Modeling of SiC :Interfaces, Transport & Devices

University of Maryland

Chris Darmody, Ziyang Xiao, Neil Goldsman,

Dev Ettisserry & Akin Akturk

Army Research Lab

Aivars Lelis, Ron Green & Dan Habersat

Outline

1. Neil Goldsman

a) Summary of Key Earlier Results

2. Chris Darmody

a) Extracting the Ideal Surface Mobility with DFT

b) Monte Carlo Modeling of SiC

3. Neil Goldsmana) Atomic Defect Levels and NO Anneal

Explanations

Modeling of SiC & GaN:Interfaces, Transport & Devices

SiC & GaN Device Virtual Fab, Design and Analysis Platform

Process & Fabrication Modeling

(Device Structure &Defect Generation)

Device Modeling(I-V & Performance)

Monte Carlo: (Transport)

Density Functional Theory

(Defects)

Σ

CoolSPICECircuit Design

Device Meet Specs?

YES

NO

E

X

P

E

R

I

M

E

N

T

Summary of Key Results:Transition Region & Atomic Origin of Defects

• Reliability: Threshold Instabilities– Due to Oxide Vacancies and Carboxyl Substitutions in SiO2 side of Trans.

Region (TR)

• Interface States: Mobility Degradation at Low Vgs. – Due to atomic defects in SiC side TR.

• Surface roughness: Mobility Degradation at High Vgs

• Transition Region: Mobility Degradation due to Disruptions in Bloch Functions and Increased Density of States.– Non-Stoichiometric Substitutions and Interstitials in SiC side of Interface

– Oxygen substituting for Carbon and Carbon Interstitials, Carbon Dimers identified and key Non-Stochiometric Structures in TR.

Summary of Key Results: Passivation

SiO2

SiC

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Summary of Key Results: Passivation

• Nitrogen:

– Passivates Carboxyl Defects in Oxide

– Passivates E’ centers in Oxide

– Passivates carbon interstitials

– But too much N generates more (+) charge & more states near CB.

– Gives rise to counter doping layer at interface

• Improves field effect mobility mainly due to counter doping.

– Acts as a dopant and fills Si vacancies in SiC

Extrinsic vs Intrinsic Mobility Comparisons and Key Result

1

μ𝑇𝑜𝑡𝑎𝑙=

1

μ𝐵𝑢𝑙𝑘+

1

μ𝑆𝑃+

1

μ𝐶+

1

μ𝑆𝑅+⋯ 𝜇𝑖 =

𝑞𝜏𝑖𝑚

𝝁 [ Τ𝒄𝒎𝟐 𝑽𝒔]Surface Field [MV/cm]

0.1 0.5 1

μ𝐵 1070

μ𝑆𝑃 1470 560 400

μ𝐴𝑅 4.4 x 107 1.8 x 106 4.8 x 105

𝝁𝒊𝒏𝒕𝒓𝒊𝒏𝒔𝒊𝒄 620 370 290

μ𝑆𝑅 350 14 4

μ𝐶 429 447 591

𝝁𝒆𝒙𝒕𝒓𝒊𝒏𝒔𝒊𝒄 193 14 4

𝝁𝑻𝒐𝒕𝒂𝒍 147 13 4

Intrinsic Surface Mobility is significantly larger than ExtrinsicIntrinsic Limit: Similar to that of Silicon

Questions?

Next, Chris Darmody will tell us the theoretically best mobility you can get in SiC from SiC/SiO2 DFT Interface

Modeling

Key Finding:Eliminate Mis-cut: Improve surface mobility to almost

700 cm2/V-sec

That’s it for Introduction

Intrinsic Surface Mobility Limit of SiC MOS Devices

Chris Darmody, Neil Goldsman

UMD 2018

Research Interest and Goals

• SiC experimentally shows low surface mobility in MOS devices

• Is this degradation intrinsic to the SiC/SiO2 interface?How good can mobility get?

• Goals: – Separate Intrinsic and Extrinsic Surface Mobility Components– Quantify and compare the intrinsic atomic-level roughness

mobility to other effects

Extrinsic

Intrinsic

Surface Roughness Mobility Models

• Existing:– Lumps intrinsic and extrinsic

factors together– Approximated using a two-

parameter mathematical form to describe the average roughness profile of the surface

• Our Model:– Extracts the atomic-interface

potential from DFT calculation using atomic-scale interface model

– Calculates scattering rate directly from extracted potential

Steps to Extract Intrinsic Atomic-Level Surface Mobility

Structural Relaxation of Pristine Interface

Self-Consistently Calculate Potential of Atomic Interface

Subtract Bulk Potential from Interface Potential to get Perturbation

Density Functional Theory

Perturbation Theory

Use Fermi’s Golden Rule to Calculate Scattering Rate

Directly Calculate Mobility from Scattering Rate

What is DFT?

• Allows us to effectively solve the many-body Schrodinger equation in a crystal

• Single Hydrogen Atom Schrodinger Equation:

−ћ2

2𝑚𝛻2 −

𝑍𝑗𝑞2

𝑟𝜓(𝑟) = 𝐸𝜓(𝑟)

• Many-Body Schrodinger Equation in Crystal:

−

𝑖

ћ2

2𝑚𝛻𝑟𝑖2 −

𝑖

𝑗

𝑍𝑗𝑞2

𝑟𝑖 − 𝑟𝑗+1

2

𝑖

𝑖′

𝑞2

𝑟𝑖 − 𝑟𝑖′𝜓(𝑟1, … , 𝑟𝑁)

= 𝐸𝜓(𝑟1, … , 𝑟𝑁)

• Replaces N-body equation with set of N Kohn-Sham equations for non-interacting particles

−ћ2

2𝑚𝛻2 + 𝑣𝐾𝑆 𝑟 𝜙𝑖 𝑟 = 휀𝑖𝜙𝑖(𝑟)

𝑣𝐾𝑆(𝑟) = 𝑣𝑒𝑥𝑡(𝑟) + 𝑣𝐻[𝜌 𝑟 ] + 𝑣𝑋𝐶[𝜌 𝑟 ] 𝜌 𝑟 = σ𝑖𝑁 |𝜙𝑖 𝑟 |2

Perturbation Theory For Surface Scattering

• Calculate Transition rate from electron in initial state 𝜓𝑖 to final state 𝜓𝑓 using Fermi’s Golden Rule

𝑅𝑖→𝑓 =2𝜋

ħ2𝜓𝑓 ∆𝑉 𝜓𝑖

2𝛿(𝐸𝑓 − 𝐸𝑖)

• Extract 3D atomic perturbation potential (ΔV) around SiC/SiO2

interface from DFT calculations

SiO2

SiC

Interface Potential Extraction

Salemi et al. Journal. Appl. Phys. 113, 2013

Perturbation Potential from Atomic Structure

SiO2

SiC

𝑉𝑥𝑦(𝑧) =1

𝐴ඵ𝑉 𝑥, 𝑦, 𝑧 𝑑𝑥 𝑑𝑦

Salemi et al. Journal. Appl. Phys. 113, 2013

Perturbation Potential Extraction

∆𝑉 = 𝑉𝑆𝑖𝐶/𝑆𝑖𝑂2 − 𝑉𝐵𝑢𝑙𝑘

∆𝑉 = 𝑉𝑆𝑖𝐶/𝑆𝑖𝑂2 − 𝑉𝐵𝑢𝑙𝑘

CalculatedPerturbation

SiC

SiO2

Details of Atomic-Level Perturbation

Oxygen Atoms

‘Virtual’ Carbon Sites

MOS Channel Electron Wavefunction

𝑅𝑖→𝑓 =2𝜋

ħ2𝜓𝑓 ∆𝑉 𝜓𝑖

2𝛿 𝐸𝑓 − 𝐸𝑖

• Assume electron free free in plane of channel and bound in z direction

• Potential quantum well near interface approximately triangular

• Wavefunction has free particle plane wave solution in x and y directions:

– 𝜓 𝑥, 𝑦 = 𝐴𝑒𝑖(𝑘𝑥𝑥+𝑘𝑦𝑦)

• Airy function solution in z direction:

– 𝜓 𝑧 =1

𝜋0∞cos

𝑡3

3+ 𝜉𝑡 𝑑𝑡=Ai[𝜉]

– 𝜉 =2𝑚𝑞 Ԧ𝐸

ћ2

1

3𝑧 −

𝐸𝑛

𝑞 Ԧ𝐸

– 𝐸𝑛 =ħ2

2𝑚

1/33𝜋𝑞 Ԧ𝐸

2𝑛 −

1

4

2/3

𝑉 𝑧 = 𝐸 𝑧 = 𝐹𝑧

1-10 nm

Quantum Well

2D Atomic Surface Scattering Rates

Energy-dependent scattering rate in each subband

Energy and field-dependent scattering rate for 1st subband

2

Field-Dependent Scattering Rate

SiO2SiC

Interface

𝜓 2 peaks closer to interface for higher surface electric fields and higher energies- Leads to increased scattering rate

Scattering Rate increases with the square of the surface field

Extrinsic vs Intrinsic Mobility Comparisons and Key Result

1

μ𝑇𝑜𝑡𝑎𝑙=

1

μ𝐵𝑢𝑙𝑘+

1

μ𝑆𝑃+

1

μ𝐶+

1

μ𝑆𝑅+⋯ 𝜇𝑖 =

𝑞𝜏𝑖𝑚

𝝁 [ Τ𝒄𝒎𝟐 𝑽𝒔]Surface Field [MV/cm]

0.1 0.5 1

μ𝐵 1070

μ𝑆𝑃 1470 560 400

μ𝐴𝑅 4.4 x 107 1.8 x 106 4.8 x 105

𝝁𝒊𝒏𝒕𝒓𝒊𝒏𝒔𝒊𝒄 620 370 290

μ𝑆𝑅 350 14 4

μ𝐶 429 447 591

𝝁𝒆𝒙𝒕𝒓𝒊𝒏𝒔𝒊𝒄 193 14 4

𝝁𝑻𝒐𝒕𝒂𝒍 147 13 4

Intrinsic Surface Mobility is significantly larger than Extrinsic

Feed Scattering Rates into Monte Carlo

• Follow an electron scattering in k-space to get transport characteristics

• Scattering mechanism chosen randomly, weighted by scattering rates

• Collect statistics about its energyand velocity over time

• Build distributions for different applied fields

−ħ2

2𝑚𝛻2 + 𝑉 𝑟 ψ𝑘 𝑟 = 𝐸ψ𝑘 𝑟

𝑑𝑘

𝑑𝑡=−𝑞𝐹

ħChange in k under applied field:

Velocity at a given k: 𝑉(𝑘) =1

ħ

𝑑𝐸(𝑘)

𝑑𝑘

SiC Scattering Rates

Bulk Scattering Simulation –Experimental Agreement

Data from Khan et al. IEEE Trans. On Elec. Dev. (2000)

Dots/Dashed = ExperimentSolid = Monte Carlo

23 °C

320 °C

High Field Effects and High Energy Tail Population Increase

T=300K

Arb

. Un

its

High field shows electrons with energy greater than bandgap –leads to impact ionization avalanching, and perhaps gate leakage

Pure Mobility Results and Overview

• Calculated reasonable field-dependent bulk mobilities from MC simulation as a function of Field and Temperature

• Developed surface roughness scattering extraction technique from atomic-level interface

• Estimated a mobility limit for an ideal surface based on the intrinsic mobility of the interface

𝜇 =Ԧ𝑣𝑑𝑟𝑖𝑓𝑡

𝐸

𝜇 =𝑑 Ԧ𝑣𝑑𝑟𝑖𝑓𝑡

𝑑𝐸

Pure mobility is distinct from field-effect mobility which contains channel charge ‘n’ implicitly

Intrinsic Vs Extrinsic Mobility Key Finding

• Extrinsic scattering mechanisms are the greatest contributing factor to low MOS channel mobility including:• Miscut (nanometer-scale) Surface Roughness• Interface Trap Coulombic Scattering

• Monte Carlo transport calculations investigate transport effects with/without miscut

• Suggest next generation SiC transistor and circuit on-axis topologies.

𝜇 = 13 Τ𝑐𝑚2 𝑉𝑠 𝜇 = 370 Τ𝑐𝑚2 𝑉𝑠

Miscut lowers mobility by ~ 10-20x

Thank You! Questions? Neil Next On Atomic Defects

Atomic View of Defect Levels and Nitrogen Passivation

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Dev Ettisserry and Neil Goldsman

A Fundamental Many Body Quantum Mechanical Perspective Density Functional Theory

Type 1 Oxygen Vacancies(Electrically Active at room temperature)

• Type 1 OVs have their +1/0 charge transition levels within the 4H-SiC BG.– Makes hole capture energetically favorable even at room temperature.

• On hole capture, they show the well-known back-bonding transformations.

• All the structurally transformed configurations are also electrically active (+1/0

CTL within the BG).

• These OVs are likely to play a role in room temperature Vth instability.

– Supports previous models like the HDL model and ESR studies.

Different structural configurations of Type 1 OVs during hole capture and release

Calculated CTLs for different OV configurations

NO Anneal: Diffusion of NO in a-SiO2

• Diffusion of NO in a-SiO2 studied using DFT-based Nudged Elastic Band (NEB)

method – different directions considered.

• Diffusion barrier = ~ 0.25 eV to 0.6 eV (typical error ~ +0.15 eV).

• NO unlikely to incorporate into bulk oxide in large numbers.

Initial state Final state

diffusion

diffusion

Incorporation of NO into near-interfacial oxide

• NO is considered to dissociate near the interface.

• What happens to atomic N??

– Studied by tracking atomic N in bulk SiO2 – Quantum Molecular Dynamics

(5ps).

• N observed to incorporate into oxide, forming stable Si-[NO]-Si defect (we call it

the ‘Nitroxyl’ defect).

• Almost barrierless, based on NEB simulation.

• ‘Nitroxyl’ defects also formed by trapping of NO in oxygen vacancies (E’ centers

– based on MD)

• Alternate configurations possible.

Incorporation of NO into near-interfacial oxide

• NO is considered to dissociate near the interface.

• What happens to atomic N??

– Studied by tracking atomic N in bulk SiO2 – Quantum Molecular Dynamics

(5ps).

• N observed to incorporate into oxide, forming stable Si-[NO]-Si defect (we call it

the ‘Nitroxyl’ defect).

• Almost barrierless, based on NEB simulation.

• ‘Nitroxyl’ defects also formed by trapping of NO in oxygen vacancies (E’ centers

– based on MD)

• Alternate configurations possible.

Incorporation of NO at 4H-SiC surface

• N and O added between

different Si-C bonds to obtain

three non-equivalent structures.

• Energy gains indicate

a) N counter-doping

b) Re-oxidation of 4H-SiC

plus E’ center generation

Interface containing

molecular NO –

reference structure

Counter-doped structure 4H-SiC re-oxidation and OV

generation

Intermediary non-

equivalent

configurations

• Validates N counter

doping as a

mechanism for

improved mobility in

NO annealed devices.

Interface modeled by

molecular dynamics

Overall Summary and Results

• Major Defect Structures Identified

• Atomic Structure of Surface Isolated

• Detailed Potential Energy of Atomic Surface Configuration Identified

• Surface Potential Used to Isolate Intrinsic from Extrinsic Mobility

• Remove Dislocations: Surface Mobility: ~ 700cm2/V-s

• Atomic configurations of E-prime Center States Identified

• Some Roles of Nitrogen Passivation on Atomic Level Identified

• Use information for optimizing NO passivation

• Expect better Transconductance Performance if/when we transition

to Planar Topologies

THANK YOU: QUESTIONS

Overall summary

• Employed Density functional theory to understand the behavior of N atoms at/near

4H-SiC/SiO2 interface during NO annealing.

• Diffusion of Molecular NO in a-SiO2 analyzed.

– Molecular NO reactions in the bulk oxide are unlikely.

• NO dissociates near interface, leading to various competing mechanisms.

– Incorporation of atomic N into the near-interfacial oxide looks energetically

feasible.

• Resulting configurations are switching oxide traps or fixed positive

charges that could limit reliability.

– Incorporation of atomic N and O at 4H-SiC surface possible.

• Leads to N counter-doping and enhanced mobility.

• Re-oxidation of 4H-SiC plus E’ center generation (which in turn degrades

reliability).

– Process optimization to balance these competing interface reactions likely to

improve device reliability and performance – need of the hour.

2D Scattering Rates for MOS Quantum Well

𝑅𝑖→𝑓 =2𝜋

ħ2𝜓𝑓 ∆𝑉 𝜓𝑖

2𝛿 𝐸𝑓 − 𝐸𝑖

• Transition rate S(k,k’) from state ห ൿ𝑘||, 𝑛 to ห ൿ𝑘||′ , 𝑛′ :

𝑆 𝑘||, 𝑘||′ , 𝑛, 𝑛′ =

2π

ћ𝑘||′ , 𝑛′ ∆𝑉 𝑘||, 𝑛

2𝛿

ħ2 𝑘||′ 2

2𝑚+ 𝐸𝑛′ −

ħ2 𝑘||2

2𝑚− 𝐸𝑛

• Energy conservation imposes allowed 𝑘||𝑓𝑖𝑛𝑎𝑙 values:

𝑘||𝑓𝑖𝑛𝑎𝑙

= (𝑘||𝑖𝑛𝑖𝑡𝑖𝑎𝑙)2+

2𝑚

ћ2(𝐸𝑚

𝑖𝑛𝑖𝑡𝑖𝑛𝑎𝑙 − 𝐸𝑚𝑓𝑖𝑛𝑎𝑙

)

• Obtain total scattering rate W(k) out of state ห ൿ𝑘||, 𝑛 by summing over all allowed final states:

𝑊2𝐷 𝑘||, 𝑛 =𝐴

(2𝜋)2

𝑛′

න𝑆 𝑘||, 𝑘||′ , 𝑛, 𝑛′ 𝑑𝑘||

′

Allowed Values for Electron Wavevector 𝑘||

𝑘||𝑓𝑖𝑛𝑎𝑙

= (𝑘||𝑖𝑛𝑖𝑡𝑖𝑎𝑙)2+

2𝑚

ћ2(𝐸𝑛

𝑖𝑛𝑖𝑡𝑖𝑎𝑙 − 𝐸𝑚𝑓𝑖𝑛𝑎𝑙

) 𝑊2𝐷 𝑘||, 𝑛 =𝐴

(2𝜋)2

𝑛′

න𝑆 𝑘||, 𝑘||′ , 𝑛, 𝑛′ 𝑑𝑘||

′

Allowed final states lie on rings