SiO2/4H-SiC Near-Interface Traps asDeduced from AC Conductance Measurements

James A. CooperJai N. Gupta Professor Emeritus of Electrical and Computer Engineering

Purdue University, West Lafayette, IN

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

GP (w )

w=

qDIT

2

ln 1+w 2t 2( )wt

(states are distributed uniformly

across the bandgap in energy)

(interface state time constant)

(normalized surface potential)

nS = ni exp uF - uS( ) (surface electron density)

F uS,uF( ) = euF e-uS + uS -1( ) + e-uF euS - uS -1( )éë

ùû

1 2

VG -VFB( ) =kT

quS + Sign uS( )

eS

COX LD

F uS ,uF( )é

ëê

ù

ûú-

QIT uS ,uF( )- QIT 0,uF( )COX

é

ëê

ù

ûú

VFB =FMS

q-

QF

COX

Calculating Surface Potential uS

potential drop across the oxide

shift due to charges in interface states

potential dropacross the

depletion region

What happens if QF isn’t uniform from place to place under the gate?

Then uS will not be uniform either!

Non-Uniform Fixed Charge QF

E. H. Nicollian and A. Goetzberger,

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

Neutral

Region

Depletion

Layer

SiO2

Gate

RandomlyDistributed Fixed

Charges QF

Electric

Field

Lines

GP (w )

w=

qDIT

2

ln 1+w 2t 2( )wt

(states are distributed uniformly

across the bandgap in energy)

GP (w )

w=

qDIT

2

ln 1+w 2t 2( )wt

P uS( )duS-¥

¥

ò

(sum over all “patches” under gate)

COX CD

GP(ω)

CP(ω)E. H. Nicollian and A. Goetzberger,

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

(probability density function for the variation

of surface potential across the interface)

Nicollian & Goetzberger Model

(interface state time constant)

dQF

duS

=kT

qCOX + CD uS ,uF( ) + CIT uS ,uF( )éë ùû

The Probability Density Function for Surface Potential

P(uS ) = P QF( )dQF

duS

CIT (uS ,uF ) = qDIT (uS ,uF )

Nicollian and Goetzberger linearized this relationship by assumingthe sample was biased well into depletion (where CD is small, << COX)and the CIT term could be ignored (i.e. DIT is small, < 5x1011 eV-1 cm-2).

Nicollian and Goetzberger assumed a Gaussian probability densityfunction for fixed charge, and converted this to a Gaussian probabilitydensity function for surface potential.

Assumptions of the Nicollian & Goetzberger Model

1. Analysis limited to biases in depletion (linear uS-VG relationship) and DIT is small.

(Allows a Gaussian distribution of surface potential.)

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

(DIT can be taken outside the integral, and the Lehovic GP /ω expression can be used.)

3. We have developed a model that eliminates all these assumptions.

8

GP (w )

w=

qDIT

2

ln 1+w 2t 2( )wt

P uS( )duS-¥

¥

ò

 

P(uS ) =1

2ps us

2exp -

(uS - u S )2

2s us

2

æ

è ç

ö

ø ÷

H. Yoshioka, et al., J. Appl. Phys.,

111, 14502 (2012).

0.394 eV

Fitting to Yoshioka, et al. GP / 𝜔 Data on 4H-SiC

Best fit usingN&G model

dry oxidation @ 1300° C, no POA

tOX = 32 nmND = 1.3x1016 cm-3

0.394 eV

Data courtesy of T. Kimoto (2017).

Yoshioka, et al. GP / 𝜔 Data on 4H-SiC

Adjusting the Width of the Curves (N & G Model)

σUS = 1, 2, 3, 4, 5, 6

0.394 eV

Data courtesy of T. Kimoto (2017).

Fitting Yoshioka’s Data with the N & G Model

Adjusting the Width of the Curves (Exact Model)

σQ = 0, 5e10, 1e11, 2e11, 5e11, 1e12 cm-2

0.394 eV

Data courtesy of T. Kimoto (2017).

Fitting Yoshioka’s Data with the Exact Model

σQ = 0, 5e10, 1e11, 2e11, 5e11, 1e12 cm-2

What’s Going On?

When the nonlinear and energy-dependent effects are accounted for, it is not possible to explain the time constant dispersion of real 4H-SiC samples using only dispersion due to fixed charge variations (Nicollian& Goetzberger model).

Reason: The nonlinear uS – VG relationship near flat-band narrows the distribution of surface potential. Increasing σQ does not increase the spread of surface potential near flat band.

Conclusion: Some other dispersion mechanism must be present!

Dispersion due Only to Interface Traps

DIT(x)

x0

δ(x)

Dispersion due to Tunneling to Near-Interface Traps

DIT(x)

x0

DIT(x)

x0

DIT(x)

How does this affect the GP/ω curve?

When states are distributed into the insulator, the

transition probability decreases exponentially

with distance, and we can write

H. Prier, Appl. Phys. Lett., 10, 361 (1967).

s N x( ) = s N 0( )exp -2k0x( ), 1 2k0( ) »1 Å

Fitting Yoshioka’s Data with the Exact Model including Tunneling

0.134 eV

0.154 eV

0.184 eV

0.204 eV

0.244 eV

0.304 eV

0.394 eV

0.134 eV

0.154 eV

0.184 eV

0.204 eV

0.244 eV

0.304 eV

0.394 eV

Fitting Yoshioka’s Data with the Exact Model including Tunneling

Assumed Distribution of States in the Oxide

The position of the interface is arbitrary, since it only affects the value of σN(0).

FWHM = 1 nm

3 nm

Atomic Profile Across the Interface

EELS, resolution <1 nm

“The thickness of a transition layer, if it exists, is less than 2 nm.”

T. Kimoto and J. A. Cooper,

Fundamentals of Silicon

Carbide Technology, Wiley,

Singapore (2014).

Fig. 6.35b, p. 218.

Simple Conceptual Picture of the Interface

s N x( ) = s N 0( )exp -2k0x( )

More Realistic Picture of the Interface

Where is the “interface”?

What is the shapeof the barrier?

Distribution of States in Energy

Values from fitting GP/ω curves.

DIT(E) function in the program.

DIT

(E)

(eV

-1cm

-2)

(EC - E) (eV)

0 0.1 0.2 0.3 0.4 0.5

1.0E+11

1.0E+12

1.0E+13

1.0E+14

Good consistency is achieved between the energy dependence assumed in the program and the energy dependence determined by

fitting to experimental GP/ω data.

DIT(E) deduced by Yoshioka using N&G model.

DIT(E) deduced from exact tunneling model.

Distribution of States in Energy

The interface state density obtained using the N – G model is close to the density

determined by fitting with the exact model.

σN(x

= 0

, E)

(cm

2)

(EC - E) (eV)

Energy Dependence of Capture Cross Section

Values from fitting GP/ω curves.

σN(E) function in the program.

The capture cross section does appear to decrease exponentially toward the conduction band, but not as rapidly as the exp(-uS) observed by Fahrner and

Goetzberger (Appl. Phys. Lett., 17, 16 (1970)).

Summary

• The Nicollian – Goetzberger model is inaccurate near flat band becauseof the nonlinear uS – VG relation. It is also inaccurate whenever DIT or σN

are strong functions of energy.

• Experimental GP/ω data on 4H-SiC can be approximately fit using theN – G model, but this gives a misleading picture of the interface.

• When the nonlinear and energy-dependent effects are taken into account,it is impossible to fit GP/ω curves on 4H-SiC using only dispersion fromfixed charge variations (Nicollian – Goetzberger model).

• We have shown that tunneling to near-interface traps gives a GP/ωdispersion that agrees well with experimental data on 4H-SiC.

• The assumed distribution of traps has a full-width at half maximum of~1 nm and a total width ~1.7 nm.

Questions?

Comments?