Band gap energy modelisa0on in Silvaco TCAD Atlas Device simulator
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1 31st RD50 Workshop (CERN) 20-22/11/2017 Band gap energy modelisa0on in Silvaco TCAD Atlas Device simulator M. Bomben LPNHE & UPD, Paris - France M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 1
2 Outline Bandgap narrowing in Silvaco Reverse/forward current level vs bandgap and temperature SimulaNon of radianon damage and impact of bandgap and temperature Reverse bias: deplenon voltage and leakage current Forward bias: forward current Conclusions and Outlook M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 2
3 BANDGAP NARROWING IN SILVACO M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 3
4 Bandgap narrowing in Silvaco M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 4
5 Bandgap narrowing: how it looks like [ev] E g Slotboom Calculated from previous formula N tot -3 [cm ] M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 5
6 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 6 Bandgap narrowing: how it looks like [ev] E g Slotboom Sentaurus Courtesy of Michael Moll N tot [cm ] Not sizeable difference
7 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 7 Test structure: effecnve doping concentranon Bulk ~ 5e16/cm 3
8 Test structure: bandgap energy in simulanon M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 8
9 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 9 Test structure: bandgap energy in simulanon No hidden adjustments here: it is what is calculated according to the formulas
10 Temperature dependence of Eg Both Silvaco Atlas and Synopsys Sentaurus use the same parameterizanon for Eg(T)*: * The very well known difference between the two is that: Eg(300K) = 1.08 ev in Silvaco Atlas Eg(0K) = ev in Synopsys Sentaurus (ó Eg(300K)~1.12 ev) * S. M. Sze, Physics of semiconductor devices. John Wiley & Sons, 1981 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN
11 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 11 How do Eg change with temperature? [ev] E g 1.1 E g (0 K) =1.124 ev E g (-20 C) = 1.2 ev SILVACO TCAD E g E g ( 0 C) = ev (+20 C) = ev E g (300 K) =1.08 ev T [K]
12 Reminder: why 1.08 ev? M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 12
13 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 13 Intrinsic concentranon vs temperature -3 [cm n i 9 ] χ 2 / ndf 1.424e+14 / 8 Norm 4.718e+19 ± 5.314e+17 n 2 ± 0 E [ev] ± a N.B.! More on this later n i ( K) = 8.29x 9 cm Eg fixed at 1.08 ev -3 n i (300 K) = 1.45x cm -3 Consistent with literature T [K]
14 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 14 Intrinsic concentranon vs bandgap 3 [1/cm n i ~-E g /2kT => OK! 6 ] T = 20 C TCAD sim. fit χ 2 / ndf / 4 Norm [1/cm ] 8.29e+09 ± Mult. Fact ± Th. En. [ev] ± 0 E g [ev] 1.08 ± Fit Function: (Mult. Fact).(x-E ) g Norm exp(- ) Th. En. EG300 [ev]
15 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 15 Bandgap narrowing in Silvaco: summary Bandgap narrowing as a funcnon of doping works as expected Bandgap narrowing with temperature works as expected Intrinsic concentranon scaling with temperature works as expected And value at K is in agreement with literature when Eg(300 K) = 1.08 ev is used Intrinsic concentranon scaling with bandgap works as expected
16 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 16 REVERSE CURRENT LEVEL VS BANDGAP
17 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 17 Structure 200 µm thick 50 µm wide n+ implant bulk concentranon
![M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 18 Reverse leakage current vs Eg and carr. vel. [A/cm] J leak 0.2 0.18 0.16 0.](/docs-images/93/111297450/images/18-3.jpg "14 0.12 0.1 12 The only relevant parameter here is Eg Eg=1.08eV Eg=1.12eV 0.08 0.06 default EG112 0.04 Syn. Th. Vel. EG112 & Syn. Th. Vel. 0.02 NO BGN 0 500 400 300 200 0 0 [V] V bias")
18 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 18 Reverse leakage current vs Eg and carr. vel. [A/cm] J leak The only relevant parameter here is Eg Eg=1.08eV Eg=1.12eV default EG Syn. Th. Vel. EG112 & Syn. Th. Vel NO BGN [V] V bias
19 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 19 Simulated leakage current vs predicnon n i ( K) = 8.29x 9 cm -3 Aw = 1e-8 cm 3 τ g ~ 4x -5 s Predicted I = qn i Aw/2/τ g ~ 1.6x -13 A Simulated I ~ 1.65x -13 A è Everything is consistent
20 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 20 Leakage current vs Temperature, Φ = 0 I [A/cm] 13 χ 2 / ndf 1.52 / 6 Prob /T ref ± 0 n ± E a ± I 1.654e 13 ± 1.16e 16 ref I vs 1/T I evaluated at V depl + 50 V (V depl does not depend from T) 14 n free to float -1 1/T [K ] I [A/cm] 13 χ 2 / ndf / 7 Prob /T ref ± 0 n 2 ± 0 E a 1.13 ± I 1.654e 13 ± 9.064e 17 ref 14 n fixed to 2-1 1/T [K ]
21 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 21 Leakage current vs Temperature, Φ = 0 I [A/cm] 13 χ 2 / ndf 1.52 / 6 Prob /T ref ± 0 n ± E a ± I 1.654e 13 ± 1.16e 16 ref I vs 1/T I evaluated at V depl + 50 V (V depl does not depend from T) 14 n free to float -1 1/T [K ] I [A/cm] Ea ~ 1.13 ev n ~ 2 13 χ 2 / ndf / 7 Prob /T ref ± 0 n 2 ± 0 E a 1.13 ± I 1.654e 13 ± 9.064e 17 ref 14 n fixed to 2-1 1/T [K ]
22 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 22 E a vs E g (300K) Φ = 0 [ev] E a TCAD Simulation Linear fit SILVACO TCAD Empirical rule: E a = E g (300)+0.05 ev Sil (300) [ev] E g
23 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 23 (Reverse -20 C scaled to 20 C)/I(20 C) I scaled /I( K) ±2% [V] V bias
24 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 24 RaNo of Reverse currents scaled to 20 C I scaled /I( K) % the accuracy on average of the rescaling Slope consistent with 1 Intercept consistent with 0 TCAD Simulation Linear fit T [K]
25 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 25 Forward current before irradianon Current [A/cm] n-on-p diode, Forward current, t = 20 E g E g E g E g E g E g = 1.08 ev = 1.09 ev = 1. ev = 1.11 ev = 1.12 ev = 1.13 ev C 0.06 As expected, larger band gap => less current Bias Voltage [V]
26 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 26 Forward current/i(1.08 ev) before irradianon I(EG300)/I( K V = 0.2 V t = 20 C χ 2 / ndf 4.42 / 3 Norm ± E g [ev] ± = Norm*exp(-EG300-E g /kt) It scales, as expected, with n i 2 ~ exp(-e g ) EG300 [ev]
27 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 27 Reverse/forward current level vs bandgap: Summary Reverse current scales with the expected funcnonal form The acnvanon energy to be used is Ea = EG ev Rescaling of leakage current works at 1% level Forward current scales as expected with exp(-e g /kt)
28 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 28 SIMULATION OF RADIATION DAMAGE AND IMPACT OF BANDGAP
29 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 29 RadiaNon damage model considered Effects of Interface Donor Trap States on IsolaNon ProperNes of Detectors OperaNng at High-Luminosity LHC F. Moscatelli et al. IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 64, NO. 8, AUGUST 2017 Perugia 2017 in the following Reminder: in my presentanon in Torino* I have showed that good agreement between simulators is found when EG300 = 1.08 ev is chosen and the thermal velocines are corrected à la Synopsys * Bomben, 28 th RD50 WS, Torino, June 2016
30 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 30 Perugia 2017, Φ = 1x 15 n eq /cm 2 I [A/cm] α(20 C) ~ 4.2e-17 A/cm χ 2 / ndf / 7 Prob /T ref ± 0 n 2 ± 0 E a ± I 4.232e ± 8.242e 13 ref Before irradianon it was 1.13 ev NormalisaNon is correct 2. Scaling as expected /T [K ]
31 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 31 ReweighNng leakage current with Ea = 1.48 ev < I(reweighted Leakage at 20 Current C) / I(20 Ratio C) > ReweighNng is accurate within 1.5% T [K]
32 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 32 Perugia 2017, Φ = 3x 15 n eq /cm 2 I [A/cm] 9 χ 2 / ndf / 7 Prob /T ref ± 0 n 2 ± 0 E a ± I 1.237e 09 ± 1.021e 12 ref α(20 C) ~ 4.1e-17 A/cm At 1e15 it was ev 1. NormalisaNon is correct 2. Scaling as expected /T [K ]
33 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 33 Extra: deplenon voltage vs temperature [V] V depl Φ = Perugia 2017 TCAD sim. pol2 fit E g = 1.08 ev T [K]
34 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 34 Extra: deplenon voltage vs temperature [V] V depl Φ = Perugia 2017 TCAD sim. pol2 fit E g = 1.08 ev Simple Taylor expansion Rather far away from E i T [K]
![Extra: deplenon voltage vs temperature [V] V depl 650](/docs-images/93/111297450/images/35-2.jpg "600 550 500 450 400 350 300 250 15 Φ = 3 - Perugia")
35 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 35 Extra: deplenon voltage vs temperature [V] V depl Φ = 3 - Perugia 2017 TCAD sim. pol2 E g = 1.08 ev It works at larger fluences as well T [K]
![M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 36 DepleNon voltage vs EG300-2 [F -2 C 30 ] 1800 1600 1400 1200 00 800 600 400 200 E g = 1.](/docs-images/93/111297450/images/36-0.jpg "08 ev E g = 1.09 ev E g = 1. ev E g = 1.11 ev E g = 1.12 ev = 1.")
36 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 36 DepleNon voltage vs EG300-2 [F -2 C 30 ] E g = 1.08 ev E g = 1.09 ev E g = 1. ev E g = 1.11 ev E g = 1.12 ev = 1.13 ev E g t = 20 C Perugia 2017 Φ=1e15 neq/cm 2 Larger bandgap values Smaller deplenon voltage V bias [V]
37 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 37 DepleNon voltage vs bandgap [V] V depl ~-E g /3kT(?) pol2 gives bezer agreement (not shown here) t = 20 C 2 χ / ndf / 3 Norm [V] ± Mult. Fact ± Th. En. [ev] ± 0 E g [ev] ± Fit Function: (Mult. Fact).(x-E ) g Norm exp(- ) Th. En Φ = 1 - Perugia 2017 TCAD sim. fit EG300 [ev]
![M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 38 Leakage current vs bandgap [A] I leak ~-E g /kt 0.45 0.4 0.35 0.](/docs-images/93/111297450/images/38-0.jpg "3 0.25 0.2 0.15 0.1 9 t = 20 C 2 χ / ndf 0.02563 / 4 Norm. [A] 4.231e ± 0 E g [ev] 1.08 ± 0.0007232 Mult. Fact. 0.9862 ± 0.02365 0.05 1.08 1.09 1.1 1.11 1.12 1.")
38 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 38 Leakage current vs bandgap [A] I leak ~-E g /kt t = 20 C 2 χ / ndf / 4 Norm. [A] 4.231e ± 0 E g [ev] 1.08 ± Mult. Fact ± EG300 [ev]
39 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 39 Forward current a{er irradianon Current [A] EG300 = 1.08 ev EG300 = 1.09 ev EG300 = 1. ev EG300 = 1.11 ev EG300 = 1.12 ev EG300 = 1.13 ev It s a resistor t = 20 C Perugia 2017 Φ=1e15 neq/cm V bias [V]
40 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 40 Forward current a{er irradianon Current [A] EG300 = 1.08 ev EG300 = 1.09 ev EG300 = 1. ev EG300 = 1.11 ev EG300 = 1.12 ev EG300 = 1.13 ev It s a resistor t = 20 C Perugia 2017 Φ=1e15 neq/cm Expected; e.g.: G. Lutz, NIM A 377 (1996) ρ ~ 2x 5 Ω cm => very close to intrinsic material V bias [V]
41 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 41 Forward current a{er irradianon vs temperature Current [a.u.] 11 E g = 1.08 ev E g = 1.09 ev E g = 1. ev E g = 1.11 ev E g = 1.12 ev = 1.13 ev E g 12 V = 0.2 V Perugia 2017 Φ=1e15 neq/cm /T [1/K]
42 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 42 Forward current a{er irradianon, E g = 1.08 EeV 2 χ / ndf / 7 I( V 11 ~ exp(-e a /kt) Norm ± E [ev] ± a A simple exponennal is the best approximanon E g = 1.08 ev V = 0.2 V Perugia 2017 Φ=1e15 neq/cm /T [1/K]
43 SimulaNon of radianon damage and impact of bandgap: Summary Reverse current snll scales with the same funcnonal form AcNvaNon energy rather different (1.48 ev) => Model dependent? To be checked with other models DepleNon voltage dependence on (T,E g ) small on ranges tested Due to posinon of traps wrt intrinsice energy To be checked with other models Forward current scales as expected with bandgap and energy M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 43
44 CONCLUSIONS AND OUTLOOK M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 44
45 Conclusions and Outlook Despite the low default bandgap value at 300 K predicnons seem to be consistent in Silvaco Atlas device simulator Reverse current scales as expected when the correct acnvanon energy is used Forward current scales as expected A{er irradianon things gets more complicated Yet the current scales with temperature with the same funcnonal form More fluences / models to be invesngated Extra: predicted deplenon voltage vs temperature needs more invesnganon (in contact with Perugia group) Outlook: the situanon is more clear; possible to make robust predicnons Silvaco used and to be used for ATLAS diginzer CollaboraNon with MPI too; see next talk M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 45
46 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 46 Acknowledgements Michael for suggesnng studies to further understand what s going on Rogelio, Perugia and MPI group for giving Silvaco a chance Luciano Bosisio (Uni. of Trieste) for great discussions LPNHE group for suppornng me My girlfriend (a biologist) for listening to me while ge default value ng mad at EG300 and...
47 THANK YOU FOR YOUR ATTENTION M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 47
48 Backup M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 48
49 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 49 Reminder It was pointed out that Silvaco thermal velocines values are different froms Synopsys ones There s a factor x2 for Synopsys on electrons thermal velocines wrt to holes
50 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 50 Forward current a{er irradianon, E g = 1.08 EeV Current [A] t = -20 C t = - C t = 0 C t = C t = 20 C E g = 1.08 ev Perugia 2017 Φ=1e15 neq/cm V bias [V]
51 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 51 Perugia 2017, Φ = 1x 15 n eq /cm 2 n free par. I [A/cm] χ 2 / ndf 0.04 / 6 Prob 1 1.0/T ref ± 0 n ± E a ± I 4.25e ± 1.09e 12 ref /T [K ]
52 M. Bomben - Band gap energy modelisanon in Silvaco TCAD Atlas Device simulator - 31st RD50 WS, CERN 52 Perugia 2017, Φ = 3x 15 n eq /cm 2 n free par. I [A/cm] 9 χ 2 / ndf / 6 Prob /T ref ± 0 n ± E a ± I 1.241e 09 ± 1.474e 12 ref /T [K ]
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