Hello,

I am simulating the breakdown behavior of a basic vertical Ga₂O₃ Schottky barrier diode using a 2D simulation. The diode lacks edge termination, with the Schottky contact covering only part of the top and the ohmic contact extending across the entire bottom. Experimental data suggests that this device should achieve a breakdown voltage of 1 kV. However, in my simulation, the electric field magnitude at 1 kV exceeds 50 MV/cm—far beyond Ga₂O₃'s critical electric field of 8 MV/cm.

I have attempted refining the mesh near the electrodes, but the more I tighten it, the higher the electric field peak becomes. Despite this, my I-V analysis still indicates breakdown at approximately 1 kV (which matches my measured results). How can I modify my simulation to produce realistic electric field values? My SDE and SDevice code are provided below. I have removed the breakdown mechanism in the code below becasue I am only interested in the electric field becasue I have already gotten the IV curves to show breakdown.

SDE:

(define Wtot 12)

(define Lsub 0)

(define Lepi 10)

(define Ltot (+ Lsub Lepi))

(define EpiDop 1.3e16)

; =================== Outer Boundary Creation =========================

;---SiC Region

(sdegeo:create-rectangle (position 0.0 0.0 0.0) (position Ltot Wtot 0.0)

"Ga2O3" "EpiSubRegion" )

; =================== Contact Definition Placement =========================

(sdegeo:define-contact-set "top_schottky" 4.0 (color:rgb 1.0 0.0 0.0) "##")

(sdegeo:define-contact-set "bot_ohmic" 4.0 (color:rgb 1.0 0.0 0.0) "##")

(sdegeo:insert-vertex (position 0 5 0))

(sdegeo:define-2d-contact (find-edge-id (position 0.0 4 0.0)) "top_schottky")

(sdegeo:define-2d-contact (find-edge-id (position Ltot 1.0 0.0)) "bot_ohmic")

(sdegeo:bool-unite (find-region-id "top_schottky"))

; =================== Constant and Analytical Profiles =========================

;---Definitions

(sdedr:define-constant-profile "Epi_Dop_Defn" "ArsenicActiveConcentration" EpiDop)

;---Windows

(sdedr:define-refeval-window "Epi_Win" "Rectangle" (position 0 0 0) (position Lepi Wtot 0.0))

;---Placement

(sdedr:define-constant-profile-placement "Epi_Place" "Epi_Dop_Defn" "Epi_Win")

; =================== Refinements =========================

;---Definitions

(sdedr:define-refinement-size "Global_Ref_Defn"

0.05 0.05 0.0

0.05 0.05 0.0 )

(sdedr:define-refinement-size "Ref.edge"

0.01 0.01 0.0

0.001 0.001 0.0 )

;---Windows

(sdedr:define-refeval-window "Global_Win"

"Rectangle" (position 0.0 0.0 0.0) (position Ltot Wtot 0.0) )

(sdedr:define-refeval-window "edge"

"Rectangle" (position 0 4.8 0) (position 0.2 5.2 0))

;---Refinement function

(sdedr:define-refinement-function "Ref.SiAct" "DopingConcentration" "MaxTransDiff" 1.0)

;---Placement

(sdedr:define-refinement-placement "Global_Ref_Place" "Global_Ref_Defn" "Global_Win" )

(sdedr:define-refinement-placement "RefPlace.edge" "Ref.edge" "edge")

Sdevice:

## Electrical contact definitions

Electrode {

{ Name="bot_ohmic" Voltage= 0.0 }

{ Name="top_schottky" Schottky Voltage= 0.0 Workfunction= @WF@}

}

## Input/Ouput files

File {

Grid= "@tdr@"

Plot= "@tdrdat@"

Current= "@plot@"

Output= "@log@"

Parameter= "@parameter@"

}

## Physics models

Plot {

eDensity hDensity

eCurrent hCurrent

ElectricField

eQuasiFermi hQuasiFermi

egradQuasiFermi hgradQuasiFermi

Potential Doping SpaceCharge

eMobility hMobility

DonorConcentration AcceptorConcentration

Doping

eVelocity hVelocity

ConductionBandEnergy ValenceBandEnergy BandGap

eQuasiFermi hQuasiFermi

}

Math {

-checkundefinedmodels

Digits= 8

Extrapolate

ErrEff(electron)= 1e2

ErrEff(hole)= 1e2

RHSmin= 1e-20

RHSmax= 1e70

RHSFactor= 1e70

Notdamped= 20

Iterations= 12

ExitOnFailure

ExtendedPrecision(128)

BM_ExtendedPrecision

NumberofThreads= 4

CdensityMin= 1e-25

SimStats

}

Solve {

Coupled(Iterations= 1000 LineSearchDamping= 0.001 ) { Poisson }

Coupled(Iterations= 1000 LineSearchDamping= 0.001 ) { Poisson Hole }

Coupled(Iterations= 1000 LineSearchDamping= 0.001 ) { Poisson Electron Hole }

NewCurrentPrefix= "BV_"

Quasistationary (

Initialstep= 1e-3 Increment= 1.55

Maxstep= 0.5 Minstep= 1.e-15

Goal { Name="top_schottky" Voltage= -1e3 }

) { Coupled { Poisson Electron Hole }

}