Study of spatial resolution and efficiency of silicon strip detectors with different readout schemes

Nuclear Instruments

and Methods in Physics Research A 356 (1995) 241-254

gi @J ELSEVIER

NUCLEAR INSTRUMENTS 8 METHODS IN PHYSICS RESEARCH SectIonA

Study of spatial resolution and efficiency of silicon strip detectors with different readout schemes W. Dqbrowski

*,

P. Grybog, M. Idzik

Faculty of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, Cracow, Poland Received 19 September

1994

Abstract The spatial resolution and efficiency of silicon strip detectors with different readout schemes considered for the ATLAS silicon tracker have been studied. A series of simulation tools has been developed for accurate modelling of the detectors and front-end electronics. All important effects like the influence of magnetic field on the charge collection in the detectors, ballistic deficit in the electronics, distributed structure of silicon strips, electronic crosstalk via the interstrip capacitance, noise injection from adjacent channels, effect of the charge collection time on timing performance of silicon strips and radiation damages to detectors and electronics have been taken into account. Two types of front-end electronics, bipolar and CMOS, and three readout schemes, analogue readout of every strip, analogue readout using capacitive charge division and binary readout, have been analysed. The spatial resolution and the efficiency have been studied for particle impact angles between - 10” and + lo”, for p-side and n-side strips separately. In the Monte Carlo analysis the Landau distribution and the electronic noise were taken into account. The effects of the electronic noise on the amplitude as well as on the time measurement were implemented in the analysis.

1. Introduction The work presented in this paper was driven by the feasibility study of different layouts of silicon strip detectors and different readout schemes for front-end electronics for the barrel section of the silicon tracker planned for the ATLAS experiment. A full evaluation of all aspects of the front-end electronics for such a detector is a very complex task and should include the following aspects: physics requirements for the spatial resolution and efficiency, radiation effects in the silicon strip detectors and frontend electronics, limitations for the power consumption, reliability and testability, cost and material budget. The impacts of the LHC environment on the silicon detectors and front-end electronics is quite well understood and a significant progress has been made in development of both detectors and electronics [1,2]. Although silicon strip detectors are used in many experiments, the conditions for a LHC experiment are quite new and some aspects should be studied more in detail.

* Corresponding

author.

0168-9002/9.5/$09.50 0 1995 Elsevier Science B.V. AI1 rights reserved SSDI 0168-9002(94)01398-5

The silicon tracker should provide a certain spatial resolution and efficiency and for any design these two parameters have to be evaluated as precisely as possible. In the first approximation these two parameters can be obtained from very few numbers like noise characteristics of the electronics, pitch and capacitances of strips, detector leakage current, and discrimination level. In the case of the ATLAS tracker, however, we have a series of effects which are not easy to evaluate using analytical formulas. The most important are the following: the required speed for the electronics approaches the intrinsic limit of the silicon detectors, i.e. the charge collection time, due to the required speed and power limitation, the available signal-to-noise ratio is relatively low, while a large total number of strips imposes an effective discrimination of noise hits, a magnetic field of 2 T causes a spread of the collected charge between adjacent strips and modifies the pulse shapes, silicon strip should give the correct timing within the bunch crossing period of 25 ns, and the effects of noise and pulse shape variation on timing are significant. We developed a flexible program for the study of spatial resolution and efficiency of systems with different detectors and electronics designs, which includes: - simulation of the pulse shapes from detectors,

242

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et al. / Nucl. I&r.

and Meth. in Plow. Rex A 356 (1995) 241-254

_ modelling of lumped equivalent circuits of strip detectors in SPICE, _ modelling of equivalent circuits for multichannel frontend electronics, - modelling of noise in the time domain. The results are finally combined with the Monte Carlo simulation of Landau fluctuations which allows us to obtain the statistical evaluation of spatial resolution and efficiency. Thus, although our study has been done having in mind basically the ATLAS tracker, the developed set of tools can be used for the evaluation of any system using silicon strip detectors. These tools guarantee correct simulations of a series of effects in the detectors and electronics which usually are considered to be important for a silicon strip system, in particular: - ballistic deficit, _ effects of pulse shape and noise on timing, _ radiation damage to detectors and electronics, - charge loss for the charge division readout scheme, _ effects of a distributed structure of strips, _ electronic crosstalk via the interstrip capacitance, _ noise injection from adjacent channels.

2. Considered schemes A series of designs of the strip detector layout and front-end electronics have been proposed for the ATLAS experiment and for other similar ones like CMS or SDC. Our goal was not to make a full analysis of any particular design but rather to consider some classes of designs. Since the number of possible schemes of detector granularity can be very big we used the total number of electronic channels as the reference point for comparison of different

schemes. This is an important parameter for any design reflecting directly on the cost and power budget. We have studied two options of the strip pitch; 50 Frn which is required to achieve a spatial resolution of the order of 10 pm, and 100 km which is rather adequate for a spatial resolution of about 20 pm. In both cases the basic detector unit is assumed to be 6 cm long. For the given strip pitch and the given total active area of the detector the same number of electronic channels can be achieved by making the strips 12 cm long with readout of every strip or by applying the capacitive charge division readout for 6 cm strips and reading out every second strip. As far as the possible schemes for front-end electronics are concerned we distinguish two general types of readout, binary and analogue. In the case of binary readout we cannot profit from the capacitive charge division and therefore only the strips of 12 cm are considered. Having an analogue readout we can apply either the readout of every strip of 12 cm or the readout of every second strip of 6 cm. To keep a certain common platform for comparison of different schemes we have assumed the same strip geometry for the direct readout and for the capacitive charge division readout; however, it might be that the chosen geometry is not the optimal one for the charge division scheme. The geometry optimisation for the charge division readout is the trade-off between the interstrip capacitance and the backplane capacitance. To avoid significant charge losses to the backplane, the interstrip capacitance should be large compared with this to backplane. This can be achieved by reducing the gap between the strips; however, this results in a big capacitive load at the preamplifier input and a high level of noise. This becomes particularly important if we take into account the fact that at the given power constraints and the required speed the

Table 1 Combinations of strip configurations and front-end electronics used for analysis CMOS front-end using deconvolution

Fast bipolar front-end

“Slow”

6

cm, 50 pm pitch strips 100 p.m pitch analogue readout (charge division)

6 cm, 50 pm pitch strips 100 pm pitch analogue readout (charge division)

12 cm, 50 p,m pitch strips 50 km pitch analogue readout

12 cm, 50 pm pitch strips 50 km pitch analogue readout

12 cm, 50 pm pitch strips 50 km pitch binary readout 6 cm. 100 pm pitch strips 200 pm pitch analogue readout (charge division)

6 cm. 100 pm pitch strips 200 p,rn pitch analogue readout (charge division)

12 cm, 100 pm pitch strips 100 pm pitch analogue readout

12 cm, 100 km pitch strips 100 p,rn pitch analogue readout

12 cm, 100 p,m pitch strips 100 pm pitch binary readout

243

W. Dqbrowski et al. / Nucl. Instr. and Meth. in Phys. Res. A 356 (1995) 241-254 increase of the equivalent input noise per unit of input capacitance will be relatively high, in the range 60-80 eI/pF. This high value drives the optimal strip geometry towards the minimum interstrip capacitance. It has been shown before [3] that even for low noise electronics with a slope of 12 el/pF there is a limited range for the increase of the interstrip capacitance where we can profit from the reducing of charge losses. Independently of the type of readout, binary or analogue, we performed an analysis for two different types of semiconductor technology used for the front-end electronics, bipolar and CMOS. The most important aspect of the technology choice is the type of input device which determines the noise performance of the system with respect to speed and power. There are a lot of other aspects connected with the choice of technology like mentioned radiation hardness, reliability, testability and cost. At this level, however, we refer only to basic noise phenomena in bipolar and CMOS transistors. All considered combinations of detector layouts and front-end electronics schemes are listed in Table 1. The details of the electronic equivalent circuits used for simulations will be discussed later.

3. Simulations

of detectors

As it was mentioned before, the required shaping time constants for the front-end electronics are in the same range as the typical charge collection times in the microstrip detectors and therefore the ballistic deficit becomes very important. In addition to this, for electrical signal analysis, microstrip detectors should be considered as lumped electrical circuits. The structure and parameters of such circuits are well identified and understood [3,4]. To evaluate these effects properly we need correct calculations of current pulses induced in strips. Obviously, the shapes of induced current pulses depend on the electric field distribution in the detector which is determined by the actual bias and the silicon bulk doping. The doping concentration can be expressed by the full depletion voltage. For our simulation we have chosen 300 p,m thick detectors with an initial full depletion voltage of 34 V, while the detectors are biased at 120 V to reduce the charge collection times. The full depletion voltage Vdep,= 34 V for a 300 )*rn thick detector corresponds to a donor concentration Nd = 5 X 10” cmm3 for n-type bulk silicon according to formula

where w is the detector thickness. We have analysed separately two types of single sided detectors made on n-type bulk material; p+ strips on the junction side, and n+ strip on the ohmic side. It is now well known that silicon strip detectors will be seriously

radiation damaged in the LHC environment resulting in type inversion of the initial n-type bulk material and after that a continuous decrease of the p-type resistivity and increase of the detector depletion voltage [S]. In fact after some time of experiment running the depletion voltage of the inverted detectors will reach the assumed bias voltage of 120 V. There are different scenarios, depending on the position of the silicon strips in the overall detector and the temperature history, which predict even much higher depletion voltages at the end of the experiment [5-71. There are two reasons for which we have assumed a relatively moderate bias voltage. First, this seems to be sufficiently low that one can expect to have no problems with the edge discharging and breakdowns reported for silicon strip detectors [8]. This might be not a problem in the future since the development of microstrip detectors working up to 500 V has been reported [9]. On the other side 120 V, even if the detector is just depleted, seems to be high enough to have no significant ballistic deficit. In the case of bigger radiation damage a higher depletion voltage will be required but this can only be better from the point of view of charge collection. In any case here we do not consider detectors which are not fully depleted. 3.1. Calculations of induced current The current signal induced in the strips by a point charge q moving in the depletion region is given according to Ramo’s theorem as [lo] i(t)

= qE, . u(t),

(2)

where E, is the weighting electric field calculated for V, = 1 V at the readout strip and V, = 0 V at all other strips and at the backplane, v(r) is the charge drift velocity. The geometry used for the calculations in the case of p+ strips of 50 pm pitch is shown in Fig. 1. The calculations of the current induced on the strips is performed in

+12ov

I I

IOOpm

I

I

Fig. 1. Schematic diagram of a single-sided strip detector and drift patterns of electrons and holes in a magnetic field.

W. Dqhrowski et al. /Nucl.

244

Instr. and Meth. in Phys. Rex A 356 (1995) 241-254 ent parameterizations of drift velocity vs temperature and doping concentrations. Applying different models and comparing the results of simulations for a simple diode with the experimental results on the charge collection time [12] the best agreement has been found for the drift velocity parameterization for high purity silicon given by Ref. [13] as

two steps. First we solve numerically Poisson’s 2D equation for the space charge region and calculate the electric field distribution E(x, yf and the weighting field E,(x. y) at the following boundary conditions: dV,/dy = 0 in the interstrip region and dV,/dx = 0 at the detector sides. The calculations have been done in a similar way like it was done before by Leslie et al. [ll] but with some more details. For 50 km strip pitch the width of p+ doping was assumed to be 10 pm while for 100 pm pitch we used a strip width of 20 pm. The doping profiles of strips are assumed to follow an error function

IFI/& “=ihl[l+(,FI,E,)n]“P’ where the effective field is given by the formula F=E+/+EXB.

erfc(k)

= 1 -erf(

k)

= +[/r,exp(--1’)

(5) For the Hall mobilities we assumed pH = 1650 crn’V_’ for electrons and p-LH= 310 cm2 V-’ SC’ for holes S -’ according to Ref. [14]. The parameters L‘,, E, and p in Eq. (4) are temperature dependent and are given by the following parameterization: - for electrons: q,, = 1.53 x 10yT-0~87 cm s-‘, E, = 1.01T’-55 Vcm-‘, p = 0.257Z’0.66, cm s-l, E, = - for holes: L‘, = 1.62 X 108T-0.5’ 1.24T’.hs Vcm-‘, /3 = 0.46T”-“. For further calculation we assume that the charge deposited by a minimum ionising particle crossing the detector is distributed uniformly along the particle track. All deposited charge is divided for buckets, each one corresponding to 0.2 pm distance of the particle track. For each bucket we assume a uniform distribution of charge along the track and a Gaussian distribution with u = 2 pm in the perpendicular direction. The Gaussian distribution in the

(3)

dt,

with the r. parameter equal to 2 pm while the concentration of donors (acceptors after type inversion) is assumed to be uniform in the n(p)-type bulk. The electric field was calculated for the following boundary conditions: V = 0 at the p+ strips and 120 V at the backplane, dV/dy = 0 on the surface in the interstrip regions and periodic boundary conditions in the x direction with a period equal to the pitch. Poisson’s equation was solved on a two-dimensional discrete uniform mesh of sizes dx = 1 km and d y = lpm. The drift velocity is determined by both the electric and the magnetic field. At a detector bias of 120 V the electric field in the depletion region reaches the range where the dependence of the drift velocity on the electric field becomes non-linear. In the literature one can find few different parameterizations of this dependence as well as differ-

before irradiation x = 24pm

strip0

1.---

x = 24um

strip1

x =24pm

stflpl

after irradiation

strip0

x = 24pm

loa Boil

z g

$

600 400 200

0 -200

--- 5

~_~~_

10

1

time hl

20

25

1000~ 800

z ;

2

*

600 . 400 : 200

!

Oi

,,l-,

r-.-__/”

-200 *

5

‘\.__ 10

IS

flrrm

20

26

ins1

Fig. 2. Examples of current signals induced on p-side strips for Vbiaa= 120 V and B = 2 T. Particle incident in the centre between strips at 0”.

W. Dqbrowski

et al. / Nucl. Instr. and Meth. in Phys. Res. A 356 (1995) 241-254

245

area of 50 pm X 6 cm in the case of 50 km pitch, and to 0.5 LA for a strip area of 100 km X 6 cm in the case of 100 km pitch. For the 100 pm pitch detectors a lower leakage current density has been assumed after irradiation since these detectors are assumed to be used at larger radii and less damaged. The detector bias is assumed to be kept all the time at 120 V. The inversion of the bulk material means also the movement of the high field region from p-side strips before irradiation to n-side strips after irradiation. Some examples of pulses generated in p-side and n-side strips for the 50 p,rn strip pitch detectors for the particles crossing the detector perpendicularly are shown in Figs. 2 and 3 respectively. In these figures we clearly see some important effects: - due to the magnetic field the current pulses at some strips are delayed which corresponds to the movement of the collected charge along the Lorentz force, - for the n-side strips where the current signal is dominated by electrons the significant signals are observed always on three strips, while for the p-side strips the spread is smaller and reduced in most cases to two strips only, - for p-side strips we observe a significant increase of the hole collection times after irradiation due to different distribution of the electric field, _ the electron collection times on n-side strips is negligibly increased after irradiation, mostly due to the fact that the junction (the high field region) is moved to n-side strips.

direction perpendicular to the track gives the average range of charge diffusion while the charge is collected by electrodes. The detailed evolution of diffusion during the collection time is ignored because in any case the charge spread due to diffusion is much less than the strip pitch and the span of carriers due to the magnetic field. For each bucket of electrons and holes moving in the depletion region we calculate the current induced in four adjacent strips according to Eqs. (21, and (4 and 5). The nominal sets of current pulses is calculated for the most probable value of deposited charge equal to 22500 electron/hole pairs. The Landau fluctuations of the deposited charge is applied only later on to the amount of total deposited charge. Since the final electrical signals are proportional to the integral of the current induced in the strips, the effect of fine structure of the current pulses due to spatial fluctuations of the number of electron/hole pairs is negligible and is ignored. The radiation damages to detectors are represented in our simulation by three most important effects: (1) the type inversion and the increase of depletion voltage, (2) the increase of leakage current, and (3) the increase of interstrip capacitance, As was mentioned before the first two effects are strongly dependent on temperature and there are different predictions for the 10 years LHC scenarios [.5-71. For our simulation we have chosen the following values corresponding to the “after irradiation” situation: (1) the n-type bulk material is inverted to the p-type and the resistivity is decreased so the depletion voltage becomes 120 V, (2) the leakage current is equal 0.5 PA for a strip

before irradiation x =24um

x = 24um

strip0

200

200

PI o

strip1

x =24um

strip2

h ,$L

I 6

g 5 0

/

10

16

-400

C

-600

E

-800

a

-1000 _$ -1200 -200 I_

-400 -600 ‘. _BM)._ ~Iwo -1200 -

tims Insi

tims L”S,

after irradiation x = 24pm

strip0

x=24um

strip1

~~ ~..,_~

x = 24pm

0

z

-200

strip2

-400 g

5 -

-600 -600 -1000 -1200 time ,“*I

Fig. 3. Examples of current signals induced on n-side strips for V,,,, = 120 V and B = 2 T. Particle incident in the centre between strips at 0”.

3.2. Detector eqnicalent circuit Our goal was to perform full electrical simulations of strip detectors and front-end electronics. The current pulses induced in strips as described above can be represented by current sources in the equivalent circuit. In addition to this the strip detector is a semiconductor structure consisting of junction p-n diodes and metal-oxide-semiconductor structures which for electrical analysis can be modelled by small signal equivalent circuits. The equivalent circuit of an AC coupled strip detector is shown in Fig. 4. This structure has been proved to be corresponding very well to real detectors [3]. The interstrip regions are modelled basically by the interstrip capacitances to first neighbours (CIl _d + CIl _m) and to second neighbours C12, as shown in Fig. 4a. The total interstrip capacitance to first neighbours is split for the capacitance between the implant strips CD _d ($ of the total) and the capacitance between metal strips CIl _m ($ of the total). Each strip is represented by a lumped RC circuit shown in Fig. 4b which allows us to take into account the effects of sheet resistances of metal strips RM and implant strips RD. The junction capacitance between the strip and the backplane ohmic contact is represented by CB capacitors, while the coupling capacitance between the implant strips and the metal readout strips is represented by CC capacitors. The R and C components form a distributed RC line which introduces some delay in the signal propagation along the strips. The basic cell corresponding to a strip length of 0.25 cm has been chosen for our simulation to keep the total number of nodes of the circuits and the computing time in a reasonable range. Let us note that the equivalent circuit of this kind allows us to simulate properly the noise contributions

Fig. 4. Full equivalent circuit of a microstrip detector used for the SPICE simulations. (a) Cross section perpendicular to strips. (b) Cross section along strips.

Table 2 Parameters

of different strip detectors

CB (pF/cm) CIl d (pF/cm) CIl~ m (pF/cm) C12 (pF/cm) RD (kbl/cm) RM (R/cm) RB (kR)

used in simulations

p-side 50/10

n-side 50/ 10

p-side 100/20

n-side 100/20

0.16 0.34 0.10 15 63 22 200

0.16 0.53 0.17 15 63 22 200

0.33 0.24 0.07 19 28 22 200

0.33 0.45 0.14 38 25 8 200

from the bias resistors RB and resistive components of strips RD and RM. For the given strip pitch there is a whole variety of different possible designs with different implant strip widths, doping concentrations, and metal strip sheet resistances resulting in different parameters of the equivalent circuits. For our simulations we have chosen some typical parameters avoiding some extreme solutions like e.g. very narrow strips resulting in small interstrip capacitances but having problems with the breakdown voltage, or very wide strips preferable for high voltage operation but resulting in very large interstrip capacitances. The parameters for 50 pm and 100 p,rn pitch with 10 pm and 20 p.rn strip width, respectively, used in the simulations are listed in Table 2. They are mostly based on the measurements of prototype detectors developed by the RD20 collaboration [IS].

4. Models for front-end electronics In the introduction we have listed a number of effects which can be evaluated properly only by full simulations of the detector equivalent circuits described above together with the front-end electronics. We used the SPICE package which is fully adequate to this purpose. The equivalent circuits of front-end electronics used in simulations are very simple but have incorporated all important parameters like noise parameters, shaping function, input impedance. open loop gain and rise time of the amplifier. This simplicity allows us to change some parameters in easy way, without tuning all the circuitry, and to study the influence of certain parameters on the overall system. Another important advantage of using simple models for electronics is that we can really simulate a multistrip equivalent detector circuit with multichannel electronics. The noise performance of the front-end electronics is basically determined by the noise parameters of the preamplifier input device and the shaping function of the overall circuitry. We consider two basic schemes for the front-end electronics: (1) a bipolar transimpedance preamplifier followed by an integrator, (2) a relatively slow CMOS charge sensitive preamplifier followed by a CR-RC shaper and an analogue signal processor. The reasons for which we have

W. Dqbrowski

inputtransistor:Id

et al. / Nucl. Instr. and Meth. in Phys. Res. A 356 (1995) 241-254

CF=I

pF

RF=~

pA, which is fully adequate for a low power design, the term OS/g, gives 125 R. The base spread resistance scales with the emitter area; however, a large emitter area results in a low current density and high sensitivity of the current gain p to radiation damages as has been shown in Ref. [ 181. For each particular design and expected levels of radiation the size of the input transistors should be optimised. A reasonable choice, as discussed in Ref. [17], allows us to keep this value as low as 35 R resulting in a total series noise resistance of 160 R. The current noise which is the shot noise of the base current is represented by the parallel noise resistance R, given as

= 400 M

Cl,=4pF+ g,=4mAlV

1 pF

MR

R, = 4kT/W,),

Fig. 5. Equivalent circuit of the bipolar front-end.

chosen these two structure were that these two schemes are considered to be used for the ATLAS silicon tracker and the examples of real circuits exists [16,17] so we can easily refer our models to the real circuits. 4.1. Bipolar

front-end

The equivalent circuit of front-end based on a bipolar input device is shown in Fig. 5. The time constant C,R, of the feedback loop in the preamplifier matches the time constant C,R, of the integrator so the overall transfer function of the circuit is the same as for a charge sensitive preamplifier followed by a CR-RC filter. The peaking time of the circuit is chosen to be 16 ns, so for the real pulses from the detector the peaking times are about 25 ns. As we have seen before (Figs. 2 and 31, some pulses induced on strips in the presence of a magnetic field are significantly delayed what results in a significant variation of the peaking time, in the range from 20 ns to 30 ns. Another important parameter of the preamplifier is the open loop gain since in this scheme the input impedance is equal to the impedance of the feedback loop divided by the open loop gain. In a multistrip system a non-zero input impedance results in the cross coupling of signals and noise between adjacent channels via the detector interstrip capacitance. Taking into account typical parameters of an available full custom bipolar process and the typical limitation for power consumption [15] we have assumed a low frequency open loop gain of 1000 and a gain-bandwidth product of 1.5 GHz. It has been shown in Ref. [15] that these parameters can be easily achieved. The voltage and the current noise sources of the input bipolar transistor are represented by the equivalent series and parallel noise resistances, R, and R, respectively. The series noise resistance for a bipolar transistors is given as R, = rhh’ + OS/g,,

247

where I, is the base current. Assuming a current gain p of 100 and a collector current of 100 pA we obtain R, = 50 kfi at room temperature. It should be stressed at the point again that the parameters assumed above correspond very well to the parameters of an existing circuit realised in a particular bipolar process; however, the same parameters can be achieved using other bipolar processes of the same class. The input capacitances of bipolar transistors which are available in these processes are usually very small, of the order of 100 fF, so we have assumed 1 pF for the input capacitance in total, including strays and bond pads. The main radiation effect in bipolar transistors is the degradation of the current gain p. This effect has been studied before and is well understood [16]. For the radiation levels foreseen for the ATLAS silicon tracker one can expect a typical decrease of /3 by 50% resulting in an increase of the base current providing the collector current will be kept at the same value. Thus, the parallel noise resistance is supposed to be decreased to the value of 25 kR after irradiation while the series noise resistance remains unchanged. The equivalent noise charge (ENC) for the described above circuit vs the external input capacitance is shown in Fig. 6. The values of ENC have been obtained in SPICE simulations for a single channel circuit and a &like input

400

200 0 0 1

2

(6)

where rbb, is the base spread resistance and g, is the transconductance. For the assumed collector current of 100

(7)

3

4

5

6

7

l

before irradiation

l

after irradiation

8

input capacitance

Fig. 6. Equivalent front-end.

noise charge

9

10

11

12

13

~ 1 14

15

[pF]

vs input capacitance

for bipolar

W. DqbrowsX-1 et al. / Nucl. Instr. and Meih. in Phvs. Rrs. A 356 (19951 Xl -2%

348

current pulse so they correspond to the way dependence is usually measured. Let us note degradation of p after irradiation results in a small increase of ENC which becomes negligible input capacitances.

how this that the relatively for large

1800 1600 1 ‘loo

2 =

,200

Y ‘ODO IJJ 800

3.2. CMOS front-end

600

There are two concepts of front-end electronics based on a MOS input device; a fast current sensitive amplifier [2] and a relatively slow amplifier followed by an analogue pulse shape processor [l]. A fast CMOS amplifier has a relatively high series voltage noise due to the inherently lower transconductance of MOS transistors compared with the bipolar ones at the same current. Therefore this solution seems to be of less interest. An interesting idea has been developed within the RD20 collaboration to use a relatively slow amplifier which allows one to design a charge sensitive amplifier with a large input transistor. The amplifier is followed by an analogue signal processor which reshapes the slow pulse to the fast one and provides good time resolution. This idea has, however, a week point since the performance of the analogue signal processor is very sensitive to the variations of pulse shapes. Having a complete simulation model for strip detectors we are able to study these effects in detail, in particular the most important one related to the time structure of current signals. The schematic diagram of the preamplifier and the shaper is shown in Fig. 7. It consists of a charge sensitive preamplifier followed by differentiating circuits and an integrator. Both blocks, the preamplifier and the CR-RC shaper, are based on the transconductance amplifiers. A shaping time constant of 75 ns is chosen, so a 3-weight deconvolution processor provides a good 25 ns time stamping [15]. The parameters of the input stage are determined by the input transistors. To obtain a reasonable transconductance we have assumed a drain current of 400 FA and a W/L ratio of 1000. For typical parameters of a 1.2 km CMOS process these result in a transconductance

400

Fig. 8. Equivalent noise charge vs input capacitance

for CMOS

front-end.

of 4 mA/V and an input capacitance of 4 pF. additional 1 pF of input capacitance is added for the bond pads and strays. For these parameters we obtain an equivalent series noise resistance R, of 2.50 0. assuming that R, = l/g,, which is somewhat ideal but for some processes quite well fulfilled. The parallel current noise in this configuration is negligible as long as the shaping time constant is relatively short, in the range of few tens of ns. The radiation effects concerning the noise parameters in MOS transistors available in different radhard processes are less coherent than in the case of bipolar transistors. Usually a small degradation of the transconductance and a small increase of the noise ideality factor is observed. Taking into account both of these effects we have assumed that after irradiation the series noise resistance will increase by 20%. i.e 11~to 300 R at the same drain current. The function of the analogue pulse shape processor (APSP) which follows the amplifier in this solution has been implemented analytically in our simulation. The signals and noise obtained at the output of the circuit shown in Fig. 7 were deconvoluted according to the weighting function of APSP. The deconvolution procedure, which basically is equivalent to a sort of reshaping for shorter time, also changes the noise. It suppresses the parallel noise and increases the series noise. Fig. 8 shows the noise vs the external input capacitance for the amplifier itself (75 ns shaping) and the deconvoluted values.

5. Extraction of signals and adding of noise

input transistor: Id = 400 FA C&=4pF+lpF g,=4mAJV CF=~ pF

RF=]

MR

Fig. 7. Equivalent circuit of the CMOS front-end.

As mentioned before we consider basically three different types of readout electronics: binary readout, analogue readout of fast signals and analogue readout of slow deconvoluted signals. Each scheme uses in a different way the information carried by electronic signals and is affected differently by noise. Therefore for different readout schemes we apply different ways how the useful informa-

W. Dqbrowski

et al. / Nucl. Instr. and Meth. in Phys. Res. A 356 (1995) 241-254

tion has been extracted and how the effects of noise are included. From the SPICE simulation we obtain the noiseless waveforms of signals at amplifier outputs and the spectrum of noise. Integrating the spectrum of output noise over the amplifier bandwidth we obtain the rms value of noise which is equal to o of a Gaussian distribution. To deal properly with the noise in the time domain we have to generate random noise waveforms and for that we have to take into account the fact that the noise at the amplifier output is partially autocorrelated due to the filtering function of the amplifier. Since many noise sources for which the effective filtering functions are different contribute to the total output noise there it is almost impossible to evaluate the effective autocorrelation function analytically. This information is, however, included in the spectrum of noise so we use a numerical procedure to generate the noise waveforms in the time domain. According to the Wiener-Khintchin theorem we find the autocorrelation function R,, (7) of noise at the preamplifier output as the Fourier transform of the noise spectrum S,, (f) obtained from SPICE: R,,(T)

= jo’S,,(g)

cos 2nTTf7df.

For the given od obtained from the integral of noise spectrum we generate a series of random noise samples spaced by 7 according to the two-dimensional Gaussian distribution p{r>(t),

rj(t+

7))

r”(t)

+ L”(t + T) - 2&T)L’(t)L’(t 24

+

T)

1 -p:(7)]

(9) where P,(T)

= R,,(r)/‘L(O)

(IO)

is the normalised autocorrelation function of the amplifier output noise. In the case of fast shaping and using pulse height information we assume that the output signal is sampled every 2.5 ns which in the case of an ideal shape of the current signal from the detector and no timing jitter would result in the sampling of the peak value. In reality the peaking time varies significantly (up to 10 ns), due to the effect of the magnetic field and different impact positions on the collection time in the detectors, and we sample not necessarily the peak value. To the sampled value of signal I! we add a random value of noise n(t) sampled from the Gaussian distribution with og. Since in this case the information used is based only on one sample we do not have to worry about the noise autocorrelation.

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The noise autocorrelation becomes important in the case of slow shaping and use of APSP. In this case the extracted information is based on three consecutive samples of a noisy waveform and the noise values for these three samples are correlated. Therefore in our simulations we generated first the noise waveforms n(t) according to the procedure described above and performed the sampling for the noisy signals c,(t) = cl(t) + n(t). These signals are deconvoluted according to the APSP algorithm. Independently we perform the deconvolution of the noise itself to obtain the rms value of the deconvoluted noise. In the case of binary readout the amplifier is followed by a discriminator providing two bit information only. A valid hit is associated with the given signal if the level of signal exceeds the discriminator threshold within the 25 ns time window. The same procedure is applied to the sparse data scan in the analogue readout before analogue information is used. A certain fraction of signals has amplitudes just above the discriminator threshold and these low pulses give most delayed responses of the discriminator since a simple level discriminator without any time walk compensation was assumed. To model this aspect correctly, again the noisy output waveforms I,, were generated and the discrimination was performed on these waveforms.

6. Monte Carlo analysis The primary goal of our study was the evaluation of two basic parameters of the silicon tracking system, namely the spatial resolution and the efficiency which can be achieved for the considered setup of silicon strip detectors and readout electronics. These are statistical parameters and can be evaluated properly only by Monte Carlo analysis taking into account the fluctuation of the amount of charge generated by particles in silicon, fluctuation of current pulse shape depending on the position and angle of particle incident, and electronic noise effects. First we apply the Monte Carlo analysis for the spatial position and angle of particle incident. In principle we consider only the tracks perpendicular to the beam direction so in the case of an ideal barrel shape of the detector all tracks would be normal to the silicon surface. In practice, due to the modularity of silicon strip detectors, we have a certain range of angles around the normal depending on the size of the single silicon crystal and the given layer radius. There are also two reasons for which the silicon detectors might be slightly tilted; one is the mechanical structure of the tracker superlayers and the other one is compensation of the Lorentz angle. To study the effect of tilt of the silicon detectors we evaluated the spatial resolution and efficiency for different angles in the range - 10” to + 10” every 2” around the normal which later on allows us to draw conclusions concerning the optimum detector tilt. For the given angle we generate a

series of events corresponding to different impact positions (every 2 pm) in the interstrip region and calculate the current signals induced in four adjacent strips. These current signals are applied to the electronic readout circuits and the output electronic responses are calculated using SPICE. This stage of calculations is performed for the most probable value of charge generated in silicon, i.e. 22500 el (the most probable value of the Landau distribution for a silicon thickness of 300 wrn). The Landau fluctuations are applied later on for the output electronic signals assuming that all electronic circuits are linear and multiplying the output amplifier signals by the ratio of the actually sampled charge from the Landau distribution to the most probable value. For the parameterization of the Landau distribution we used the approximation proposed by Bichsel [19]. For each different setup and each impact angle 50000 particles were incident in the region between two adjacent readout strips. The output signals, including the noise as described in Section 5, were analysed in terms of efficiency and spatial resolution. For the efficiency we assumed that the discriminator threshold will be set at 4a of noise. This applies to the binary readout as well as to the sparse data scan in the case of analogue readout. It is now commonly agreed that in a system of low occupancy like the ATLAS silicon tracker the noise rate has to be kept low and the condition of 4a for the threshold is proposed by others as well [20]. For the spatial resolution we extract the rms value of the (incident position - reconstructed position) distribution. For the binary readout the reconstructed position is associated with the centre of hit strip in

al

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the cases when only one strip show a signal above the threshold, and with the central position between two adjacent strips in the cases when two strips show signals above the threshold. In practice we do not observe events with three fired strips. Using the pulse height information in the analogue readout the reconstructed position is associated with the centre of gravity where the signals taken for analysis are not limited only to these passing the 4a threshold. Here we assume that if one channel has a signal above the threshold. the sparse data scan logic allows one to read out the neighbour channels even if these are below threshold. Otherwise a significant fraction of events would give signals above the threshold only on one strip and the pulse height information cannot be used to improve the spatial resolution. A second level of discrimination is required to not take into the analysis signals which are comparable to or smaller than the noise. Therefore different cuts (2a, 3u, 4~) were tried for the obtained output signals to find the optimum one giving the best spatial resolution. In most cases the best spatial resolution is given by the cut at 3cr or 4~. Going down below 3a we introduce more false information due to the accepted noise than the useful one carried by small signals at neighbouring strips. This second level of discrimination is supposed to be implemented in the software at the stage of data analysis and not in the front-end hardware. Later on we present only the best obtained spatial resolutions. Typical histograms obtained for the reconstructed positions in the case of a 50 p,rn pitch detector with the p-side readout, for 0” and 6” impact angles, are shown in Fig. 9a

bipolar digital

impact angle of 6 deg

bipolar charge division

bipolar digital

Fig. 9. The histograms of position resolution for different readout schemes. (a) 0” impact angle. (b) 6” impact angle.

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and 9b respectively. Let us notice some characteristic features: for an impact angle of 0” the centres of the histograms are shifted by about 30 pm due to the magnetic field compared with the expected positions at 25 pm for the chosen geometry, for impact angle of 0” most events are single hit events and even for the readout using pulse height information the system behaves more like a digital one with the characteristic rectangular shapes of histograms, an impact angle of 6” increases the span of the region on the p-side in which holes are collected and causes bigger shifts of the histogram centres, due to the bigger span of holes most of the events are double hit events resulting in significantly better spatial resolutions in the cases of readout using pulse height information.

,. Results For each configuration of strip detector, for both the p-side and the n-side, and for different types of front-end electronics we extracted the efficiency and the spatial resolution as a function of the impact angle. The analysis was performed for two sets of parameters for strip detectors and front-end electronics, before and after irradiation. The summarised results are presented in Figs. 10-13. Fig. 10 shows the plots for p-side strips of 50 pm pitch. Let us notice that the setups with CMOS readout electronics, including deconvolution, show some problems

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with the efficiency, even before irradiation. This is partially due to the higher noise compared with the bipolar front-end but mainly due to significant signal losses in the deconvolution process because of non-ideal current signals from strips. For all types of bipolar front-ends the efficiency is practically 100%. A little loss of efficiency after irradiation is observed for the bipolar analogue readout of every strip and the bipolar digital readout, i.e. for 12 cm long detectors. The spatial resolution vs the angle shows a characteristic profile with a minimum around 6-7” for all setups. This is the angle at which we have the optimum ratio of single hit to double hits events. Let us remark that this impact angle introduces an additional span of collected holes on the p-side in the same direction as the magnetic field. The Lorentz angle for holes at the chosen bias conditions is about 4”, thus for the impact angle 4” the Lorentz angle is compensated. As a result most of the events are single hit ones at this point and all systems give a resolution around 14 km as is expected for a pure digital system, i.e. 50 pm/m. The obtained results indicate clearly an optimum tilt angle of this kind of detectors, i.e. p-side with 50 pm pitch, of about 6”. Fig. 11 shows the results for the same detector geometry but read out on the n-side. Now the positive impact angles compensate partially the Lorentz angle for electrons which is about 20”, significantly larger than for holes. Because of this large Lorentz angle the charge is always collected by more than one strip resulting in smaller average signals. For the negative impact angles we observe a significant drop of efficiency for the systems with readout of every strip, but not for the systems with charge

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Fig. 11. Efficiency and spatial resolution for n-side 50 pm pitch detectors.

division readout. This is because in most cases significant signals appear on three adjacent strips and due to charge division mechanism fractions of signals from the edge strips are fed back to the central strip increasing the signal on it. The behaviour of the spatial resolution on the n-side is quite different from that on the p-side. For the negative

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impact angles the spatial resolution is limited by noise and is even worst than expected for an ideal digital system. The optimum impact angle is about 10” but the curves are quite flat in this region. Comparing the results for the p-side and n-side we notice that the optimum impact angle (the tilt angle of the detector) for which we obtain the best spatial resolution is about the same for each side. Thus, for

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Fig. 12. Efficiency and spatial resolution for p-side 100 pm pitch detectors

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et al./Nucl.

Instr. and Meth. in Phys. Res. A 356 (1995) 241-254

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Fig. 13. Efficiency

and spatial resolution for n-side 100 p,m pitch detectors.

a double sided small stereo angle detector we can choose a tilt of about 6-8” which will fully satisfy the optimisation for both sides. This, however, is true only for 50 p,rn pitch detectors. Another interesting result which is worth to stress is the spatial resolution obtained with the digital readout. For the optimum angle this can be significantly better than pitch/\/i?. We obtained 9 pm for each side which is not far away from 7 km which corresponds to the ideal situation with 50% of single hit events from 25 li,rn regions around the strip centres and 50% of double hit events from 25 km centre interstrip regions. Figs. 12 and 13 show the results for 100 pm pitch detectors. Here again we observe a significant inefficiency for the setups with CMOS front-end electronics. Because of the wider pitch, generally, we have more single hit events compared with the 50 km pitch detectors. This is clearly visible in the case of spatial resolution for the p-side. In the relatively large range of impact angles the spatial resolution is almost the same for all considered schemes which means that all systems behave like the digital one, also those using the pulse height information. The optimum tilt angle for the p-side is now larger, above 10”. In the n-side we profit significantly from the pulse height information since the span of electrons due to the magnetic field is still comparable with the pitch. Therefore we obtain a good percentage of double hit events which improve the spatial resolution. As a result the spatial resolution for the n-side is better than for the p-side. The optimum tilt angle for the n-side is now -2” and it does not coincide with the optimum tilt for the p-side. Thus, in

the case of a double sided small stereo angle detector the tilt should be chosen somewhere between -2” and 10” to make a reasonable compromise between the n-side and the p-side resolution.

8. Conclusions We have developed a set of simulation programs which allows us to study the detailed effects in silicon strip detectors as well as the performance of silicon strip systems. The Monte Carlo analysis performed for different setups of strip detectors and front-end electronics show clearly that for the silicon strip system, like the silicon tracker for the ATLAS experiment, the noise requirements for the front-end electronics are essentially completely driven by the efficiency. The considered bipolar front-end electronics shows very good performance when used in three different configurations, i.e. analogue readout of every strip, capacitive charge division readout and digital readout. The spatial resolution obtained with the CMOS front-end could be acceptable; however, this kind of CMOS front-end is not acceptable as far as the efficiency is concerned. In most cases considered the spatial resolution varies significantly, up to a factor of 2, with the particle impact angle. Thus, we can gain significantly in spatial resolution by a proper tilt of the detectors. For 50 pm pitch detectors this optimum tilt is about 6-8” and is the same for the p-side and the n-side readout; thus, in double sided small stereo angle detectors both sides can be used in the opti-

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mum way. This is not true for 100 pm pitch detectors for which the optimum tilt angles are different for the p-side and n-side. The fact that the 50 pm pitch is preferable in the aspect considered above is due to the specific value of the magnetic field of 2 T. Generally, the radiation effects which have been taken into account do not cause any major problem. The degradation of spatial resolution is typically in the range of 20%. We observe somewhat bigger effects for some particular impact angles which we do not see as a problem since even for an optimum tilt of the detector the impact angles will vary in the range of a few degrees around the optimum value.

Acknowledgements This work was supported by the Polish State Committee for Scientific Research (project no. SPUB-206/94 and no. 8 S 501 040 06).

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