1. Treinamento: Testes Paramétricos em Semicondutores Setembro 2012
Section 4 – Capacitance Measurement Basics
Cyro Hemsi
Engenheiro de Aplicação

2. Agenda Technology Area Where Capacitance Measurement is Used
Fundamental of Capacitance Measurement
Basic Techniques to Achieve Accurate Capacitance Measurement

3. Technology Area Where Capacitance Measurement is Used

4. What is Capacitance ?
Capacitance is amount of charge stored between the electrodes when applying a unit voltage.
Basic Equations
Electrode
W: Width
L: Length
e0: Permittivity of vacuum A
d: Distance
e: Relative permittivity
A: Area of electrode
Relation of Charge and Applied Voltage V
Dielectrics
Q: Total charge
Positive charge
V: Applied voltage
Negative charge
Most important equation to remember!!

5. Physical Dimensions of Semiconductor Devices
Thickness of dielectrics can be determined from the gate capacitance.
Source
Drain
Gate
Semiconductor
Substrate L W d
Cgb
Cgs
Cgd
Gate-Source Overwrap
MOS FET
Inter Connection
Gate
Dielectrics
Inter layer dielectrics d
Thickness of interlayer dielectrics can be determined from the capacitance between interconnecting wires.
Cgb: Gate to body capacitance
Cgd: Gate to drain capacitance
Cgs: Gate to source 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.
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.

6. Why Are MOSFET Capacitance Measurements Important?
SEQ.
Why Are MOSFET Capacitance Measurements Important?
Note that the value of the capacitance varies with applied DC voltage
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
Capacitance versus voltage measurement +
Physical device parameters
(area, work function, etc.)
Key Device Parameters
Mathematical Calculations

7. Doping Profile of Semiconductor Devices
Distribution of boundary defect density by comparing CV curve measured by high frequency(>1 kHz) and low frequency (<10 Hz) CV measurement.
Thickness of gate dielectrics can be extracted from Cmax.
N-MOS Cap
Space Charge
(depletion) Layer
p-Si Cg Cd
Gate Dielectrics Ld V
Low Frequency
High Frequency
Doping profile can be extracted from the Cmax and Cmin.
Ld: Depth of depletion layer
q: Charge of electron
Na: Density of acceptor
Vth V
Threshold voltage can be extracted from the intersection point of Cmin and extrapolation of CV curve.
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.

8. Capacitance Measurements for Solar Cell
Equivalent circuit model is determined by frequency sweep of impedance to optimize extra circuit to convert DC power generated by solar cell to AC Power. -
N-type Rs Rp
Frequency C
Junction Leakage
Space Charge Layer
P-type
Junction Capacitor +
Residual Resistance
Photo current
Schematic of Solar Cell
Impedance Spectroscopy
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.
AC Level (mVpp)
Mott-Schottky Plot
Drive-level Capacitance Profiling (DLCP)

9. Mobility Measurement of Organic Semiconductor Materials
T. Okachi et al. / Thin Solid Films 517 (2008) 1331–1334
Organic Material 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.
Cgeo: Geographical capacitance
tt: Carrier transit time
m: Mobility of carrier
Improvement of mobility of organic material is most critical to put it to practical use.

10. Electrical Field by Applied Bias
Characterization of Electrostatic Capacitive MEMS (Micro Electro Mechanical System) Sensor
Also, displacement of diaphragm is caused by the applied external bias voltage.
Electrostatic capacitive MEMS sensor detects displacement of diaphragm by mechanical stimulations like acceleration, pressure or sonic wave as a modulation of electrostatic capacitance.
Bias Voltage or Displacement
Capacitance C0
Mechanical Stimulus
Diaphragm Spring
Fixed Electrode
Electrical Field by Applied Bias
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.

11. Importance of On-Wafer Capacitance Measurement
On-wafer measurement becomes standard to develop various devices.
Probe
Wafer Chuck
Wafer
Semi-auto prober
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.
To carry out accurate capacitance measurement, specific attention is necessary.

12. Fundamental of Capacitance Measurement

13. Basic Equations Related to Capacitance Measurement
Equation to Measure Capacitance
Derivation
Stimulus
Capacitance is calculated from the measured charge and amplitude of applied step voltage.
Step Voltage
Capacitance is calculated from the measured current and ramp rate of applied ramp voltage.
Ramp Voltage
Capacitance is calculated from the measured impedance and frequency of applied AC signal.
AC Voltage
Most widely-used method by capacitance meter

14. Function of Each Terminal of Capacitance Meter
Agilent 4284A
Keep “0V” in AC manner by active feedback.
So called “Virtual Ground”, not actual ground.
Auto Balancing Bridge I
voltage of the test signal applied to DUT
HCUR
HPOT
LPOT
LCUR
DUT
current that flows through DUT V
0 V A V I
LCUR
LPOT
HPOT
HCUR
Connect terminals based on its functionalities is important to measure capacitance correctly.
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

15. Equivalent Circuit Model and Equations to Extract Capacitance
Appropriate Parameter
Parallel Model
Complex Vector
Equations
Admittance Plane Im Cp Rp
Cp-Rp
Cp-G
Cp-D
Cp-Q Re Y
G: Conductance
D: Dissipation factor
Q: Quality factor
Appropriate Parameter
Series Model
Complex Vector
Equations
Impedance Plane Im Re Cs
Cs-Rs
Cs-D
Cs-Q Rs Z
Choosing appropriate measurement parameter is essential to extract capacitance correctly.

16. How Do Capacitance Meters Work?
Auto-Balancing Bridge Method
Virtual ground V2 Rs
I1 = I2 R2 Hc Lc
DUT Hp I2 I1 Lp
virtual ground of the Op Amp V1
Auto Balancing Bridge Method
The auto balancing bridge can be conceptualized as an Op Amp circuit. Ohm's law applies: V=I*R . The device is stimulated by an AC signal, with the actual voltage applied to the device being monitored at the H (high) terminal. The L (low) terminal is driven to 0 volts by the virtual ground of the Op Amp. The current, I2, through the range resistor is equal to the current through the DUT. Therefore, the output voltage is proportional to the current through the device. Voltages and current are automatically balanced, thus giving rise to its name. To cover a wide frequency range, a null-detector and a modulator are used instead of an amplifier in practical circuits.
Hc; Signal Source
Hp: Potential Meter
Lc: Current meter
Lp: Potential Meter to Lock the phase of measurement signal.
Impedance is calculated by Z = V1*R2/V2.
Z = =
V2 = I2 x R2 I2 V1 V2
V1R2
Impedance is calculated by Z = V1*R2/V2.

17. Four Terminal Pair (4TP) Measurement Method
Measurement Circuit
4TP:
Minimize residual impedance V ～ ～ Lc Lp Hp A Hc
Measurement Path
Shields:
Minimize stray capacitance
Current flow:
Minimize inductive coupling
Connection with DUT
Auto Balancing Bridge Method using 4TP Cabling
The most commonly used cabling method is the four terminal pair, or “4TP” method.
Any time you add cables to a measurement setup you inevitably create additional sources for measurement error. There are three main sources of error:
Residual impedance in the cables
Stray capacitance between cables or to ground
Mutual inductance caused by the current flow between adjacent cables
Any of these factors can act to reduce the impedance measurement range. To mitigate these factors we need to do the following:
Eliminate the effects of the residual impedance by using a 4-cable or Kelvin style connection.
Shield the cables to eliminate stray capacitance
Eliminate the mutual inductance effect by allowing an induced current to flow through the outer conductor in opposition to the applied current flowing through the center conductor
The 4TP method achieves these goals.
DUT
Virtual ground

18. B1500A Capacitance Measurement Coverage
EasyEXPERT 4.x
QSCV
HFCV
Ultra-HFCV
B1500A
(SMU)
B1500A
(MFCMU)
4294A
1 kHz
5 MHz
110 MHz
Using EasyEXPERT and the B1500A, you can create CV-IV solutions from 1 kHz to 5 MHZ using standard DC probes (4TP connection). You can also make quasi-static CV (QSCV) measurements using the SMUs.
Agilent can supply positioner-based CV-IV switching solutions that do not degrade the measurement performance of the analyzer. Positioner-based switching solutions with measurement resolution of 0.5 mV and 10 fA, 1 fA, or 0.1 fA are available. Of course, Agilent also offers three different switching matrices for more advanced needs (B2200A, B2201A, and E5250A). Using the B2200A and B2201A switching matrices in conjunction with the B2220A interface and an approved low-leakage probe card, you can achieve current measurement resolutions of 1 fA (B2200A) and 10 fA (B2201A) all the way to the probe tips.
In addition, Agilent will soon be able to supply EasyEXPERT application tests to control the 4294A as well. This makes using the 4294A much easier to use and reduces the learning curve. Note that for frequencies above 5 MHz, you cannot use switching matrices. Direct connections using RF probes with ground-signal (GS) or ground-signal-ground (GSG) configurations are required.
Standard (>25 A) dielectrics
Thin-gate (<25 A) dielectrics

19. Basic Techniques to Achieve Accurate Capacitance Measurement

20. 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.

21. Measurement Parameter
Error Caused by Using Inappropriate Selection of Equivalent Circuit Model
Actual Device
Measurement Parameter
Measured Value Cp Rp
Cp-Rp
Error caused by measurement parameter mismatch
Cs-Rs Cs
Cp-Rp
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. Rs
Cs-Rs
Inappropriate selection of measurement parameter increases measurement error.

22. Measurement Parameter Selection for Actual Device
Parameter to select
Conditions
MOS-FET
Source
Gate
Drain Cp Rp
Cp-Rp
Cp-G
Cp-D
Cp-Q
Gate Resistance
AND
Gate
Contact resistance of via
Sub Cs Rs
Gate Leakage
Junction Resistance
Cs-Rs
Cs-D
Cs-Q
AND Cp Rp
Relatively thick dielectrics of technology node over 90 nm will satisfy either of above. Rs
For more shrunk process, parameter extraction using multi-frequency is necessary.
Actual Equivalent Circuit

23. Error Caused by Cablings
Residual Inductance
LCR Meter
Residual Resistance
Device to Measure
Output terminals of LCR Meter
Calibration Plane
Parasitic Capacitance
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.
Influence of residual inductance Increases along with a square of frequency
Total impedance measured by LCR Meter
Lres
Rres
Cpar
Cdev
Higher frequency results in larger measurement error
Additional Error
Not related to the measurement frequency

24. Minimizing Error from Cablings
Eliminate parasitic capacitance of cable extension by using coaxial cable and connect shield to the shield of the test leads.
Connect shield of cable extensions at end of cable each other to minimize residual inductance.
Connect shield of test leads each other to terminate four terminal pair.
LCR Meter
LCR Meter
Test Leads
Cable Extension
Probe
HCUR
HPOT V
LPOT
LCUR
LPOT
HPOT
HCUR
Output Terminals
LCUR A
Make unshielded part as short as possible to minimize residual inductance and
Extends output to the device to measure near as possible by using the test leads of LCR meter
Test Leads for LCR Meter
Measurement Current
Current return to HCUR

25. END Of section 4