Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf...

D.P. Ettisserry,N. Goldsman

Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation in

4H-SiC Power MOSFETs

Dev EttisserryECE Department

UMD College Park

Advisor: Prof. Neil Goldsman

10th ARL Workshop on SiC Electronics08/13/2015

UMD College Park

Overview

• Introduction• Reliability issues in 4H-SiC MOSFETs (Problem statements).• Integrated Modeling Approach

• Density Functional Theory plus related modeling tools.• High-temperature reliability modeling.• NO passivation and device reliability.• Summary



Problem statementsCritical reliability concern – High-temperature Vth instability*

Room-Temperature ΔVth[1] High-Temperature ΔVth

[2]

* Measurements by our collaborators at U.S. Army Research Lab, Adelphi, MD.[1] A. J. Lelis et. al, IEEE T-ED, 55, no.8, 1835, 2008.[2] A. J. Lelis et. al, IEEE T-ED, 62, no.2, 316, 2015.

Development of Passivation processes• After identifying the root-causes of reliability degradation, how can we alter

device processing to mitigate them???• Effect of commonly used NO passivation.


Integrated Modeling Approach

Density of States

Interatomic Forces

Ground state energy

Electron density

DFT

Trap levels and

Activation energies

Molecular dynamics

Passivation processes

Reliability / performance-

limiting mechanismsand models

GoodMOSFET!!!

Integrated Modeling

Bridging the gap between fundamental physics and

MOSFET engineering

TCAD / Rate equations


Density Functional Theory• Schrodinger wave equation that accounts for all the electrons and nuclei in

the system and their interactions.

• The kinetic and potential energies are altered by quantum effects like Pauli’sexclusion – not quantifiable.

• DFT provides a tractable accurate solution for the ground state eigenvalues(energy) and electron density.

– Replaces the complicated interacting system Hamiltonian by a sum of non-interacting Hamiltonians.

– Uses electron density (one function in space) as the fundamental propertyinstead of ψtot.

∑∑∑∑∑≠≠ −

+∇−−

+−

−+∇−=

JI JI

JII

I Iji jiIi Ii

I

ii

e RReZZ

Mrre

RreZ

mH

22

22

,

22

2

21

221

2ˆ

Total wavefunction


Energy Levels of Defects from DFT

Interstitial defect

no: of electrons

bulk with Charged

Defect

Fermilevel

Valenceband

Chemicalpotential

Energy of Bulk w/o defect

(DFT)

Energy of Bulk w/ defect

(DFT)

• The defect formation reaction for different charge states

𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 + 𝐷𝐷 + 𝑞𝑞𝑒𝑒− → { [𝐷𝐷 + 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏]𝑞𝑞 }

• The feasibility of defect formation is given by its formation energy

𝐸𝐸𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓,𝑞𝑞 = 𝐸𝐸[𝐷𝐷+𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏]𝑞𝑞 − 𝐸𝐸𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 − µ𝐷𝐷 − 𝑞𝑞(𝐸𝐸𝐹𝐹 + 𝐸𝐸𝑣𝑣)

Example• Stability of the defect in its chargedstate q, and its trap level obtained fromformation energy vs Fermi level plot.

• Charge Transition Level (CTL), representing the thermodynamic trap level, is the intersection between two formation energy curves.

D & q


High-temperature reliability modeling of 4H-SiC MOSFETs

• Amorphous SiO2 model generation• Role of oxide defects in reliability degradation.• Transient modeling of high-temperature Vth

instability.

[1] D.P. Ettisserry, N. Goldsman, A. Akturk, and A.J. Lelis, “Negative bias-and-Temperature-assisted activation of oxygen-vacancy hole traps in 4H-SiC MOSFETs,” accepted for publication by the Journal of Applied Physics.[2] D.P. Ettisserry et. al., “Modeling of oxygen-vacancy hole trap activation in 4H-SiC MOSFETs using Density FunctionalTheory and Rate Equation Analysis,” accepted for oral presentation at the Intl. Conference on Simulation of SemiconductorProcesses and Devices (SISPAD), 2015.


• ΔVth vs log-stress time is linear.• Typically attributed to oxygen

vacancies (direct two-way tunnelingmodel [1, 2]).– Also, ESR evidence.3, 4

Reliability issues in 4H-SiC MOSFETs

Room-Temperature ΔVth[1]*

Critical reliability concern – High-temperature threshold voltage instability (ΔVth)

High-Temperature ΔVth[5]*

• ΔVth vs log-stress time is linear till ~125oC – due to switching hole traps.

• For T>125oC, excessive aggravation inΔVth .

Why???

[5] A. J. Lelis et. al, IEEE T-ED, vol. 62, no.2, pp.316-323, 2015.* Measurements by our collaborators at U.S. Army Research Lab, Adelphi, MD.

[1] A. J. Lelis et. al, IEEE T-ED, vol. 55, no.8, pp.1835–1840, 2008.[2] A. J. Lelis, and T. R. Oldham, IEEE Trans. Nuclear Science, vol. 41, no. 6, pp. 1835–1843, 1994.[3] J. F. Conley, P. M. Lenahan, A. J. Lelis, and T. R. Oldham, Appl. Phys. Lett. 67, 2179 (1995).[4] J. T. Ryan, P. M. Lenehan, T. Grasser, and H. Enichlmair, Appl. Phys. Lett. 96, 223509 (2010).


Amorphous SiO2 model generationMethod 1 – Sequential Back-bond Break (SBB Method)• New method – Exploits the periodicity of supercell models, inherent in DFT.• Represents bond-switched regions of oxide (high-amorphousness).

Method 2 – Quantum molecular dynamics• Represents non-bond-switched regions of oxide (low-amorphousness).


Amorphous SiO2 model – structural properties

• Bond angle and bond length distributionsagree well with other models generatedusing molecular dynamics [1].

• Pair correlation functions agree well withexperimental reports [2]. Further workwith larger models will be helpful toconfirm the results.

[1] F. Devynck et. al., Phys. Rev. B 76, 075351 (2007).[2] A. C. Wright., J. Non Crys. Solids, 179, 84-115 (1993).


• The structural and electronicproperties of OVs in ‘bond-switched’ oxide regions (SBBmodel) was studied.

Oxygen vacancy (OV) defects in SBB models

Structures of OV in ‘bond-switched’ oxide regions:(1) Basic Low-energy Dimer, (2) High-energy forward-projected (fp), (3) High-energy back-projected (bp)

• Upon hole capture, basic dimer spontaneously forms positive fp.

• fp thermally transforms to bp.• Also, fp and bp are stable when

neutral.


Electrical activity of OVs in SBB models

Electrical activity of OV in high disorder regions:• All configurations are electrically active permanently.• The +1/0 CTL moves to right consistently, as the OV assumes higher energy

configurations – predicts formation of ‘fixed’ positive charges.• These OVs in bond-switched regions contribute to room temperature Vth

instability.– Supports previous models [1,2].

[1] J. F. Conley, P. M. Lenahan, A. J. Lelis, and T. R. Oldham, Appl. Phys. Lett. 67, 2179 (1995).[2] J. T. Ryan, P. M. Lenehan, T. Grasser, and H. Enichlmair, Appl. Phys. Lett. 96, 223509 (2010).


Oxygen vacancies (OV) in MD models• Studied structural and electronic

properties of OVs in ‘non-bond-switched’ oxide regions (lowamorphousness).

Configurations of OV in silicon dioxide:Neutral:(1) Basic Low-energy Dimer,Positive (upon hole capture)(1) Low energy dimer (2) High-energy forward-projected (fp-bb1), (3) High-energy back-projected (bp-bb1),(4) High-energy forward-projected (fp-bb2), (5) High-energy back-projected (bp-bb2),

[1] M.A. Anders et.al., IIRW pp. 16-19, Oct. 2014.

• Thermal barriers for transformation calculated using DFT-based Nudged Elastic Band (NEB) method.

How do these structures behave electrically??


Electrical properties of Oxygen vacanciesElectrical activity of Oxygen Vacancy:

• Basic neutral dimers are electrically inactive.

• Higher energy configurations are active.


Under NBTS, neutral dimers are ‘activated’ to form active forward-projected and back-projected structures.


Transient modeling of OV hole trap activation• What is the time dependence of activation process??? • Solve Arrhenius rate equations bases on DFT-calculated activation barriers!

- Activation barriers from DFT- k12 and k21 from SRH model

𝑏𝑏12 = σ𝑣𝑣𝑡𝑡𝑡𝑝𝑝 𝑇𝑇(𝑧𝑧,𝐹𝐹)


• The time-dependent total concentration of activated hole traps (positive charges) is translated to voltage shift.

• |Δ𝑉𝑉 (𝑡𝑡)| = 𝑞𝑞 𝑁𝑁 ∑𝑖𝑖=26 𝑥𝑥𝑖𝑖(𝑡𝑡)𝐶𝐶

Transient modeling of OV hole trap activation

[1] A. J. Lelis et. al, IEEE T-ED, vol. 62, no.2, pp.316-323, 2015.



RT Vth instability post HTGB stress

• The model explains:– Short-term reliability degradation [1].– Long-term reliability degradation [1].– ESR observations [2].

[1] A. J. Lelis et. al, IEEE T-ED, vol. 62, no.2, pp.316-323, 2015.[2] M.A. Anders et.al., IIRW pp. 16-19, Oct. 2014.

High amorphousregion


NO Passivation of E’ centers

[1] D.P. Ettisserry et. al., “Mechanisms of Nitrogen incorporation at 4H-SiC/SiO2 interface during Nitric Oxide passivation –A first principles study,” accepted for oral presentation at the Intl. Conference on Silicon Carbide and Related Materials(ICSCRM), 2015.


Oxygen vacancy – NO treatment• NO molecule could be ‘trapped’ by oxygen vacancy to form

‘nitroxyl’ configuration.• ‘Nitroxyl’ can also be formed by incorporation of atomic

Nitrogen into oxide lattice near the interface.

• NO in oxide could lead to switching oxide traps, or fixed positive charges.

Overall effects of NO:– Carboxyl hole trap removal under dilute

NO - MitigatesΔVth [1].– NO can be counter productive –

switching oxide traps.– NO mitigates interface traps [2].– Thus, optimized NO passivation

mitigates Vth instability.

[1] D.P. Ettisserry et. al., J. Appl. Phys. 116, 174502 (2014).[2] G. Y. Chung et al., IEEE EDL, vol. 22, no. 4, pp. 176-178, 2001.


Other effects on NO treatment – Counter-doping• NO can incorporate at the interface.

– Nitrogen substitution of C or counter-doping.

• Improved channel mobility [1].

– It could re-oxidize 4H-SiC surface.

– Create additional oxygen vacancy defects due to ‘scarcity’ of oxygen.

• Optimization of NO passivation is extremely important for improved MOSFETs !!!!

[1] G. Liu et al., IEEE EDL, vol. 34, no. 2, pp. 181-183, 2013.


Overall summary• Unified Density functional theory with device modeling techniques.

– Can solve practical problems encountered by semiconductor device physicistsand process engineers.

• Reliability and mobility models in semiconductor devices.• High Temperature ΔVth in 4H-SiC MOSFETs.

– Due to the activation of electrically ‘inactive’ oxygen vacancies to formswitching oxide hole traps over time.

– Long term reliability degradation is due to residual activated hole trap centers.• Passivation effects using molecular dynamics

– Nitric Oxide• Controlled NO could be effective, Excess NO can have adverse effects.• Counter-doping during NO passivation is energetically feasible.


Thank you, Questions?


Additional defects involved in hole trapping

• Role of carbon-related defects• Stability-providing bonding mechanisms


• Atomic carbon has been suggested to be emitted into the oxideduring 4H-SiC oxidation [1].

• Our DFT based molecular dynamics simulation of atomic carbon inSiO2 resulted in the rapid formation of Si-O-C-Si bridges.

Single carbon interstitial in SiO2 – DFT Based Molecular Dynamics simulation

• The existence of carbon-containing interlayers has been observed inTEM measurements [2].

initial final

[1] Y. Hijikata, H. Yaguchi, and S. Yoshida, Applied Physics Express 2, 021203 (2009).[2] T. Zheleva, A. Lelis, G. Duscher, F. Liu, I. Levin, and M. Das, Appl. Phys. Lett. 93, 022108 (2008).

C interstitialSi-O-C-Si bridge

Yellow – CBlue - SiRed - O


Formation of carboxyl defect from Si-O-C-Si bridges in SiO2

• Exothermic reaction, energyreleased = ~2 eV

• Activation barrier = 0.5 eV

Carboxyl: Likely Defect !!

• Carboxyl defect, Si-[C=O]-Si, are more stable than Si-O-C-Sidefect – based on simple octet rule.

• Simple bond energy based calculations indicated ~3.2 eV energyrelease.

• The kinetics of conversion of Si-O-C-Si bridge to carboxylconfiguration was studied using nudged-elastic band method.


• Based on bandgap alignment, a +2 to neutral charge transition level is observed forcarboxyl defect within the 4H-SiC bandgap (at Ev,4H-SiC + 1.4 eV) – implies thatthe charge is electrically active.

Electrical activity of carboxyl defects in 4H-SiC MOSFETs

• The defect is predicted to be aborder trap.

• For 4H-SiC Fermi level > 1.4 eV,defect is neutral.

• For 4H-SiC Fermi level < 1.4 eV,defect is in +2 state (hole trap).

• Thus, the defect is a border hole trapcausing Vth instability.


• In the neutral state, Si-C band length corresponds to that in 4H-SiC.

• Weak bond due to the electronegative carboxyl oxygen imparting partial positivecharge to carbon – Coulomb repulsion between partially positive Si and C.

• The bond can be broken by radiation or high applied bias and temperature makingit positively charged (h+ trapping) – similar to Si-Si precursor bond in E’ centers.

Structural transformations in the carboxyl defect

• In the stable +2 state, significantpuckering and back-bonding ofpositive Si with oxygen wasobserved – similar to O vacancyhole traps.

• This structural change impartsstability in +2 state.

• Significant resemblance with well-established E’ center hole traps.


• In the neutral state, at high ELF of 0.89,two lone pairs on Oxygen are distinctlyvisible.

• By comparing with Lewis perspective ofbonding, this indicates a carbon-oxygendouble bond (C=O).

• In the stable +2 state, at a high ELF of0.89, a single lone pair was observed oncarboxyl oxygen.

Bonding in the carboxyl defect - ELF• This indicates a triple bond

between C and O.

• Apart from puckering, the increasein C-O bond order from 2 to 3imparts stability to the defect in +2state. ESR invisible in 0 and +2.

Si SiC

O

Si SiC

O

Si SiC

O

O

h+

h+

• Mobility degradation in 4H-SiC MOSFETs


• Drift Diffusion simulation of 4H-SiC MOSFET.• Algorithm for trap characterization.


Performance issues in 4H-SiC MOSFETs

[1] N. Saks et. al., APL 77, No. 20, 3281 (2000).[2] J.M. Knaup et al., PRB 71, 235321 (2005)

Critical performance concern – Very low channel electron mobility

Typical Dit spectrum [2]Poor Hall and effective mobility [1]

• Very poor Hall mobility.• Even poorer effective mobility.• Very high density of interface traps near the conduction band edge.

– Poor quality of interface.

Identify the number of distinct defects, their atomic make-up, their energy levels andindividual concentrations.

2D-Device Simulation of a SiC power MOSFET

50A DMOSFET cross section

• Solve equations simultaneously.• Allows us to calculate I-V

characteristics based on the internalstructural detail of the device andprobe inside the device whereexperiments can not reach.

[1] S. Potbhare et al., IEEE TED, 55, no 8, pp. 2029-2040, 2008.[2] S. Potbhare et al., J. Appl. Phys., 044515, 2006.[3] S. Potbhare, et al., IEEE TED, 55, No.8, pp. 2061-2070, 2008. [4] S.K. Powell et al., J. Appl. Phys. 92, 4053 (2002).


( ) ( ) ( )TzzFNNemTkT

iOTit

BC ,,

1163*

2

⋅+

=επµ

Coulomb Scattering Mobility

Trapped Charge

Bulk MobilityBulk Phonons and Impurity Scattering

( ) min

minmax

1

300

µµµ

µ γ

η

+

+

−

=B

B

ref

B

ND

TT

Doping

Surface Roughness Mobility

( ) ( )TFLemmET

SRdcSR

12

122**

3

2 ⋅∆

=⊥

µ

Step HeightCorrelation

Length

( ) ( )||ETvT sat

HF =µ

High Field Mobility

Saturation Velocity

Experimentally Verified Mobility Models

( )3

1

⊥⊥

+=TE

BEATSPµ

Surface Phonon Mobility


• Interface trap density modeled as exponential –represents experiments [1,2]

Methodology: Trap characterization

[1] V.V. Afanas’ev, et al., Phys. Stat. sol (a), vol. 162, pp. 321-337, 1997. [2] N.S. Saks et al, APL. 76, 2250 (2000).

Part 1 - Drift-Diffusion Simulation


• Energy gap is discretized into N parts.

Part 2 - Algorithm

• Assume m traps, sample space is NCm.

1.6 3.2

h1

h3

h2

• Pick a set { Ej }, (j = 1 to m) from the sample space.

• For a given gate bias andtemperature, find fermilevel and f (E) from DDsimulation.

1 equation, m unknowns


• Find total occupied trapdensity.

Methodology: Trap characterization (contd..)

.

.

.

Temp 1

Temp p

Is [h1,h2,…hm] same for all T

T1

Tp

Defects are at [E1 E2…Em]

Missing some defects.

Repeat with new m !

(n+1)Xm

mX1

(n+1)X1

(n+1)XmmX1

(n+1)X1

1 1 ……. 1 N_tot

1 1 ……. 1 N_tot

• To form a system of equations, the process is repeated for n voltages, n>m


Methodology: Trap characterization (contd..)

Next step: Use DFT to find atomic nature of defect

Results: Major mobility-limiting traps• Based on the methodology, three trap types are predicted.• Temperature invariance < 20 %

• E1 : 2.8-2.85 eV (2.3 X 1011 / cm2)• E2 : 3.05 eV (5.4 X 1011 / cm2)• E3 : 3.1-3.2 eV (1 X 1012 / cm2)

• Trap energies match with traps determined by experiments • DLTS [1] and • C-V measurements [2]

[1] A.F. Basile et al., J. Appl. Phys. 109, 064514 (2011). [2] N.S. Saks et al., Appl. Phys. Lett. 76, 2250 (2000).


Trap identification from DFT

• Considered trap levels of two possible SiC defects.

– Si vacancy [1,2].– Carbon dimer defect [3,4].

[1] C.J. Cochrane et al., Appl. Phys. Lett. 100, 023509 (2012).[2] M.S. Dautrich et al., Appl. Phys. Lett. 89, 223502 (2006).[3] F. Devynck et al., Phys. Rev. B 84, 235320 (2011).[4] X. Shen et al., J. Appl. Phys. 108, 123705 (2010).D.P. Ettisserry,

N. Goldsman

• No trap level seen near the conduction band edge from Si vacancy.

– Unlikely to be a major cause of poor mobility.

• C dimer defect gave trap levels close to conduction band edge.

– Similar to the energy extracted by our methodology.

• By comparison, the nature of defect at 3.1-3.2 eV could be Carbon dimer.


Overall summary

• Proposed a methodology that combines drift-diffusion simulation and density functional theory to predict:

– The existence of three types of mobility reducing defect in SiC/SiO2 interface.

– High density of interface trapping likely from Carbon dimer defects in SiCside of the interface.

• Unified Density functional theory with device modeling techniques.– Can solve practical problems encountered by semiconductor device physicists

and process engineers.• Reliability and mobility models in semiconductor devices.


Thank you, Questions?

Backup slides


• In the neutral state, at high ELF of0.9, two lone pairs on Oxygen aredistinctly visible.

• By comparing with Lewisperspective of bonding, this showsC-O single bond.

• In the stable +2 state, a single lonepair was seen on carboxyl oxygen -indicates a C=O double bond.

• Apart from puckering, increase inC-O bond order from 1 to 2 impartsstability to the defect in +2 state.

Bonding in the H2-passivated carboxyl defect• Resembles carboxyl defect and

continues to act as hole trap – H2has no/minimal effect. ESRinvisible defect in 0 and +2states.

h+

Si SiC

O

SiO

h+

H

Si SiC

O

Si SiC

O

HH

H

H

H


Switching oxide hole trap model• Holes tunnel into and out of near-interfacial

border hole traps, causing Vth instability.– Two-way tunneling model– Explains room temperature Vth instability [1].– Depth of oxide traps into which holes tunnel

change at a rate of ~2Ǻ per decade of stresstime.

• Predicts ΔVth vs log-stress time to belinear, as seen experimentally.

Room Temperature ΔVth - background

• Well-known switching oxide hole trap = E’ centers (Oxygen vacancy) [2].– Traditionally held responsible for Vth instability in 4H-SiC and Si MOSFETs.– Observed using electron spin resonance spectroscopy [3, 4].


C-related defects ???


Problem statementsCritical reliability concern – High-temperatureVth instability*

Room-Temperature ΔVth[1]

High-Temperature ΔVth[2]

* Measurements by our collaborators at U.S. Army Research Lab, MD.[1] A. J. Lelis et. al, IEEE T-ED, 55, no.8, 1835, 2008.[2] A. J. Lelis et. al, IEEE T-ED, 62, no.2, 316, 2015.[3] N. Saks et. al., APL 77, No. 20, 3281 (2000).[4] J.M. Knaup et al., PRB 71, 235321 (2005)

Critical performance concern – Very lowchannel electron mobility

Typical Dit spectrum [4]

Poor Hall and effective mobility [3]


Nitric Oxide Diffusion


Bandgap alignment


Thermal transitions between OV configurations• Activation barriers for thermal transitions between various OV configurations (in low disorder

oxide regions).• Calculated from DFT (Nudged Elastic Band method).

• Barriers are generally lower for positively charged states → negative bias is critical for trap activation.

Activation barrier calculations


Switching oxide hole trap model• Holes tunnel into and out of near-interfacial

border hole traps, causing Vth instability.– Two-way tunneling model– Explains room temperature Vth instability [1].– Depth of oxide traps into which holes tunnel

change at a rate of ~2Ǻ per decade of stresstime.

• Predicts ΔVth vs log-stress time to belinear, as seen experimentally.

Room Temperature ΔVth - background

• Well-known switching oxide hole trap = E’ centers (Oxygen vacancy) [2].– Traditionally held responsible for Vth instability in 4H-SiC and Si MOSFETs.– Observed using electron spin resonance spectroscopy [3, 4].


C-related defects ???

• Under NBTS, inactive neutral dimers are ‘activated’ to form electrically active structures.

• What is the time dependence of activation process??? - Very critical to Vth stability

𝑑𝑑𝑥𝑥1𝑑𝑑𝑡𝑡 = −𝑏𝑏12𝑒𝑒

−𝐸𝐸12𝑏𝑏 𝑇𝑇 𝑥𝑥1 + 𝑏𝑏21𝑒𝑒

−𝐸𝐸21𝑏𝑏 𝑇𝑇 𝑥𝑥2

𝑑𝑑𝑥𝑥2𝑑𝑑𝑡𝑡

= − 𝑏𝑏21𝑒𝑒−𝐸𝐸21𝑏𝑏 𝑇𝑇 + 𝑣𝑣0𝑒𝑒

−𝐸𝐸23𝑏𝑏 𝑇𝑇 + 𝑣𝑣0𝑒𝑒

−𝐸𝐸25𝑏𝑏 𝑇𝑇 𝑥𝑥2 + 𝑏𝑏12𝑒𝑒


+ 𝑣𝑣0𝑒𝑒−𝐸𝐸32𝑏𝑏 𝑇𝑇 𝑥𝑥3 + 𝑣𝑣0𝑒𝑒

−𝐸𝐸52𝑏𝑏 𝑇𝑇 𝑥𝑥5𝑑𝑑𝑥𝑥3

𝑑𝑑𝑡𝑡= − 𝑣𝑣0𝑒𝑒



−𝐸𝐸35𝑏𝑏 𝑇𝑇 𝑥𝑥3 + 𝑣𝑣0𝑒𝑒




𝑑𝑑𝑥𝑥5𝑑𝑑𝑡𝑡

= − 𝑣𝑣0𝑒𝑒−𝐸𝐸52𝑏𝑏 𝑇𝑇 + 𝑣𝑣0𝑒𝑒






𝑑𝑑𝑥𝑥4𝑑𝑑𝑡𝑡 = − 𝑣𝑣0𝑒𝑒





�𝑖𝑖=1

6

𝑥𝑥𝑖𝑖 = 1

Transient modeling of OV hole trap activation - 1

- Activation barriers from DFT- k12 and k21 from SRH



Density Functional Theory (2)• Bonn-Oppenheimer approximation

– Nuclei are much more massive than electrons. So, they are consideredstill.

– Thus, the electronic Hamiltonian becomes

– The nuclei-nuclei potential can be separately calculated.

• Hohenberg-Kohn theorem 1– The ground state energy, E[n(r)], of a multi-body system is a unique

functional of electron density, n(r).

• Hohenberg-Kohn theorem 2– The n(r) which minimizes E[n(r)] is the true ground state n(r)

corresponding to the solution of SWE.

• While the energy functional is the sum of all kinetic and potentialenergies, the effect of QM interactions are not explicitly known. Inshort, the mathematical form of the functional is unknown.


Molecular dynamics from DFT• Can determine the time evolution of atoms in a system.• From DFT, force on individual atom is calculated.• Force on atom i due to j’s= - (gradient of energy in ground state, E) From DFT

• Verlet Algorithm for tracking the position of atoms in time:𝑑𝑑2

𝑑𝑑𝑡𝑡2 𝑅𝑅𝑖𝑖 =𝐹𝐹𝑖𝑖𝑀𝑀𝑖𝑖

𝑅𝑅𝑖𝑖 𝑡𝑡 + Δ𝑡𝑡 = 2𝑅𝑅𝑖𝑖 𝑡𝑡 + 𝑅𝑅𝑖𝑖 𝑡𝑡 − Δ𝑡𝑡 +Δ𝑡𝑡 2

𝑀𝑀𝑖𝑖𝐹𝐹𝑖𝑖(𝑅𝑅𝑗𝑗)

Discretization in time to solve the differential equation.

From Newton’s law:

𝐹𝐹𝑖𝑖 𝑅𝑅𝑗𝑗 = −𝜕𝜕𝐸𝐸𝜕𝜕𝑅𝑅𝑖𝑖

• By tracking Ri, the trajectories of atoms are calculated.• Can study

• diffusion,• chemical reactions (passivation), etc

Effect of temperature included externally (velocity rescaling)


Electrical activity of defects in 4H-SiC MOSFETsWhich defects matter in 4H-SiC MOSFETs ?

• The Fermi Level is restricted tomove within 4H-SiC bandgap.

• Bandgap lineup between 4H-SiCand SiO2 is very critical.• Calculated from DFT or internal

photoemission [1].

Bandgap lineup procedure using DFT [2]

Defect in SiO2 or 4H-SiC or interface

InactiveActive

Charge Transition Level located within

4H-SiC BG?Y N

[2] C. G. Van de Walle et. al., Phys. Rev. B 34, no. 8, pp. 5621- 5634 (1986).

[1] V. V. Afanas’ev et. al., J. Appl. Phys. 79, 3108 (1996).


Density Functional Theory


Density Functional Theory - Flow


• The by-product of NO passiation reaction with the carboxyl defect is theNCO molecule – important to know if this creates new defects.

• NCO molecules are large – seen to be trapped inside SiO2 void.

• Reacts with NO molecule to give N2 and CO2.

Significance of isocyanate molecule (NCO)

Observations:• Intermediate product include

nitrosil isocyanate – activationbarrier of 0.2 eV.

• This is followed by a cyclicintermediate.

• N2 and CO2 are formed withenergy release of ~ 3 eV.

• N2 and CO2 diffuses outrelatively easily, completing thedefect passivation reaction.

• NCO is unlikely to create newdefects in SiO2.


3. Overall results on Passivation1

– Studied the mechanism of NO treatment of carboxyl defect.

• NO was seen to remove the defect.

• Excess NO seen to result in positive charge build-up.

• Controlled NO passivation to improve Vth instability.

• By-products of the reaction do not create additional defects.

– Was seen to create hole traps similar to the original carboxyl defects.

– Unlikely to be effective in improving Vth instability.

• NO passivation

• H2 passivation

[1] D.P. Ettisserry, N. Goldsman, A. Akturk, and A. Lelis, under review with the Journal of Applied Physics.

• F passivation– Passivates E’ and carboxyl – related hole traps completely. Effect of

dielectric constant reduction requires further study.


• In the neutral state, at high ELF of0.9, two lone pairs on Oxygen aredistinctly visible.

• By comparing with Lewisperspective of bonding, this showsC-O single bond.

• In the stable +2 state, a single lonepair was seen on carboxyl oxygen -indicates a C=O double bond.

• Apart from puckering, increase inC-O bond order from 1 to 2 impartsstability to the defect in +2 state.

Bonding in the H2-passivated carboxyl defect• Resembles carboxyl defect and

continues to act as hole trap – H2has no/minimal effect. ESRinvisible defect in 0 and +2states.

h+

Si SiC

O

SiO

h+

H

Si SiC

O

Si SiC

O

HH

H

H

H


Amorphous SiO2 model generation

Method 1• New method – Exploits the periodicity of supercell models, inherent in DFT.

– An Si-O-Si linkage is randomly broken.– The disconnected Si is puckered by 166 pm to back-bond with rear oxygen, making the Oxygen

triply coordinated.– One of the original Si attached to the triply coordinated O is broken and puckered to generate a

new triply coordinated O.– Process is repeated until the puckered Si meets the original dangling O, repairing the damage.

• Represents regions of oxide with high-amorphousness.

Method 2• Melt-and –quench Molecular dynamics.• Represents regions of oxide with low-amorphousness.

Important considerations• In theory, one could form infinite number of equations in the over-

determined system – but works only for carefully chosen lowvoltages.

• To minimize errors, the algorithm is applied at low voltages. Voltages at which the equations are formed are chosen in such

a way that change in Fermi level is large (or large f(E)). Also, Trap-filling happens at low voltages.

• It should be made sure that the Fermi level is such that it falls in the“region of interest” for traps (in case of SiC, near conduction band).

Limitation:• Cannot resolve mid-gap trap energies. All the mid-gap traps are fully occupied even at low gate bias

due to large SiC/SiO2 work-function difference.


• Chemical bonding can be studied using Electron LocalizationFunction (ELF).

• ELF is the conditional probability of finding an electron in thevicinity of another electron with the same spin – gives a measure ofPauli’s exclusion.

• Defined such that high ELF implies high electron localization –indicates lone pairs, bonding pairs and dangling bonds.

• These different electron localizations occur at local maxima in ELF.

• Plotted as isosurfaces at different values to distinctly “see”chemical bonding.

• ELF used to study bonding transformations in defects during holecapture – help to identify defect stabilizing mechanisms.

Electron Localization Function [1] from DFT

[1] B. Silvi and A. Savin, Nature 371, 683–686 (1994).


BTS measurements

[1] B. Silvi and A. Savin, Nature 371, 683–686 (1994).

Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf...

Documents

Transcript of Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf...