integrated modeling of high-temperature gate-bias …neil/sic_workshop/presentations_2015/pdf...
TRANSCRIPT
![Page 1: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/1.jpg)
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
![Page 2: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/2.jpg)
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
D.P. Ettisserry,N. Goldsman
![Page 3: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/3.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 4: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/4.jpg)
D.P. Ettisserry,N. Goldsman
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
![Page 5: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/5.jpg)
D.P. Ettisserry,N. Goldsman
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
![Page 6: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/6.jpg)
D.P. Ettisserry,N. Goldsman
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
![Page 7: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/7.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 8: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/8.jpg)
D.P. Ettisserry,N. Goldsman
• 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).
![Page 9: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/9.jpg)
D.P. Ettisserry,N. Goldsman
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).
![Page 10: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/10.jpg)
D.P. Ettisserry,N. Goldsman
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).
![Page 11: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/11.jpg)
D.P. Ettisserry,N. Goldsman
• 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.
![Page 12: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/12.jpg)
D.P. Ettisserry,N. Goldsman
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).
![Page 13: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/13.jpg)
D.P. Ettisserry,N. Goldsman
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??
![Page 14: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/14.jpg)
D.P. Ettisserry,N. Goldsman
Electrical properties of Oxygen vacanciesElectrical activity of Oxygen Vacancy:
• Basic neutral dimers are electrically inactive.
• Higher energy configurations are active.
[1] M.A. Anders et.al., IIRW pp. 16-19, Oct. 2014.
Under NBTS, neutral dimers are ‘activated’ to form active forward-projected and back-projected structures.
![Page 15: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/15.jpg)
D.P. Ettisserry,N. Goldsman
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)
![Page 16: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/16.jpg)
D.P. Ettisserry,N. Goldsman
• 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.
[2] M.A. Anders et.al., IIRW pp. 16-19, Oct. 2014.
![Page 17: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/17.jpg)
D.P. Ettisserry,N. Goldsman
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
![Page 18: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/18.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 19: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/19.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 20: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/20.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 21: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/21.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 22: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/22.jpg)
D.P. Ettisserry,N. Goldsman
Thank you, Questions?
![Page 23: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/23.jpg)
D.P. Ettisserry,N. Goldsman
Additional defects involved in hole trapping
• Role of carbon-related defects• Stability-providing bonding mechanisms
![Page 24: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/24.jpg)
D.P. Ettisserry,N. Goldsman
• 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
![Page 25: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/25.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 26: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/26.jpg)
D.P. Ettisserry,N. Goldsman
• 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.
![Page 27: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/27.jpg)
D.P. Ettisserry,N. Goldsman
• 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.
![Page 28: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/28.jpg)
D.P. Ettisserry,N. Goldsman
• 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+
![Page 29: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/29.jpg)
• Mobility degradation in 4H-SiC MOSFETs
D.P. Ettisserry,N. Goldsman
• Drift Diffusion simulation of 4H-SiC MOSFET.• Algorithm for trap characterization.
![Page 30: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/30.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 31: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/31.jpg)
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).
D.P. Ettisserry,N. Goldsman
![Page 32: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/32.jpg)
( ) ( ) ( )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
D.P. Ettisserry,N. Goldsman
![Page 33: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/33.jpg)
• 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
D.P. Ettisserry,N. Goldsman
![Page 34: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/34.jpg)
• 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
D.P. Ettisserry,N. Goldsman
• Find total occupied trapdensity.
Methodology: Trap characterization (contd..)
![Page 35: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/35.jpg)
.
.
.
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
D.P. Ettisserry,N. Goldsman
Methodology: Trap characterization (contd..)
![Page 36: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/36.jpg)
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).
D.P. Ettisserry,N. Goldsman
![Page 37: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/37.jpg)
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.
![Page 38: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/38.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 39: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/39.jpg)
D.P. Ettisserry,N. Goldsman
Thank you, Questions?
![Page 40: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/40.jpg)
Backup slides
![Page 41: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/41.jpg)
D.P. Ettisserry,N. Goldsman
• 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
![Page 42: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/42.jpg)
D.P. Ettisserry,N. Goldsman
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].
[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).
C-related defects ???
![Page 43: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/43.jpg)
D.P. Ettisserry,N. Goldsman
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]
![Page 44: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/44.jpg)
D.P. Ettisserry,N. Goldsman
Nitric Oxide Diffusion
![Page 45: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/45.jpg)
D.P. Ettisserry,N. Goldsman
Bandgap alignment
![Page 46: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/46.jpg)
D.P. Ettisserry,N. Goldsman
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
![Page 47: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/47.jpg)
D.P. Ettisserry,N. Goldsman
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].
[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).
C-related defects ???
![Page 48: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/48.jpg)
• 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
−𝐸𝐸12𝑏𝑏 𝑇𝑇 𝑥𝑥1
+ 𝑣𝑣0𝑒𝑒−𝐸𝐸32𝑏𝑏 𝑇𝑇 𝑥𝑥3 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸52𝑏𝑏 𝑇𝑇 𝑥𝑥5𝑑𝑑𝑥𝑥3
𝑑𝑑𝑡𝑡= − 𝑣𝑣0𝑒𝑒
−𝐸𝐸32𝑏𝑏 𝑇𝑇 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸34𝑏𝑏 𝑇𝑇 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸35𝑏𝑏 𝑇𝑇 𝑥𝑥3 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸23𝑏𝑏 𝑇𝑇 𝑥𝑥2
+ 𝑣𝑣0𝑒𝑒−𝐸𝐸43𝑏𝑏 𝑇𝑇 𝑥𝑥4 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸53𝑏𝑏 𝑇𝑇 𝑥𝑥5
𝑑𝑑𝑥𝑥5𝑑𝑑𝑡𝑡
= − 𝑣𝑣0𝑒𝑒−𝐸𝐸52𝑏𝑏 𝑇𝑇 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸56𝑏𝑏 𝑇𝑇 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸53𝑏𝑏 𝑇𝑇 𝑥𝑥5 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸25𝑏𝑏 𝑇𝑇 𝑥𝑥2
+ 𝑣𝑣0𝑒𝑒−𝐸𝐸65𝑏𝑏 𝑇𝑇 𝑥𝑥6 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸35𝑏𝑏 𝑇𝑇 𝑥𝑥3
𝑑𝑑𝑥𝑥4𝑑𝑑𝑡𝑡 = − 𝑣𝑣0𝑒𝑒
−𝐸𝐸43𝑏𝑏 𝑇𝑇 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸46𝑏𝑏 𝑇𝑇 𝑥𝑥4 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸34𝑏𝑏 𝑇𝑇 𝑥𝑥3 + 𝑣𝑣0𝑒𝑒
−𝐸𝐸64𝑏𝑏 𝑇𝑇 𝑥𝑥6
�𝑖𝑖=1
6
𝑥𝑥𝑖𝑖 = 1
Transient modeling of OV hole trap activation - 1
- Activation barriers from DFT- k12 and k21 from SRH
D.P. Ettisserry,N. Goldsman
![Page 49: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/49.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 50: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/50.jpg)
D.P. Ettisserry,N. Goldsman
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)
![Page 51: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/51.jpg)
D.P. Ettisserry,N. Goldsman
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).
![Page 52: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/52.jpg)
D.P. Ettisserry,N. Goldsman
Density Functional Theory
![Page 53: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/53.jpg)
D.P. Ettisserry,N. Goldsman
Density Functional Theory - Flow
![Page 54: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/54.jpg)
D.P. Ettisserry,N. Goldsman
• 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.
![Page 55: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/55.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 56: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/56.jpg)
D.P. Ettisserry,N. Goldsman
• 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
![Page 57: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/57.jpg)
D.P. Ettisserry,N. Goldsman
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.
![Page 58: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/58.jpg)
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.
![Page 59: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/59.jpg)
D.P. Ettisserry,N. Goldsman
• 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).
![Page 60: Integrated Modeling of High-Temperature Gate-Bias …neil/SiC_Workshop/Presentations_2015/pdf only...Integrated Modeling of High-Temperature Gate-Bias (HTGB) Reliability Degradation](https://reader031.vdocuments.us/reader031/viewer/2022030819/5b3019b47f8b9af0648e4cc3/html5/thumbnails/60.jpg)
D.P. Ettisserry,N. Goldsman
BTS measurements
[1] B. Silvi and A. Savin, Nature 371, 683–686 (1994).