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Systemic Errors in the MOS Conductance Technique Supported by the II-VI Foundation Cooperative Research Initiative S. Swandono, D. T. Morisette, and J. A. Cooper School of Electrical and Computer Engineering and Birck Nanotechnology Center

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SLIDE 1

Systemic Errors in the MOS Conductance Technique

  • S. Swandono, D. T. Morisette, and J. A. Cooper

School of Electrical and Computer Engineering and Birck Nanotechnology Center Purdue University, West Lafayette, IN

Supported by the II-VI Foundation Cooperative Research Initiative

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SLIDE 2

Physics of the MOS Conductance Technique

COX CD GP(ω) CP(ω)

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SLIDE 3

COX CD GP(ω) CP(ω)

  • K. Lehovic, Appl. Phys. Lett., 8, 48 (1966).

Lehovic Distributed-State Model

(uniform distribution of states in energy) (interface state time constant)

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SLIDE 4

Non-Uniform Fixed Charge QF

  • E. H. Nicollian and A. Goetzberger,

Bell Syst. Tech. J., 46, 1055 (1967).

Neutral Region Depletion Layer SiO2 Gate Randomly Distributed Fixed Charges QF Electric Field Lines

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SLIDE 5

COX CD GP(ω) CP(ω)

  • E. H. Nicollian and A. Goetzberger,

Bell Syst. Tech. J., 46, 1055 (1967).

(normalized surface potential) (probability density function for the variation

  • f surface potential across the interface)

Nicollian & Goetzberger Model

(Distribution of states in energy) (sum over all “patches” under gate) (interface state time constant)

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SLIDE 6
  • W. Fahrner and A. Goetzberger,
  • Appl. Phys. Lett., 17, 16 (1970).

Interface State Capture Cross Section σN Surface Potential uS

Earliest Data on σN(E) in Silicon (1970)

Exponential decrease of σN toward the band edge.

?

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SLIDE 7

Measured Capture Cross Sections in 4H-SiC

σN(E) (cm2) EC - E (eV)

0.1 0.2 0.3 0.4 0.5 1e-20 1e-18 1e-16 1e-14

1 2 3

  • M. Das, Ph.D. Thesis,

Purdue Univ., Dec. 1999.

3 1 2

This Work

?

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SLIDE 8

Assumptions of the Nicollian–Goetzberger Model

  • 1. Analysis limited to biases in depletion (linear uS-VG relationship).

(This allows the Gaussian probability distribution for fixed charge to be translated into a Gaussian probability distribution of surface potential uS.)

  • 2. Interface-state parameters (DIT, σN) vary slowly with energy.

(DIT can be taken outside the integral over surface potential.)

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SLIDE 9

Procedure to Quantify Errors

  • 1. Use an exact calculation that eliminates assumptions made by

Nicollian & Goetzberger.

  • 2. Assume a Gaussian distribution of fixed charge P(QF),

and use the exact us-Vg relationship to calculate the probability distribution of surface potential P(uS).

  • 3. Choose specific values for DIT, σN, and σQ, and generate a

GP/ω vs. ω curve.

  • 4. Regard the GP/ω vs. ω curve as experimental data.
  • 5. Use the original Nicollian-Goetzberger model to extract the

apparent interface trap density DIT, standard deviation of surface potential σUS, and capture cross section σN.

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SLIDE 10

Assumptions of the Nicollian–Goetzberger Model

  • 1. Analysis limited to biases in depletion (linear uS-VG relationship).
  • 2. Interface-state parameters (DIT, σN) vary slowly with energy.
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SLIDE 11

The uS-VG Relationship

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10 20

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1 2 Surface Potential us VG-VFB (V)

EC-EF = 0.2 eV EC-EF = 0.5 eV EC-EF = 0.8 eV 4H-SiC TOX = 40 nm ND = 2e16 cm-3 Accumulation Depletion

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SLIDE 12

Effect of Non-Uniform Fixed Charge QF

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SLIDE 13
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10 20

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1 2 VG-VFB (V)

Gaussian QF TOX = 40 nm σQ = 2e11 cm-2

Surface Potential uS

Mapping P(QF) to P(us)at EC-EF = 0.8 eV

EC-EF =0.8 eV

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SLIDE 14
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10 20

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1 2

Surface Potential uS

VG-VFB (V)

Gaussian QF TOX = 40 nm σQ = 2e11 cm-2 EC-EF =0.5 eV

Mapping P(QF) to P(us)at EC-EF = 0.5 eV

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SLIDE 15
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10 20

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1 2

Surface Potential uS

VG-VFB (V)

Gaussian QF TOX = 40 nm σQ = 2e11 cm-2 EC-EF =0.2 eV

Mapping P(QF) to P(us)at EC-EF = 0.2 eV

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SLIDE 16

0.5 1 1.5 2 2.5 1.E-08 1.E-04 1.E+00 1.E+04 1.E+08 1.E+12 GP/ω (nF cm-2) ωτ

Effect of Bias Point (Fermi Level)

TOX = 40 nm DIT =8.48e10 eV-1 cm-2 σQ = 2e11 cm-2 EC-EF = 0.5 eV EC-EF = 0.8 eV EC-EF = 0.2 eV

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SLIDE 17

Effect of Oxide Thickness

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SLIDE 18
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10 20

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1 2

Surface Potential uS VG-VFB (V)

Gaussian QF σQ = 2e11 cm-2 EC-EF = 0.5 eV

Mapping P(QF) to P(us)at TOX = 10 nm

EC-EF = 0.5 eV

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SLIDE 19
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10 20

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1 2

Surface Potential uS VG-VFB (V)

19 Gaussian QF σQ = 2e11 cm-2 EC-EF = 0.5 eV EC-EF = 0.5 eV

Mapping P(QF) to P(us)at TOX = 40 nm

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SLIDE 20
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20

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1 2 3 4 5

Surface Potential uS VG-VFB (V)

Gaussian QF σQ = 2e11 cm-2 EC-EF = 0.5 eV EC-EF = 0.5 eV

Mapping P(QF) to P(us)at TOX = 150 nm

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SLIDE 21

Effect of Oxide Thickness

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.E-03 1.E+00 1.E+03 1.E+06 1.E+09 1.E+12

GP/ω (nF cm-2) ω (rad s-1)

150nm 40nm 10nm

σQ = 2e11 cm-2 DIT = 8.48e10 eV-1 cm-2 EC-EF = 0.5 eV

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SLIDE 22

Assumptions of the Nicollian–Goetzberger Model

  • 1. Analysis limited to biases in depletion (linear uS-VG relationship).
  • 2. Interface-state parameters (DIT, σN) vary slowly with energy.
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SLIDE 23

Measured DIT(E) in 4H-SiC

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SLIDE 24

Question: How much error is introduced by an exponentially increasing DIT? To find out, choose a bias point in the linear region

  • f the uS–VG relationship, (EF deep in the bandgap,

far from the CB). Here the only distortion is due to the exponential DIT.

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SLIDE 25

Choose a bias point with EF far from the CB

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10 20

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1 2 Surface Potential us VG-VFB (V)

EC-EF =1.3 eV 4H-SiC TOX = 40 nm ND = 2e16 cm-3 Accumulation Depletion

EC Ei

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SLIDE 26

1E+05 1E+06 1E+07 1E+08 1E+09 1E+10 1E+11 1E+12 1E+13 0.5 1 1.5 2 DIT ( cm-2 eV-1) EC - E (eV) α = 0 α = 0.2

EC-E = 1.3 eV DIT0 = 1.09e8 eV-1 cm-2

Exponential Model for DIT(E)

Uniform

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SLIDE 27

0.0E+0 2.0E-3 4.0E-3 6.0E-3 8.0E-3 1.0E-2 1.2E-2 1.E-16 1.E-12 1.E-08 1.E-04 1.E+00 1.E+04

GP/ω (nF cm-2)

ω (rad s-1)

Impact of Exponential DIT(E)

TOX = 40 nm EC-EF = 1.3 eV σQ = 2e11 cm-2

Exponential DIT Uniform DIT

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SLIDE 28

Combined Effects

  • Non-linear uS – VG relationship
  • Exponential DIT(E)
  • σN assumed constant (uniform with respect to energy)
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SLIDE 29

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1.E-03 1.E+00 1.E+03 1.E+06 1.E+09 1.E+12

GP/ω (nF cm-2)

ω (rad s-1)

σQ = 2e11 cm-2 α = 0.2

TOX = 10 nm, (EC-EF) = 0.5 eV

Exact Calculation Fit using Nicollian- Goetzberger model

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SLIDE 30

Total Error in DIT(E) at TOX = 10 nm

1.E+10 1.E+11 1.E+12

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

DIT (cm-2 eV-1) EC-E (eV)

Apparent Real EC – EF = 0.5 eV σQ = 2e11 cm-2 α = 0.2

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SLIDE 31

1.E-18 1.E-17 1.E-16 1.E-15 1.E-14 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

σN (cm2) EC-E (eV)

Apparent Real

Total Error in σN(E) at TOX = 10 nm

EC – EF = 0.5 eV σQ = 2e11 cm-2 α = 0.2

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SLIDE 32

2 4 6 8 10 12 14 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12

GP/ω (nF cm-2) ω (rad s-1)

TOX = 40 nm, (EC-EF) = 0.5 eV

Exact Calculation Fit using Nicollian- Goetzberger model

EC – EF = 0.5 eV σQ = 2e11 cm-2 α = 0.2

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SLIDE 33

1.E+10 1.E+11 1.E+12 0.2 0.4 0.6 0.8

DIT (cm-2 eV-1) EC-E (eV)

Apparent Real

Total Error in DIT(E) at TOX = 40 nm

EC – EF = 0.5 eV σQ = 2e11 cm-2 α = 0.2

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SLIDE 34

1.E-18 1.E-16 1.E-14 1.E-12 1.E-10 1.E-08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

σN (cm2) EC-E (eV)

Apparent Real

Total Error in σN(E) at TOX = 40 nm

ϒ = 0.749

EC – EF = 0.5 eV σQ = 2e11 cm-2 α = 0.2

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SLIDE 35

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12

GP/ω (nF cm-2) ω (rad s-1)

TOX = 150 nm, (EC-EF) = 0.5 eV

Exact Calculation Fit using Nicollian- Goetzberger model

EC – EF = 0.5 eV σQ = 2e11 cm-2 α = 0.2

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SLIDE 36

1.E+10 1.E+11 1.E+12 0.2 0.4 0.6 0.8

DIT (cm-2 eV-1) EC-E (eV)

Apparent Real

Total Error in DIT(E) at TOX = 150 nm

EC – EF = 0.5 eV σQ = 2e11 cm-2 α = 0.2

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SLIDE 37

1.E-18 1.E-16 1.E-14 1.E-12 1.E-10 1.E-08 0.2 0.4 0.6 0.8

σN (cm2) EC-E (eV)

Apparent Real

Total Error in σN(E) at TOX = 150 nm

γ = 0.921

EC – EF = 0.5 eV σQ = 2e11 cm-2 α = 0.2

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SLIDE 38

Exponential σN(E) toward CB. σUS decreasing toward CB. Exponential DIT(E) near CB.

  • W. Fahrner and A. Goetzberger,
  • Appl. Phys. Lett., 17, 16 (1970).

Surface Potential uS

DIT(E) σUS(E) σN(E)

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SLIDE 39

Apparent σUS vs. Energy

Apparent σUS EC – E (eV)

TOX = 40 nm, σQ = 2x1011 cm-2 TOX = 40 nm, σQ = 5x1010 cm-2 TOX = 10 nm, σQ = 2x1011 cm-2 Tox = constant σUS ratio ≈ σQ ratio σQ = constant σUS ratio < Tox ratio

Exponential DIT

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SLIDE 40

Conclusions

  • A rapidly increasing DIT(E) and a non-linear uS-VG relationship

cause errors in the MOS conductance technique.

  • Data extraction is more accurate with thinner oxides.
  • The apparent energy dependence of σN is an artifact caused

by an increasing DIT(E) and a non-linear uS-VG relationship.

  • We are creating calibration curves to estimate the actual

interface state parameters from the apparent parameters measured on real devices.

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SLIDE 41

Thank you!

Supported by the II-VI Foundation Cooperative Research Initiative

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SLIDE 42

Numerical Model for GP(ω)

Single-level interface state Loop over QF Loop over energy Sum over QF distribution (different “patches” under the gate) Probability of finding this QF value Surface potential in this “patch” Sum over bandgap energy around EF Fermi function evaluated at the state energy

where

State time constant