Impact of Charge Collection Efficiency and Electronic Noise on the Performance of Solid-state 3D Microdetectors

Impac o cha ge collec ion e icency and elec onic noise on he pe o mance o solid s a e 3D-mic ode ec o s J P ie o-Pena1, F G´omez1,2, C Gua diola3,MC Jim´enez-Ramos4,5, J Ga c´ıa L´opez4,5, A Ba a o-Rold´an4,5, M Baselga6, J Pa do-Mon e o7and C Fle a8 1Depa amen o de F´ısica de Pa ´ıculas, Uni e sidade de San iago de Compos ela, 15782-San iago de Compos ela, Spain 2G upo de Imagen Molecula , Ins i u o de In es igaci´on Sani a ia, 15706-San iago de Compos ela, Spain 3Labo a oi e de Physique des 2 in inis I `ene Jolio -Cu ie (IJCLab-UMR9012) Uni e si ´e Pa is-Saclay, O say, 91405 F ance 4Cen o Nacional de Acele ado es, 41092 Se illa, Spain 5Depa men o A omic, Molecula and Nuclea Physics, Uni e sidad de Se illa, 41012 Se illa, Spain 6ETP (KIT), He mann- on-Helmhol z-Pla z 1, 76344 Eggens ein-Leopoldsha en, Ge many. Now a Deu sches Elek onen-Synch o on DESY, No kes asse 85, 22607 Hambu g, Ge many 7G upo de F´ısica M´edica e Bioma em´a icas, Ins i u o de In es igaci´on Sani a ia, San iago de Compos ela, 15706 Spain. 8Ins i u o de Mic oelec ´onica de Ba celona, Cen o Nacional de Mic oelec ´onica (IMB-CNM, CSIC), Bella e a 08193 Spain E-mail: [email p o ec ed] Abs ac . Mic odosime y has been adi ionally pe o med h ough gaseous p opo ional coun e s, al hough in ecen yea s di e en solid s a e mic odosime e s ha e been p oposed and cons uc ed o his ask. In his pape we analyze he esponse o solid s a e de ices o mic ome ic size wi h no in insic gain de eloped by CNM-CSIC (Spain). The e a e wo majo aspec s o he ope a ion o hese de ices ha a ec he econs uc ion o he p obabili y dis ibu ions and momen a o s ochas ic quan i ies ela ed o mic odosime y. Fo mic ome ic olumes he d i and di usion o he cha ge ca ie s gi es ise o a pa ial cha ge collec ion e iciency in he pe iphe al egion o he deple ed olume. Such e ec p oduce a pe u ba ion o he econs uc ed pulse heigh (i.e. impa ed ene gy) dis ibu ions wi h espec o he ac ual mic odosime ic dis ibu ions. The ele ance o his de ia ion depends on he size, geome y and ope a ion condi ions o he de ice. On he o he hand, he elec onic noise om he single e en eadou se -up poses a limi on he minimum de ec able lineal ene gy when he mic odosime e size is educed. This a icle add esses hese issues o p o ide a amewo k on he physical cons ain s o he design and ope a ion o solid s a e mic odosime e s. Impac o CCE and noise on silicon-based 3D-mic ode ec o s 2 1. In oduc ion High ene gy p o on and hea ie ion ex e nal beam he apy p esen s ce ain adiobiological and physical p ope ies ha allows be e esul s han con en ional pho on and elec on ex e nal adio he apy in se e al ypes o cance . Pa icle he apy is capable o inducing mo e damage o he umo issue a cellula and sub-cellula le els compa ed o pho on he apy o compa able mac oscopic dose le els and a be e dose con o ma ion o he a ge olume (Du an e & Loe le 2010). The a ionale behind his beha io is ha p o ons and ions can ha e a much highe Linea Ene gy T ans e (LET) han ha p oduced by cha ged pa icles p esen in con en ional pho on and elec on he apy, and his highe concen a ion o ene gy deposi ion leads o mul iple clus e ed single-s and and double-s and b eaks o cellula DNA. This amoun o damage p o okes a highe numbe o cell inac i a ion and apop osis han wi h pho on beams, since ha damage is mo e di icul o epai (B enne & Wa d 1992). The inc eased numbe o acili ies capable o p o iding hese ypes o ea men has been inc easing in he las yea s all a ound he wo ld (Dosanjh, Amaldi, Maye , Poe e e al. 2018, Pa icle The apy Co-Ope a i e G oup 2019). In pa icle he apy he dose is e alua ed in e ms o pho on isoe ec i e dose, which is calcula ed as he p oduc o he physical dose (abso bed dose o wa e ) and he ela i e biological e ec i eness o RBE (IAEA 2008). RBE is dependen on physical and biological ac o s, such as LET and se e al o he biological p ocesses ha di e as a unc ion o he a ge issue (B i en, Pe e s & Mu ay 2001, Pagane i 2014). The B agg peak, o he s opping ange o he ions, coincides wi h he egion o maximum RBE. To cha ac e ize he pho on isoe ec i e dose, i is impo an o know he ene gy deposi ion along he pa icle acks a sub-mic ome ic le els (K ¨ame & Scholz 2000). As he adi ional dosime ic quan i ies used in pho on and elec on ex e nal adio he apy a e based on a e age alues o deposi ed ene gy in la ge egions and in ol ing a la ge numbe o e en s, hey canno be used o he small scales needed in pa icle he apy. A mic oscopic scales, he s ochas ic na u e o he adia ion-ma e in e ac ions equi es quan i ies based on dis ibu ion p obabili ies ins ead o me ics based on expec a ion alues. The ole o mic odosime y is o p o ide he ull desc ip ion o hese quan i ies. Fo mic odosime y applica ions, issue equi alen gaseous p opo ional chambe s (TEPC) a e he mos commonly used de ec o s. Thei p inciple o ope a ion is based on he use o a gas a a e y low p essu e wi h he same mass s opping powe ha a ce ain olume o issue equi alen solid issue, allowing o simula e a issue equi alen mic oscopic si e h ough he use o a gaseous mac oscopic si e. The main disad an age o hese de ec o s is ha wall-e ec s can cause dis o ions in hei eading. These e ec s can be a oided by using an i e a ion o he TEPC de ec o s called wall-less TEPC. Rega dless, any model o TEPC will ha e millime ic spa ial esolu ion due o i s mac oscopic size and show pile-up e ec s unde beams o high luence a e (as in Impac o CCE and noise on silicon-based 3D-mic ode ec o s 3 clinical beams, wi h luence a es g ea e han 108pa icles s−1cm−2). They a e di icul o ope a e due o he use o high ol ages, gas supply equi emen s and hei size makes mo ing hem a ea on i s own. All hese ac s make hem un easible o daily po en ial quali y assu ance and limi he p ac ical use o hese de ices in clinical ix u es. Despi e all hese d awbacks, he TEPC echnology has been he s anda d o mic odosime ic measu emen s up o now, and ecen ly, new e sions o hese de ec o s ha e been in oduced, such as he mini-TEPC, which can imp o e mos o he pe o mance limi a ions associa ed wi h hei size. (Colau i, Con e, Sel a, Chi io i, Pola, Bo o , Fazzi, Agos eo & Ciocca 2017, Fa ahmand, Bos, De Na do & Van Eijk 2004, De Na do, Cesa i, Don`a, Mag in, Colau i, Con e & To nielli 2004, Kliauga 1990). Solid s a e adia ion de ec o s a e commonly used o pe o m he dosime ic cha ac e iza ion o adia ion ields, and p esen ad an ages such as as esponse and good ene gy esolu ion. This amily o de ec o s, ha ing a highe mass densi y in he ac i e olume han a gas-based de ec o , can be manu ac u ed down o mic ome ic and submic ome ic dimensions, and hus close o he ac ual cell o cellula s uc u e sizes o in e es , allowing i s use o mic odosime y applica ions. No only can solid-s a e de ec o s ha e high ene gy esolu ion, as signal p ocessing and a small size, bu hey a oid some o he disad an ages o he TEPC, as hey do no need high ol age bias and exhibi an o e all easie de ice ope a ion. The use o h ee-dimensional a chi ec u e was p oposed o silicon de ec o s (Pa ke , Kenney & Segal 1997) in he ields o medical imaging and pa icle acking in high ene gy physics (Pelleg ini, Lozano, Ullan, Ba es, Fle a & Pennica d 2008). This con igu a ion would be able o educe he loss o cha ge ca ie s due o apping e ec and sho en he cha ge collec ion ime compa ed o adi ional plana solid-s a e de ec o s. In he 3D con igu a ion, he ol age equi ed o p o oke ull deple ion in he bulk is also educed, and o hin de ices o up o 50 µm hickness he capaci ance o a 3D mic o-s uc u ed solid-s a e de ec o is a leas wo o de s o magni ude lowe han o adi ional plana de ec o s (Pelleg ini, Ga cia, Balbuena, Cab uja, Lozano, O a a & Ullan 2009). The signal o noise a io (SNR) is imp o ed since SNR is in e sely p opo ional o he capaci ance (Spiele 2005). Ne e heless, solid s a e de ices also ha e some p oblems o hei own ha limi hei use ulness in dosime y. In he case o silicon, i s non equi alence o issue bo h in mass ene gy abso p ion coe icien and s opping powe coe icien makes i necessa y o apply co ec ion ac o s in o de o ob ain he mic odosime ic dis ibu ions in wa e . I is impo an ha he ype o de ices desc ibed in his a icle a e aligned wi h i s sensi i e olume pe pendicula o he p opaga ion di ec ion o he beam, as a misalignmen can p oduce a di e en mean cho d leng h o he beam pa icles, a ec ing he econs uc ed lineal ene gy spec a (Bols , Gua elli, T an & Rosen eld 2018). Also, silicon de ices a e suscep ible o adia ion damage which deg ades hei pe o mance wi h o al dose. Addi ionally, he e can be a loss o collec ed cha ge p oduced om he ack ioniza ion due o ecombina ion ha a ec s he econs uc ion o he impa ed ene gy dis ibu ions, hus modi ying he mic odosime ic spec a. This e ec is summa ized Impac o CCE and noise on silicon-based 3D-mic ode ec o s 4 usually h ough he cha ge collec ion e iciency dependence on he ack impac posi ion. E en hough new de elopmen s in low-gain a alanche diodes (LGAD) use in insic ampli ica ion o enhance SNR (Pelleg ini, Fe n´andez-Ma ´ınez, Baselga, Fle a, Flo es, G eco, Hidalgo, Mandi´c, K ambe ge , Qui ion e al. 2014), his ampli ica ion is s ill limi ed and he lack o in insic ampli ica ion in cu en 3D silicon de ec o echnology comp omises he signal o noise a io o de ices in he mic ome e and sub-mic ome e dimensions. In his pape he ac i e olume and cha ge collec ion p ope ies o a cylind ical silicon mic odosime e de eloped by IMB-CNM (CSIC, Spain) was s udied. In he case o he de ice employed o his wo k, he ou pu signal is conside ed p opo ional o he impa ed ene gy in he sensi i e olume. F om he spec a gi en by he de ec o signal, o he mic odosime ic quan i ies can be calcula ed. To e alua e he cha ge collec ion p ope ies o he de ice, a model o cha ge collec ion e iciency as a unc ion o he dis ance o he cen e o he ac i e a ea was de eloped and hen compa ed wi h expe imen al da a om es uns conduc ed a he synch o on o he Fondazione CNAO (Pa ia, I aly) using a ca bon ion beam and a CNA (Se ille, Spain) using a p o on mic obeam. Addi ionally, he de ec ion limi o 3D mic os uc u ed de ec o s as a unc ion o hei size is s udied by means o a simple model ha akes in o accoun elec onic noise om he eadou elec onics. 2. Ma e ials and me hods 2.1. Silicon mic odosime e The mic odosime e employed in his wo k is a new ype o h ee dimensional diode designed and de eloped by IMB-CNM (CSIC) a hei acili ies in Ba celona, Spain (Gua diola, Qui ion, Pelleg ini, Fle a, Es eban, Co ´es-Gi aldo, G´omez, Solbe g, Ca abe & Lozano 2015). The de ec o is comp ised o se e al indi idual senso s o uni cells a anged in an a ay capable o indi idual eadou o he de ec ion o ene gy deposi ion e en s. These cells ha e a h ee-dimensional cylind ical s uc u e e ched inside he silicon bulk wi h an implan ed p+ cha ge collec ing elec ode su ounded by a concen ic n+ elec ode ench. The cylind ical cell axis is pe pendicula o he silicon wa e plane. A scanning elec on mic oscope image and a schema ic c oss sec ion o he de ice can be seen in igu e 1. Al hough he ab ica ion p ocess allows he p oduc ion o de ec o s wi h di e en diame e o he cylind ical senso s, in he de ice employed in his wo k we ha e se he he physical size o he silicon cylinde as 20 µm in diame e bu due o he elec ic ield dis ibu ion o he de ice he sensi i e size o he cylinde is 15 µm in diame e . In his way he size and shape o he silicon sensi i e olume is simila o hose o mammalian cell (Ginzbe g, Ka i & Ki schne 2015). The diame e o he cen al implan ed elec ode is 4 µm and he wid h o he n+ ench is 3 µm. The senso s in he silicon die a e a anged in a squa e ma ix wi h p-elec ode Impac o CCE and noise on silicon-based 3D-mic ode ec o s 5 Figu e 1. C oss sec ion schema ic o he de ec o (no o scale, le ) along wi h an elec on mic oscope image o he 3D-mic ode ec o op- iew ( igh ). indi idual eadou . The pi ch be ween wo consecu i e de ec o cen e s in his pa icula de ice is 200 µm al hough his can also be a ied i desi ed. All he n-elec odes a e connec ed o he same pad on he opposi e side o he a ay o bias connec ion. In his wo k, only he eadou om one indi idual cell a a ime was ully ins umen ed, keeping he es o he senso s g ounded. The hickness o he sensi i e olume is 5.5±0.5 µm. The ene gy esolu ion was es ima ed om measu emen s as 12% ull-wid h a hal - maximum (FWHM) a 660 keV. Mo e in o ma ion abou he ab ica ion p ocess and Technological Compu ed Assis Design (TCAD) simula ions o he deple ion olume and cha ge collec ion can be ound a (Fle a, Es eban, Baselga, Qui ion, Pelleg ini, Gua diola, Co ´es-Gi aldo, L´opez, Ramos, G´omez e al. 2015). These de ec o s a e designed o pe o m mic odosime ic measu emen a nominal luence a e in had on he apy, allowing an ins umen al e i ica ion o he lineal ene gy spec a a di e en dep h and posi ions in a phan om (G´omez, Fle a, Es eban, Qui ion, Pelleg ini, Lozano, P ezado, Dos San os, Gua diola, Mon a ou e al. 2016, P ie o-Pena, G´omez, Fle a, Gua diola, Pelleg ini, Done i, Gio danengo, Gonz´alez-Cas a˜no & Pa do- Mon e o 2019). Thei design p oduces a high con o ma ion o he deple ed egion o a olume o app oxima ely 900 µm3. The in insic ield g adien s p esen in he de ice oge he wi h he cha ge d i and di usion p o oke ha in he mic odosime e cell pe iphe y he cha ge collec ion e iciency exhibi s a ela i ely as decay o ze o alues. Pa ially deple ed silicon olumes p esen in he de ice lead o ecombina ion o he ioniza ion cha ge and pa ial cha ge collec ion. Due o he in insic echnological limi s in he mic oelec onics manu ac u ing p ocesses, his cha ge collec ion ansi ion is no negligible in gene al e ms and can a ec he econs uc ed mic odosime ic spec um om he silicon mic o-cell. This issue has been add essed in he p esen s udy o e alua e i s signi icance and he limi a ion i poses o ac ual mic odosime e geome ies. All he esul s p esen ed in his wo k a e shown in e ms o ene gy deposi ion in silicon. Howe e , he silicon ene gy deposi ion spec a can be con e ed o issue equi alen ma e ial by a look up able me hodology like ha used in (P ie o-Pena e al. 2019). Impac o CCE and noise on silicon-based 3D-mic ode ec o s 6 2.2. Elec ical simula ions Elec ical simula ions we e conduc ed wi h a TCAD so wa e, Sen au us Synopsys. This so wa e sol es he Poisson equa ion o he s udied geome y. TCAD simula ions gi e a de ailed desc ip ion o he elec ical ield o he mic odosime e as well as he ansien o a hea y ion h ough any angle o he de ice, gi ing he cha ge collec ion. The simula ed de ice is a 20 µm diame e n- ype (wi h a doping concen a ion o 8.61 ×1011 cm−3) mic odosime e . The silicon wa e s which he silicon de ec o s a e ab ica ed om ha e a hickness o 5.5 ±0.5 µm, wi h he hickness o his de ec o sample de e mined o be 5.3 µm. The silicon dioxide cha ge su ace densi y used is 1011 cm−2. The elec ical simula ions we e ca ied ou wi h 0 V, 5 V and 10 V bias ol age. Expe imen al measu emen s wi h 5 MeV alpha pa icles indica e a ull deple ion o he mic odosime e sensi i e olume a a 5 V bias ol age (Fle a e al. 2015). The ansien simula ions use he He yIon so wa e unc ion, wi h pa icles ha ha e an LET in silicon (Linea Ene gy T ans e unc ion) o 1.282 10−5pC/µm impinging pe pendicula ly o he su ace o he mic odosime e . 2.3. Expe imen al se -up The cha ac e iza ion o hese de ices wi h ion he apy beams we e pe o med using a 115.25 MeV A−1 12C ion beam a Fondazione CNAO (Pa ia, I aly). This synch o on acili y has an ac i e scanning p o on and ca bon ion beam. Du ing he measu emen s we used he signal om a mono-ene ge ic pencil beam c ossing 20 cm o ai be ween he nozzle exi and he measu ing ins umen . Se e al measu emen s we e ca ied ou placing he mic odosime e behind a a iable dep h o polyme hyl me hac yla e (PMMA, densi y 1.186 g cm−3). The dep h was con olled using a mo o ized emo e wedge sys em. The wedge sys em is o med by wo 10◦PMMA wedges allowing a a iable dep h o 3 mm o 40 mm wi h an unce ain y o he dep h o app oxima ely 30 µm. PMMA is a issue-equi alen ma e ial, allowing o pe o m measu emen s in he ields o mic odosime y and adiobiology, he main scope o hese de ec o s. The se o mic odosime ic spec a ob ained co e om he beam en ance pla eau up o he B agg peak o he ion beam used. The mic odosime e was connec ed o a CAEN A1422H Hyb id cha ge sensi i e p eampli ie and o a CAEN N968 spec oscopy shaping ampli ie . Then, he esul ing pulse heigh was digi ized h ough an Amp ek MCA8000D mul ichannel analyze placed in he expe imen al oom, connec ed ia E he ne o a compu e in he con ol oom whe e he spec a we e s o ed. The p e ious wo k done using he CNAO clinical beam 12C ion beam o CNAO wi h he cylind ical mic odosime e s (P ie o-Pena e al. 2019) exhibi a easonable ag eemen wi h he Mon e Ca lo simula ions. Ne e heless, expe imen al pulse heigh dis ibu ions (using any bias ol age in he ange o 0-20 V) always show a ele an ail wi h high numbe o coun s in he low-ene gy pa o he spec a and a small shi when compa ed wi h espec o he peak posi ion in he simula ed impa ed ene gy dis ibu ions, as can Impac o CCE and noise on silicon-based 3D-mic ode ec o s 7 Figu e 2. Expe imen al spec um (blue do ed line) measu ed wi h he IMB 3D mic ode ec o and FLUKA Mon e Ca lo simula ion ( ed solid line) o 115.25 MeV A−1 12C ions a e sing 25.20 mm o PMMA (P ie o-Pena e al. 2019). be seen in igu e 2, aken wi h no bias ol age. Elec onic noise con ibu ions, ampli ie baseline shi s o pile-up e en s ha e no been ound o be able o gene a e his dis o ion o he measu ed da a om he mic odosime e s. The e ec o spec ome y dis o ion in silicon mic osenso s has been epo ed p e iously in di e en de ices wi h high g anula i y eadou (Gimenez, Ballab iga, Campbell, Ho swell, Llopa , Ma chal, Sawhney, Ta oni & Tu ecek 2011, Campbell, Heijne, Hol´y, Id´a aga, Jakubek, Lebel, Le oy, Llopa , Posp´ısil, Tlus os & Vykydal 2008). I is hypo hesized ha his beha io is p oduced by in insic ield g adien s and cha ge di usion ha modi y he eco ded spec a by he mic osenso , p o oking pa ially deple ed olumes leading o ecombina ion and pa ial cha ge collec ion in he pe iphe y o he mic ocylinde . 2.4. Mon e Ca lo simula ions The expe imen al wo k was benchma ked agains a Mon e Ca lo simula ion o he beam ene gy deposi ion in an indi idual cell o he de ec o . Mon e Ca lo simula ions we e pe o med using he FLUKA Mon e Ca lo code (Fe a i, Sala, Fasso Impac o CCE and noise on silicon-based 3D-mic ode ec o s 8 Figu e 3. Pulse heigh spec um o 600 keV p o on beam in acuum aken a he IBIC beam a CNA (Se ille, Spain). & Ran 2005, B¨ohlen, Ce u i, Chin, Fass`o, Fe a i, O ega, Mai ani, Sala, Smi no & Vlachoudis 2014), de eloped by CERN and INFN. The e is a p ede ined con igu a ion in he code o i s use in had on he apy (”HADROTHE apy”) ha was selec ed o he simula ions, changing he de aul h esholds o he anspo o all pa icles, mul iple sca e ing and del a ay p oduc ion and co ec ions o o m ac o o Comp on Sca e ing. A s ic e addi ional limi o he kine ic ene gy h eshold was selec ed, changing i o 1 keV. This op ion was selec ed o ep oduce he expe imen al esul s mo e accu a ely wi hou adding oo much addi ional compu a ion ime, as de ailed in (B¨ohlen, Ce u i, Dosanjh, Fe a i, Gudowska, Mai ani & Quesada 2010). Fo each geome y a simula ion wi h 105his o ies was compu ed. The es ima ed ela i e s a is ical unce ain y o he simula ion in he pla eau egion o he B agg cu e is less han 2%. The code was commissioned agains a wa e dep h dose dis ibu ion o he same CNAO expe imen al beam measu ed wi h a Peak inde a iable wa e column and a PTW 34080 B agg-peak chambe , simila o a p ocedu e desc ibed elsewhe e (G´omez e al. 2016). The simula ion esembles he pencil beam’s main cha ac e is ics, such as ene gy and angula sp ead a he exi window o he gan y oge he wi h Impac o CCE and noise on silicon-based 3D-mic ode ec o s 9 he anspo ac oss he PMMA wedge and myla window and o he ma e ials o he de ec o me allic case and silicon suppo . 2.5. Cha ge Collec ion E iciency model The econs uc ed impa ed ene gy in he de ec o ac i e olume is ob ained om he pulse heigh dis ibu ion o he senso . Each e en pulse heigh is he e conside ed as he con olu ion o he ac ual ene gy deposi ion along he silicon de ec o wi h he e ec i e cha ge collec ion e iciency map. Fo he de ailed e alua ion o he Cha ge Collec ion E iciency (CCE) we used he Ion Beam Induced Cha ge (IBIC) echnique p o on mic obeam acili y a CNA (Se ille). Du ing he i adia ion he beam was scanned h ough he de ec o and he eadou was pe o med h ough a synch onized ampli ie and digi ize chain. The kine ic ene gy o he p o on beam employed was 600 keV in di e en es uns conduc ed in acuum. Figu e 3 shows he pulse heigh spec a o 0 V and 3 V bias ol age in he IBIC p o on beam. A phenomenological model o he CCE was de eloped o desc ibe he expe imen al esul s and Mon e Ca lo simula ions. He e, no only he impa ed ene gy was eco ded, bu also he posi ion and di ec o cosines o he ajec o y o he pa icles when hey en e in o he de ec o olume. Ioniza ion was gene a ed in a 0.05 µm s ep oxel geome y, acco ding o FLUKA dis ibu ions, along he s aigh line a e sing he de ec o olume wi h an angle equal o he cosines o he pa icle. I was conside ed ha o he pa icles and ene gy used he la e al s aggling was negligible when compa ed wi h he dimensions o he de ec o (Be ge , Cou sey, Zucke , Chang e al. 1998). Once he ioniza ion cloud along he ack is p oduced, each cha ge oxel is weigh ed wi h he poin dependen model CCE unc ion, and hen all he weigh ed cha ge con ibu ions a e e en ually added o ob ain he expec ed signal o each e en . The CCE unc ion cons uc ed is based on exponen ial unc ions wi h dependence on bo h he dis ance o he cen al axis o he cylinde ( ) and he dep h a e sed by he pa icle (h). Radial and e ical dependence a e sepa a ed in he model. A six-pa ame e unc ion was cons uc ed as shown in he ollowing equa ion: F( , h) = ( )⊗g(h) (1) ( ) = 1 + e−g 1 1−e−g 21−eg ( − 2) 1 + eg ( − 1)(2) g(h) = 1 + e−ghh1 1−e−ghh21−egh(h−h2) 1 + egh(h−h1)(3) whe e and ha e he alues o he adius and heigh ( om he geome ical cen e o he cylinde ), 1and h1a e he poin s in which he CCE unc ion eaches a alue o 0.5, 2and h2a e he poin s in which he unc ion goes o ze o, and g and gza e he g adien s o he exponen ial decay. Addi ionally, he e ical h componen has a ha d limi in h=2.75 µm due o he de ec o dimensions ( hickness o 5.5 µm). Impac o CCE and noise on silicon-based 3D-mic ode ec o s 16 Mos p obable lineal ene gy, ymp (keV µm-1) 0 50 100 150 200 250 300 350 400 Peak posi ion di e ence (keV µm-1) 0 2 4 6 8 10 12 14 16 18 Figu e 10. Peak shi in keV/µm o all measu ed poin s wi h he cylind ical mic osenso along he B agg cu e as a unc ion o he mos p obable lineal ene gy, ymp. de ec o leakage cu en and α,β,γ,δand κa e noise pa ame e s associa ed o he elec onic eadou chain due o shun and se ies esis ance, senso bias cu en and ampli ie con ibu ions (Radeka 1974, Be uccio & Pullia 1993). Fo his wo k, we ha e conside ed sizes Lo cylind ical mic ode ec o s om 0.1 µm up o 40 µm wi h Cin anging om 0.01 pF up o 5.3 pF and Id om 1 pA up o 950 pA. These alues we e aken acco ding o ou expe ience wi h simila de ices. We used pa ame e s om he s a e o he a elec onics (CR-110 e e ence shee n.d.) o calcula e ha ENC would yield alues be ween 260 up o 290 elec ons o a shaping ime o 1 µs espec i ely (α= 43 pF−2µse2;β= 15 pF; γ= 8 µs−1pA−1e2;δ= 800 pA; κ= 5 ×104 e2). We ha e conside ed wo scena ios, namely: when he ack incidence is o be pa allel o he cylinde axis conside ed abo e, hus ha ing < l >=L(denomina ed axial) and when he e is µ- andomness wi h < l >=2 3L(denomina ed iso opic). Fo he noise sepa a ion we ha e assumed ha he FWHM equi alen noise ene gy would be 2.35 imes he ENC mul iplied by he a e age ene gy wpe ion-elec on pai , hus p o iding a h eshold on he ene gy impa ed de ec ion aken as wo imes his FWHM (Radeka 1974)  h ≥2×ENC ×2.35 ×W Impac o CCE and noise on silicon-based 3D-mic ode ec o s 17 0 5 10 15 20 25 30 35 40 0 1 2 3 4 5 6 7 8 9 10 Size o mic odosime e (µm) Limi o lineal ene gy de ec ion (keV/µm) Silicon iso opic Diamond iso opic Silicon axial Diamond axial Figu e 11. Limi o de ec abili y o lineal ene gy in cylind ical mic o–dosime e s wi h equal diame e and heigh Las a unc ion o L. Do ed and con inuous lines co espond o diamond and silicon de ec o s unde iso opic condi ions espec i ely. Dashed and do -dashed lines co espond o diamond and silicon de ec o s o axial incidence espec i ely. This p o ides also a co esponding limi on he lineal ene gy de ec ion in he o m o y h = h < l > ≥4.7×ENC ×W < l > Thus we can e alua e he co esponding limi s o he de ec ion o he lineal ene gy conside ing hese cylind ical mic ode ec o s o di e en size L. Figu e 11 shows he limi s on he de ec ion o lineal ene gy in he de ec ing ma e ial as a unc ion o he de ec o size bo h o iso opic and pa allel o he cylinde axis incidences. In his Figu e we ha e included bo h diamond and silicon senso s jus o guide he eade in e ms o he physical limi s expec ed om he di e en cha ac e is ics o he sensi i e media. In he axial incidence scena io, he capabili y o ex end he de ec ion ange o 1 keV/µm would be achie ed in silicon when he size o he mic osenso is equal o bigge han 4.4 µm while in he case o diamond his would imply a senso o 16 µm hickness. Addi ionally, i is clea ha sub-mic on mic odosime e s would be only use ul o highly ionizing pa icles, since o silicon (diamond) de ices o 1 µm we would only be able o de ec adia ion wi h lineal ene gy o e 4.5 keV/µm (15.7 keV/µm). This conclusion Impac o CCE and noise on silicon-based 3D-mic ode ec o s 18 ends o exclude he easibili y o solid s a e mic odosime e s as adequa e de ices o ack s uc u e measu emen in he egion a ound 0.1 µm o below, a leas o non in insic gain senso s. Those limi s a e e en la ge o he iso opic condi ions whe e, o example, o achie e a de ec ion limi below 1 keV/µm i would be needed a senso o 6.7 µm size in silicon while o diamond his limi yields a alue o 25 µm. In ac he use o de ices o en hs o mic ons would yield alues close o he Linea Ene gy T ans e han he s ochas ic lineal ene gy conside ed in mic odosime ic dis ibu ions. O cou se, he esul s o his sec ion could be ecalcula ed conside ing he pa icula elec onic noise, senso cha ac e is ics and eadou unde s udy. 4. Conclusions Solid-s a e de ices can be employed o measu e mic odosime ic spec a. Cha ge collec ion e iciency (CCE) and elec onic noise pose limi a ions on hei pe o mance since hey can a ec he ideli y o he mic odosime ic dis ibu ions and he h esholds o lineal ene gy de ec ion. Fo he cylind ical de ice s udied in his wo k wi h 15 µm diame e and 5.5 µm hickness, he in insic ield g adien s and cha ge di usion in he sensi i e olume o he de ec o modi y he eco ded spec a by inducing a cha ge collec ion e iciency s ongly dependen on he posi ion o he ene gy deposi ion e en . These pe u ba ions modi y he aw expe imen al mic odosime ic spec a in a sys ema ic way, p oducing an a i icial enhancemen o he low lineal ene gy egion. In he p esen wo k his e idence was ound in 12C beam measu emen s a CNAO. In o de o ep oduce his sys ema ic e ec we cons uc ed a i s phenomenological model o he CCE by using an exponen ial unc ion and six pa ame e s ela ed o he physical dimensions o he mic os uc u ed de ec o . Elec ical simula ions using TCAD a di e en biasing ol ages and p o on beam IBIC es s pe o med o s udy he ac i e olume inside he mic odosime e s we e addi ionally used o alida e he CCE model. Mon e Ca lo simula ions we e modi ied by using his model o compu e he pa ial cha ge collec ion in he simula ed ene gy deposi ion e en s. Recons uc ed spec a including CCE e ec showed conside able ag eemen wi h he expe imen al esul s. The mos p obable lineal ene gy in hese expe imen al spec a is shi ed wi h espec o he expec a ion alue ob ained wi h Mon e Ca lo simula ions. This shi along he B agg cu e holds a linea ela ionship wi h he lineal ene gy. Addi ionally o he dis o ion o he low lineal ene gy spec a, he elec onic noise con ibu ion se s a heo e ical limi on he smalles de ec able lineal ene gy o mic os uc u ed solid s a e de ices. Conside ing a cylind ical de ice wi h equal diame e and heigh L, he lineal ene gy h eshold would be in e sely p opo ional o his pa ame e . Fo example, o de ec ing e en s o 1 keV/µm, he dimension Lshould be g ea e han 4.4µm whe eas in diamond his size should be a leas 16 µm. Impac o CCE and noise on silicon-based 3D-mic ode ec o s 19 Acknowledgmen s C Gua diola has ecei ed unding om he Eu opean Union’s Ho izon 2020 esea ch and inno a ion p og am unde he Ma ie Sklodowska-Cu ie g an ag eemen No 745109. M C Jim´enez-Ramos acknowledge suppo om he Spanish p ojec RTI2018-098117-B- C21 unded by Minis y o Science, Inno a ion and Uni e si ies. Re e ences Be ge , M. J., Cou sey, J., Zucke , M., Chang, J. e al. (1998). 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