Systemic Errors in theMOS Conductance Technique

S. Swandono, D. T. Morisette, and J. A. CooperSchool of Electrical and Computer Engineering and Birck Nanotechnology Center

Purdue University, West Lafayette, IN

Supported by the II-VI Foundation Cooperative Research Initiative

Physics of the MOS Conductance Technique

COX CD

GP(ω)

CP(ω)

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)

Non-Uniform Fixed Charge QF

E. H. Nicollian and A. Goetzberger,Bell Syst. Tech. J., 46, 1055 (1967).

NeutralRegion

DepletionLayer

SiO2

Gate

RandomlyDistributed Fixed

Charges QF

ElectricFieldLines

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 variationof surface potential across the interface)

Nicollian & Goetzberger Model

(Distribution of states in energy)(sum over all “patches” under gate)

(interface state time constant)

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

Interface StateCapture Cross

Section σN

Surface Potential uS

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

Exponential decrease ofσN toward the band edge.

?

Measured Capture Cross Sections in 4H-SiCσ N

(E)

(cm

2 )

EC - E (eV)0.1 0.2 0.3 0.4 0.50

1e-20

1e-18

1e-16

1e-14 1

2

3

M. Das, Ph.D. Thesis, Purdue Univ., Dec. 1999.

3

1 2This Work

?

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.)

Procedure to Quantify Errors1. 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 aGP/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.

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.

The uS-VG Relationship

-70-60-50-40-30-20-10

01020

-3 -2 -1 0 1 2

Surf

ace

Pote

ntia

l u s

VG-VFB (V)

EC-EF = 0.2 eV

EC-EF = 0.5 eV

EC-EF = 0.8 eV

4H-SiCTOX = 40 nmND = 2e16 cm-3

AccumulationDepletion

Effect of Non-Uniform Fixed Charge QF

-70-60-50-40-30-20-10

01020

-3 -2 -1 0 1 2

VG-VFB (V)

Gaussian QFTOX = 40 nmσQ = 2e11 cm-2

Surf

ace

Pote

ntia

l uS

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

EC-EF =0.8 eV

-70-60-50-40-30-20-10

01020

-3 -2 -1 0 1 2

Surf

ace

Pote

ntia

l uS

VG-VFB (V)

Gaussian QFTOX = 40 nmσQ = 2e11 cm-2

EC-EF =0.5 eV

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

-70-60-50-40-30-20-10

01020

-3 -2 -1 0 1 2

Surf

ace

Pote

ntia

l uS

VG-VFB (V)

Gaussian QFTOX = 40 nmσQ = 2e11 cm-2

EC-EF =0.2 eV

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

0

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

G P/ω(n

Fcm

-2)

ωτ

Effect of Bias Point (Fermi Level)

TOX = 40 nmDIT =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

Effect of Oxide Thickness

-70-60-50-40-30-20-10

01020

-3 -2 -1 0 1 2

Surf

ace

Pote

ntia

l u S

VG-VFB (V)

Gaussian QFσQ = 2e11 cm-2

EC-EF = 0.5 eV

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

EC-EF = 0.5 eV

-70-60-50-40-30-20-10

01020

-3 -2 -1 0 1 2

Surf

ace

Pote

ntia

l u S

VG-VFB (V)19

Gaussian QFσQ = 2e11 cm-2

EC-EF = 0.5 eV

EC-EF = 0.5 eV

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

-140

-120

-100

-80

-60

-40

-20

0

20

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Surf

ace

Pote

ntia

l uS

VG-VFB (V)

Gaussian QFσQ = 2e11 cm-2

EC-EF = 0.5 eV

EC-EF = 0.5 eV

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

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

G P/ω

(nF

cm-2

)

ω (rad s-1)

150nm40nm

10nm

σQ = 2e11 cm-2

DIT = 8.48e10 eV-1 cm-2

EC-EF = 0.5 eV

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.

Measured DIT(E) in 4H-SiC

Question: How much error is introduced by an exponentially increasing DIT?

To find out, choose a bias point in the linear region of the uS–VG relationship, (EF deep in the bandgap, far from the CB).

Here the only distortion is due to the exponential DIT.

Choose a bias point with EF far from the CB

-70-60-50-40-30-20-10

01020

-3 -2 -1 0 1 2

Surf

ace

Pote

ntia

l u s

VG-VFB (V)

EC-EF =1.3 eV

4H-SiCTOX = 40 nmND = 2e16 cm-3

AccumulationDepletion

EC

Ei

1E+05

1E+06

1E+07

1E+08

1E+09

1E+10

1E+11

1E+12

1E+13

0 0.5 1 1.5 2

D IT( c

m-2

eV-1

)

EC - E (eV)

α = 0

α = 0.2EC-E = 1.3 eVDIT0 = 1.09e8 eV-1 cm-2

Exponential Model for DIT(E)

Uniform

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

G P/ω

(nF

cm-2

)

ω (rad s-1)

Impact of Exponential DIT(E)

TOX = 40 nmEC-EF = 1.3 eVσQ = 2e11 cm-2

Exponential DIT

Uniform DIT

Combined Effects

• Non-linear uS – VG relationship

• Exponential DIT(E)

• σN assumed constant (uniform with respect to energy)

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

G P/ω

(nF

cm-2

)

ω (rad s-1)

σQ = 2e11 cm-2

α = 0.2

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

ExactCalculation Fit using

Nicollian-Goetzberger

model

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

1.E+10

1.E+11

1.E+12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

D IT(c

m-2

eV-1

)

EC-E (eV)

Apparent

Real

EC – EF = 0.5 eVσQ = 2e11 cm-2

α = 0.2

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

σ N(c

m2 )

EC-E (eV)

Apparent

Real

Total Error in σN(E) at TOX = 10 nm

EC – EF = 0.5 eVσQ = 2e11 cm-2

α = 0.2

0

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

G P/ω

(nF

cm-2

)

ω (rad s-1)

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

ExactCalculation

Fit usingNicollian-

Goetzbergermodel

EC – EF = 0.5 eVσQ = 2e11 cm-2

α = 0.2

1.E+10

1.E+11

1.E+12

0 0.2 0.4 0.6 0.8

D IT(c

m-2

eV-1

)

EC-E (eV)

Apparent

Real

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

EC – EF = 0.5 eVσQ = 2e11 cm-2

α = 0.2

1.E-18

1.E-16

1.E-14

1.E-12

1.E-10

1.E-08

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

σ N(c

m2 )

EC-E (eV)

Apparent

Real

Total Error in σN(E) at TOX = 40 nm

ϒ = 0.749

EC – EF = 0.5 eVσQ = 2e11 cm-2

α = 0.2

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

G P/ω

(nF

cm-2

)

ω (rad s-1)

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

ExactCalculation

Fit usingNicollian-

Goetzbergermodel

EC – EF = 0.5 eVσQ = 2e11 cm-2

α = 0.2

1.E+10

1.E+11

1.E+12

0 0.2 0.4 0.6 0.8

D IT(c

m-2

eV-1

)

EC-E (eV)

Apparent

Real

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

EC – EF = 0.5 eVσQ = 2e11 cm-2

α = 0.2

1.E-18

1.E-16

1.E-14

1.E-12

1.E-10

1.E-08

0 0.2 0.4 0.6 0.8

σ N(c

m2 )

EC-E (eV)

Apparent

Real

Total Error in σN(E) at TOX = 150 nm

γ = 0.921

EC – EF = 0.5 eVσQ = 2e11 cm-2

α = 0.2

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)

Apparent σUS vs. Energy Ap

pare

nt σ

US

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 = constantσUS ratio ≈ σQ ratio σQ = constant

σUS ratio < Tox ratio

Exponential DIT

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

• We are creating calibration curves to estimate the actualinterface state parameters from the apparent parametersmeasured on real devices.

Thank you!

Supported by the II-VI Foundation Cooperative Research Initiative

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