Fully Depleted Monolithic Active Microstrip Sensors: TCAD simulation study of an innovative design concept
Lorenzo De Cilladi, Thomas Corradino, Gian-Franco Dalla Betta, Coralie Neubüser, Lucio Pancheri
AArticle
Fully Depleted Monolithic Active Microstrip Sensors:TCAD simulation study of an innovative design concept
Lorenzo De Cilladi * , Thomas Corradino , Gian-Franco Dalla Betta , Coralie Neubüser andLucio Pancheri on behalf of the ARCADIA collaboration Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino (Italy) Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, 10125 Torino (Italy) Dipartimento di Ingegneria Industriale, Università degli Studi di Trento, 38123 Trento (Italy) Trento Institute for Fundamental Physics and Applications - Istituto Nazionale di Fisica Nucleare (TIFPA-INFN),38123 Trento (Italy) * Correspondence: [email protected]: date; Accepted: date; Published: date
Abstract:
The paper presents the simulation studies of 10 µ m pitch microstrips on a fully depletedmonolithic active CMOS technology and describes their potential to provide a new and cost-effectivesolution for particle tracking and timing applications. The Fully Depleted Monolithic Active MicrostripSensors (FD-MAMS) described in this work, which are developed within the framework of the ARCADIAproject, are compliant with commercial CMOS fabrication processes. A TCAD simulation campaign wasperformed in the perspective of an upcoming engineering production run with the aim of designingFD-MAMS, studying their electrical characteristics and optimising the sensor layout for enhancedperformance in terms of low capacitance, fast charge collection and low-power operation. A very finepitch of 10 µ m was chosen to provide very high spatial resolution. This small pitch still allows readoutelectronics to be monolithically integrated in the inter-strip regions, enabling the segmentation of longstrips and the implementation of distributed readout architectures. The effects of surface radiationdamage expected for total ionising doses of the order of 10 to 10 krad were also modelled in thesimulations. The results of the simulations exhibit promising performance in terms of timing andlow power consumption and motivate R&D efforts to further develop FD-MAMS; the results willbe experimentally verified through measurements on the test structures that will be available at thebeginning of 2021. Keywords:
Particle detectors; silicon detectors; monolithic sensors; microstrip sensors; CMOS; TCADsimulations; fast timing.
1. Introduction
Charged particle tracking and timing are fundamental tools for both physics research and fornumerous applications. Although a number of detection techniques are available, silicon detectorshave become largely employed due to their versatility and to the parallel strong developments of thesemiconductor industry. Various flavours of silicon sensors have been developed to meet the specificrequirements of different experiments and applications, such as high spatial resolution, fast chargecollection, low power consumption, high radiation tolerance and low cost per unit area.Silicon detectors are divided in two categories, namely hybrid and monolithic detectors. The formerare made of two separate silicon elements, the sensor and the chip, which are interconnected throughexternal bump or wire bonding. While the sensor hosts the sensing volume only, the chip integratesthe front-end readout electronics. On the contrary, monolithic sensors, which are emerging as a validalternative to hybrid detectors, embed the front-end electronics in the same silicon substrate which hosts a r X i v : . [ phy s i c s . i n s - d e t ] J a n of 26 the sensing volume, with benefits in terms of material budget, production yield and fabrication cost, asthey are produced with commercial microelectronics processes [1–3].Due to their characteristics, monolithic sensors have recently raised a wide interest in differentresearch fields; studies, proposals and developments have been made for applications in high energyphysics (HEP) [4–6], X-ray imaging [7,8], medical particle imaging [9] and space experiments [10].The state of the art includes three main types of monolithic sensors. The first type, called DepletedField Effect Transistors (DEPFETs), is capable of low noise operation thanks to low sensor inputcapacitance [11]. DEPFET detectors have been developed and used for HEP applications [12], for X-rayimaging in space [13] and for free electron laser experiments [14]. The main limitation of DEPFETs isthe need to reset their internal gate which can be quickly saturated by the leakage [15], thus making thistechnology not suitable for environments with high levels of non-ionising radiation.A second approach consists in the SOI (Silicon-On-Insulator) monolithic sensors. SOI sensors embeda buried-oxide layer separating a thin low-resistivity silicon layer, which hosts the integrated readoutcircuitry, from a thicker high-resistivity substrate, which serves as the sensitive detection region [16,17].This technology allows a low capacitance to be obtained [17]; however, SOI sensors suffer from back-gateeffect and have a reduced radiation hardness, due to accumulation of positive holes charges in the buriedoxide layer after irradiation [18]. Strategies have been found to overcome these limitations and to recoverfrom the Total Ionising Dose (TID) [19], but, as a consequence, the fabrication process of SOI sensors havebecome highly specialised and not compliant with standard microelectronics production processes. Thisresults in increased cost per unit area, which is a critical issue for large-area detector applications.A third flavour of monolithic sensors is represented by CMOS sensors [20]. CMOS sensors werealready in use for light detection when they were first proposed for charged particle tracking at thebeginning of the 2000s [21]. Over the last years, important advancements in CMOS sensors allowedthem to be employed in many applications, eventually leading to very large scale productions for particletrackers at collider experiments. The STAR pixel detector, which took data at the Relativistic Heavy IonCollider (RHIC) from 2014 to 2016, was the first large area monolithic pixel tracker ever built, for a total of0.16 m [22]. These dimensions have been exceeded by the newly-constructed Inner Tracking System ofthe ALICE experiment at CERN, in which a total detector surface of about 10 m is covered by ALPIDECMOS monolithic active pixel sensors (MAPS) [4].These achievements demonstrate the level of maturity and reliability that CMOS sensors haverecently reached. However, there is still room for further improvements, especially in terms of chargecollection speed and radiation hardness, and possibility to push previous limits in terms of low powerdensity, high spatial resolution and SNR.Pixel detectors are the first choice for small scale applications and for vertex trackers atcollider experiments [2] as they have an intrinsic capability of providing a two-dimensional positioninformation [23]. On the other hand, microstrip sensors [24] are largely used as particle detectors forspace applications and are a competitive option for particle trackers due to their high spatial resolution,simpler readout and much lower power density (i.e. power consumption per unit area) compared to pixeldetectors. Large experiments at particle colliders have largely employed silicon hybrid strip sensors in thepast, and are still developing and assembling new large-area trackers based on this technology, as in thecase of the Phase-2 Upgrades of the CMS Outer Tracker [25] and of the ATLAS Strip Inner Tracker [26]. A monolithic sensors is called “active” if it integrates a signal amplifier inside each pixel or strip. of 26
Recent space experiments equipped with silicon hybrid microstrip trackers include FERMI-LAT [27],DAMPE [28], PAMELA [29] and AMS-02 [30]. Strip-like sensors integrated in a monolithic technologyhave been proposed by combining the outputs of 55 µ m × µ m [31] or 40 µ m × µ m [32] pixels in eachcolumn or row of a pixel matrix.Spatial resolution of 1.25-1.3 µ m was achieved using hybrid silicon microstrip sensors with 25 µ mpitch [33]. However, it has recently been demonstrated with fully depleted double-SOI monolithic pixelsensors that the 1 µ m limit can be exceeded by semiconductor detectors [34]. The keys to a high spatialresolution with analogue readout are a fine microstrip pitch, a low sensor thickness to reduce Coulombscattering and delta-ray emission, and an increased SNR, which can be achieved by reducing the leakagecurrent and the sensor input capacitance to the readout electronics, but which is ultimately limited by thenoise of the front-end electronics [24,33,35].This paper presents the first investigation, design and simulation studies of CMOS Fully DepletedMonolithic Active Microstrip Sensors with 10 µ m pitch for charged particle detection. Properly optimisedsensor layouts may allow sub-micron resolution, improved radiation hardness and fast timing performancethanks to full depletion [6,36] in a power-saving and cost-effective commercial technology. Moreover, afurther advantage of monolithic microstrips is the potential complexity reduction of the detector assemblycompared to hybrid microstrip detectors. In fact, since many readout functions can be monolithicallyintegrated on the same chip which hosts the sensing volume, 1-by-1 strip bonding to the external readoutelectronics would not be needed anymore. We have hence studied and designed the FD-MAMS within theframework of the INFN ARCADIA project in order to provide an innovative solution for satellite-basedspace trackers and for large area particle detectors at future collider experiments.The results of the Technology Computer-Aided Design (TCAD) simulation campaign which alloweddifferent MAMS design flavours to be compared in terms of sensor capacitance, reference voltage values,leakage current and charge collection time and efficiency are presented; the effects of the inclusion of asilicon dioxide (SiO ) layer on top of the sensor and of surface radiation damage on the sensor operatingparameters are explored; the study of charge sharing between groups of adjacent strips when particleswith different Linear Energy Transfer (LET) traverse the sensor is reported. A selection of the MAMSpresented in this paper is going to be implemented in test structures which were submitted in November2020 for an engineering production run.The paper is organised as follows: Section 2 presents the sensor concept for the ARCADIA fullydepleted CMOS monolithic microstrip sensors and illustrates the simulation campaign that was performedfor the sensor design optimisation; Section 3 describes and discusses the results of the simulations; Section 4presents the conclusions, the future perspectives and the planned tests for the ARCADIA monolithicmicrostrip sensors.
2. The ARCADIA sensor concept
The ARCADIA project and its precursor, SEED (Sensor with Embedded Electronics Development),designed an innovative sensor concept [37,38] based on a modified 110 nm CMOS process developedin collaboration with LFoundry and compatible with their standard 110 nm CMOS process. Up to 6metal layers can be stacked on top of the sensor, for a total metal and insulator thickness of about 4-5 µ m.The ARCADIA collaboration is developing a scalable event-driven readout architecture to cover large The TCAD simulations were produced using the Synopsys ® Sentaurus (Version O-2018.06-SP2) software. of 26 detection surfaces (O(cm )) while maintaining ultra-low power consumption. The target for pixel sensorsis 10-20 mW/cm at high rates O(100 MHz), but for less dense particle environments (e.g. in spaceapplications) a dedicated low-power operation mode implements a cyclic pulling of the data packets fromeach section of the pixel matrix and disables most of the serialisers and data transceivers, further reducingthe total power consumption of the chip.In our project, an n-on-n sensor concept enabling full substrate depletion over tens or hundreds ofmicrons and allowing full CMOS electronics to be implemented was employed. A simplified view of thesensor cross section is visible in Figure 1. The process allows to achieve sensor thicknesses from 50 to400 µ m. A high resistivity n-type substrate was used and constitutes the active volume. The sensing n-wellnode, located on top of the sensor, collects the electrons produced by ionisation due to particles traversingthe active detection volume.N-doped and p-doped wells intended to host pMOSFETs and nMOSFETs respectively are shielded bya deep p-well, which allows the integration of full CMOS electronics and, hence, more complex digitalfunctions, when necessary. In fact, the deep p-well prevents the n-wells hosting pMOSFETs from competingwith the n-doped sensing node in the collection of the charge, thus avoiding loss of charge collectionefficiency. Figure 1.
ARCADIA monolithic sensor concept. The dotted arrows indicate the drift path of electrons(e) and holes (h) generated by a particle crossing the sensor. The voltages V nwell and V back applied to thesensor contacts are shown in green.
A p+ boron-doped region sits at the backside of the n-substrate, thus forming a pn-junction; whena negative bias voltage V back is applied to the backside p+ contact, sensor depletion starts from thepn-junction at the bottom of the sensor and eventually extends to the whole sensor, if the backside voltageis sufficiently large. Since the high voltage needed for sensor depletion is applied at the backside, itis possible to maintain the voltage V nwell applied to the front n-well electrode below 1 V and to uselow-voltage integrated electronics (1.2 V transistors) which is more radiation-resistant and has lower noise.Full sensor depletion allows fast charge collection by drift (beneficial to enhance the timing performance),higher charge collection efficiency, deeper collection depth and larger SNR; it also leads to improvedradiation tolerance, as charge losses by trapping are reduced [5]. Since thicker sensors need higher backside of 26 bias voltage to reach full depletion, termination structures composed of multiple floating guard rings areused to avoid early breakdown at the edges of the pn-junction.An additional n-type epitaxial layer, with lower resistivity than the substrate, is integrated betweenthe n-type substrate and the deep p-wells. Its aim is to better control the potential barrier below thedeep p-well, in order to delay the onset of the punch through current described in details in Paragraph 2.2.2.The feasibility of this sensor concept and approach to Fully Depleted monolithic CMOS sensorswas proven in the framework of the SEED project [37,38]. The upcoming ARCADIA engineering runwill include different design flavours of FD-CMOS monolithic sensors, both pixelated and strip-like.Large-area (1.3 × ) pixel demonstrators with embedded CMOS electronics and pixel test structures(0.5 × × ) without integrated readout circuitry [39] are foreseen, with pitches rangingfrom 10 to 50 µ m. The test structures will include as well the innovative MAMS and will allow a detailedcharacterisation of these sensors. The 3D TCAD simulation campaign performed to design the firstFD-MAMS will be presented and discussed in the following.
3D TCAD simulations were employed as a tool to optimise the sensor layout and performance. Theuse of 3D simulations is necessary to have a more realistic domain and results which are more accurateand less affected by boundary conditions. Furthermore, we were also interested in studying the chargecollection dynamics after a particle crosses the sensor, and this is more straightforward with 3D simulations.A fine pitch of 10 µ m was chosen for the microstrips in order to explore the characteristics and performanceof a sensor layout which pushes the requirements on both spatial and timing resolution. Different sensorthicknesses foreseen for the production runs were simulated. Variations in the sensor layout and operatingparameters were tested to study and optimise the sensor response. The simulated sensor flavours takeinto account the limitations imposed by the foundry’s sensors fabrication process, especially for the n-welland p-well sizes. The strip simulations investigated sensor flavours which pushed the design to the limitsof the process requirements. Figure 2.
Example TCAD 3D sensor domains for ARCADIA microstrips (top row) and corresponding crosssections (bottom row). (a) Standard simulation domain for sensors with the deep p-well. (b) Addition ofn-wells above the deep p-wells. (c) Simulated ARCADIA microstrips without deep p-wells. of 26
All the TCAD simulations were performed at a temperature of 300 K. A standard simulation domainincluding three 50 µ m long, 50 µ m thick, 10 µ m pitch microstrips is shown as an example in Figure 2 (a).The n-doped substrate is shown in green, the epitaxial layer in yellow, the microstrip sensing n-wells inred, the p-wells in blue and the less doped deep p-well in light blue. The default value for V nwell is 0.8 V.The p-wells, instead, are kept at a voltage V pwell = In this Section, the simulations performed to extract the sensor electrical characteristics and to studythe charge collection dynamics are briefly illustrated. Shared definitions and conventions on simulationsetups and operating parameters were agreed for the whole ARCADIA simulation campaign and arealso described in [39]. The strip length in the upcoming production run will be 1.2 cm. However, MAMSwith lengths of 50 µ m were simulated in order to run a large set of TCAD simulations in a reasonablecomputational time. The results were then scaled to the desired length.2.2.1. Depletion voltageSensor depletion starts at the backside, where the pn-junction between the n-type substrate and thep+ contact is located. If no negative bias voltage is applied to the backside contact, the sensor is not fullydepleted and the collection n-wells are not isolated. This means that a resistive path exists between then-type sensing nodes (see Figure 3, on the left). Therefore, if a voltage difference is applied between twoadjacent n-wells, a current will flow between them.As the negative voltage applied to the backside contact increases, the space charge region enlargesthrough the high resistivity substrate, eventually merging with the depletion volume which surroundsthe pn-junctions formed between the n-type substrate or epitaxial layer and the deep p-wells. At thispoint, the sensor is fully depleted, the resistive path between the sensing nodes is closed and the collectionn-wells are isolated; this is shown in Figure 3, on the right. In this condition, no current (except for theleakage current) will flow among adjacent n-wells even when different voltages are applied to them. of 26 Figure 3.
Depletion process in ARCADIA microstrips. On the left: cross section of a sensor before fulldepletion is reached. On the right: cross section of a fully depleted MAMS. The orange lines indicate theedge of the depletion region.
This behaviour can be observed in the orange example IV curve in Figure 4 ( I nwell , unbalanced ). Thesimulated domain shown in Figure 2 (left) was used. In this simulation, a voltage unbalance of 10 mVwas applied between adjacent strips: the first n-well was biased at 0.79 V, the central one at 0.8 V and thethird one at 0.81 V. The curve shows the current measured at the sensing node of the central strip as afunction of | V back | . A current of about 1 nA is measured at V back = − nA. This baseline corresponds to the leakage current (green IV curve, I nwell , leakage ).The backside voltage at which the single microstrips become isolated and the plateau is reached is thesensor depletion voltage V dpl ; this voltage is evaluated as the intersection point between the exponentialdecay fitting of the IV curve decreasing segment and the baseline. |V back | [V] | C u rr e n t | [ A ] I pwell I nwell , unbalanced I nwell , leakage V pt V dpl V pd C a p a c i t a n c e [ f F / m ] ARCADIA TCAD simulation C sens C sens (V pt ) Figure 4.
Example characteristic IV and CV curves extracted from TCAD simulations of ARCADIAmonolithic sensors. The red vertical axis refer to the sensor capacitance ( C sens ) CV curve. of 26 Figure 5 shows the simulated electrostatic potential and electric field maps at V back = V dpl in a crosssection of a 3-strip domain with all the n-wells at V nwell = Figure 5.
Electrostatic potential map (left) and electric field map (right) for a group of three ARCADIAmicrostrip sensors at V back = V dpl . The electric field lines are plotted on top of both maps. V back exceeds a certain value, a hole current flowing between the shallow p-doped backside regionand the (deep) p-well exponentially increases. This condition is known as punch-through and the holecurrent is the punch-through current [40]. We define the voltage corresponding to the onset of thepunch-through as V pt . The onset of the punch-through currents can be observed from the blue IV curve inFigure 4 ( I pwell ), which shows the absolute value of the current measured at the top p-well contacts as afunction of | V back | . The dip in the curve, corresponding to the point of sign inversion of the current, wasdefined as V pt . The simulation domain includes three 50 µ m long, 50 µ m thick, 10 µ m pitch microstrips. Inthis case, the n-wells are all biased at V nwell = V back = V pt as a safe reference sensor operating voltage; this isthe operating point for all the results shown in the following, if not stated differently. The sensor powerdensity can be defined as pd = V back · ( I pwell + I nwell ) A , where I nwell and I pwell are the currents flowing at thesensing node and at the top p-well contacts respectively, and A is the top surface area of the simulatedmicrostrip domain. In order to quantify the maximum acceptable backside bias voltage that limits theabsorbed power density, the value V pd at which pd = was extracted from the simulated IVcurves (see Figure 4).Figure 6 shows the hole current density at two different | V back | > | V pt | in the simulation domain usedto extract the I pwell curve of Figure 4. On the left, a backside voltage exceeding V pt by 1 V was chosen, whileon the right V back was set to V pd . An increase in the hole current density of several orders of magnitudecan be observed below the deep p-wells and in the substrate. of 26 Figure 6.
Hole current density in a simulated sensor domain including three microstrips in punch-throughcondition at two different V back . Care had to be taken to ensure that | V dpl | < | V pt | in the designed sensors. In this way, full depletionis reached before the onset of the punch-through. Moreover, the voltage operating range between V dpl and V pt , defined as ∆ V op = | V pt − V dpl | , should be large enough to ensure safe operation in full depletionbefore the onset of the punch-through even if deviations from the simulated design occur in the sensorfabrication process.2.2.3. Leakage currentThe same sensor domain and n-well voltage configuration used for the extraction of V pt was alsoused to evaluate the sensor leakage current I leak . The leakage current is defined as the current flowing atthe collection nodes in full depletion and in absence of external stimuli, such as particles or radiation. Theleakage current as a function of the backside bias voltage is shown in Figure 4 as a green curve ( I leak ). Inthe example shown in Figure 4, a value of 10 fA was extracted for I leak at V back = V pt .2.2.4. Sensor capacitanceThe sensor CV curve was simulated through AC simulations with a frequency of 10 kHz using thesame sensor domain employed for V pt and I leak evaluation, with V nwell = C sens , which is the input capacitance seen by the DC-coupled front-end electronics,originates from the lateral capacitance between the collection n-well and the surrounding p-wells. It isthus important to minimize this contribution by a careful selection of the distance between the edge of thecollection n-well and the p-wells; we call this distance "gap" (see Figure 1). An example CV curve is shownin red in Figure 4, with the capacitance per unit length considered. In the example of Figure 4, a value ofabout 0.33 fF/ µ m was obtained at V back = V pt .It has to be mentioned that in these sensors the depletion voltage does not necessarily correspond tothe voltage of minimum capacitance. The reason for this is the presence of the epitaxial layer, which islocated far from the backside pn-junction and has a lower resistivity than the substrate. Therefore, thedepletion of the epitaxial layer begins after the depletion of the substrate and progresses more slowlywith voltage. Full depletion of the whole sensor, including the epitaxial layer, and minimum capacitance Dose [Mrad]10 I n t e g r a t e d d e n s i t y [ c m ] Q ox Q ox (pre-irradiation) N accint N accint (pre-irradiation) N donint N donint (pre-irradiation) Figure 7.
Dependence of the oxide charge density Q ox , acceptor integrated interface trap state density N accint and donor integrated interface trap state density N donint on the dose for the surface radiation damage modeldescribed in [41]. Pre-irradiation values are shown as horizontal dotted lines. are only reached at | V back | > | V dpl | . From this point, both capacitance and leakage current values will beintended at V back = V pt .A central focus of the layout optimisation was the minimisation of the sensor capacitance. In fact, lowinput capacitance to the DC-coupled CMOS readout electronics allows for low-noise readout, low analogpower [5] and, in particular, SNR maximisation. Large input capacitance worsens the noise levels and thespeed of the front-end electronics [6].2.2.5. Surface radiation damageIn the simulation campaign performed to study the properties of MAMS, a silicon dioxide (SiO )layer was added on the top-side of the sensor. In addition to this, surface damage was modeled to evaluatethe effects of Total Ionising Dose (TID) on the sensor electrical properties.The impact of surface radiation damage was modeled following the AIDA-2020-D7.4 report [41]. Themodel introduces fixed positive oxide charges and band-gap acceptor/donor defect levels (trap states) atthe Si-SiO interface. The concentrations of oxide charges and defect levels start from a fixed value beforeirradiation (i.e. with the only inclusion of the SiO surface layer, at dose =
0) and increase with the doseprovided to the sensors. The dependence of the oxide charge density Q ox [charges · cm − ], of the acceptorintegrated interface trap state density N accint [cm − ] and of the donor integrated interface trap state density N donint [cm − ] on the dose is shown in Figure 7. Pre-irradiation values, shown as dotted horizontal lines inFigure 7, are Q ox = · charges · cm − , N accint = · cm − and N donint = · cm − .In the simulation campaign, the effects of the inclusion of the SiO layer and of the radiation damageon the leakage current, sensor capacitance, depletion voltage and punch-through voltage were investigatedand will be discussed in Section 3.2.2.6. Transient simulationsTCAD transient simulations were run to study the sensor charge collection process in response toparticles traversing the simulated microstrip domain. These simulations also let us identify the mostrelevant layout parameters to be optimised for improving the sensor performance in terms of fast anduniform charge collection irrespective of the particle incidence position. The transient simulations employ the Synopsys ® Sentaurus TCAD
HeavyIon model, described in [42]. The
HeavyIon model gives an analyticaldescription of the amount of charge generated within a 3D cylindrical distribution along the incidentparticle track. Two main parameters have to be passed to the
HeavyIon model: the linear Energy Transfer(LET), defined as the average deposited charge per unit length, and the transverse size of the chargedeposition volume generated around the particle trajectory. We chose the charge transverse distributionprofile to be gaussian around the particle track.
Figure 8.
Best-case and worst-case scenarios considered in the TCAD transient simulations. The microstripsare represented as adjacent grey blocks and the particle traversing the domain is shown as an orangecylinder. The nomenclature used to identify the microstrips (from 1 to 5) is illustrated.
Two extreme cases in terms of particle impact position were studied to evaluate the uniformity ofcharge collection time and charge collection efficiency. Particle trajectories perpendicular to the sensorsurface were considered. In the best-case scenario, the particle impact point corresponds to the centre ofa microstrip, which is the centre of a collection n-well. On the contrary, in the worst-case scenario, theparticle traverses the sensor at the edge between two adjacent microstrips, i.e. in the middle of a p-well. InFigure 8 the two cases and the corresponding numbering of the strips are illustrated. This conventionalstrip nomenclature will be used in the following when referring to transient simulations.In order to save computational time, a reduced TCAD simulation domain that employs the symmetrieswas used. This reduced domain corresponds to a quarter of the full domain, with the particle incidentin the corner of the domain instead of in the centre. An example for the best-case scenario is shown inFigure 9. The collected charge and current signals were then scaled to reproduce the full domain case,which includes nine or ten 100 µ m long microstrips in the best-case and worst-case scenario respectively(Figure 8). These numbers and size of strips guarantee that that the amount of deposited charge reachingthe borders of the simulation domain is negligible. The correctness of this strategy was verified andconfirmed by comparing the results of a simulation with a quarter domain and of a simulation with fulldomain. Figure 9.
Example reduced TCAD domain used in transient simulations (best-case scenario). Themicrostrips are labelled following the nomenclature illustrated in Figure 8. A crossing particle is representedas an orange cylinder hitting the corner of the simulated reduced domain.
An example of current signals I nwell ( t ) measured at the microstrip sensing nodes when a particlecrosses the microstrip domain is shown in Figure 10 (left). We defined as charge collection efficiency forthe i-th strip (CCE i ) the integral of the current signal I nwell , i ( t ) extracted from the i-th strip and normalisedat the total charge Q tot deposited in the sensor by the particle, according to the formula CCE i ( t ) = (cid:82) t I nwell , i ( t (cid:48) ) dt (cid:48) Q tot = (cid:82) t I nwell , i ( t (cid:48) ) dt (cid:48) LET · d Si (1)where d Si is the sensor thickness. The total charge collection efficiency CCE for the whole simulateddomain is defined as CCE ( t ) = N strips ∑ i = CCE i ( t ) (2)where N strips is the total number of strips in the simulated domain. The total CCE at the end of thecharge collection process (i.e. at t = t end =
30 ns, which was observed to be large enough for completecharge collection) has to be equal to 100% in the absence of recombination:
CCE ( t = t max ) = i as a function of time is shown in Figure 10, on the right, for strip number 1. The timesneeded for collecting the 95% and 99% of the total deposited charge were evaluated and referred to as t and t , respectively. These values were compared for different design options and used to select thelayouts of the fastest sensor flavours.The spatial mesh of the transient simulations was forced to be finer around the particle trajectory tomore accurately simulate the charge deposition and the drift of electrons and holes from their generationpoints along the particle track towards the electrodes. Additionally, the time step of the transientsimulations was fine tuned to guarantee the necessary accuracy while keeping the computational timerequirement economical. We observed that these adjustments prevented the simulations from givingunphysical results. Figure 10.
Simulated current signals (left) and corresponding charge collection efficiency CCE i (right) inthe best-case and worst-case scenarios for strip number 1 in an example 50 µ m thick microstrip domain. Aparticle track with an LET of 1.28 · − pC/ µ m was simulated. Since MAMS are an interesting candidate for tracking detectors in space applications, the chargecollection was studied not only for minimum ionising particles (MIPs) but also for heavy nuclei of interestfor in-orbit astroparticle experiments. The LET values of carbon and oxygen ions were studied in G
EANT µ m,or 1.28 · − pC per µ m in silicon for MIPs could be reproduced. The G EANT µ m thick silicon layer immersed in air and with a transverse size of 1 × . The particle gun waspositioned 15 cm in front of the centre of the silicon layer. The G4EmPenelopePhysics physics list was usedto model the electromagnetic processes and the necessary precision on the energy deposited within thesilicon was achieved with a maximum step size of 1 µ m [44]. The LETs for carbon (C + ) and oxygen(O + ) ions at their minimum ionisation were computed from their most probable energy loss (i.e. themost probable value of the straggling or Landau functions [45,46]). Figure 11 shows the LET as a functionof the particle energy obtained for C and O ions traversing 50 µ m of silicon. The energies E min at whichC and O ions are at the minimum of ionisation were found to be 35 GeV and 60 GeV, respectively. Thecorresponding LETs are 45.6 · − pC/ µ m and 83.0 · − pC/ µ m, which results in 36 and 65 times theMIP value. This is consistent with the expected scaling from the Bethe-Bloch formula.We were especially interested in studying the charge sharing among the microstrips surrounding theparticle impact point and the charge collection time at different LETs. This will be reported and discussedin Section 3. Figure 11.
Dependence of the LET on the energy of carbon ions (C + , blue) and oxygen ions (O + , orange)incident on 50 µ m thick silicon. The LET values were evaluated through Geant4 simulations. The redvertical lines indicate the minimum ionisation energies for the two particle species.
3. Results and discussions
In this section, the results of the TCAD simulation campaign will be presented. Their implicationswill be discussed and their connections to the design objectives will be highlighted. As mentioned inSection 1, the main targets of the FD-MAMS design were the following.1. To enhance the spatial resolution. A very fine pitch of 10 µ m was chosen to reach this goal. Intrinsicspatial resolution in case of digital readout would be equal to pitch √ = µ m √ (cid:39) µ m, which can befurther improved thanks to charge sharing and with an analog readout.2. To minimise the sensor capacitance C sens at V back = V pt . A low sensor capacitance is particularlyimportant to keep low electronic noise and, consequently, to maximise the SNR.3. To obtain fast and uniform charge collection, irrespective of the particle incidence position. This willenhance the sensor timing capabilities and will reduce the dead-time between successive particledetections.For reasons of space available for MAMS in the first ARCADIA engineering run, only a few sensorflavours could be included. Hence, a simulation campaign was needed to identify the best performingsensor layouts. The deep p-well, when present, was kept the same size as the p-well. The expression"p-well and deep p-well" will be contracted and referred to as "(deep) p-well". In the legends of the figures,the abbreviation "dpw" will be used for deep p-well. layer and surface damage A first group of TCAD simulation studies was aimed at investigating the effects of the SiO layer andof surface TID damage on the FD-MAMS characteristics. The model that we employed was presented inParagraph 2.2.5. As can be seen from Figure 12, for one of the selected 50 µ m thick microstrip layouts, theinclusion of the SiO layer with a minimum concentration of traps and oxide charges ( dose =
0) determinesa small increase of about 5% in the leakage current I leak from 20.8 fA to 22.0 fA. The sensor capacitance C sens is strongly affected by the inclusion of the SiO layer, as it increases by 31% from 0.26 fF/ µ m to 0.34 fF/ µ m.Both I leak and C sens are found to rise with increasing dose. The minimum dose that we considered is50 krad, as the model is not validated for lower doses [41]. Figure 13, instead, shows the effect of the SiO layer and of the TID on V dpl and on V pt . The effect of the dose on these two values is smaller than in the case of I leak and C sens . Furthermore, V dpl and V pt are influenced by the dose in opposite directions, whichresults in a slight increase in the operating range ∆ V op with increasing dose. Dose [Mrad] C u rr e n t [ p A ] ARCADIA TCAD simulation I leak dose = 0no SiO layer 0.20.30.40.50.60.7 C a p a c i t a n c e [ f F / m ] C sens dose = 0no SiO layer Figure 12.
Leakage current I leak (green) and sensor capacitance C sens (red) as a function of the total ionisingdose for a 50 µ m thick microstrip sensor. The values obtained in simulations with and without the SiO layerin the absence of irradiation are shown as horizontal lines and referred to as "dose = 0" and "no SiO layer"respectively. Dose [Mrad] V o l t a g e [ - V ] ARCADIA TCAD simulation V pt V pt (dose = 0)V pt (no SiO layer)V dpl V dpl (dose = 0)V dpl (no SiO layer) Figure 13.
Depletion voltage V dpl (blue) and punch-through voltage V pt (orange) as a function of the totalionising dose for a 50 µ m thick microstrip sensor. The values obtained in simulations with and without thesilicon dioxide layer in the absence of irradiation are shown as horizontal lines. layer wasfound to be due to the introduction of positive oxide charges at the Si-SiO interface [39]. In fact, the modelthat we adopted foresees a significant positive oxide charge concentration Q ox = 6.5 · charges/cm − already at dose = 0. These positive oxide charges attract free electrons from the n-type silicon epitaxiallayer towards the Si-SiO interface in the gap and determine an increase in the electron concentration around the heavily n-doped collection well, as illustrated in Figures 14 and 15. This electron accumulationbehaves as an extension of the collection n-well. Figure 14.
Schematic illustration of the electron accumulation in the gap between the collection n-well andthe surrounding p-wells due to the positive oxide charges introduced at the Si-SiO interface. Figure 15.
Electron density in an example microstrip simulation domain without (left) and with (right) theSiO layer on top of the sensors. The sizes of both the collection n-well and of the gap were found to contribute to C sens . Therefore,both n-well and (deep) p-well sizes were adjusted to find the optimal layout for C sens minimisation. Itwas observed the inclusion of the SiO layer influences C sens in different ways for different gap sizes.Hence, C sens with and without the SiO layer was evaluated. Figure 16 shows the trend of C sens as afunction of the gap size for 50 µ m thick microstrips. The different sensor thicknesses considered (50, 100and 300 µ m) were found not to influence the sensor capacitance. Both the case with fixed minimum-sizen-well and variable (deep) p-well (blue curves) and the case with fixed minimum-size (deep) p-well andvariable n-well (orange curve) were studied. The dash-dotted lines refer to simulations without the surfaceSiO layer, whereas solid lines to the case with SiO layer included with minimal oxide charge and trapconcentration.The reason for which smaller gaps with fixed n-wells could not be investigated is referred to as channel choking , a condition that inhibits sensor operation; this condition is explained in Section 3.3. Thevertical grey band in Figure 16 and in the following ones corresponds to the forbidden region due to theconstraints on n-well and (deep) p-well minimum sizes imposed by the fabrication process. The leftmostlimit of the grey band is still permitted.Variations of n-well and of (deep) p-well size do not lead to the same C sens for the same gap size. Afixed n-well size with SiO layer included shows a trend that is not monotonic, but has a minimum at slightly less than 0.34 fF/ µ m. This effect is caused by the electron accumulation in the gap at the Si-SiO interface. However, the difference in C sens between the minimum-capacitance option and the sensor layoutat the edge of the forbidden region is lower than 2%. There was, as expected, no benefit found from havinglarge n-wells. The sensor capacitance increases with the n-well size, as can be seen from the blue curve inFigure 16. Therefore, we chose the best layout for minimum C sens to have the smallest possible n-well sizeand sufficiently small (deep) p-well. Gap size [ m] C a p a c i t a n c e [ f F / m ] ARCADIA TCAD simulation fixed p-wellfixed n-wellno SiO with SiO Figure 16. C sens as a function of the gap size for different sensor layout configuration. The vertical greyband is the forbidden region due to fabrication constraints; its leftmost limit is still permitted. Figure 17 compares the sensor capacitance for layouts with deep p-well (orange curve) and withoutdeep p-well (green curve). All the sensor flavours feature the minimum n-well size permitted by thefabrication process. On the one hand, removing the deep p-well could help in further reducing the sensorcapacitance. On the other hand, this choice would strongly affect the sensor bias voltage operating range,as discussed in the following section.
Gap size [ m] C a p a c i t a n c e [ f F / m ] ARCADIA TCAD simulation fixed n-well, no dpwfixed n-well, with dpwno SiO with SiO Figure 17.
Sensor capacitance C sens as a function of the gap size for different sensor layout configurationswith and without the deep p-well. We found the influence of the n-well size on the operating voltages to be negligible compared to theeffect of the (deep) p-well size. Therefore, for the sake of capacitance minimisation, we fixed the n-wellsize at the smallest possible value. With this assumption, Figure 18 presents the effect of the (deep) p-wellsize effect on V dpl and on V pt for 50 µ m thick sensors. Both the cases with (orange curves) and withoutdeep p-well (green curves) were considered and compared. The voltage values are reported for the case ofdose = 0.In all the layouts considered in Figure 18, the onset of the punch through happens at voltagessufficiently larger than the depletion voltage. Outside of the forbidden region (grey band), the operatingrange ∆ V op is always between 4.2 V and 6.2 V, or between the 23% and the 41% of V dpl . This is a sufficientlylarge operating range for safe sensor operation, even in the hypothesis of possible doping inhomogeneitiesamong adjacent microstrips or slight deviations from the doping design values. Similar observations on ∆ V op have been made for 100 µ m thick and 300 µ m thick sensors. Gap size [ m] V o l t a g e [ - V ] channel choking ARCADIA TCAD simulation no dpwwith dpwV pt V dpl Figure 18.
Sensor depletion voltage V dpl and punch-through voltage V pt as a function of the gap sizefor different sensor layout configurations. The orange region indicates the forbidden region due to theobserved channel choking . As a general trend, it can be observed in Figure 18 that smaller (deep) p-wells result in larger V dpl and V pt . This can be interpreted as follows. Large p-doped surfaces below the (deep) p-wells create widerpn-junctions with the n-doped epitaxial layer, thus facilitating the depletion of the underlying epitaxiallayer at lower voltages. On the other hand, large (deep) p-wells also lower the potential barrier thatprevents the direct flow of holes towards the substrate. This results in the earlier onset of the punchthrough hole current between the (deep) p-wells and the backside p+ region. Sensors without the deepp-well showed higher reference voltages. In fact, the presence of a deep p-well reduces the epitaxial layerthickness below the p-wells, thus requiring a lower voltage to achieve both full depletion and the onset ofpunch-through currents.Finally, for sensors with too large deep p-well, a phenomenon that we defined as channel choking wasobserved. This consists in the closure of the conductive channel below the collection n-well due to thelateral merging of the closely adjacent depletion regions formed at the junctions between the deep p-wellsand the n-epitaxial layer. In this situation, in the simulations performed to extract V dpl , no current flowsamong the n-wells at low values of V back , even though the space charge region of the backside junction hasnot reached the surface yet. In this condition, the I nwell , unbalanced curve, that corresponds to the orange curve shown in Figure 4, appears flat and no V dpl can be extracted. This means that the n-wells are alreadyisolated from one another at V back = I nwell measured at the sensing node, is inhibited by the strong potential barrier present below then-wells. No channel choking was observed for sensor layouts without the deep p-well.For completeness, Figure 19 (left) illustrates the dependence of V pt and V dpl on the sensor thicknessfor the sensor layout with minimum sizes for the n-well and for the (deep) p-well. The trend is linearover a wide range of thicknesses, both with and without the deep p-well. Also the operating voltage ∆ V op = V pt − V dpl linearly increases with the sensor thickness, as shown in Figure 19 (right). The sensorthickness investigated was extended down to 20 µ m, well below the smallest thickness (i.e. 50 µ m) of thesensors that will be produced in the first ARCADIA engineering run. The reason for this will become clearin Paragraph 3.5.1, as the study of very thin sensors was functional for enhancing the speed of the chargecollection process and, consequently, for improving the sensor timing performance. Figure 19.
Dependence of V dpl and V pt (left) and of the operating voltage range ∆ V op (right) on the sensorthickness. The voltage V pd at which the power density is 0.1 mW/cm was found to be about 4-5 V above V pt for50 µ m thick microstrips, 7-8 V for 100 µ m thick microstrips and 18-20 V for 300 µ m thick microstrips whenthe deep p-well was included. nwell The V nwell voltage was varied with the aim of finding possible improvements in the sensorperformances. The results are shown in Figure 20 (left), where the vertical red line indicates the defaultvalue of 0.8 V. A minimum V nwell of about 0.5 V is necessary to satisfy the condition | V pt | > | V dpl | . Moreover,an increase in V nwell has several interesting effects. First of all, it allows the sensor full depletion to bereached at lower (in absolute value) backside voltages. Secondly, it also shifts the onset of the punchthrough towards larger | V back | , thus increasing the operating range ∆ V op . Finally, as shown in Figure 20(right), larger V nwell implies lower sensor capacitance. Figure 20. V dpl and V pt (left) and sensor capacitance (right) as a function of V nwell . The vertical red lineindicates the default value of V nwell = As described in Paragraph 2.2.6, TCAD transient simulations were used to study the charge collectiondynamics. In order to select the layouts with the optimal performance in terms of fast and uniform chargecollection, the effect of the (deep) p-well size on the charge collection time at V back = V pt was evaluated.The time t needed to collect 95% of the total charge deposited in the simulated sensor domain is plottedin Figure 21 for 50 µ m thick sensors and LET = 1.28 · − pC/ µ m (1 MIP) as a function of the gap size andwith fixed minimum n-well size. Gap size [ m] t [ n s ] ARCADIA TCAD simulation no dpwwith dpwbest-caseworst-case
Figure 21. t as a function of the gap size for best-case and worst-case scenarios. Microstrips with large gaps, hence small (deep) p-wells, are to be preferred for fast charge collection.The reason for this is a higher | V pt | , which enables sensor operation at a larger | V back | . The consequentstronger electric field in the sensor results in higher charge velocity in the silicon substrate. For the samereason, microstrip sensors without deep p-well revealed a significantly faster charge collection in both thebest-case and the worst-case scenario. Flavours with small (deep) p-wells also show very uniform chargecollection for different particle incidence positions. The difference in t for the best-case and worst-casescenarios is below 0.1 ns for the fastest permitted options. This result is also achieved thanks to the finemicrostrip pitch of 10 µ m. The channel choking, as described in Section 3.3, limits the deep p-well size asthe potential barrier below the sensing node slows down the electron collection. This problem, as shown in Figure 21, can be avoided by removing the deep p-well.Figure 22 demonstrates that the proposed MAMS guarantee fast sensor response also under heavilyionising particles. The charge collection time is only weakly proportional to the charge deposited by theincident particle within an LET range of [1.28; 128] · − pC/ µ m. A 50 µ m thick sensor was considered inFigure 22, and the LET values corresponding to 1 MIP, carbon (C) ion and oxygen (O) ion at their minimumof ionisation are highlighted as vertical green lines. Moreover, t is added to show that the time neededfor complete charge collection is only slightly larger than t , due to a small fraction of charge collectedby the strips adjacent to the central one. However, t and t were never found to exceed 2 ns and 3 nsrespectively in 50 µ m thick sensors. Linear Energy Transfer [10 pC/ m] T i m e [ n s ] t t best-caseworst-case Figure 22. t (blue) and t (red) as a function of the LET for best-case and worst-case scenarios. | V pt | . However, we alsoinvestigated other ways to increase | V pt | and to speed up the charge collection. In particular, as shown inSection 3.4, a larger V nwell is capable of shifting the onset of the punch-through current towards larger | V back | . Therefore, we explored the effects of V nwell on the charge collection time.In a strip readout system, timing information can be retrieved only from the strips collecting mostof the charge (i.e. strip(s) number 1, following the nomenclature of Figure 8), as they provide a signalwith sufficiently large SNR. Therefore, in order to study the sensor timing performance and after verifyingthrough t that the total deposited charge is quickly collected in the whole simulation domain, weconsidered the time t central needed to collect 95% of the charge in the central strip(s).Figure 23 shows the dependence of t central at V back = V pt and with LET = 1.28 · − pC/ µ m on thevoltage applied to the sensing node. A 50 µ m thick sensor with a layout optimised for fast charge collectionwas considered. A significant improvement could be reached at larger V nwell . For the option without deepp-well and at V nwell = t central is 0.84 ns in the best-case and 0.94 ns in the worst-case scenario. If weassume an electron drift saturation velocity of ∼ · cm/s in silicon at a temperature of 300 K [47], theminimum drift time for electrons that have to cover a 50 µ m distance is 0.5 ns. This explains the saturationobserved in Figure 23 and demonstrates the fast charge collection and the promising timing capabilities ofthe proposed MAMS. V nwell [V] t c e n t r a l [ n s ] ARCADIA TCAD simulation no dpwwith dpwbest-caseworst-case
Figure 23. t central as a function of the voltage V nwell applied to the sensing node for best-case and worst-casescenarios. The vertical red line indicates the default value of V nwell = A way to further reduce the collection time is to explore thinner sensors. Figure 24 demonstrates thatthe charge collection time t central is proportional to the sensor thickness. For these simulations, V nwell wasset to the 0.8 V and a 1 MIP LET was considered. Even at thicknesses as large as 300 µ m, t central does notexceed 6 ns. In the best-case scenario without the deep p-well, reducing the sensor thickness from 50 µ mto 40 µ m, 30 µ m and 20 µ m results in a decrease in t central of 15%, 33% and 50%, respectively. Analogousproportionality was observed for t . Therefore, for future production runs, thinner sensors could beconsidered for the enhancement of the timing performance. Sensor thickness [ m] t c e n t r a l [ n s ] ARCADIA TCAD simulation no dpwwith dpwbest-caseworst-case
Figure 24. t central as a function of the sensor thickness for best-case and worst-case scenarios. A set of TCAD simulations was dedicated to study the charge sharing among adjacent microstripswhen particles with different LETs traverse the sensor. Charge sharing is relevant for improving the spatialresolution, especially with analog readout, and is enhanced by fine microstrip pitches and large sensorthicknesses. On the contrary, it is reduced at higher V back for a fixed sensor thickness.In Figure 25, the case of a 300 µ m thick sensor at V back = V pt is presented for the best-case scenario.The total charge collected by each strip (identified using the nomenclature of Figure 8) is plotted versus the LET. The black horizontal line indicates a possible charge threshold corresponding to 10% of a MIP at thesingle strip level. A comparison with the sensors that will be produced in the first ARCADIA engineeringrun will allow deeper investigation on the charge sharing, a fine tuning of the simulations and studiesaimed at evaluating the spatial resolution of 10 µ m pitch MAMS. Linear Energy Transfer [10 pC/ m] T o t a l c o ll e c t e d c h a r g e [ p C ] ARCADIA TCAD simulation strip 1strip 2strip 3strip 4strip 510% MIP
Figure 25.
Charge sharing among adjacent microstrips. The total charge collected by strips 1 to 5 (followingthe nomenclature illustrated in Figure 8) is shown as a function of the LET.
4. Conclusions
In this work, we presented detailed TCAD simulations of CMOS-based FD-MAMS, which may finduse for tracking and timing in particle and nuclear physics, space and medical applications. The results ofthe TCAD simulation campaign, performed to design the 10 µ m pitch FD-MAMS, demonstrate their veryfast and uniform charge collection, which encourages their practicality for various applications, even underheavily ionizing particles. The effect of surface ionizing radiation damage was investigated, and the layoutparameters were optimized to achieve a minimum capacitance, beneficial for electronic noise reduction.The possibility to operate the sensor in full depletion and at low-power density (i.e. before the onset ofthe punch through current) was verified in the simulations. A preference for small collection diodes andsmall (deep) p-wells emerged for obtaining lower capacitance and faster sensor response. Additionally,these simulations confirmed the possibility of monolithically integrating readout architectures in theinter-strip regions for strips of 10 µ m pitch. The first FD-MAMS samples will be produced in the upcomingARCADIA engineering production run at the beginning of 2021 and will allow the simulation results to becompared with experimental data from electrical characterisation, laser and beam irradiation tests. Thepromising results of the first simulation campaign on FD-MAMS will translate into further R&D activitiesto enhance the sensor performance in terms of low capacitance and high timing and spatial resolution. Appendix A. Expected effects from epitaxial layer thicknesses
Possible variations in the epitaxial layer thickness of [-15%; +30%] communicated by the foundry withrespect to the reference value induced us to investigate their effect on the operating parameters. While thesensor capacitance was observed not to be influenced, both V dpl and V pt showed a linear dependence onthe epitaxial layer thickness. This behaviour is presented in Figure A1. -15% reference +15% +30% Epitaxial layer thickness V o l t a g e [ - V ] ARCADIA TCAD simulation V pt V dpl Figure A1. V dpl and V pt as a function of the epitaxial layer thickness, expressed as percentage variationwith respect to the reference thickness. Acknowledgments:
The research activity presented in this article has been carried out in the framework of theARCADIA experiment funded by the Istituto Nazionale di Fisica Nucleare (INFN), CSN5. The activity has also beensupported by the project "Dipartimento di Eccellenza", Physics Department of the University of Torino (Dipartimentodi Fisica - Università degli Studi di Torino), Italy, funded by MUR.
Author Contributions:
Data curation, Lorenzo de Cilladi; Formal analysis, Lorenzo de Cilladi; Investigation, Lorenzode Cilladi; Supervision, Coralie Neubüser and Lucio Pancheri; Writing – original draft, Lorenzo de Cilladi; Writing –review & editing, Thomas Corradino, Gian-Franco Dalla Betta, Coralie Neubüser and Lucio Pancheri.
Conflicts of Interest:
The authors declare no conflict of interest.
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