UNCLASSIFIED

U.S. Army Research, Development and Engineering Command

Daniel B. Habersat

Neil Goldsman (UMD), and Aivars Lelis

Mobile Ion Effects on SiC MOS Bias-

Temperature Instability Measurements

14-15 Aug 2014 1

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Outline

• Overview of modeling approach

• Simulation results

– Sweep time (rate)

– Stress time

– Temperature

• Comparison with experimental data

• Conclusion

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MODELING APPROACH

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Method of Analysis

• Self-consistently solve: – Poisson equation in semiconductor and

oxide

– Ion transport in oxide

– Ion charge conservation

• Solutions of: – ψ potential

– n,p electron and hole concentration

– nA, nC anion and cation concentration

• Extract: – ψs = ψ-ψb band bending

– VFB ={VGB | ψs=0} flatband

– Vmid ={VGB | ψs= –ψb) midgap

– Vinv ={VGB | ψs= –2ψb) inversion

d2𝜓

d𝑥2= −𝜆𝜓 𝑝 − 𝑛

𝑝 d𝑥𝑥∈𝑜𝑥 ,∀𝑡

= 𝑝𝑡𝑜𝑡

𝐽𝑝 = −𝑞 𝑝𝜇d𝜓

d𝑥+ 𝐷

d𝑝

d𝑥

𝜕𝑝

𝜕𝑡= −

1

𝑞

d𝐽𝑝

d𝑥− 𝑅

-0.5

0

0.5

1

1.5

2

2.5

3

-15 -10 -5 0 5 10 15

Surf

ace

Ban

d B

en

din

g ψ

s [V

]

Applied Bias VGB [V]

V_inv

V_mid

V_FB

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[1] G. Greeuw and J. F. Verwey, J. Appl. Phys., vol. 56, no. 8, pp. 2218–

2224, 1984.

[2] M. W. Hillen, G. Greeuw, and J. F. Verweij, J. Appl. Phys., vol. 50, no.

7, pp. 4834–4837, Jul. 1979.

[3] Y. Shacham‐Diamand, A. Dedhia, D. Hoffstetter, and W. G. Oldham,

J. Electrochem. Soc., vol. 140, no. 8, pp. 2427–2432, Aug. 1993.

[4] B. Tuttle, Phys. Rev. B, vol. 61, no. 7, pp. 4417–4420, Feb. 2000.

Mobility Models and Ion

Transport

• Ions are assumed to freely move through the oxide, under the influence of local field (drift) and ion concentrations (diffusion)

• The gate contact and semiconductor interface are both impermeable to ions (charge conservation)

• Data comes from published experiments measuring mobility of ions in SiO2, generally Arrhenius-like

• Mobility μ can be correlated roughly with “transit time” tt, the amount of time taken to drift across oxide thickness tox under an applied field E

• Region of interest (as defined by operating conditions):

– 25°C – 200°C

– μs – 1,000 hrs

– ~15 V on gate

– 500 Å SiO2 typical

𝑡𝑡 =𝑡𝑜𝑥𝜇𝐸

𝜇 𝑇 = 𝜇0 exp −𝐸𝑎

𝑘𝐵𝑇

Tran

sit

Tim

e [

s]

500 Å SiO2

3 MV/cm

5

1E-6

1E-4

1E-2

1E+0

1E+2

1E+4

1E+6

1E+8

-25 0 25 100 200 500

1E-20

1E-18

1E-16

1E-14

1E-12

1E-10

1E-08

1E-06

1 2 3 4

Mo

bili

ty [

cm2 /

V s

]

1000/T [°K-1]

Na Li K Cu H

Temperature [°C]

+

+

+

+

+

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Simulation Scenarios

• Goal: to mimic realistic stress-and-measure sequences while exploring impacts of various sequencing parameters – sweep time,

– stress time, and

– temperature.

VGB VGB VGB t

VGB VGB VGB t

VGB VGB VGB t

constant T

constant T

versus T

ΔV + +

+ + + +

+

SiC SiO2

+ – – +

+ –

+ –

+ –

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SWEEP TIME (RATE)

Simulation Results

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Sweep Rate Analysis

VGB VGB VGB t

constant T

• Parameters – Sweep time varied

– Stress time fixed, 0s

– Temperature fixed, 150°C

– Structure is 500Å SiO2 on top of 4H:SiC, doping profile similar to typical DMOSFET

– 1x1012 cm-2 Na+ or K+ ions

1E-6

1E-4

1E-2

1E+0

1E+2

1E+4

1E+6

1E+8

-25 0 25 100 200 500

1E-20

1E-18

1E-16

1E-14

1E-12

1E-10

1E-08

1E-06

1 2 3 4

Mo

bili

ty [

cm2 /

V s

]

1000/T [°K-1]

Na

K

500 Å SiO2

3 MV/cm

Temperature [°C]

Tra

nsit

Tim

e [

s]

+

+

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x

t

Raw Simulation Data

(Typical Na+)

VG

B

VG

B

VG

B

t

ψ [V]

oxide semiconductor

-15

0

15

SiC SiO2

+ +

+ + + +

+

SiC SiO2

+ – – +

+ –

+ –

+ –

E [V/m] 3x108

0x108

-3x108 SiC SiO2

log n [m-3]

SiC SiO2

log p [m-3]

1016

1018

1020

1022

1024

1026

SiC SiO2

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VGB VGB VGB t

Detailed Movement of Ions

During Bias Ramp (Na+)

-1

-0.5

0

0.5

1

-15 -10 -5 0 5 10 15

Ion

Dis

pla

cem

en

t C

urr

en

t [(αCox

)-1]

Applied Bias VGB [V]

30 MV/s 3 kV/s 300 mV/s

~1 μs ~10 ms ~100 s

~100 s ~10 ms

~1 μs

log p [m-3]

log p [m-3] log p [m-3]

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Surface Band Bending – Applied

Bias Relationship (Na+)

~100 s ~10 ms ~1 μs

VGB VGB VGB t

-0.5

0

0.5

1

1.5

2

2.5

3

-10 -5 0 5 10

Surf

ace

Ban

d B

en

din

g ψ

s [V

]

Applied Bias VGB [V]

30 MV/s 3 kV/s 300 mV/s

Vinv up

Vinv down

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VGB VGB VGB t

Inversion Voltage Versus

Sweep Time, Na+

2E+2

2E+1

2E+0

2E-1

2E-2

2E-3

2E-4

2E-5

2E-6

1E-1

1E+0

1E+1

1E+2

1E+3

1E+4

1E+5

1E+6

1E+7

1E+8

1 1.5 2 2.5 3 3.5 4 4.5

Slew

Rat

e [

V/s

]

Applied Bias VGB [V]

Vinv up

Vinv down

Sw

eep T

ime [

s]

~100 s

~10 ms

~1 μs

ΔVinv=Vdown–Vup

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VGB VGB VGB t

Inversion Hysteresis Versus

Sweep Time

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

-2.5

-2

-1.5

-1

-0.5

0

1E-2 1E+0 1E+2 1E+4 1E+6 1E+8

ψs H

yste

resi

s (ΔVinv)

[V

]

Slew Rate [V/s]

Na

K

Sweep Time [s]

“fast” “slow” “ultra-fast”

+

+

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“True” Ion Shift

UNCLASSIFIED

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STRESS TIME

Simulation Results

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Stress Time Analysis

VGB VGB VGB t

constant T

• Parameters – Sweep time fixed, 2s

– Stress time varied

– Temperature fixed, 150°C

– Structure is 500Å SiO2 on top of 4H:SiC, doping profile similar to typical DMOSFET

– 1x1012 cm-2 Na+ or K+ ions

1E-6

1E-4

1E-2

1E+0

1E+2

1E+4

1E+6

1E+8

-25 0 25 100 200 500

1E-20

1E-18

1E-16

1E-14

1E-12

1E-10

1E-08

1E-06

1 2 3 4

Mo

bili

ty [

cm2 /

V s

]

1000/T [°K-1]

Na

K

500 Å SiO2

3 MV/cm

Temperature [°C]

Tra

nsit

Tim

e [

s]

+

+

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Inversion Voltage Versus

Stress Time (K+)

1E-3

1E-2

1E-1

1E+0

1E+1

1E+2

1E+3

1E+4

1 1.5 2 2.5 3 3.5 4 4.5

Stre

ss T

ime

[s]

Applied Bias VGB [V]

Vinv down Vinv up

K+ Transit Time (390 s)

3 MV/cm @ 150°C

μ=4.3x10-15 cm2/V s

VGB VGB VGB t

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Inversion Voltage Hysteresis

Versus Stress Time

-2.5

-2

-1.5

-1

-0.5

0

0.001 0.01 0.1 1 10 100 1000 10000

ψs H

yste

resi

s (ΔVinv)

[V

]

Stress Time [s]

Na

K

VGB VGB VGB t

+

+

14-15 Aug 2014 17

“True” Ion Shift Na+ Transit Time (0.83 ms)

3 MV/cm @ 150°C

μ=2.0x10-9 cm2/V s

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TEMPERATURE

Simulation Results

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Temperature Analysis

VGB VGB VGB t

versus T

• Parameters – Sweep time fixed, 2s

– Stress time fixed, 1000s

– Temperature varied

– Structure is 500Å SiO2 on top of 4H:SiC, doping profile similar to typical DMOSFET

– 1x1012 cm-2 Na+ or K+ ions

1E-6

1E-4

1E-2

1E+0

1E+2

1E+4

1E+6

1E+8

-25 0 25 100 200 500

1E-20

1E-18

1E-16

1E-14

1E-12

1E-10

1E-08

1E-06

1 2 3 4

Mo

bili

ty [

cm2 /

V s

]

1000/T [°K-1]

Na

K

500 Å SiO2

3 MV/cm

Temperature [°C]

Tra

nsit

Tim

e [

s]

+

+

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Inversion Voltage Versus

Temperature

-50

-25

0

25

50

100

150

200

300

500

1 1.5 2 2.5 3 3.5 4 4.5 Inversion Voltage Vinv [V]

ideal Vinv

Vinv up

Vinv down

ideal Vinv + Q/Cox

Tem

pe

ratu

re T

[°K

]

1

1.5

2

2.5

3

3.5

4

4.5

1 1.5 2 2.5 3 3.5 4 4.5

10

00

/T [

°K-1

]

Inversion Voltage Vinv [V]

ideal Vinv

Vinv up

Vinv down

ideal Vinv + Q/Cox

Na K + +

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Inversion Voltage Hysteresis

Versus Temperature

-50 -25 0 25 50 100 150 200 300 400 500

-2.5

-2

-1.5

-1

-0.5

0

1 1.5 2 2.5 3 3.5 4 4.5

Inve

rsio

n V

olt

age

Hys

tere

sis Δ

Vin

v [V

]

1000/T [°K-1]

K

Na

Increasing

stress time

Temperature [°C]

Increasing

sweep time

+

+

14-15 Aug 2014 21

Increasing

sweep time

“True” Ion Shift

UNCLASSIFIED

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EXPERIMENTAL

COMPARISON

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Decrease in Instability at 25°C

– Mobile Ions?

• Experimental ΔVinv versus stress time at 25°C

• Two samples from the same wafer – “clean” shows typical log-time

positive instability (charge trapping)

– “dirty” shows a negative instability at longer times (mobile ions?)

• ΔVinv at 25°C simulated for 1x1012 cm-2 Na+ and K+, then scaled to fit

• Neither ion (nor their combination) appears to adequately explain time dependence of the observed negative instability trend…!

• Requires excessive amounts of K+ (>1013 cm-2), not supported by supplemental data -0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

1E+1 1E+2 1E+3 1E+4

Inve

rsio

n In

stab

ility

ΔVinv

[V]

Stress Time [s]

"clean" "dirty?" K Na

+

+

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Decrease in Instability as T is

increased – Mobile Ions?

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 50 100 150 200 250

Inve

rsio

n In

stab

ility

ΔVinv

[V]

Temperature [°C]

A B C D E

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

0 50 100 150 200 250

Inve

rsio

n In

stab

ility

ΔVinv

[V]

Temperature [°C]

K ΔV, 1E12

Na ΔV, 1E12

Experimental Simulation

+

+

14-15 Aug 2014 24

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Conclusions

• Parameter effects

– Sweep time

• Fast sweeps (<< transit times) “freeze” the ions in place

• Slow sweeps (>> transit times) ions follow the bias, counter charge trapping

• Med. sweeps (~ transit time) maximizes instability

– Stress time

• Only matters when sweep is <~ transit time

• Saturates around scale of transit time

– Temperature

• No direct effect, mostly modulation of the mobility

• Effects are subject to the rules for both sweep and stress time

• Initial comparisons of a free ion transport and ideal semiconductor model with experimental data:

– Does not appear to explain room-temperature stress time dependence of some negative instabilities

– K+-like ion can roughly match temperature-dependent instability, though low temperature fit is poor

– Na+ could be present, but no definitive evidence either way so far

• Possible improvements to this work include:

– Mechanisms other than “free transport” (e.g., trapping, neutral associations, etc.)

– Including effects from other charge mechanisms such as interface and oxide traps (shifts are not simply additive)

– Presence of multiple ion species or other mobile structures

– Extend model to MOSFET structure, calculate ID-VGS (potential to incorporate into UMD 2-D model)

– Inverting the simulation: what mobility model & charge density are needed to reproduce experimental data? How about a “mobility spectrum” analysis similar to that used in QMSA for Hall effect?

– Modeling assumed the bias ramp always started with ion charge at gate, whereas experimental devices start in indeterminate condition and data was measured sequentially (back-and-forth stress & measure does not return ions to initial condition)

– Device properties for the model could have been chosen incorrectly

14-15 Aug 2014 25