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

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

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Technology Area Where Capacitance Measurement is Used 3

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

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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 SourceDrain Gate Semiconductor Substrate L W d Cgb Cgs Cgd Gate-Source Overwrap MOS FET Inter Connection Cgb: Gate to body capacitance Cgd: Gate to drain capacitance Cgs: 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. 5

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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 Page 6 SEQ.

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Doping Profile of Semiconductor Devices N-MOS Cap Space Charge (depletion) Layer p-Si Cg Cd Gate Dielectrics Ld V 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 layer q: Charge of electron Na: Density of acceptor Doping profile can be extracted from the Cmax and Cmin. Ld: Depth of depletion layer q: Charge of electron Na: Density of acceptor Thickness of gate dielectrics can be extracted from Cmax. 7

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Space Charge Layer N-type P-type Residual Resistance + - Photo current Junction Capacitor Junction Leakage RsRp Frequency Rp Rs C AC Level (mVpp) Schematic of Solar CellImpedance Spectroscopy Drive-level Capacitance Profiling (DLCP)Mott-Schottky Plot 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. Carrier density distribution over the depletion width is obtained from the slope of 1/Cp 2 to Voltage plot (Mott-Schottky plot ) Defect density distribution is obtained from the Cp to AC voltage amplitude of capacitance measurement plot. 8

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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 t t : Carrier transit time : Mobility of carrier d Vdc Mobility of carrier is obtained from the maximum frequency of negative differential susceptanceΔB= {C1( )Cgeo}. : angular velocity of measurement signal. Mobility of carrier is obtained from the maximum frequency of negative differential susceptanceΔB= {C1( )Cgeo}. : angular velocity of measurement signal. Improvement of mobility of organic material is most critical to put it to practical use. 9

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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 C0C0 0 Mechanical Stimulus 10

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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. 11

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Fundamental of Capacitance Measurement 12

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Basic Equations Related to Capacitance Measurement Step Voltage Ramp Voltage AC Voltage Equation to Measure Capacitance StimulusDerivation Basic 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. 13

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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 LCURLPOTHPOTHCUR A V LCUR LPOT HPOT HCUR 0 V V I I Auto Balancing Bridge Connect terminals based on its functionalities is important to measure capacitance correctly. 14 Keep 0V in AC manner by active feedback. So called Virtual Ground, not actual ground. 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-Rp Cp-G Cp-D Cp-Q Series Model Cs-Rs Cs-D Cs-Q CpRp Cs Rs Re Admittance Plane Im Re Appropriate Parameter Complex Vector Equations Parallel Model Appropriate Parameter Complex Vector Equations Impedance Plane G: Conductance D: Dissipation factor Q: Quality factor Im Choosing appropriate measurement parameter is essential to extract capacitance correctly. Z Y 15

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How Do Capacitance Meters Work? Virtual ground Z = = V 2 = I 2 x R 2 I2I2 V1V1 V2V2 V1R2V1R2 V2V2 Hc R2R2 Hp Lp Lc Rs DUT V1V1 I2I2 I 1 = I 2 I1I1 Auto-Balancing Bridge Method Page 16 virtual ground of the Op Amp Impedance is calculated by Z = V 1 *R 2 /V 2.

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Four Terminal Pair (4TP) Measurement Method Hc Measurement Circuit Measurement Path Connection with DUT V DUT LcLp Hp Virtual ground A 4TP: Minimize residual impedance Shields: Minimize stray capacitance Current flow: Minimize inductive coupling Page 17

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B1500A Capacitance Measurement Coverage 5 MHz110 MHz1 kHz QSCV B1500A (MFCMU) 4294AB1500A (SMU) HFCVUltra-HFCV EasyEXPERT 4.x Thin-gate (<25 A) dielectrics Standard (>25 A) dielectrics Page 18

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Basic Techniques to Achieve Accurate Capacitance Measurement 19

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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. 20

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Error Caused by Using Inappropriate Selection of Equivalent Circuit Model Actual Device CpRp Cs Rs Measurement Parameter Cp-Rp Cs-Rs Cp-Rp Cs-Rs Measured Value 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. 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. 21

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Measurement Parameter Selection for Actual Device Gat e Sub SourceDrainGate Cp Rp Rs Actual Equivalent Circuit Gate Resistance Gate LeakageJunction Resistance Contact resistance of via Conditions Parameter to select AND Cp Rp Cp-Rp Cp-G Cp-D Cp-Q AND Cs Rs Cs-Rs Cs-D Cs-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 22

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Error Caused by Cablings Cdev Cpar Rres Lres Total impedance measured by LCR Meter LCR Meter Output terminals of LCR Meter Calibration Plane Device to Measure Residual Inductance Residual Resistance Parasitic Capacitance 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 23

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HCUR HPOT LPOT LCUR Minimizing Error from Cablings LCURLPOT 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. Probe Cable Extension Measurement Current Current return to HCUR 24

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END Of section 4

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