a Xi :2505.05632 2 [physics.ins-de ] 25 Jun 2025
Compensa ed LGAD op imisa ion h ough an de Pauw es s uc u es
A. Fondaccia,b,∗
, T. C ocib, D. Passe ic,b, R. A cidiaconod,e, N. Ca igliae, M. Fe e oe, M. Cen is Vignali , M. Bosca din ,
G. Pa e nos e , R. S. Whi ee, A. R. Al amu ae, V. Solag,e, A. Mo ozzib, F. Mosca ellih,b
aDipa imen o di Fisica, Uni e si `a degli S udi di Pe ugia, Via Alessand o Pascoli, 06123, Pe ugia, I aly
bIs i u o Nazionale di Fisica Nuclea e (INFN) - Sezione di Pe ugia, Via Alessand o Pascoli, 06123, Pe ugia, I aly
cDipa imen o di Ingegne ia, Uni e si `a degli S udi di Pe ugia, Via Go edo Du an i, 93, 06125, Pe ugia, I aly
dDipa imen o di Scienze del Fa maco, Uni e si `a del Piemon e O ien ale, La go Donegani, 2, 28100, No a a, I aly
eIs i u o Nazionale di Fisica Nuclea e (INFN) - Sezione di To ino, Via Pie o Giu ia, 1, 10125, To ino, I aly
Fondazione B uno Kessle (FBK), Via Somma i e, 18, 38123, T en o, I aly
gDipa imen o di Fisica, Uni e si `a degli S udi di To ino, Via Pie o Giu ia, 1, 10125, To ino, I aly
hIs i u o O icina dei Ma e iali (IOM) CNR - Sede di Pe ugia, Via Alessand o Pascoli, 06123, Pe ugia, I aly
Abs ac
A new gain implan design has ecen ly been in oduced o enhance he adia ion esis ance o low-gain a alanche diodes (LGADs)
o he ex eme luences an icipa ed in u u e had on collide s like FCC-hh. This design u ilises an enginee ed compensa ion o wo
opposing ypes o doping implan s, equi ing a ho ough analysis o hei e olu ion due o i adia ion. To his end, he expe imen al
measu emen s o hei ini ial es s uc u es ha e been compa ed wi h Technology CAD simula ions bo h be o e and a e i adia ion.
F om he measu emen -simula ion compa ison ega ding C-V cha ac e is ics, he dono emo al a high ini ial dono concen-
a ions (>1016 a /cm3) used in Compensa ed LGADs has been s udied, along wi h how dono co-implan a ion in luences he
bene icial e ec o ca bon o slow accep o emo al. Fu he mo e, an inno a i e applica ion o an de Pauw es s uc u es, ypi-
cally employed by ound ies o moni o p ocess quali y, has been implemen ed. The doping emo al o he single implan s used in
Compensa ed LGADs has been es ima ed by examining he a ia ion in shee esis ance wi h i adia ion h ough hese s uc u es.
Keywo ds: Silicon senso s, 4D- acking, Radia ion ha dness, Compensa ed LGAD, TCAD simula ion.
1. In oduc ion
Fu u e had on collide s, such as FCC-hh, will ha e inc eas-
ingly c owded en i onmen s, and ime will be an essen ial pa-
ame e o be added o e en analysis [1]. Timing esolu ions o
ens o picoseconds will enable he sepa a ion o he acks in
ime (4D- acking), leading o ewe acks pe e en and, hus,
a mo e s aigh o wa d analysis.
Low-gain a alanche diodes (LGADs) [2] can p o ide he
necessa y iming esolu ion [3] h ough in e nal signal ampli i-
ca ion. Howe e , hei adia ion esis ance is inadequa e o u-
u e had on collide s. The gain implan , c ucial o signal mul-
iplica ion, deac i a es unde i adia ion (Fig. 1 le ) h ough he
accep o emo al mechanism [4], deg ading LGAD iming es-
olu ion. Mos adia ion- ole an LGADs o da e can su i e up
o 2.5·1015 neq/cm2[5], while he expec ed luence in he FCC-
hh’s inne mos egion will exceed 1017 neq/cm2.
A new gain implan design [6], achie ed h ough he com-
pensa ion o wo dopan s o opposi e ype (Fig. 1 igh ), has
ecen ly been in oduced o enhance he adia ion esis ance o
LGADs o ex eme luences. Bo h implan s will unde go dop-
ing emo al wi h i adia ion; i enginee ed co ec ly, hei di -
e ence will emain ai ly cons an , po en ially ex ending he
li espan o Compensa ed LGADs beyond 1017 neq/cm2.
∗Co esponding au ho
Email add ess: [email p o ec ed] (A. Fondacci)
Figu e 1: Gain implan e olu ion wi h i adia ion in s anda d (le ) and Com-
pensa ed ( igh ) LGADs. The op line e e s o non-i adia ed de ices, and he
bo om one o samples i adia ed a 1016 neq/cm2.
2. Fi s p oduc ion o Compensa ed LGADs
The i s Compensa ed LGADs we e manu ac u ed by Fon-
dazione B uno Kessle (FBK) in la e 2022 on 30 µm hick
high- esis i i y ac i e subs a es [7]. Di e en combina ions o
bo on (p+) and phospho us (n+) doses ha e been in es iga ed
o he gain implan , as epo ed in he spli able 1. Fu he -
mo e, ca bon has been co-implan ed in one wa e o in es iga e
i s e ec in slowing accep o emo al when also phospho us
a oms a e p esen in he same olume o he bo on.
P ep in submi ed o Nuclea Ins umen s &Me hods in Physics Resea ch, Sec ion A June 27, 2025
Wa e No p+dose n+dose C dose
5 1 1
6 2a 1
7 2b 1
8 2b 1
9 2c 1
10 3a 2
11 3b 2
12 3b 2
13 3b 2 1
14 3c 2
15 5a 4
Table 1: Spli able o he i s Compensa ed LGADs manu ac u ed by FBK in
la e 2022. Fo he dose coding, a <b<c and 2c <3a. Fu he mo e, W5 is a
s anda d LGAD epo ed o e e ence.
The samples ha e been ex ensi ely cha ac e ised be o e and
a e i adia ion1wi h elec ical and ansien measu emen s [7].
F om I-V cha ac e is ics2, i has been obse ed ha he in-
c ease o he cu en wi h bias, due o he in e nal mul iplica-
ion, seems o be main ained up o he highes luences, mean-
ing a highe adia ion esis ance compa ed o s anda d LGADs.
Mo eo e , a iming esolu ion a ound 40 ps has been measu ed
wi h samples i adia ed a 2.5·1015 neq/cm2, indica ing ha
Compensa ed LGADs can each iming pe o mances simila
o he s anda d LGADs.
3. TCAD in es iga ion
Compa ing expe imen al measu emen s wi h TCAD simu-
la ions can p o ide addi ional insigh s o designing he nex
ba ch o op imised Compensa ed LGADs. In de ail, he dono
emo al a e a high ini ial dono concen a ions (>1016 a /cm3)
used in LGADs can be assessed, he in e play be ween accep-
o and dono emo al can be s udied, and las ly, he impac o
dono doping on he bene icial e ec o ca bon in slowing down
accep o emo al can be e alua ed.
To his end, he s a e-o - he-a Synopsys®Sen au us TCAD
sui e has been used, and he adia ion damage has been aken
in o accoun by using he las elease o he Pe ugia adia ion
damage model [8]. In he la e , accep o and dono emo al
a e pa ame ised acco dingly o he ollowing equa ion [9]:
NA,D(ϕ)=NA,D(0) ·e−cA,D·ϕ(1)
whe e cA,Dis he accep o (dono ) emo al coe icien depend-
ing on he ini ial accep o (dono ) concen a ion NA,D(0), and
ϕis he i adia ion luence in neq/cm2. The cA alues a e
known ac oss a wide ange o NA(0) based on s udies o s an-
da d LGADs [10], while he li e a u e on cD alues is limi ed o
ND(0) up o 1014 a /cm3[11].
1Senso i adia ion was done a he JSI TRIGA Ma k II neu on eac o in
he luence ange [4 ·1014,5·1015]neq/cm2.
2I-V measu emen s be o e i adia ion ha e been made a +20 ºC, whils
cha ac e isa ions a e i adia ion ha e been pe o med a -20 ºC.
3.1. C-V cha ac e is ics
As C-V cha ac e is ics a e well known o ca y in o ma ion
ela ed o doping p o iles, hey ha e been selec ed o begin
compa ing measu emen s and simula ions. Speci ically, i has
s a ed wi h he C-Vs o wa e 12 (W12), ollowing he me hod-
ology epo ed in [12] and b ie ly summa ised below:
1. Calib a e he subs a e hickness and doping concen a ion
in he TCAD en i onmen using he C-V measu emen s o
p-i-n diodes;
2. Inco po a e Gaussian i s om compensa ed gain implan
SIMS in o he simula ed de ice o c ea e a Compensa ed
LGAD, hen e i y he ag eemen be ween C-V measu e-
men s and simula ions be o e i adia ion.
3. Selec he igh cA o he gi en NApeak (0)3 om he ac-
cep o emo al pa ame isa ion [10] and a y cDun il C-V
measu emen s and simula ions ag ee a e i adia ion.
The emo al coe icien s ha enable he simula ions o align
wi h he measu emen s a e cD=6.50·10−16 cm2and cA=2.50·
10−16 cm2[12], and cD∼2·cAassuming he same dependence
on he ini ial doping densi y and conside ing he 3 −2 ini ial
concen a ion o implan ed bo on and phospho us.
Mo ing o he W13, which is simila o W12 bu ea u es ca -
bon co-implan a ion, a good ag eemen be ween measu emen s
and simula ions (Fig. 2) was ob ained wi h he p e iously ex-
ac ed cDand wi h cA=8.26 ·10−17 cm2. The la e being
one- hi d o he p e ious cAcon i ms he expe imen al obse a-
ion [7] ha ca bon slows accep o emo al in he same way as
in s anda d LGADs [10], e en in he p esence o phospho us in
he gain implan egion.
Figu e 2: P e- and pos -i adia ion W13 C-V measu emen s and simula ions.
Each band is he plane a ea co e ed by he amily o cu es ob ained by mea-
su ing di e en samples o he same wa e unde he same condi ions.
3.2. Shee esis ance
A new me hod o in es iga ing doping emo al by obse ing
changes in shee esis ance wi h i adia ion has been explo ed.
3The C-V cha ac e is ics a e sensi i e o changes in he peak concen a ion
o he ac i e gain implan [13]. The e o e he cA(cD) o he peak is used o
scale down he en i e bo on (phospho us) p o ile.
2
Consequen ly, measu emen s and simula ions o an de Pauw
es s uc u es [14] ha e been compa ed. These ou - e minal
s uc u es, commonly u ilised by ound ies o moni o p ocess
quali y, allow o he measu emen o he shee esis ance o a
gi en dopan laye by applying a known cu en be ween wo
e minals and p obing he ol age d op ac oss he o he wo.
A an de Pauw es s uc u e can be eplica ed in a 3D simu-
la ion domain, and he shee esis ance can be calcula ed by ol-
lowing he measu emen p ocedu e. Thus, he doping a ia ion
wi h i adia ion can be de e mined by uning he doping p o ile
in he TCAD en i onmen un il i ep oduces he expe imen al
a ia ion in shee esis ance wi h luence. Fo comple eness,
a an de Pauw es s uc u e o each doping implan used in
Compensa ed LGADs was included in he ba ch (Fig. 3).
Figu e 3: Layou o he an de Pauw es s uc u es included in he i s ba ch
o Compensa ed LGADs eleased by FBK in la e 2022.
Beginning wi h he NPLUS implan 4, Fig. 4 illus a es he
p o ile e olu ion which enables he ep oduc ion o he expe -
imen al a ia ion in shee esis ance wi h i adia ion (Fig. 5).
The black cu e ep esen s he non-i adia ed scena io and de-
pic s he NPLUS p ocess simula ion, calib a ed on a SIMS, im-
plan ed in o he p- ype high- esis i i y subs a e. The black ci -
cle and diamond o e lap in Fig. 5 e i ies ha all he implan ed
NPLUS a oms a e elec ically ac i e.
The wo a e -i adia ion p o iles in Fig. 4 esul om in-
c easing he subs a e doping concen a ion based on he accep-
o c ea ion pa ame isa ion [10], he eby educing he NPLUS
ail. This ep oduces he shee esis ance a ia ion wi h i a-
dia ion (Fig. 5), demons a ing ha he NPLUS implan is no
a ec ed by dono emo al and con i ming he quali y o he
accep o c ea ion pa ame isa ion embedded in he Pe ugia a-
dia ion damage model.
Conside ing a p- ype implan on a p- ype subs a e, such as
he PGAIN o W5, he subs a e con ibu es o he measu ed
shee esis ance wi h a pa asi ic e ec , as he s udied laye and
he subs a e a e no sepa a ed by a deple ion egion. How-
e e , he simula ion can ep oduce his pa asi ic con ibu ion;
he e o e, aluable in o ma ion can be ob ained by compa ing
measu emen s and simula ions, e en in his case.
4Doping implan used by FBK o make he collec ion elec ode in LGADs.
Figu e 4: NPLUS doping p o ile e olu ion wi h i adia ion. The subs a e dop-
ing is inc eased acco dingly o he accep o c ea ion pa ame isa ion.
Figu e 5: P e- and pos -i adia ion shee esis ance measu emen s and simula-
ions o he NPLUS implan . The e o ba s ep esen a small pe cen age o he
a e age alue, wi h hei expansion caused by he scale being highly magni ied.
Fig. 6 shows he e olu ion o W5’s PGAIN p o ile wi h i -
adia ion, which allows o he ep oduc ion o he changes
in he expe imen al shee esis ance (Fig. 7). The black
cu e illus a es a p ocess simula ion calib a ed using SIMS,
while he pos -i adia ion cu es ha e been de i ed by apply-
ing he accep o emo al (gain implan ) and c ea ion (subs a e)
pa ame isa ions o he o me . In pa icula , o ep oduce he
expe imen al da a, he app op ia e cA o each gain implan
poin had o be used in he accep o emo al pa ame isa ion,
and i was no possible o use he cAo he peak o all o hem,
esul ing in mo e scaled ails. This indica es ha he measu e-
men o shee esis ance is mo e sensi i e o changes in he in e-
g al o he ac i e gain implan concen a ion, which also consid-
e s he educ ion o p o ile ails, a he han a ia ions in peak
concen a ion only, as is he case o C-V cha ac e is ics.
4. Conclusion
The cha ac e isa ion o he i s Compensa ed LGAD p o o-
ypes buil by FBK in 2022, which u ilise he compensa ion
o wo opposi e- ype dopan s o he gain implan , showcased
hei po en ial o ex ending iming measu emen s o ex eme
luences (>1017 neq/cm2) an icipa ed in u u e had onic collid-
e s like FCC-hh.
3
Figu e 6: W5 PGAIN doping p o ile e olu ion wi h i adia ion. The subs a e
doping inc eases ollowing he accep o c ea ion pa ame isa ion, while he gain
implan doping dec eases acco dingly o he accep o emo al pa ame isa ion.
Figu e 7: P e- and pos -i adia ion shee esis ance measu emen s and simula-
ions o he W5 PGAIN implan .
Mo eo e , by compa ing expe imen al da a wi h TCAD sim-
ula ions be o e and a e i adia ion, doping emo al due o i a-
dia ion has been in es iga ed, o e ing insigh s o u u e Com-
pensa ed LGAD ba ches. The Pe ugia adia ion damage model
was applied wi hin he TCAD en i onmen o accu a ely assess
i adia ion e ec s.
P ecisely, he measu emen -simula ion compa ison o C-V
cha ac e is ics acili a ed he s udy o dono emo al a high ini-
ial dono concen a ions (>1016 a /cm3) used in Compensa ed
LGADs, es ima ing a dono emo al a e abou wice ha o
accep o emo al, assuming he same unc ional o m o bo h
mechanisms. I was also con i med ha dono doping in he
compensa ed gain implan does no a ec he bene i s o ca bon
co-implan a ion in slowing accep o emo al.
Las ly, o he i s ime, measu emen s and simula ions o
an de Pauw es s uc u es be o e and a e i adia ion ha e
been compa ed o alida e he change in shee esis ance as a
me hod o assessing doping emo al. This app oach can inde-
penden ly es ima e he a ia ion o each doping implan used in
Compensa ed LGADs, u ilising a dedica ed an de Pauw es
s uc u e o each o hem. Fo ins ance, analysis o he NPLUS
implan es s uc u e demons a ed insensi i i y o dono e-
mo al due o i s high ini ial phospho us concen a ion. Gi en
i s po en ial, his me hodology will be applied o he new n- ype
LGAD ba ch cu en ly in p oduc ion a FBK.
Decla a ion o compe ing in e es
The au ho s decla e ha hey ha e no known compe ing i-
nancial in e es s o pe sonal ela ionships ha could ha e ap-
pea ed o in luence he wo k epo ed in his pape .
Acknowledgmen s
This p ojec has ecei ed unding om he Eu opean Union’s
Ho izon 2020 Resea ch and Inno a ion P og amme unde
GAs Nos 101004761 (AIDAinno a) and 101057511 (EURO-
LABS), he PRIN MUR p ojec 2022RK39RF ‘ComonSens’,
and he Eu opean Union (ERC, CompleX, 101124288). Views
and opinions exp essed a e howe e hose o he au ho s only
and do no necessa ily e lec hose o he Eu opean Union o
he Eu opean Resea ch Council. Nei he he Eu opean Union
no he g an ing au ho i y can be held esponsible o hem.
Re e ences
[1] ECFA De ec o R&D Roadmap P ocess G oup, The 2021 ECFA de ec o
esea ch and de elopmen oadmap, Tech. ep., Gene a (2020). doi:
10.17181/CERN.XDPL.W2EX.
[2] G. Pelleg ini, e al., Technology de elopmen s and i s measu emen s o
Low Gain A alanche De ec o s (LGAD) o high ene gy physics appli-
ca ions, Nucl. Ins um. Me h. A 765 (2014) 12–16. doi:10.1016/j.
nima.2014.06.008.
[3] N. Ca iglia, e al., Beam es esul s o a 16ps iming sys em based on
ul a- as silicon de ec o s, Nucl. Ins um. Me h. A 850 (2017) 83–88.
doi:10.1016/j.nima.2017.01.021.
[4] G. K ambe ge , e al., Radia ion e ec s in Low Gain A alanche De ec-
o s a e had on i adia ions, JINST 10. doi:10.1088/1748-0221/
10/07/P07006.
[5] R. S. Whi e, e al., Cha ac e isa ion o he FBK EXFLU1 hin senso s
wi h gain in a high luence en i onmen , Nucl. Ins um. Me h. A 1068
(2024) 169798. doi:10.1016/j.nima.2024.169798.
[6] V. Sola, e al., A compensa ed design o he LGAD gain laye , Nucl.
Ins um. Me h. A 1040 (2022) 167232. doi:10.1016/j.nima.2022.
167232.
[7] V. Sola, e al., The i s ba ch o compensa ed LGAD senso s, Nucl. In-
s um. Me h. A 1064 (2024) 169453. doi:10.1016/j.nima.2024.
169453.
[8] A. Mo ozzi, e al., TCAD simula ions o adia ion- ole an silicon sen-
so s, PoS VERTEX2023 (2024) 060. doi:10.22323/1.448.0060.
[9] M. Moll, e al., In es iga ion on he imp o ed adia ion ha dness o silicon
de ec o s wi h high oxygen concen a ion, Nucl. Ins um. Me h. A 439
(2000) 282–292. doi:10.1016/S0168-9002(99)00842-6.
[10] M. Fe e o, e al., Radia ion esis an LGAD design, Nucl. Ins um. Me h.
A 919 (2019) 16–26. doi:10.1016/j.nima.2018.11.121.
[11] R. Wuns o , e al., In es iga ions o dono and accep o emo al and long
e m annealing in silicon wi h di e en bo on/phospho us a ios, Nucl.
Ins um. Me h. A 377 (1996) 228–233. doi:10.1016/0168-9002(96)
00217-3.
[12] A. Fondacci, e al., Tcad in es iga ion o Compensa ed LGAD Senso s
o ex eme luence, Nucl. Ins um. Me h. A 1068 (2024) 169811. doi:
10.1016/j.nima.2024.169811.
[13] T. C oci, e al., TCAD simula ions o non-i adia ed and i adia ed low-
gain a alanche diodes and compa ison wi h measu emen s, JINST 17
(2022) C01022. doi:10.1088/1748-0221/17/01/C01022.
[14] L. J. an de Pauw, A Me hod o Measu ing Speci ic Resis i i y and
Hall E ec o Discs o A bi a y Shape, pp. 174–182. doi:10.1142/
9789814503464_0017.
4
