Study on Saturation of Sipm for Scintillator Calorimeter Using UV Laser

Study on Saturation of SiPM for scintillator calorimeter using UV laser

Naoki Tsuji, The University of Tokyo Linghui Liu, Wataru Ootani, Kosuke Yoshioka, Makoto Gonokami, Yusuke Morita CHEF2019 at Fukuoka, 25-29 November 2019

1 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

International linear Collider (ILC)

Future high energy frontier machine Electron-positron collider Lepton, elementary particle Low background → precise measurement

Ecm : 250 - 500 GeV Initial plan : 250 GeV Extendable to 1 TeV Search for new physics Precise measurement of Higgs Precise measurement of top quark Search for dark matter

2 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

International Large Detector (ILD)

ILD consists of vertex detector, central tracker, EM calorimeter, hadron calorimeter, and muon tracker Particle Flow Algorithm (PFA) Each particle is detected by the best suited detectors Improved jet energy resolution It is necessary to classify charged particle and neutral particle precisely ➡High granularity calorimeter is required.

3 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Sc-ECAL

Scintillator Electromagnetic CALorimeter (Sc-ECAL) Technology option of EM calorimeter for ILD Based on scintillator strips readout by SiPM 5 × 45 × 2 mm3 scintillator strip Virtual segmentation : 5mm × 5mm with strips in x-y conﬁguration Timing resolution < 1 ns Low cost

Silicon PhotoMultiplier (SiPM) Made up of multiple APD pixels operated in Geiger mode Excellent photon-counting capability Small size Low bias operation

Hamamatsu Photonics K.K., 4 /19 Opto-semiconductor Handbook “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Saturation of SiPMs

SiPM saturation can be an issue for Sc-ECAL Pile-up hits in small and dense EM shower When a large number of photons are injected to SiPM, output of SiPM can be saturated due to limited number of pixels ) det

Saturation curve is usually measured by direct injecting fast laser pulse (~400 nm) to SiPM Time constant of emission of scintillation light (few ns) is not negligible compared to recovery time of SiPM cell (dozens ns) Our idea is to measure the SiPM saturation with Number of excited pixels (N scintillation light excited by UV pulse laser The measured saturation curve can directly

be used for saturation correction in Sc-ECAL Number of incident photons (Nseed) Hamamatsu Photonics K.K., Opto-semiconductor Handbook

5 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

SiPMs for Sc-ECAL

Hamamatsu MPPC S12571 series MPPC : Product name of Hamamatsu SiPM Small pixel size : 10 / 15 μm Active area : 1 × 1 mm2 Breakdown voltage : 65 V Crosstalk : IR photons from No Trench isolation avalanche in ﬁred pixel can trigger adjacent pixels S12571-015P Hamamatsu MPPC S14160 series Small pixel size : 10 / 15 μm Active area : 1.3 × 1.3 / 3 × 3 mm2 Breakdown voltage : 38 V 0.5 μm trench isolation → low crosstalk Crosstalk probability (%)

Trench : Separation

between adjacent pixels in Overvoltage (V) order to reduce crosstalk Hamamatsu Photonics K. K., PD18

6 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Trench technique of new MPPC Hamamatsu Photonics K. K., PD18 MPPC S14160 series employ trench technique Low crosstalk Low operation voltage No reduction of ﬁll factor Longer tail due to larger cell capacitance Longer recovery time

Saturation is improved for new MPPC?

Low crosstalk Provided by → saturation ↓ S14160 (w/ trench) Hamamatsu Photonics Longer recovery → saturation ↑

S12572 (w/o trench) 7 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Experimental setup

Laser 190 nm laser : Scintillation excitation, invisible to MPPC 470 nm laser : No scintillation excitation, directly detected by MPPC Setup for Sc-ECAL 5 × 45 × 2 mm3 scintillator strip (EJ-212) with center dimple

MPPC w/o trench : S12571-015P Setup Active area : 1.0 × 1.0 mm2 Scintillator strip (wrapped strip + PCB) Pixel pitch : 15 μm 4489 pixels Injection hole MPPC w/ trench : S14160-1315PS Active area : 1.3 × 1.3 mm2 Cavity MPPC Pixel pitch : 15 μm 7296 pixels

8 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Experimental setup

Excite scintillation light with fast fsec UV pulse laser Laser light is split using half mirror (to scintillator, to photodiode) Incident light intensity is monitored with photodiode MPPC S12571-015P with over voltage of +4 V (Recommended voltage by Hamamatsu) MPPC S14160-1315PS with over voltage of +4 V ( 〃 ) Signal attenuations (10 - 40 dB) used to avoid saturation of electronics

Photodiode (S12689-02)

Variable ND ﬁlters

Prism Half mirror MPPC Scintillator

Laser Attenuator Al mirror Amp Trigger signal Waveform Delay digitizer 9 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Experiment setup Scintillator Photodiode & PCB Incident light intensity controlled with three ND ﬁlters

Cut oﬀ contamination of other wavelength light

Laser Light is split using half mirror Half mirror

Photodiode

Variable ND ﬁlters

Prism Half mirror MPPC Scintillator

UV laser Attenuator Al mirror Amp Trigger signal Waveform Delay digitizer 10 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Signal waveform

Waveform is compared among 190 nm laser, 470 nm laser, and Sr90 190 nm laser, Sr90 → MPPC detects scintillation light 470 nm laser → MPPC detects laser light directly Almost the same waveform b/w 190 nm and Sr90 Faster signal for direct injection of 470 nm laser ➡Suggesting that injected UV laser really excites scintillation light !

S12571-015P (MPPC w/o trench) S14160-1315PS (MPPC w/ trench)

190 nm laser 190 nm laser 470 nm laser 470 nm laser Sr90 Sr90

11 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Analysis

Digitized waveform is integrated to estimate charge. The charge is then converted into number of photoelectrons being divided by single photoelectron charge. Single photoelectron charge is obtained from dark noise signal found in oﬀ-time

region MPPC charge chargeH Entries 44629 Mean 0.2499 Signal of scintillation light 3500 Std Dev 0.04832

S12571-015P(MPPC w/o trench) Event number 3000

2500

2000

1500

1000

500

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Single charge [10^10e] Integration range (100 ns) Charge value MPPC charge h2 Signal of scintillation light 104 Entries 42862 Mean 0.0002862 S14160-1315PS (MPPC w/ trench) Pedestal Std Dev 0.003065

Event number 103

Gain value 102 Single p.e.

Integration range (100 ns) −0.02 −0.01 0 0.01 0.02 0.03 0.04 Single charge [10^10e] 12 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Laser intensity

Incident light intensity is monitored with photodiode Laser light is split using half mirror

Photodiode current is converted to Nseed using calibration constant obtained at low light intensity where no saturation is anticipated

(Nseed : number of photoelectrons when assuming no saturation) Eﬀect of crosstalk and after-pulse is not corrected yet

Linear regionUV of scanS12571-015P without attenuator (MPPC w/o trench) Linear region UVof S14160-1315PSscan without attenuator (MPPC w/ trench)

180 140 160

120 140 N_detected[p.e.] N_detected[p.e.]

100 120

100 80

80 60 60 40 40

20 20

−9 −9 0 ×10 0 ×10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 current[A] current[A]

13 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Saturation curve with 190 nm laser

Over-saturation is observed for both MPPCs

N.B. still some uncertainties in estimation for signal attenuation factors We observed that the attenuation factor depends on light intensity Probably due to change in signal shape caused by MPPC saturation

UV scan ofUV S12571-015P scan of S12571-015P (MPPC w/o trench) UV scan ofUV S14160-1315PS scan of S14160-1315PS (MPPC w/ trench) 9000 18000 8000 0dB 0dB 10dB 16000 10dB 7000 20dB 20dB 14000 N_detected[p.e.] 30dB N_detected[p.e.] 30dB 6000 40dB 12000 40dB 5000 10000

4000 Npixel = 4489 8000

Npixel = 7296 3000 6000

2000 4000 Preliminary Preliminary 1000 2000

0 0 0 5000 10000 15000 20000 25000 30000 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 N_seed[p.e.] N_seed[p.e.]

14 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Saturation curve with 470 nm laser

Saturation curve using 470 nm laser is measured to compare with 190 nm laser Stronger saturation compared to 190 nm laser is observed Over-saturation is still observed for both MPPCs Due to after pulse and delayed crosstalk?

N.B. still some uncertainties in estimation for signal attenuation factors

470 nm scan of 470S12571-015P nm laser scan (MPPC w/o trench) 470 nm scan of S14160-1315PS470 nm laser scan (MPPC w/ trench) 9000 0dB 18000 0dB 8000 10dB 10dB 16000 20dB 20dB 7000 14000 N_detected[p.e.] 30dB N_detected[p.e.] 30dB 6000 40dB 40dB 12000 5000 10000

4000 Npixel = 4489 8000

Npixel = 7296 3000 6000

2000 4000 Preliminary Preliminary 1000 2000

0 0 0 5000 10000 15000 20000 25000 30000 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 N_seed[p.e.] N_seed[p.e.]

15 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Comparison of 190 nm and 470 nm laser

Significant difference between saturation curves with 190 nm and 470 nm laser The effect of time constant of scintillation light emission is observed Can be a big impact on saturation correction

ComparisonComparison of S12571-015Pwith 190nm and (MPPC 470nm w/o laser trench) ComparisonComparison of S14160-1315PS with 190nm and (MPPC 470nm w/ laser trench) 9000 18000 8000 190 nm laser 16000 190 nm laser 7000 470 nm laser

N_detected[p.e.] 14000 N_detected[p.e.] 470 nm laser 6000 12000 5000 10000

4000 Npixel = 4489 8000

Npixel = 7296 3000 6000

2000 4000 Preliminary Preliminary 1000 2000

0 0 0 5000 10000 15000 20000 25000 30000 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 N_seed[p.e.] N_seed[p.e.]

16 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Comparison of two MPPCs with 190 nm laser

Normalized by sensor area, PDE and crosstalk probability to compare saturation curves between two MPPCs MPPC w/ trench is less saturated compared to MPPC w/o trench Few plots above the linear function (because of wrong attenuation factor?) [For S14160-1315PS (w/ trench)] (Lower crosstalk → saturation ↓) ＞ (Longer recovery time → saturation ↑) Eﬀect of longer recovery time is small because of scintillation emission time Comparison of MPPCs with 190 nm laser Comparison with two types of MPPCs (S14160-1315PS and 12571‒015P) ] 2

30000

25000 S14160-1315PS (w/ trench) 20000 S12571-015P (w/o trench) N_detected[p.e.]/area/(1+CT)

15000

10000

Preliminary Number of detected photons [p.e./mm 5000

3 0 ×10 0 10 20 30 40 50 60 70 80 90 100 17 /19 NumberN_seed[p.e.]/area/PDE/(1+CT) of photons [p.e./mm2] “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Comparison of two MPPCs with 470 nm laser

S12571-015P (w/o trench) is less saturated compared to S14160-1315PS (w/ trench) [For S14160-1315PS (w/ trench)] (Lower crosstalk → saturation ↓) ＜ (Longer recovery time → saturation ↑) Eﬀect of longer recovery time is large because of short duration of laser pulse

Comparison of MPPCs with 470 nm laser Comparison with two types of MPPCs (S14160-1315PS and 12571‒015P)

S14160-1315PS (w/ trench)

) [p.e.] 30000 S12571-015P (w/o trench) CT

25000

20000 N_detected[p.e.]/area/(1+CT) /area/PDE/(1+P

det 15000 = N 10000 nor_det

N Preliminary 5000

3 0 ×10 0 10 20 30 40 50 60 70 80 90 100 18 /19 Nphoton[p.e.]N_seed[p.e.]/area/PDE/(1+CT) = Nseed/area/PDE/(1+PCT) “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Summary & To do

Saturation curves for MPPCs are measured using scintillation light excited by fast UV-laser Saturation recovery with scintillation light is observed. It should be taken into account for saturation correction The measured saturation curves can directly be used for correction

Saturation curves are measured for two types of MPPCs for Sc-ECAL (w/ and w/o trench) The eﬀect of longer recovery time of S14160 (MPPC w/ trench) is found small for scintillation light Longer-tail eﬀect is observed when the measurement of fast pulse

To do Investigate light intensity dependence of attenuation factor Compare with theoretical model of saturation

19 /19 Backup

20 /10 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Attenuation factor MPPC

Dynamic range of DAQ is not suﬃcient to cover whole light HV intensity range

Need signal attenuation to avoid saturation in electronics Attenuator 10-40 dB attenuator used Amp There is a frequency dependence of attenuator Waveform Attenuation rate depends on input pulse shape digitizer

Waveform comparison with 0dB vs 10dB (S12571-015P) Waveform comparison with 0dB vs 10dB (S14160-1315PS)

0 dB 0 dB 10 dB 10 dB

21 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

At low light intensity, Variation of waveform background is dominant

Background Variation of waveform depending on light intensity was observed Scintillation Eﬀect of constant background light at low light intensity At higher light intensity, Background light comes from optical setup and laser reﬂection background is negligible Faster than scintillation light because directly injected to Scintillation MPPC

Signiﬁcant contribution from fast component of background Background at low light intensity

Waveform comparison with 0dB attenuator (S12571-015P) Waveform comparison with 0dB attenuator (S14160-1315PS)

Background Background

Scintillation

22 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Variation of waveform

Eﬀect of SiPM saturation at high light intensity Saturation deforms waveform at very high light intensity

These eﬀects change the attenuation rate depending on light intensity Not yet calibrated

Waveform comparison with 40dB attenuator (S12571-015P) Waveform comparison with 40dB attenuator (S14160-1315PS)

Saturated Saturated

Not saturated Not saturated

23 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Attenuation Calibration

Attenuation rate is optimized with factor and offset : Nopt = A * Npe + B Fit with linear function and calculate coefficients to match the lines Specious factor and offset are used at high light intensity Saturation and waveform variation change the attenuation rate depending on light intensity Fit with polynomial function

ComparisonUV scan without with attenuator 0dB vs. 10dB and 10dB(S12571-015P) attenuator ComparisonUV scan with with 30dB 30dB vs.and 40dB 40dB (S12571-015P) attenuator

8000 160 7000 30 dB 140 0 dB N_detected[p.e.] N_detected[p.e.] 6000 120

100 ×3.39 5000 ×3.63

80 4000

60 3000

40 2000 ×3.45 (Attenuation rate) 20 10 dB 40 dB ×3.11 1000 0 0 20 40 60 80 100 120 140 160 180 4000 6000 8000 10000 12000 14000 16000 18000 20000 N_incident[p.e.] N_incident[p.e.]

24 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Attenuation Calibration

CalibratedUV scan results without with attenuator 0dB vs. and 10dB 10dB (S12571-015P) attenuator CalibratedUV resultsscan with with 30dB 30dB and vs. 40dB 40dB attenuator (S12571-015P)

8000 160

140 7000 N_detected[p.e.] N_detected[p.e.] 120

100 6000

5000 40 dB 60 10 dB 40 4000 20 30 dB 0 dB 0 0 20 40 60 80 100 120 140 160 180 4000 6000 8000 10000 12000 14000 16000 18000 20000 N_incident[p.e.] N_incident[p.e.]

25 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Comparison of two types of MPPCs

S12571-015P These plots contain the diﬀerence of active area, crosstalk probability and PDE between two types of MPPCs

Nseed and Ndet are divided by each active area, crosstalk probability, PDE for comparison purpose

Nseed is converted into number of inserted photon (Nphoton) PDE (%) Ndet is converted into normalized number of detected photons (Nnor_det) Then, we can see directly saturation tendency of each MPPC Overvoltage (V) Crosstalk probability (%)

26 /19 Overvoltage (V) “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Waveforms with 0dB attenuator Attenuationattenuation factor 0dB ratio vs. 10dB

1 peak

0.8

x3.38772 0.6

0.4 x3.15034

0.2 x3.1103

9 ×10− 1 1.2 1.4 1.6 1.8 2 2.2 2.4 current

UV scan without attenuator and 10dB attenuator

160

140

N_detected[p.e.] 120

100

0 0 20 40 60 80 100 120 140 160 N_incident[p.e.] 27 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Waveforms with 10dB attenuator Waveforms with 30dB attenuator

Waveforms with 40dB attenuator Waveform transition with 0 - 40dB attenuator

28 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Attenuationattenuation factor 0dB ratio vs. 10dB Attenuationattenuation factor 10dB ratio vs. 20dB

peak peak 1

0.9 0.8 0.8

0.7 x3.38772 x3.49093 0.6 0.6

0.5 0.4 x3.15034 0.4 x3.33339

0.3 0.2 x3.21422 x3.1103 0.2

9 9 ×10− 0.1 ×10− 1 1.2 1.4 1.6 1.8 2 2.2 2.4 3 3.5 4 4.5 5 5.5 6 6.5 7 current current

Attenuationattenuation factor 20dB ratio vs. 30dB Attenuationattenuation factor 30dB ratio vs. 40dB

peak peak 1 1

0.9

0.8 0.8 0.7 x3.55659 x3.60312 0.6 0.6

0.5 x3.63195

0.4 x3.5701 0.4

0.3 x3.49469 x3.45095 0.2 0.2

9 6 ×10− 0.1 ×10− 10 12 14 16 18 20 22 24 26 28 0.05 0.1 0.15 0.2 0.25 current current 29 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Waveforms with 0dB attenuator Attenuationattenuation factor 0dB ratio vs. 10dB

peak 1.6

1.4

1.2 x3.38914 1

0.8 x3.23162 0.6

0.4 x3.08691

0.2 9 ×10− 1 1.2 1.4 1.6 1.8 2 current

UV scan without attenuator and 10dB attenuator

180

160

N_detected[p.e.] 140

120

100

0 0 20 40 60 80 100 120 140 160 180 N_incident[p.e.] 30 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Waveforms with 10dB attenuator Waveforms with 30dB attenuator

Waveforms with 40dB attenuator Waveform transition with 0 - 40dB attenuator

31 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Attenuationattenuation factor 0dB ratio vs. 10dB Attenuationattenuation factor 10dB ratio vs. 20dB

1.8 peak 1.6 peak

1.6 1.4

1.4 1.2 x3.38914 1.2 x3.46571 1 1 0.8 x3.23162 0.8 x3.27096 0.6 0.6 0.4 x3.35106 x3.08691 0.4

0.2 9 9 ×10− 0.2 ×10− 1 1.2 1.4 1.6 1.8 2 3 3.5 4 4.5 5 5.5 6 current current

Attenuationattenuation factor 20dB ratio vs. 30dB Attenuationattenuation factor 30dB ratio vs. 40dB

2.2

peak peak 1.8 2 1.6 1.8

1.6 1.4

1.4 1.2 x3.80956 x3.7942 1.2 1

1 x3.36394 0.8 x3.67675

0.8 0.6

0.6 x3.51893 0.4 x3.53735 0.4 0.2 −9 −9 0.2 ×10 ×10 10 12 14 16 18 20 20 30 40 50 60 70 80 90 current current 32 /19 “Study on Saturation of SiPM for scintillator calorimeter using UV laser”, CHEF2019 at Fukuoka Naoki Tsuji, The University of Tokyo

Comparison with two types of MPPCs

The difference of two plots should be consistent with the difference of PDE However, S14160-1315PS is less saturated compared with S12571-015P even after correction Need further verification We plan to do the same measurement with fast 400 nm laser UV comparison of MPPCs S14160-1315PS (New MPPC w/ trench)

) [p.e.] 10000 CT S12571-015P 8000 (Standard MPPC w/o trench)

6000 /area/PDE/(1+P N_detected[p.e.]/area/(1+CT) det = N 4000 nor_det N

2000 Preliminary

3 0 ×10 0 20 40 60 80 100 33 /19 Nphoton[p.e.]N_seed[p.e.]/area/PDE/(1+CT) = Nseed/area/PDE/(1+PCT)