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    On-Chip Spiral Inductors for

    RF Applications

    Juin J. Liou

    Electrical and Computer Engineering Dept.University of Central Florida, Orlando, FL, USA

    University ofCentral Florida

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    Research Activities

    Affiliation: Professor, Electrical and Computer Engineering Dept.

    Director, Solid State Electronics Lab and Device

    Characterization Lab, University of Central Florida

    Research Area: Semiconductor device modeling/simulation, RF device/IC

    design, and semiconductor manufacturing

    L

    is

    t ofRe

    ce

    nt Proje

    cts:

    1. Study and modeling of reliability of GaAs heterojunction bipolar transistors

    (Air Force, Alcatel Space)

    2. RF CMOS reliability modeling and simulation (Intersil Corp., Conexant

    Systems)

    3. Design and modeling of on-chip electrostatic discharge (ESD) protection

    structures (Semiconductor Research Corp., Intersil Corp., Intel Corp., NIST,TSMC)

    4. Parameter extraction of VBIC bipolar transistor model (Lucent Tech.)

    5. Statistical modeling of Si devices and ICs (Lucent Tech.)

    6. Design and modeling of junction field-effect transistors (Texas

    Instruments/SRC)

    7. Design and modeling of passive components for RF ICs

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    Outline

    Background

    Design and Modeling Concept Advanced Inductor Structures

    Advanced Inductor Modeling

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    In contrast with digital circuits which use mainlyactive devices, on-chip passive components arenecessary and imperative adjuncts to most RFelectronics. These components include inductors,capacitors, varactors, and resistors

    For example, the Nokia 6161 cellphone contains 15ICs with 232 capacitors, 149 resistors, and 24inductors

    Inductors in particular are critical components in

    low noise amplifiers, oscillators and other tunedcircuits

    The lack of an accurate and scalable model for on-chip spiral inductors presents a challenging

    problem for RF ICs designers

    Motivations

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    RF Low Noise Amplifier(LNA)

    Inductorsoccupy a large percentageofthechip

    areaandareoftenthe performanceandcost

    limitingelementsin RF ICs

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    Outline Background

    Design and Modeling Concept

    Advanced Inductor Structures

    Advanced Inductor Modeling

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    Typical Square Shaped Spiral Inductor

    builton Si Substrate

    On-chip spiral inductors are used when a relatively small inductance

    (i.e., several nH) is needed. Otherwise off-chip inductors are used

    Performance of the spiral inductor depends on the number of turns, line

    width, spacing, pattern shape, number of metal layers, oxide thickness

    and conductivity of substrate

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    Equivalent Circuitofa Lumped (Single-

    ) Model forSpiral Inductors

    Except for the series

    inductance, all

    components in the modelare parasitics of the

    inductor and need to be

    minimized

    This model is widely used,but it is not very accurate

    and not scalable

    SiC SiR

    oxC

    sL

    sR

    sC

    SiC SiR

    oxC

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    ComponentsofLumpedModel

    SiC SiR

    oxC

    sL

    sR

    sC

    SiC SiR

    oxC

    LS consists of the self

    inductance, positive

    mutual inductance, and

    negative mutual

    inductance

    CS is the capacitance

    between metal lines

    RS is the series resistanceof the metal line

    COX

    is the capacitance of

    oxide layer underneath the

    spiral

    RSi and CSi are the coupling

    resistance and capacitance

    associated with Si substrate

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    Quality Factorand Self-Resonant Frequency

    The quality factorQ is an extremely important figure of merit for theinductor at high frequencies. The most fundamental definition forQ is

    Basically, it describes how good an inductor can work as an energy-

    storage element. In the ideal case, inductance is pure energy-storage

    element (Q approaches infinity), while in reality, parasitic resistance and

    capacitance reduce Q. This is because the parasitic resistance consumesstored energy, and the parasitic capacitance reduces inductivity (the

    inductance can even become capacitive at high frequencies).

    Self-resonant frequencyfSR marks the point where the inductor turns to

    capacitive.

    !

    ederDissipatAveragePow

    edEnergyStorQ [

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    Quality Factor

    pR pC sC

    sR

    sL

    Equivalent circuit of the

    one terminal grounded

    inductor

    ? A

    ! psss

    pss

    sssp

    p

    s

    s CCLL

    CCR

    RRLR

    R

    R

    LQ 2

    2

    21

    1[

    [

    [

    2

    2

    22

    1

    ox

    poxSi

    Siox

    p

    R

    RR

    !

    [

    222

    22

    1

    1

    SiSiox

    SiSiSiox

    oxpRCC

    RCCCCC

    !

    [

    [

    torsonanceFacSelfossFactorSubstrateLR

    L

    s

    s Re![

    Note: RP and CP give rise to substrate eddy and displacement currents, respectively

    WhenRPapproaches infinity, the substrate loss factor approaches unity (ideal case)

    Q can be improved by making the silicon substrate either a short or an open

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    Physical MechanismsofSubstrate Loss

    Both the eddy and displacement currents contribute to the

    substrate loss and degrade the inductor RF performance

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    Effectof InductorQfactoron Circuit

    Performance

    ;! KR 2

    1Term

    nHLg 6!

    nH

    s 5.0!

    RFC

    2Term

    AQ1010

    Low Noise Amplifier

    0 1 2 3 4

    0.0

    0.5

    1.0

    1.5

    2.0

    2.5

    3.0

    3.5

    4.0

    4.5

    m2:

    Freq=2.4 GHz

    NF=2.057 dB

    F=5

    m1:

    Freq=2.4 GHz

    NF=0.898 dB

    F=25

    m1

    m2

    NoiseFigure(dB)

    Frequency (GHz)

    0 1 2 3 4

    2

    4

    6

    8

    10

    12

    14

    m2:

    Freq=2.4 GHz

    S21

    =10.487 dB

    F=5

    m1:

    Freq=2.4 GHz

    S21

    =12.001 dB

    F=25

    m1

    m2

    S21

    (dB)

    Frequency (GHz)

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    Effectof InductorQfactoron Circuit

    Performance

    Colpitts Oscillator

    Circuit

    AQ500 pFC 2002 !

    pC 401!

    ;! KR 10nHLc

    200!

    1 10 100 1000

    -170

    -160

    -150

    -140

    -130

    -120

    -110

    -100

    -90

    -80

    m2:

    Noise Frequency=100 KHz

    Phase Noise=-126.996 dBc

    Quality Factor=10

    m1:

    Noise Frequency=100 KHz

    Phase Noise=-140.841 dBc

    Quality Factor=30

    m2

    m1

    Phase

    Noise

    (dB

    c)

    Noise Frequency (KHz)

    Inductor is often the component

    limiting the cost and performance in

    RFICs!

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    ImprovedModel withMore Accurate

    Series Resistance

    1siC

    1siR

    1oxC

    2siC

    2siR

    2oxC

    dcLdcR

    2sR

    2sL

    1sR

    1sL

    1sM 2sM

    R increases with increasing frequency skin effect

    This model uses several frequency-independent components to

    describe frequency-dependent series resistance

    0 2 4 6 8 10

    0

    1

    2

    3

    4

    5

    6

    7

    8

    QualityFactor

    Frequency (GHz)

    Measured

    Conventional T Model

    One LoopTwo Loops

    0 2 4 6 8 10

    2

    4

    6

    8

    10

    R

    ;)

    Frequency (GHz)

    Measured

    Conventional TModel

    One Loop

    Two Loop

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    ImprovedModel with Additional R and

    C Components

    subC subR

    oxC

    subC subR

    oxC

    20

    L

    20

    R

    cC

    subC subR

    oxC

    cC

    sC

    20

    R

    20

    L

    21

    R 21

    R

    scR

    scR

    2m

    L2m

    L

    0.1 1 10

    0

    2

    4

    6

    8

    10

    12

    14

    16

    DifferentialQualityFactor

    Frequency (GHz)

    easurement (w=15 Qm,D=220Qm,N=4)

    Proposed odel

    Fixed RL mode l

    (extracted at f=4GHz)

    This model uses a double- frequency equivalent circuit to

    account for the frequency-dependent nature ofL and R

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    ImprovedModel with Additional

    Horizontally Coupled R and C

    0.1 1 10

    0

    1

    2

    3

    4

    5

    6

    7

    8

    9

    Quality

    a

    tor

    Frequen y GHz)

    SquareSpiral Indu tor

    R=60Qm, W=14.5Qm, S=2Qm

    Model w/o Rsub

    & Csub

    roposedModel

    Measurements:

    2.5 Turn

    6.5 Turn

    1siC

    1siR

    1oxC

    2siC

    2siR

    2oxC

    0sL0s

    R

    sC

    subR

    subC

    1sL

    1sR

    This model adds R and C to account for the horizontal coupling

    in Si substrate

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    Outline Background

    Design and Modeling Concept

    Advanced Inductor Structures

    Advanced Inductor Modeling

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    Structure with patterned ground shield

    0.1 1 10

    0

    1

    2

    3

    4

    5

    6

    7

    8

    Q

    Frequency (GHz)

    PGS

    SGS

    NGS (19;-cm)

    Ground shielding reduces the effective distance between the spiral and groundand thus reduces the substrate resistance. But solid ground shield (SGS) canreflect EM field in the substrate and reduce Q factor. Patterned ground shield canavoid this effect. Drawback of ground shielding is an increased coupling

    capacitance due to an reduced distance between the metal and ground.

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    Structure with Suspended Spiral

    Inductor suspended above the structure to reduce the

    substrate coupling resistance and capacitance

    0 2 4 6 8 10 12 14 16 18 20

    0

    2

    4

    6

    8

    10

    Conventional L

    Suspended L

    Conventional Q

    Suspended Q

    Frequency (GHz)

    Inductance

    (nH)

    0

    10

    20

    30

    40

    50

    QualityFactor

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    Structure with Substrate Removal

    Portions of substrate are moved using deep-trench

    technology to reduce the substrate coupling resistance and

    capacitance

    st1 Metal

    nd2 Metal

    BPSG

    ViaHole

    Si Pillar

    1 100

    2

    4

    6

    8

    10

    12

    14

    Q

    Fr y ( z)

    Induct rw/o Tr nch

    Inductorw/ Tr nch

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    Structure with Vertical Spiral

    Spiral is placed vertically on the substrate to reduce magnetic

    field coupling to substrate

    0 1 2 3 40

    2

    4

    6

    8

    10

    12

    14

    Quality

    Factor

    Fr uency ( z)

    Model-Before PDM

    Measured-Before PDM

    Model-AfterPDMA

    Measured-AfterPDMA

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    Structure with Multiple Metal Layers and

    Vertical Shunt

    The series resistance is reduced with increasing number of

    vertical shunt among the metal layers (case of M3 has no

    vertical shunt). But this approach can increase COX

    and thus

    reduce the self-resonant frequency.

    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

    12

    M2/M3/M4M3/M4M2/M3M3

    Resistance(;)

    Qmax

    -Factor

    Total metal Layer Thickness ( m)

    Qmax

    Rdc

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    Structure with Horizontal Shunt

    The metal line is split into multiple paths so that the effective

    series resistance is reduced and Q factor is increased

    0.1 1 10

    -2

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18

    20

    22

    QualityFactor

    Frequency (GHz)

    1 // Path

    2 // Path

    3 // Path

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    Structure with Tapered Line Width

    EM loss is most significant in center of spiral. The metal line

    width is tapered to reduce the magnetically induced losses in

    the inner turns

    0.1 1 10

    0

    10

    20

    30

    40

    50

    QualityFactor

    Frequency (GHz)

    Optimized (Inner Turns Tapered)

    W=40Qm

    W=25Qm

    W=10Qm

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    Structure with Stacked Metal Layers

    The stacked structure increases effective metal length, which

    increases the inductance without increasing the chip area

    0 2 4 6 8-0.2

    0.0

    0.2

    0.4

    0.6

    0.8

    1.0

    1.2

    QualityFactorInductance

    Frequency (GHz)

    Quality

    Factor

    -2

    0

    2

    4

    6

    8

    10

    12

    Inductance

    (n

    )

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    Structure with Non-Symmetrical and

    Symmetrical Winding

    The symmetrical winding improves the RF performance

    because 1) it has less overlap which reduces the series

    capacitance and 2) the geometric center is exactly the magnetic

    and electric center, which increases the mutual inductance

    a b

    1 Met l

    2 Met l

    Via

    OverLap

    OverLap

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    Structure with Non-Symmetrical and

    Symmetrical Winding

    0 2 4 6 8 10

    1.0

    1.5

    2.0

    2.5

    3.0

    3.5

    4.0

    4.5

    5.0

    5.5

    QualityFactor

    Fre uency( )

    Non- y etr ical Inductor

    Sy etr ical Inductor

    fS

    R

    (

    )

    Inductance(n )

    Non-Sy etr ical Inductor

    Sy etr ical Inductor

    Q factor of the symmetrical inductor is improved, but the self-

    resonant frequency is degraded due to an increased ac potential

    difference between neighboring turns in the symmetrical inductor

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    Dual-Layer Symmetrical Winding

    Q factor of the symmetrical inductor can be further increased

    using a dual-layer structure

    Port 2Port

    2Metal

    1Metal

    Via

    0.

    0.

    0.

    .0 1.

    1.

    1.

    1.

    .0 2.2 2.

    2.

    2.

    0.0

    0.5

    1.0

    1.5

    2.0

    2.5

    .0

    3.5

    .0

    4.5

    5.0

    Quali

    actor

    QBW

    )

    Fr

    uency

    !z)

    Single"

    #

    urns

    Dual"

    #

    urns

    Single 3#

    urns

    Dual 3#

    urns

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    Structure with Non-Square Pattern

    For hexagonal and octagonal inductors, less metal length is needed to achievethe same number of turns. Thus series resistance is compressed and Q factor

    improved. On the other hand, the square shaped inductor will be more area

    efficient. For example, for a square area on the wafer, square shape will utilize

    100% of the area, whereas hexagonal, octagonal and circular shapes use 65%,

    82.8% and 78.5% respectively

    0 1 2 3 4 5

    0

    1

    2

    3

    4

    5

    6

    7

    Qu

    $

    lit

    %F

    $

    &

    to

    '

    F( )

    qu)

    n0 1

    (2

    Hz)

    3

    qu4 ( )

    H)

    x4

    gon4

    l

    5

    0

    t4

    gon4

    l

    Ci( 0

    ul4 (

    Fixed

    inductanceof 5 nH

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    Structure with Non-Square Pattern

    0 2 4 6 8 10 12

    0

    1

    2

    3

    4

    5

    6

    L

    eff

    (nH)

    Frequency (GHz)

    Octagonal Inductor

    Square Inductor

    The square inductor possesses a higher peak inductance but a lower self-resonant frequency (i.e., frequency at which L is zero). This is because

    the longer metal line of square inductor induces a larger metal to substrate

    capacitance, which reduces the inductance at high frequencies. For low

    frequencies, the inductor depends mainly on the length of the spiral wire,

    and the square pattern possesses a larger inductance.

    Fixed outer

    diameter

    0 2 4 6 8 10 12

    0

    2

    4

    6

    8

    10

    12

    14

    16

    18

    QualityFactor

    Frequency (GHz)

    Octagonal Inductor

    Square Inductor