1

Treinamento:Testes Paramétricos em

Semicondutores

Setembro 2012

Cyro HemsiEngenheiro de Aplicação

Section 4 – Capacitance Measurement Basics

2

Agenda

• Technology Area Where Capacitance Measurement is Used

• Fundamental of Capacitance Measurement

• Basic Techniques to Achieve Accurate Capacitance Measurement

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Technology Area Where Capacitance Measurement is Used

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What is Capacitance ?

Capacitance is amount of charge stored between the electrodes when applying a unit voltage.

L: LengthW: Width

d: Distance

V

Electrode

Dielectrics

Positive charge

Negative charge

Basic Equations

A e: Relative permittivityA: Area of electrode

e0: Permittivity of vacuum

d

W

d

AC 00 L

CVQ

Q: Total charge V: Applied voltage

Relation of Charge and Applied Voltage

Most important equation to remember!!

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Physical Dimensions of Semiconductor Devices

• Each capacitance represents actual physical dimensions and it is really important information to adjust conditions of manufacturing processes like lithography, etching, deposition time etc.

• Also, those parasitic capacitances are important to determine the gate delay of electric circuit in the logic devices.

Gate Dielectrics

Source Drain

Gate

SemiconductorSubstrate

L

W

dCgb

Cgs

Cgd

Gate-Source Overwrap

Gate-Source Overwrap

MOS FET Inter Connection

Cgb: Gate to body capacitanceCgd: Gate to drain capacitanceCgs: Gate to source capacitance

Inter layer dielectrics

d

Thickness of interlayer dielectrics can be determined from the capacitance between interconnecting wires.

Thickness of dielectrics can be determined from the gate capacitance.

Overwrap width between the gate electrode and drain or source area can be determined from the gate to drain or gate to source capacitances.

Why Are MOSFET Capacitance Measurements Important?

Capacitance versus voltage measurement

+Physical device parameters (area, work function, etc.)

Mathematical Calculations

•Gate oxide capacitance•Gate oxide thickness•Substrate impurity

concentration•Fermi potential•Flat band capacitance•Flat band voltage•Surface charge density•Fixed depletion layer

charge•Threshold voltage

Key Device Parameters

Note that the value of the capacitance varies with applied DC voltage

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SEQ.

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Doping Profile of Semiconductor Devices

N-MOS Cap

Space Charge (depletion)

Layer

p-Si

Cg

Cd

Gate DielectricsLd

V

CdCgCgCd

minc

CgCmax

V

High Frequency

Low Frequency

Vth

• CV characteristics of MOS-CAP (MOS-FET) is one of most important measurement item because it reveals various parameters related to the manufacturing process and device operation.

Threshold voltage can be extracted from the intersection point of Cmin and extrapolation of CV curve.

Distribution of boundary defect density by comparing CV curve measured by high frequency(>1 kHz) and low frequency (<10 Hz) CV measurement.

Doping profile can be extracted from the Cmax and Cmin.

Ld: Depth of depletion layerq: Charge of electronNa: Density of acceptor

LdεAε

dsi0c qNa

ε2εd

si0L V

Thickness of gate dielectrics can be extracted from Cmax.

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Space Charge Layer

N-type

P-type

Residual Resistance

+

-

Photo current

Junction Capacitor

Junction Leakage

0.E+00

2.E+13

4.E+13

6.E+13

-5.0 -2.5 0.0 2.5 5.0

Voltage [V]

1/C

p2 [

F-2

]

157

158

159

160

161

162

163

0 200 400 600 800

Vpp [mV]

Cp

[nF

]

Re|Z|

Im|Z

|

Rs Rp

0

Frequency

RpRs

C

AC Level (mVpp)

Schematic of Solar Cell Impedance Spectroscopy

Drive-level Capacitance Profiling (DLCP)Mott-Schottky Plot

Capacitance Measurements for Solar CellEquivalent circuit model is determined by frequency sweep of impedance to optimize extra circuit to convert DC power generated by solar cell to AC Power.

Carrier density distribution over the depletion width is obtained from the slope of 1/Cp2 to Voltage plot (Mott-Schottky plot )

Defect density distribution is obtained from the Cp to AC voltage amplitude of capacitance measurement plot.

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Mobility Measurement of Organic Semiconductor Materials

Organic Material

Cgeo: Geographical capacitance

T. Okachi et al. / Thin Solid Films 517 (2008) 1331–1334

tt: Carrier transit timem: Mobility of carrier

2

3

4

Vdc

dtt

d

Vdc

Mobility of carrier is obtained from the maximum frequency of negative differential susceptance −ΔB=−w{C1(w)−Cgeo}.w: angular velocity of measurement signal.

Improvement of mobility of organic material is most critical to put it to practical use.

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Characterization of Electrostatic Capacitive MEMS (Micro Electro Mechanical System) Sensor

• Mechanical characteristics of MEMS sensor can be obtained from its capacitance to voltage characteristics.

• Electrical capacitance measurement is easier and faster than the measurement by a mechanical stimulus.

• Also frequency dependency of capacitance reveals mechanical response of the diaphragm spring.

Fixed Electrode

Diaphragm Spring

Electrostatic capacitive MEMS sensor detects displacement of diaphragm by mechanical stimulations like acceleration, pressure or sonic wave as a modulation of electrostatic capacitance.

Also, displacement of diaphragm is caused by the applied external bias voltage.

Electrical Field by Applied Bias Bias Voltage or

Displacement

Capacitance

C0

0

Mechanical Stimulus

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Importance of On-Wafer Capacitance Measurement

• Advantage of On-wafer Measurement– Quick evaluation and lower cost are possible because packaging is not necessary.

• Challenges– There are many possible course of error from the cablings, wafer chuck, probing etc.

Semi-auto prober

Wafer Chuck

Probe

Wafer

To carry out accurate capacitance measurement, specific attention is necessary.

On-wafer measurement becomes standard to develop various devices.

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Fundamental of Capacitance Measurement

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Basic Equations Related to Capacitance Measurement

CVQ

dtdV

CIdtdQ

CdVdQ

AtV

jωtjωCexpI

exp(jωt)V

AI

dtdV

IC

IV

Z

f2πω

0tΔV

0t0V

ΔVΔQ

C

Step Voltage

Ramp Voltage

AC Voltage

Z ω1

CIm

Equation to Measure Capacitance

StimulusDerivationBasic

Equation

Most widely-used method by capacitance meter

Capacitance is calculated from the measured charge and amplitude of applied step voltage.

Capacitance is calculated from the measured current and ramp rate of applied ramp voltage.

Capacitance is calculated from the measured impedance and frequency of applied AC signal.

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Function of Each Terminal of Capacitance Meter

Agilent 4284A

Advantages of Auto Balancing Bridge Method• High accuracy (0.05 % basic accuracy)• Wide frequency range (20 Hz to 100 MHz)• Various choices are available based on frequency range and functions. Agilent 4284A, 4285A, E4980A, E4981A, 4294A, B1500A

LCUR LPOT HPOT HCUR

AV

LCURLPOTHPOTHCUR

0 VV

I

I

I

VZ

Auto Balancing Bridge

Connect terminals based on its functionalities is important to measure capacitance correctly.

Keep “0V” in AC manner by active feedback.So called “Virtual Ground”, not actual ground.

voltage of the test signal applied to DUT

current that flows through DUT

DUT

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Equivalent Circuit Model and Equations to Extract Capacitance

Cp-RpCp-GCp-D Cp-Q

Series Model

Cs-RsCs-DCs-Q

Cp Rp

Cs

Rs

Cs1

Rs

Re

Rp

1

Admittance Plane

Cp

Im

Re

Appropriate Parameter

Complex Vector Equations

Parallel Model Appropriate Parameter

Complex Vector Equations

Impedance Plane

G: ConductanceD: Dissipation factorQ: Quality factor

CpjRpV

I

ZY

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Y

CpIm

YRpRe

1 RpG /1

CpRpY

YD

1

Im

Re DQ /1

Im

CsjRs

I

VZ

1

)Im(

1

ZCs

)Re(ZRs

Cs

Rs

Z

ZD

)Im(

)Re(

Choosing appropriate measurement parameter is essential to extract capacitance correctly.

Z

Y

How Do Capacitance Meters Work?

Virtual groundVirtual ground

Z =

=

V2 = I2 x R2

I2

V1

V2

V1R2

V2Hc R2

Hp Lp

Lc

Rs

DUT

V1

I2

I1 = I2

I1

Auto-Balancing Bridge Method

Page 16

virtual ground of the Op Amp

Impedance is calculated by Z = V1*R2/V2.

Four Terminal Pair (4TP) Measurement Method

Hc

Measurement Circuit

Measurement Circuit

Measurement Path

Measurement Path

Connection with DUT

Connection with DUT

V

DUT

Lc Lp Hp

～～

Virtual groundVirtual ground

A

4TP:Minimize residual impedance

Shields:Minimize stray capacitance

Current flow:Minimize inductive coupling

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B1500A Capacitance Measurement Coverage

5 MHz 110 MHz1 kHz

QSCVB1500A

(MFCMU)4294AB1500A

(SMU)

HFCV Ultra-HFCV

EasyEXPERT 4.x

Thin-gate (<25 A) dielectrics

Standard (>25 A) dielectrics

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Basic Techniques to Achieve Accurate Capacitance Measurement

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Possible Sources of Measurement Error

• Inappropriate selection of measurement parameter

– Capacitance is extracted based on the equation of the equivalent circuit model for selected measurement parameter.

– Mismatch of equation and equivalent circuit model causes measurement error.

– Selection of appropriate measurement parameter (equivalent circuit ) is important.

• Parasitic capacitance, residual resistance and inductance

– Cablings between the instruments and device affects measurement results.

– Minimizing influence of cablings are critical to achieve accurate measurement.

• Inappropriate execution of compensation

– Compensation is commonly used to remove the influence from the cablings.

– But inappropriate compensation has a devastating impact on measurement results.

– Compensation have to be done in correct manner!!

• Parasitic capacitance of wafer probing system.

– On-wafer measurement has a specific error caused by a parasitic of the wafer chuck not considered when measuring discrete components.

– Special care is required for on-wafer capacitance measurement.

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Error Caused by Using Inappropriate Selection of Equivalent Circuit Model

Actual Device

Cp Rp

Cs

Rs

Measurement Parameter

Cp-Rp

Cs-Rs

Cp-Rp

Cs-Rs

Measured Value

222

232

1 RsCs

RsCsCsCpm

CsCsm

CpCpm

22

1

CpRpCpCsm

Error caused by

measurement parameter mismatch

Inappropriate selection of measurement parameter increases measurement error.

Quick Tips:If measured capacitance value is stable when measurement frequency is changed, the selection of measurement parameter is appropriate, because error component has frequency dependency.

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Measurement Parameter Selection for Actual Device

Gate

Sub

Source DrainGate

Cp Rp

Rs

Actual Equivalent Circuit

Gate Resistance

Gate Leakage Junction Resistance

Contact resistance of via

Conditions Parameter to select

RpRs

CpRs

1

ANDCp Rp

Cp-Rp Cp-GCp-D Cp-Q

RsRp

AND

CpRp

1

Cs

Rs

Cs-Rs Cs-DCs-Q

Relatively thick dielectrics of technology node over 90 nm will satisfy either of above.

For more shrunk process, parameter extraction using multi-frequency is necessary.

MOS-FET

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Error Caused by Cablings

CdevCpar

RresLresTotal impedance measured by LCR Meter

LCR Meter

Output terminals of LCR Meter

Calibration Plane

Device to

Measure

Residual Inductance

Residual Resistance

Parasitic Capacitance

)(

1

CdevCparjLresjRresZm

Additional Error Not related to the measurement frequency

Influence of residual inductance Increases along with a square of frequency

Rres is Included in the Rs when using Cs-Rs mode. But in Cs-Rp mode, Rres is included in the error of measured capacitance.

Higher frequency results in larger measurement error

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HCUR

HPOT

LPOT

LCUR

Minimizing Error from Cablings

LCUR LPOT HPOT HCUR

LCR Meter

Test Leads for LCR Meter

Output Terminals A

V

LCR Meter

Extends output to the device to measure near as possible by using the test leads of LCR meter

Eliminate parasitic capacitance of cable extension by using coaxial cable and connect shield to the shield of the test leads.

Make unshielded part as short as possible to minimize residual inductance and

Connect shield of test leads each other to terminate four terminal pair.

Test Leads

Connect shield of cable extensions at end of cable each other to minimize residual inductance.

ProbeCable Extension

Measurement Current

Current return to HCUR

END Of section 4