fied

tion

ing

file

en a

ution

n is

trckt

Solves for the transient response of the circuit. This card requires a.tran

card in the circuit file. In addition thetranckt may be used in lieu of

trckt .(Default: False)

acdcckt

Solve the small signal ac circuit while sweeping DC source(s). This c

requires a.dc and.ac card in the circuit file. In additiondcacckt may be

used in lieu ofacdcckt . (Default: False)

hbckt

Solves the large signal ac circuit using the harmonic balance simul

This card requires the HB simulator module and the.hb analysis card in

the circuit file. A sweeping of the DC and/or AC source can be speci

with the.hbac and/or the.hbdc card in the circuit file. (Default: False)

hboutfile

The basis for the name of the file to store the solution at a given simula

point. To this name an extension of “.sol” is added for the data forΨ, n, and

p. An extension of “.trm” is added to the name for the data file contain

the terminal characteristics. A “.nds” extension is added for the data

containing the circuit node solutions.

savestep

During a sweep of a source in a harmonic balance simulation,savestep is

used to specify how often the harmonic balance solution is saved giv

file basis specified byhboutfile . At each integer multiple of the given

value, the last letter of the output file name is incremented and the sol

is saved to that file. A value of 0 means only the last completed solutio

saved. (Default: 0)


Users Manual

ance

fied

hbinfile

Use the given file name as the starting point for the next harmonic bal

simulation. This file contains the “.sol” extension and it must be speci

when the file name is given.

NEW EXAMPLE

solve acckt

solve hbckt hboutfile=hbsolnA hbsavestep=15


Users Manual

and

COMMAND TRAP

This new card is used in the specification of the traps inside the device

at interfaces. It has a similar format to that of theprofile card.

SYNTAX

trap [Parameters]

NEW PARAMETERS

EXAMPLES


Users Manual

circuit

ndard

ctrode

.

circuit

oked

ce

ps up

ramps

for the

t

ndary

. It

tion is

as

ecified in

value

5.3 The Circuit File

A separate circuit file is needed to specify the linear circuit surrounding the PISCES device. The

file contains a SPICE-like net list to describe the connections of the external circuitry. The sta

SPICE linear elements are provided along with a special element for specifying the ele

connections for the linear devices. The standard analysis capabilities are provided with the.op , .dc ,

.ac, and.tran cards. In addition there are specialty dot cards for the harmonic balance analysis

Thecontact card in PISCES contains a parameter which is used to specify the file name for the

file. Even if a circuit file is specified for boundary conditions, the boundary conditions are not inv

unless one of the circuit solves is specified on thesolve card. Therefore, the recommended sequen

of cards in PISCES is as follows:

solve init outfile=soln.initsolve v1=1.0 vstep=1.0 nstep=4 num=1solve v2=0.25 vstep=0.25 nstep=5 num=2solve v1=5.0 v2=1.5 outfile=soln.dcinitsolve opckt outfile=soln.opsolve trckt

In this sequence, an initial solution is computed and saved in the file soln.init. The next card ram

the voltage on electrode number one which could be a drain or collector. The third solve card

up the voltage on electrode two which could be a gate or base. The fourth card solves

approximate operating point and stores that solution. The fifthsolve card accesses the circui

boundary conditions and solves for the operating point solution with the inclusion of circuit bou

conditions. The finalsolve card specifies a transient simulation with circuit boundary conditions

could just as easily specify an ac, dc, or harmonic balance circuit analysis. When the simula

restarted or fails, one can now use theload card to restart from any location at which is solution h

been saved.

The next set of pages provides description of the elements and analyses cards that can be sp

the circuit file. At the end of the chapter some limitation on node numbers and information on

specifications is outlined for the user.


Users Manual

is

COMMAND COMMENT LINES

Any line with an* in the first column is considered a comment and

ignored during parsing.

* This is a comment


Users Manual

ard.

The

fined

COMMAND NUMERICAL DEVICE

Nxxxxxxxx N1 . . . Ni

The PISCES device is specified by the numerical device element c

xxxxxxxx uniquely identifies the device andN1 through Ni are the

numerical nodes to which the device is connected in the circuit.

number of node connections must equal the number of electrodes de

in the PISCES deck otherwise the simulation will abort.

Nldmos 14 3 0


Users Manual

or

h

t

d are

COMMAND STANDARD ELEMENTS

Rxxxxxxxx N1 N2 val

Lxxxxxxxx N1 N2 val

Cxxxxxxxx N1 N2 val

The the R, L, andC identifies the element as either a resistor, inductor,

capacitor respectively.N1 andN2 are the numeric node numbers to whic

the element is connected. Theval variable represents the value of tha

element. The standard MKS units can be used to specify values an

described later in this document.

Rfeeback 23 81 1e3

Lpackage 87 63 93n

Cintercon 9 38 2.33p


Users Manual

ork

.

, C,

ngth,

each

the

nly

ffect

COMMAND TRANSMISSION LINE

Txxxxxxxx N1 N2 GND R L C G Len Nsections

This element specifies a two port (common ground) distributed T-Netw

transmission line as shown in the figure.N1 andN2 are the numeric node

numbers at each end of the line andGND is the common ground contact

The distributed nature of the line is created by T-sections where R, L

and G specify the resistance per unit length, the inductance per unit le

the capacitance per unit length, and the admittance per unit length.Len is

the total length of the line in unit lengths andNsections is the number of

T-sections used to simulate the line. Hence, the inductance of

T-section is given byl = L*Len /(2*Nsections ), the resistance is given

by r = R*Len /(2*Nsections ), the capacitance is given byc = C*Len /

Nsections , and the admittance is given byg = G*Len /Nsections . Note

that the circuit portion of any simulation is very small compared to

device simulation. Hence, a relatively large number of sections not o

improves the transmission line model, but also does not realistically a

the device simulation.

Tmatch 8 10 0 0 28n 100p 0 1 200

Tmatch 7 9 0 0 14n 50p 0 2 200

Tinput 2 3 0 1u 82n 54p 3n 5 100

rl

c g

r l

Figure 5.1 One T-section of a transmission line defined with N sections.


Users Manual

ear

the

e

ain

ear

the

ols

ely.

COMMAND DEPENDENT SOURCES

Gxxxxxxxx N+ N- n+ n- val

Exxxxxxxx N+ N- n+ n- val

G andE specify a linear voltage controlled current source and a lin

voltage controlled voltage source.N+ and N- specify the positive and

negative nodes of the source. Current flows from the positive node to

negative node.n+ and n- specify the voltage nodes which control th

sources.val is the transconductance (in mhos) or the voltage g

respectively.

Fxxxxxxxx N+ N- Vname val

Hxxxxxxxx N+ N- Vname val

F and H specify a linear current controlled current source and a lin

current controlled voltage source.N+ and N- specify the positive and

negative nodes of the device. Current flows from the positive node to

negative node.Vname specifies the voltage source whose current contr

the devices.val is the current gain or transresistance (in ohms) respectiv

Gcond 0 12 20 0 1m

Egain 10 0 20 0 50

Fgain 0 40 32 33 12

Ftran 23 0 52 42 1k


Users Manual

rce

is

ode

for

ource

r

DC

ces.

the

COMMAND INDEPENDENT SOURCES

Vxxxxxxxx N+ N- <source description>

Ixxxxxxxx N+ N- <source description>

V and I specify an independent voltage source and current sou

respectively.N+ andN- are the numerical nodes to which the source

connected. Current flows from the positive node to the negative n

through the source.

The source descriptions are as follows. A voltage source is used

reference, but all descriptors can be used with a current source.

DC Sources

Vname 1 0 [dc] [value]

Thedc specifies the source as a DC source and the value is the given s

value. Neitherdc norvalue need to be specified. If onlyvalue is specified

then the source is assumed to be a DC source of that value. If neithedc

norvalue or if onlydc is specified then the source is assumed to be of

value zero.

Vgate 5 0 dc 2.3 Vcc 1 0 5.0

AC Sources

Vname 1 0 [dc] [DCvalue] ac [ACvalue]

Theac specifies this source as being AC and is required on all AC sour

ACvalue specifies the amplitude of the ac small signal generated by


Users Manual

lies a

ribed

here

e of

source. If no value is given,ACvalue is assumed to be 1.0. An optionaldc

specification may be place on the source to indicate that it also supp

DC bias.

Vperturb 5 0 dc 2.3 ac 0.1

Vinput 9 0 ac 0.6

TRANSIENT SOURCES

Vname 1 0 <transient source type>

Transient sources can take on a number of different function as desc

by the following functions.

Piece-wise Linear (pwl)

Vname 1 0 pwl t0 v0 t1 v1 t2 v2 t3 v3 . . .

Piece-wise linear sources are described by a discontinuous function w

each (time, voltage) point is connected by a linear change in the valu

the source. The points in the function are given as:

if t0 != 0 then the voltage at t=0 is set equal to the voltage at t = t0.

Vinput 10 0 pwl 0 0.0 1n 0.0 2n 0.5 10n 2.0 20n 2.0 21n 0.0

Time Value

t0 v0

t1 v1

t2 v2

... ...


Users Manual

ier

ear

Periodic Square Pulse (pulse)

Vname 1 0 pulse v1 v2 td tr tf pw per

A pulse is simply a piece-wise linear function specified in an eas

manner to define a periodic function. The variables are defined as:

and the function takes on the following values as a piece-wise lin

function:

Vname 1 0 pulse -0.5 0.5 10n 1n 1n 50n 100n

Variable Description

v1 initial value

v2 pulsed value

td time delay

tr rise time

tf fall time

pw pulse width

per period

Time Value

0.0 v1

td v1

td+tr v2

td+tr+pw v2

td+tr+pw+tf v1

per+td v1

per+td+tr v2

... ...


Users Manual

the

onic

Sinusoidal Function (sin)

Vname 1 0 sin Vo Va freq td theta

This source takes on the following sinusoidal functional values within

time ranges specified. Note that this does not define a source for harm

balance, but rather defines a source for transient analysis.

where:

Vname 1 0 sin 3.3 0.5 50Meg 0.0 0.0


Vo DC offset value

Va sinusoid amplitude

freq frequency in HZ

td delay time

theta damping factor

0 t td< < Vo

td t< Vo Va e t td–( )theta–( ) 2π freq t td+( )( )sin+


Users Manual

nal

Exponential Pulse (exp)

Vname 1 0 exp v1 v2 td1 tau1 td2 tau2

The exponential source takes on the following exponential functio

values within the time ranges specified.

where:

Vname 1 0 exp -1.5 0.75 3n 25n 50n 10


v1 initial value

v2 pulsed value

td1 rise delay time

tau1 rise time constant

td2 fall delay time

tau2 fall time constant

0 t td1< < V1

td1 t td2< < V1 V2 V1–( ) 1 et td1–( )–tau1

-----------------------–

–

+

td1 t td2< < V1 V2 V1–( ) 1 et td1–( )tau1

--------------------–

–

V1 V2–( ) 1 et td2–( )tau2

--------------------–

–

+ +


Users Manual

nal

ource

t a

s and

ysis.

Single Frequency FM (sffm)

Vname 1 0 sffm vo va fc mdi fs

The sffm source takes on the following single frequency FM functio

value over all time:

where:

Vname 1 0 sffm 0.0 1m 108Meg 5 40k

Harmonic Balance Source

Vname 1 0 hb Vo Vmag freq theta

Harmonic balance source are used to define the large signal ac s

applied to the circuit during harmonic balance analysis. Note tha

sinusoidal transient source is ignored during harmonic balance analysi

likewise, a harmonic balance source is ignored during transient anal


Vo DC offset voltage

Va amplitude

fc carrier frequency

mdi modulation index

fs signal frequency

Vo Va 2π fc t mdi 2π fs t( )sin+( )sin+


Users Manual

ype.

ies:

All ac sources in the HB simulation must be specified with this source t

The parameters are defined as follows:

Hence the source takes on the following values for the given frequenc

Vname 1 0 hb 0.0 0.5 1.2G -90


Vo DC offset voltage

Vmag amplitude of sinusoid

freq frequency of sinusoid

theta phase of sinusoid (deg.)

Frequency Value

DC Vo

freq

0.0

Vm theta( )cos jVm theta( )sin+

n freq×


Users Manual

rcuit

ed in

o

but

e of

or no

.

the

ally

e of

uring

es the

COMMAND OPTIONS CARD

The.options card is used to set numerical parameters related to the ci

simulation.

SYNTAX

.options [gmin=value] [rmin=value] [area=value] [ltertol=value]

[ltevtol=value] [lteitol=value] [ltelim=value]

PARAMETER

gmin

Thegmin parameter specifies the smallest value for a conductance us

the circuit simulation. Agmin conductor is placed from every node t

ground. This additional large resistance adds a leakage current,

guarantees that the matrix is not singular. Note that too small a valu

gmin may cause ill- conditioning. For most applications,gmin could be

set to zero and hence, have no affect. However, if there are very few

passive components in the circuit,gmin has to be larger than zero

(Default: 1.0e-12 mhos).

rmin

Thermin parameter is used to specify a small resistance for places in

circuit where a small short-circuit is required. This resistance is typic

used for an inductor connecting a voltage source solely to an electrod

the PISCES device. Inductors are replaced with a zero volts source d

DC analysis and hence, a zero resistance in this situation can caus


Users Manual

t the

st

ld be

r is a

For

ugh

ation

s for

user

the

r by

ith

he

If the

dt is

rror

he

matrices to go singular. Likegmin , the effect ofrmin is minimal. Only a

small voltage is typically lost across the resistor and it guarantees tha

matrix is not singular. Thermin parameter can be set to zero for mo

cases, but should a matrix inversion error occur, this parameter shou

set to some small inconsequential value. (Default: 1.0e-12 ohms)

area

PISCES solves a device in only two dimensions. The area paramete

scaling factor for all currents in order to provide a quasi-3d solution.

most applications, this parameter refers to the width of the device altho

symmetry (like in BJT’s) could meanarea is equal to twice the device

length or more.

ltertol, ltevtol, lteitol, ltelim

These four parameters are used in the calculations of the local trunc

error during transient analysis. For most applications, the default value

these parameters are sufficient, but a brief description is provided for a

who may want to adjust the time step controls of the circuit portion of

simulation. For a more detailed description, please refer to the pape

Bank, etc.

ltertol : The relative tolerance for calculating the errors associated w

each time step. (Default: 0.001)

ltevtol : The absolute error tolerance for voltages. (Default: 1mV)

lteitol : The absolute error tolerance for currents. (Default: 1pA)

ltelim : The limit on the value for the norm of the error tolerance. If t

norm is greater than this value, the time step is reduced and repeated.

norm is less than this value, the time step is accepted and the next

calculated. (Default: 1.0)

In order to increase the accuracy in the overall solution, the relative e

tolerance (ltertol ) can be decreased. Likewise, in order to relax t


Users Manual

he

,

sis.

ence,

accuracy,ltertol is increased. In order to affect only the voltage or t

current,ltevtol or lteitol should be adjusted in the same manner asltertol .

Finally, in order to tighten the time steps,ltelim can be reduced or likewise

to relax the time steps ltelim is increased.

All these parameters only affect the circuit portion of the transient analy

In most cases, the device simulation tends to limit the time steps, and h

these parameters should rarely be changed.

EXAMPLES

.options gmin=0.0 rmin=0.0 area=100


Users Manual

and

d to

cards

ces

e the

ep

e,

equal

COMMAND ANALYSIS CARDS

A set of analysis cards provides the user a way to specify the limits

conditions on the different types of analysis. Note that PISCES is use

select the desired analysis via the solve card; hence, multiple analyses

can exist in one file.

Operating Point Simulation

.op

Compute the operating point solution.

DC Sweep Simulation

.dc Sname1 start1 end1 step1 [Sname2 start2 end2 step2]

The .dc card allows for the sweeping of DC sources. Up to two sour

may be swept simultaneously where the second source is swept insid

first source. The.dc requires at least one source and set of swe

parameters to be specified. Thestart parameters refers to the start valu

the end parameter refers to the end value, and thestep refers to the

stepping value. The source is stepped until its value is greater than or

to its end value.

.dc Vin 0.0 0.5 0.05


Users Manual

are

The

ient

e

time

DF

. The

The

be

qual

t is

AC Simulation

.ac [dec || lin] numsteps startf endf

The.ac card specifies a small signal sweep in frequency. All ac sources

swept over the specified frequencies as determined by this card.

sweeping can be linear or logarithmic as specified by thelin or dec

parameter. Thelin parameter means thenumsteps are taken linearly from

startf to endf . The dec parameter means thatnumsteps are taken

logarithmically and there arenumsteps per decade.

.ac lin 10 1k 10k

.ac dec 5 100k 1G

Transient Simulation

.tran tstep tstop [tstart tmax]

The .tran card specifies the time range and time steps for a trans

analysis. Thetstep parameter specifies the initial time step. If th

backward Euler method is selected on the PISCES method card, this

step is used throughout the entire PISCES/circuit simulation. If the B

method is selected on the PISCES method card, thentstep is the initial

time step and time step estimation is used to select all future values

tstop parameter specifies the time at which the simulation stops.

tstart parameter specifies the point in time from which the solution is to

saved. If this parameter is not given, the solution is saved from time e

to zero. Thetmax parameter is the maximum time step to be taken. If i


Users Manual

time.

lance

The

. The

s if

f

t.

not given, the maximum is calculated based upon the value of the stop

This ratio is set at compilation and has a default value of 0.1.

.tran 0.1n 25n

.tran 0.1n 25n 0.0 5n

Harmonic Balance Simulation

.hb f1 order [f2] [f3] [f4] . . .

.hbdc Sname start end step [Sname start end step] . . .

.hbac Sname start end step [Sname start end step] . . .

.hbfr Sname start end step fnum [Sname start end step] . . .

.hbss nstep a|d|f Sname start end {fnum} [a|d|f Sname . . .

These analysis cards are used to specify various types of harmonic ba

analysis. The.hb card is required and describes the Fourier expansion.

f1 parameter specifies the first fundamental frequency and is required

subsequentf# parameters specify the higher fundamental frequencie

inter-modulation distortion analysis is to be performed. Theorder

parameter is the number of harmonics used in the Fourier expansion.

The .hbdc , .hbac , .hbfr , and .hbss card specifies any sweeping o

sources. The.hbdc causes the HB sourceSname to have its DC bias

swept from thestart value to theend value instep steps. The sources

listed later on the card are swept inside the sources listed first.

The.hbac causes the HB sourceSname to have its large signal AC value

swept in magnitude fromstart value toend value instep steps. The

sources listed later on the card are swept inside the sources listed firs

The .hbfr card causes the HB sourceSname to have it frequency value

swept fromstart value to end value in step steps. In addition, the

fundament frequency numberfnum is adjusted to this value as well.


Users Manual

that

only

uch

z

tion

en

The .hbss allows for simultaneous sweeps of multiple sources such

the specified value is adjusted for each and every source. Therefore,

one value is specified for the number of steps,nstep . Each sourceSname

has either its ac magnitude, DC value, or frequency value (a | d | f) swept

from start value toend value with the samenstep steps. If frequency is

swept, then the fundamental value is adjusted as given byfnum .

Multiple cards may be contained in the same simulation. For s

situations, the sources on.hbss are swept inside the source on.hbfr which

are swept inside the sources on the.hbac card, which are swept inside the

sources on the.hbdc card.

.hb 1.2G 8

.hbac Vin 0.25 4.0 0.25

Sweep sourceVin from 0.25 to 4.0 by 0.25. Do a HB simulation at 1.2 GH

with 8 harmonics.

.hb 849.5Meg 5 850.5Meg

.hbss 16 Vin1 a 0.25 4.0 Vin2 a 0.25 4.0

Sweep the magnitude of the ac voltage ofVin1 andVin2 from 0.25 to 4.0

volts in 16 steps. Hence, during each stepVin1 andVin2 take on the same

value. This sweep description is designed to do inter-modulation distor

analysis by setting the frequency ofVin1 to 849.5MHz and that ofVin2 to

850.5MHz. The.hb card specifies a 5th order expansion at the two giv

frequencies.


Users Manual

alpha-

.3e-5,

5.4 NODE NUMBERS

The node numbers in the net list must be unique positive integers. Negative numbers and

numeric characters will cause an error.

5.5 SCALING FACTORS

The values in the net list may be specified in decimal notation (1.2), exponential notation (4

10e4) or using a scaling factor (1k). The scaling factors are defined as follows:

Unit Symbol Scaling

tera t 1012

giga g 109

mega meg 106

kilo k 103

centi c 10-2

milli m 10-3

micro u 10-6

nano n 10-9

pico p 10-12

femto f 10-15

atto a 10-18


CHAPTER 6Examples

e first

efficient

ted by

GaAs

ing a

takes

circuits

e first

he photo

ds are

6.1 Description

This chapter provides many examples of using the new features provided in PISCES2H-B. Th

section is devoted to examples that exercise the improved numerics and demonstrates more

convergence. In the following section, some applications for the new models are demonstra

showing the effect of quantum mechanics on MOS CV characteristics and the effect of traps in a

diode. The third section focuses on simulations with external boundary conditions by show

variety of different analysis methods. The final section gives a number of examples that

advantage of the harmonic balance module to find large signal responses of some common RF

including a demodulator, mixer, and power amplifier.

6.2 Examples Exercising the Improved Numerics

There are two examples that demonstrate the improvement in the numerics in PISCES. Th

example addresses the effect of newton projection on the convergence of a non-planar avalanc

diode. The second example involves a high frequency simulation of a _____. The new metho

capable of finding a solution whereas the old methods tended to struggle.


Examples

antum

ucture.

nation,

two of

6.2.1 Convergence in a Non-Planar Avalanche Photo Diode

6.2.2 High Frequency Analysis

6.3 Applications for the New Physical Models

Examples are provided for the three new models in PISCES. The first examples invoke the qu

mechanical models which are used to calculate the modified CV characteristics of a MOS str

The third example demonstrates the affect of dynamic traps in a GaAs diode.

6.3.1 C-V Characteristics Using van Dort QM Model

6.3.2 AC Analysis of MOSFET Using Hansch QM Model

6.3.3 Traps in a GaAs Diode

6.4 Circuit Boundary Conditions

6.4.1 Diode with External Circuit Components and DistributedContact Resistance

PISCES boundary conditions include distributed contact resistances, limited surface recombi

external resistances/capacitances, and linear circuit boundary conditions. This example uses


Examples

n order

rodes. In

circuit

owing

6.2b

d

d high

nitude

e

these boundary conditions simultaneously, contact resistance and circuit boundary condition, i

to the plot the IV characteristics of a diode with external resistances.

A diode has external resistors on each electrode and a feedback resistor between the two elect

addition, electrode two has a distributed contact resistance as shown in Figure 6.1 Next to the

diagram, the IV characteristics are given for the configuration. Note the large leakage current fl

through the feedback resistance.

The input deck for PISCES and circuit description is provided in Figure 6.2a and Figure

respectively. The distributed contact resistance is specified on the firstcontact card and the circuit

boundary conditions are invoked by specifying ackfile on the secondcontact card. The circuit

description is given in the circuit file nameddiode.ckt. The solution for the circuit simulation is store

in diode.raw and is in a format that can be read by Berkely’s version of SPICE3.

Figure 6.3 contain plots of the current flow lines when the distributed contact resistance is low an

relative to the N- region, respectively. Notice that the current flow change based upon the mag

of the distributed resistance.

R1 = 1k

Rf = 100k R2 = 2k

P N+

Rcontact

Vin

Figure 6.1 (a) Circuit diagram for diode with extrinsic bulk resistance and distributedcontact resistance. (b) The IV response of the structure shows a large leakagcurrent generated by the feed back resistance.

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

-5 -4 -3 -2 -1 0 1 2Vin (Volts)

Iin (

mA

)

(a) (b)


Examples

k

title diode with contact resistance and circuit BC’s

$ create meshmesh rect nx=70 ny=11

x.mesh n=1 l=0x.mesh n=70 l=10y.mesh n=1 l=0y.mesh n=11 l=0.2

region num=1 ix.lo=1 ix.hi=70 iy.lo=1 iy.hi=11 silicon

$ electrodeselectr num=1 ix.lo=1 ix.hi=1 iy.lo=1 iy.hi=11electr num=2 ix.lo=50 ix.hi=70 iy.lo=1 iy.hi=1

$ uniform doping for simplicitydoping p.type conc=1e15 uniformdoping n.type conc=2e19 uniform x.left=4

$ place distribute resistance on contact #2contact num=2 con.res=1e-3’

$ specify circuit filecontact cktfile=diode.ckt

$ set modelsmodel consrh conmob fldmob bgn

$ do initial solutionsymb carr=2 newtonmethod trapsolve init

$ ramp up voltage on diodesolve v1=0 vstep=-1.0 nstep=5 elect=1

$ set circuit logfile in Berkeley spice3f4 formatlog cktfile=diode.raw spice.out

$ do dc sweepsolve dcckt

* test for multiple boundary conditions

* initial start value for sourcevin 1 0 -5

* completely surround device with resistancesr1 1 3 1krf 3 4 100kr2 4 0 2k

* device specificationnd 3 4

* analysis specification.dc vin -5 2 0.25

* circuit options.options area=100 rmin=0 gmin=0

Figure 6.2 (a) PISCES input deck for DC sweep of diode surrounded by resistive networwith a distributed contact resistance. (b) Net list describing circuit diagram.

(a) (b)


Examples

at are

6.4.2 Transient Response of a BJT Inverter

Transient analysis allows for automatic time stepping to minimize the number of time steps th

required. To demonstrate this capability, a simple BJT inverter is switch from itson state to itsoff state

and back to itson state. A circuit diagram and the transient response is provided in Figure 6.4.

Figure 6.3 Current flow lines for a diode with (a) a low contact resistance and (b) with alarge contact resistance.

(a) (b)

Vcc

VinRin = 10k

Rcc = 5k

Rf = 100kVout

Rl=50k

Figure 6.4 Circuit diagram of simplified BJT inverter and the response of that invertergiven a pulse input.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 2 4 6 8 10

Vou

t (V

olts

)

Time (ns)

(a) (b)


Examples

hm is

time

t of the

ints in

The PISCES input deck and the circuit file are shown in Figure 6.5. The time stepping algorit

selected in the PISCES deck on themethod card with the2nd andtauto parameter set to true to

invoke the TR-BDF method describe by Bank. The circuit portion of the code calculates its own

step independent of PISCES. PISCES then decides which time should be taken: its own or tha

circuit where typically the smaller of the two is selected. In addition, PISCES handles break po

the input response by forcing a time point at that specific location.

$ transient analysis of bjt inverter

$ load mesh filemesh infile=bjt.msh

$ set-up circuit informationcontact cktfile=inv.ckt

$ set models for BJT invertermodel srh auger bgn conmob fldmob

$ do symbolic factorization and$ set numerical methodssymb newton carrier=2method itlimit=20 biaspart 2nd tauto

$ initial device solutionsolve init

$ ramp up voltage on drainsolve v1=0 vstep=1 nstep=5 elect=1

$ solution logfilelog cktfile=inv.raw spice.out

$ do transient analysis of circuitsolve tranckt

* Circuit description for a BJT inverter

* apply transient piece-wise linear function at* input of the invertervin 4 0 pwl 0 0 0.2n 0 0.4n 5 5n 5 5.2n 0 1 0vcc 1 0 dc 5.0

* surrounding circuitryrcc 1 2 5krbb 4 3 10kr31 2 3 100k

* load of next stagerl 2 0 50k

* BJT devicenq1 2 3 0

* set device size.options area=1

* transient analysis initial step and stop time.tran 0.1n 10n

Figure 6.5 (a) PISCES input deck for transient simulation of bjt inverter. (b) Net listdescribing circuit diagram.

(a) (b)


Examples

tions.

is dual

anges

e base

meter

6.4.3 Gain vs. Bias Condition for a BJT Amplifier

In this example, an BJT amplifier is analyzed for its small signal gain for various bias condi

Hence, the simulation requires both a DC sweep and an ac small signal perturbation. Th

simulation capability allows a user to analyze how the small signal performance of a device ch

with variations in the bias condition.

Figure 6.6 shows the circuit diagram for the BJT amplifier and the small signal gain versus th

bias. Vin(DC) is swept from 0.5V to 1.0V in tightly space voltage steps while Vin(ac) is applied at a

relatively low frequency in order to negate high frequency effects.

The PISCES input deck and the circuit file is given in Figure 6.7. In the PISCES deck, the para

to specify a joint ac/DC analysis isacdcckt on thesolve card. In the circuit file, the circuit

configuration is described in a SPICE-like format and a.ac card and a.dc card specifies the limits on

Vcc

Vin(DC)

Vin(ac) Rin = 50k

Rcc= 75k

Rf = 10M

Vout

05

101520253035404550

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

Vin(DC) (Volts)V

out(a

c)/V

in(a

c) (

Vol

ts)

Figure 6.6 (a) Circuit diagram for BJT amplifier with (b) the small signal response fordifference bias conditions on the gate.

(b)(a)


Examples

When

ncy.

ser does

quency

pability

lifier.

of

the two analysis. The.ac card specifies the same start and end frequency with only a single step.

this is encountered on the.ac card, the small signal simulation is performed only at that one freque

Single frequency ac analysis is used because it is the only one desired for this example. The u

have the option to do multiple frequency simulations in an ac/DC simulation.

6.5 Harmonic Balance Analysis

Harmonic balance analysis provides a technique to do large signal sinusoidal analysis in the fre

domain rather that the time domain. The next three example demonstrate the power of this ca

by solving for the large signal response of a AM demodulator, a BJT mixer, and MOS power amp

All three involve some simple circuitry in order to obtain the desired response.

$ find bias for maximum gain in amplifier

$ load mesh generated by bjt.pismesh infile=bjt.msh

$ load circuit BC’scontact cktfil=amp.ckt

$ set modelsmodel srh auger bgn conmob fldmob

$ do init solutionsymb newton carrier=2method itlimit=20 trapsolve initsolve v1=0.0 vstep=1.0 nstep=5 elect=1

$ solve for small signal at multiple DC biaseslog cktfile=amp.logsolve acdcckt

* test for analysis of inverter

* initial biasesvin 12 0 dc 0.5 ac 1.0vcc 11 0 dc 5.0

* bias circuitryrin 12 2 50krcc 11 1 75krf 1 2 10Meg

* numerical devicenq1 1 2 0

* set circuit options.options area=200 rmin=1e-12 gmin=1e-12

* DC and ac sweep.dc vin 0.5 1.0 0.005.ac lin 1 1 1

Figure 6.7 (a) PISCES input deck for determining small signal gain versus bias conditionBJT amplifier. . (b) Net list for circuit and analysis limits.

(a) (b)


Examples

l on a

litude

ths out

t signal

rder to

of this

ge 37),

single

erate

6.5.1 Large Signal Analysis of AM Demodulator

A simple AM demodulator, consisting of a diode, resistor, and capacitor, is fed a 5kHz signa

15MHz carrier as shown in the circuit diagram in Figure 6.8a. The diode rectifies the amp

modulated input voltage F(t). The output capacitor and resistor, acting as a low pass filter, smoo

the resultant signal. The output, less the DC offset, is shown in Figure 6.8b. Note that the outpu

is not a pure sine wave and some improvements are needed in the circuit and device in o

optimize the results.

The PISCES input deck and the circuit file are shown in Figure 6.9. The interesting aspect

simulation is how the input signal is represented. In describing harmonic balance sources (pa

only a single frequency is specified; hence, the expression for must be reduced to

sinusoids. This reduction is easily accomplished using trigometric identities in order to gen

Equation 6.1.

(6.1)

whereωc is the carrier frequency andωs is the signal frequency.

Vbias

Vin(t)

Cfilter Rload

Vout

Vin t( ) 112--- 2π 5x103( )t( )sin+

2π 5x106( )t( )sin=

Figure 6.8 Circuit diagram of AM demodulator. An 5KHz signal on a 5MHz carrier is fedinto the demodulator.

-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.5

-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5Time (ms)

Vou

t (V

olts

)

(a) (b)

F t( )

F t( ) ωct( )sin 0.25 ωc ωs–( )t( )cos ωc ωs+( )t( )cos–( )+=


Examples

equency

comes

arrier

cy are

Another issue of concern is convergence. Harmonic balance convergence is based upon the fr

of the simulation and the amount of power or amplitude in the input signals. When either be

large, convergence may become difficult. In order to facilitate improved convergence, the c

frequency is ramped up from 0.0V to the 1.0V desired in the simulation by including the.hbac card

in the circuit net list. The solutions for the intermediate steps in ramping the carrier frequen

include in the output file, but those results are easily dismissed during analysis.

$ PISCES simulation deck for am demodulator

$ load mesh generated by diode.pismesh in=diode.msh

$ tell PISCES about circuit descriptioncontact cktfile=am.ckt

$ do symbolic factorizationsymb newton carr=2

$ set numerical methods for PISCES and HBmethod biasparthbmeth gmrestart=10 maxiter=40

$ set simulation modelsmodels temp=300 srh auger conmob fldmob

$ do initial solution and operating point solutionsolve initsolve v1=0.0 vstep=0.2 nstep=3 elect=1solve opckt

$ set circuit solution file and do HB$ analysis to find demodulated signallog column.out cktfile=am.logsolve hbckt

* a simple AM demodulator

* 15MHz carrier plus 5kHz signalVcar 1 0 hb 0.65 0.0 15Meg 0Vsigm 2 1 hb 0.0 0.25 14.995Meg 90Vsigp 3 2 hb 0.0 -0.25 15.005Meg 90

* rectifierNdiode 3 4

* load resistance and filtering capacitanceCfilter 4 0 0.013urload 4 0 5k

* frequencies of interest.hb 15Meg 5 5k

* ramp up ac carrier signal magnitude for* improved convergence.hbac Vcar 0.0 1.0 0.1

* circuit options.options gmin=0 rmin=0 area=100

Figure 6.9 (a) PISCES input deck for analyzing AM demodulator. (b) Net list describingcircuit diagram and analysis limits.

(a) (b)


Examples

ard as

l, and

ilters

in the

ed by

nt to

g the

rmonic

6.5.2 BJT Mixer to Down Covert a 2Mhz Signal to 100KHz

This example consists of a simple single BJT mixer using an HP25 transistor from Hewlett Pack

shown in Figure 6.10. The input to the circuit is driven by a 2.1MHz LO and a 2.0MHz RF signa

mixes the signal down to 100kHz. A tuned resonant RLC circuit with a high Q in the collector f

out mixing products other than 100 kHz. The noise in the output, also shown in Figure 6.10, is

micro-voltage range thus providing a very clear output signal. This distortion can be reduc

increasing the Q of the resonator and reducing the RF power level.

The PISCES input file and circuit file are shown in Figure 6.11 In this example, it is very importa

ramp up the DC bias on the mixer. This biasing is done in the PISCES file by first increasin

voltage on the collector and then the voltage on the base. Upon obtaining the DC bias the ha

balance simulation can then be executed with better convergence behavior.

Vout

Vlo

Vs

R = 15kHzC = 66.667nFL = 37.995mH

Vcc

-10

-5

0

5

10

15

20

25

-10 -5 0 5 10

Noi

se (µ

V)

Time (µs)

Figure 6.10 (a) BJT Mixer that down converts a 200MHz to a 100kHz signal. (b) The noisein the 100kHZ output signal.

(a) (b)


Examples

rovide

MOS

rasitics

ifier is

m the

t by an

6.5.3 Analyzing Gain and Efficiency in a MOS Power Amplifier

The modeling of an RF device coupled with parastics, matching network, and bias network can p

insight into the performance of a discrete power amplifier. Figure 6.12 shows the intrinsic LD

device with parastics at the chip level due to the pad and interconnect. In addition to the pa

shown, there are additional parasitics for the packaging. The input and output of the ampl

connected through matching networks that are tuned for the individual device and isolated fro

DC bias by a capacitor. A biasing network sets the operating point and is isolated from the inpu

title HP25 w/ 3-emitter, 2-base, 1-collector

$ load mesh for structure

$ set finite recombination on emittercontact num=3 surf.rec vsurfn=1e5 vsurfp=1e5contact cktfil=hp25mix.ckt

$ do symbolic factorization, set numerical meth-ods and modelssymbol carrier=2 newtonmethod itlim=50 p.tol=1e-7 c.tol=1e-7models temp=300 bgn srh auger conmob fldmob

$ initial solvesolve init

$ sweep v1 (collector) up to 10 voltssolve v1=1 nstep=9 elect=1 vstep=1

$ sweep V2 (base) up to 0.7 voltssolve v2=0.1 nstep=5 elect=2 vstep=0.1

$ specify output file and do HB analysislog cktfile=hp25mix.log column.outsolve hbckt

* Single-device BJT mixer based on the HP-25* Q = 100, LO v=0.15

* bias voltagesVcc 4 0 10.0Vlo 1 0 hb 0.7 0.15 2.1Meg 0

* input signalVs 2 1 hb 0.0 0.01 2.0Meg 0

* resonant RLC circuitL1 4 3 37.995e-6C1 4 3 66.667e-9R1 4 3 15k

* HP25 bjtMbyte 3 2 0

* harmonic balance limits.hb 2.1Meg 6 0.1Meg

* circuit issues.options gmin=1e-12 area=5 rmin=1e-12

Figure 6.11 (a) PISCES input deck for analyzing BJT Mixer. (b) Net list describing circuitdiagram and analysis limits.

(a) (b)


Examples

r to the

raded

device

rce and

- LDD

akdown

higher

t

ll P

he gain

t

d

inductance.A PISCES deck and net list for the device and circuit is created in a similar manne

previous examples and thus not provided here.

The physics of the device plays an important role in its performance. A laterally diffused g

channel enhances RF performance, prevents punch-through, and increases the

transconductance. A p+ sinker (represented by a side contact electrode) connects the sou

substrate together to eliminate extra bond wires and provide for a back side contact. An n

decreases the electric field at the drain side of the device and optimizes Rds(on), BVdss, and Cdg. A

metal field plate reduces the electric fields at the edge of the gate thereby increasing the bre

voltage and reducing Cdg.

The response of interest is the gain and efficiency as shown in Figure 6.13. The gain rolls off at

power levels (Pin > 30 dbm) because the device operates in gm compression region and the outpu

power is limited by the saturation current. The power added efficiency (PAE) is low for a smaout

because the device drains more power in Class A operation. Efficiency increases until just after t

starts to decrease. At this point, Pin approaches Pout resulting in very little power added to the inpu

signal.

Drain

Gate

Backside Source

P+ Sinker

N+P- Channel

P- Epi

N- Ldd

N+

P+ Enhance

P+ Substrate

Cgs(E)

Cds(E)

Cdg(E)

Rsource

Rgate

Cds(P)

Rds(P)

Cgs(P)

Rgs(P)

P = Due to PadE = Due to Electrode/Interconnect

Figure 6.12 Cross section of an LDMOS transistor with parasitics represented as lumpeelements


Examples

device

hen it

uency

.9dbm,

ts full

omain

e

In addition to examining a calculated result of the simulation, one can analyze the state of the

at various levels in the simulation. For example, the device performance begins to degrade w

enters gm compression. Figure 6.14 shows the voltage on the drain in the time domain and freq

domain as the device enters this region. The three power levels correspond to a output of 19

28.5dbm, and 33.5 dbm. At the low power level the voltage on the drain is able to swing to i

limits. As the power increases, the voltage becomes limited on how low it can swing. The time d

0

15

30

45

60

75

16 18 20 22 24 26 28 30 32 340

5

10

15

20

25

ExperimentalSimulated

Efficiency

Gain

Pout (dbm)

PA

E (%

)Gai

n (d

bm)

Figure 6.13 Gain and power added efficiency for LDMOS power amplifier.

02468

101214161820

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

Vdr

ain

(V)

Time (ns)

0

1

2

3

4

5

6

7

8

ωo 2*ωo 3*ωo 4*ωo 5*ωoFrequency

| Vdr

ain|

(V

)

Figure 6.14 (a) Time domain voltage and (b) spectrum of the voltage on the drain of thLDMOS transistor in a power amplifier as the device enters gm compression.

(a) (b)


Examples

signal

at the

ysical

s the

ximum

plot and the frequency plot reflect that change by two different mechanisms. The time domain

flattens out when it swings low. The spectrum reflects this effect with the addition of harmonics

higher frequencies.

This example clearly shows the power of the harmonic balance device simulation. The ph

characteristics of an advance technology impact simulation significantly. Hence, this tool allow

design engineer to analyze and optimize a robust devices in order to achieve the ma

performance.


Examples


References

ing at

telli.2.

Ac-

nsac-

sient985.

is ofSI-

OSisco,

nol-A:

References

[1] Troyanovsky, Boris.Frequency Domain Algorithms for Simulating Large Signal DistortionSemiconductor Devices. Dissertation Submitted to the Department of Electrical EngineerinStanford University. November 1997.

[2] Johnson, B., T. Quarles, A. R. Newton, D.O Pederson, and A. Sangiovanni- VincenSPICE3 Version 3f User's Manual. Berkeley: Regents of the University of California, 199

[3] McCalla, William J. Fundamentals of Computer-Aided Circuit Simulation. Boston: Kluwer ademic Publishers, 1993.

[4] Laux, S. E. “Techniques for small-signal analysis of semiconductor devices.” IEEE Trations on Electronic Devices, Vol. ED-32, No. 10, pp. 22028-2037, 1985.

[5] Bank, R., W. M. Coughran, W. Fichtner, E. H. Grosse, D. J. Rose, and R. K. Smith, “Transimulation of silicon devices and circuits.” IEEE Transactions on Electron Devices, Oct. 1pp. 1992-2007.

[6] B. Troyanovsky, F. Rotella, Z. Yu, R. Dutton, and J. Sato-Iwanga. “Large Signal AnalysRF/Microwave Devices with Parasitics Using Harmonic Balance Device Simulation.” SAMI. Fukuoka, Japan: Nov. 1996.

[7] Gordon Ma, Wayne Burger, Chris Dragon, and Todd Gillenwater. “High Efficiency LDMPower FET for Low Voltage Wireless Communications.” Proceedings of IEDM. San FrancCA: December 1996.

[8] Alan Wood, Chris Dragon, and Wayne Burger. “High Performance Silicon LDMOS Techogy for 2GHz RF Power Amplifier Applications.” Proceeding of IEDM. San Francisco, CDecember 1996.


References


Documents

Supplemental Manual for PISCES2H-B - Stanford …fmr/research/docs/HBpisces.pdf · Supplemental Manual for PISCES2H-B Harmonic Balance Module, Circuit Boundary Conditions, and