Polarization in Diamond Internal Charge Trapping Jannis Fischer - - PowerPoint PPT Presentation

Polarization in Diamond

Internal Charge Trapping Jannis Fischer

DESY Zeuthen

September 16th, 2013

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Contents

1

Basic Equations

2

Transport algorithm

3

Result

4

Outlook

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Trapping mechanisms

Traps

EV EC Et,2 Et,1 Eg EF

Look at initial, neutral state Traps below EF ≈ EV + Eg

2 are filled → Donor-like

Traps above EF ≈ EV + Eg

2 are empty → Acceptor-like

Each trap type described by function ft(x) : [0, d] → [0, 1] In initial neutral crystal: ft = 1 for Donor-like, ft = 0 for Acceptor-like Then: ft(x) = nT (x)

NT

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Trapping mechanisms

Capture/Emission Equations

Beginn with Generation/Trapping/Emission rates: Generation: 36 · 104cm−1 d

∆x · Φ

(Φ: Flux of incoming particles, d: Thickness, ∆x: cell spacing) Prompt Recombination: Next slide Trapping: ∆nT(x) = −∆n(x) = n(x)C tr

e ∆t

• 1 − nT (x)

NT

• (nT: Trapped electron density, NT: Trap density, n mobile electron

density, C tr

e = σnvth,nNT)

Detrapping: ∆nT(x) = −nT(x)C em

e

∆t (C em

e

= C tr

e 1019 exp

• −∆E

kT

• , ∆E: Depth of Trap)

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Trapping mechanisms

Prompt Recombination

Problem: How to include that some electron hole pairs will immeadiately recombine after generation? Look at CCE measurements of good crystals, use empirical formula

Diamond CCEvsHV fit

CCE −1,500 −1,000 −500 500 1,000 1,500 Voltage (V) −600 −400 −200 200 400 600 SC01013 SC01530 SC01683 SC01735 SC01756 SC01760 SC01761 NonLinearFit1 NonLinearFit2 NonLinearFit3 NonLinearFit4 NonLinearFit5 NonLinearFit6 NonLinearFit7

A,B,C,D>0 parameters

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Transport Algorithm

Steps in Simulation:

1 Generate charges uniformly in crystal, save number of generated

charges Qgen

2 Reduce this charge by prompt recombination (dependent on local

electric field)

3 Do transport: Start at negative electrode (for electrons) 4 In each cell calculate trapping and emission, change n, nT accordingly 5 Move leftover charge to next bin, count this number of moved

charges to Qmov

6 At end of crystal: CCE =

2Qmov NCellsQgen

7 Do the same for holes in opposite direction 8 Recalculate local electric field from Poisson equation using FEM 6 / 11

Transport Algorithm

Parameters

Parameter Value Thickness 5 · 10−2cm

• No. of Cells

100 Incoming Particle Flux 1000cm−2 Trap concentration 1015cm−3 Temperature 300K Time step ∆t 1s External HV 100V Trap Energy

1 4Eg

Prompt Recombination: CCE(E) = 1 − 1 1 + exp

• −5·10−2·E−38

11

• (1)

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Results

Charge distribution

Trapped Charge Distribution (t=300s)

Charge Density / cm-2 5e+10 1e+11 1.5e+11 2e+11 2.5e+11 3e+11 Cell No. 20 40 60 80 100 nT pT 8 / 11

Results

Electric Field

Internal Electric field

Electric field / Vcm-1 −8,000 −7,000 −6,000 −5,000 −4,000 −3,000 −2,000 −1,000 1,000 Cell No. 20 40 60 80 100 120 9 / 11

Results

CCE development

CCE vs time

CCE 50 60 70 80 90 100 time / s 50 100 150 200 250 300 10 / 11

Outlook

Which parameters should be examined first?

This should be discussed.

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