c

c

Double particle resolution in STAR silicon drift detectors

I

R.Bellwiedd, R.BeuttenmuUeP, W.Chena, D.DiMassimoa, L.Doud, H.Dykeb, A. Frenchd, J.RHalld, G. WXoEman', THumanicb, A.I.Kotovab~e, LV.Kotovb*ey,l, H.W.KmeP, ZU", C.J.Liawa, D.Lynna,

L.Ray', V.L.Rykovd, S.U.Pandeyd, CSrunead, J.Schambach', J.Sedlmeir", E.Sugarbake9 J.Takahashid, W.K.Wdsond

.Brookhaven National Laboratory 6dL - G 3693 ' The Ohio State University University of Texas Austin a Wayne State University

IHEP, Protvino

3 Abstract

The inner tracking detector of the STAR experiment at the BNL Relativistic Heavy Ion Collider will consist of a three layer barrel suucture of 216 silicon drift detectors. Calculations of the two-hit resolution achievable for these detectors are presented in this article. The effects on two-hit resolution of the electronic's response function, frequency of signal digitization and noise level are discussed.

1. INTRODUCTION The Silicon Vertex T a k e r (SVT) improves considerably

the momentum resolution, main interaction vertex position resolution and secondary vertex resolution for the STAR experiment [l]. The ability of SVT detectors to resolve nearby hits is important for two-parcicle correlation measurements and studies of short-lived particles. The SVT consists of 216 bidirectional Silicon Drift Detectors (SDD) with a maximum drift distance of 30 mm. Detailed description of the SDD design is presented in [2].

Electrons czeated by the ionizing particle in the SDDs, drift towards collecting anodes. The drift time of the electrons gives the distance between anodes and the crossing point of the particle. Diffusion and mutual electrostatic repulsion cause the drifting elearon cloud to spread out. As a redt, the arrival time of electrons at the anode has an approximately Gaussian distribution (31 with the width depending on the amplitude and drift time. The number of electrons created in the SDD by a minimum ionizing particle is about 25OOO. This allows us to determine the location in the drift direction of the center of gravity of the whole electron cloud with a precision of a few micrometers [4].

In this paper we show what resolution one can expect from the SVT detectors for close hits. We use a method deveIoped in [A to calculate the errors in amplitudes and drift coordinates of two hits with signals overlapping at the preamplifier-shaper output.

lConesponding author. phone: (614)-292-4775; fax: (614>-292- 4833; -ail: ko t~~@m~.~hio - s ta t e . edu

11. METHOD Our goal is to determine the amplitudes Ql,l and centroids

Till of two superimposed pulses using a set of N experimental samples si. The method of maximum likelihood [SI is used for estimation of paramem and their variances. According to the maximum likelihood method the values of the parameters are determined by minimization of the functional:

. N N

where gik are the elements of the inverse covariance matrix of the measurement errors, si are the experimental samples, qi are the values of the fitting function at the time ti, and X is the vector of deviations between samples and fitting curve.

The fiuing function q(t,A), where A = (Qt, 92, TI, Tz), is linearized by linear expansion around starting values of Ao. The expression for the linear expansion of qi is:

The matrix equation for the values of AA, which minimize (l), is

rAA = N, where

and

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spc- cific commercial product, process, or service by trade name, trademark, manufac- turer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

, ' ,. The covariance matrix M Of Variables AA is given by [6]

In our case Bg'lB' = r. as shown in [5], and the equation for M becomes:

M = I'-'.

111. FITTING FUNCTION AND NOISE COVARIANCE

For simplicity, following [XI. we take the Gaussian response MATRIX

function with the width 01 for the preamplifier-shaper

-"

45

40

2 o ' =

30

25

10

15 r

cloud with udord to a Gaussian output signal with U' = CT; + This function transforms a Gaussian input signal of an electron

5

fitting function for two-hits is

where u1 and Q' are the values of a known function Q = a(Q, T) in the points (Q1,Tl) and (Q1,T'). In the real experiment the function Q = u(Q, T) could be obtained from calibration data. For these calculations a "calibration" was done as follows: signal width for different drift times and amplitudes was simulated by a "slow SDD signal simulator" [7] and approximated by the polynomial expression:

Q(Q,T) = JPdQ) x Pm(T),

where m is the polynomial order. Good approximation was achieved for m=3. The output signal widths simulated for hits with amplitudes 125OOe ( i M I P ) and 125OOOe (5MIP) and

?he following noise sources are taken into accounc anode leakage current shot noise, series equivalent voltage noise of the input ampUer, and Poisson fluctuations in the pulse shape. The noise covariance at the output, from [SI, is:

fft = 20rw are shown in fig.1.

where q is the value of the electron charge. The fust term is the contribution of the shot noise of the anode leakage current I = vq. The second term is the contribution of the series noise, where C is the total input capacitance and e t is the physical spectral density of the amplifier series noise. The third term is the contribution of the Poisson fluctuations with the input signal waveform f',,(t).

*

Fig. 1 Approximarion of the signal width by polynomial expression for amplitudes 05 MIP and 5 MIP.

Iv. CONSTANTS USED IN CALCULATIONS

The most important parameters of the front end electronics for tw+hit resolution are: noise level, response function width and sampling frequency. Two versions of preamplifier-shapers with the width 0 of response functions of 52 ns and 97 ns and a noise level less than 4OOe for both designs have been developed for the SVT. The following values have been used in calculations: equivalent noise charge (ENC) of the &es noise = 400e. us = 207w and 40ns. The sampling frequency for the SVT is 26.77 MHz. CalcuIations with different frequencies were performed to show how resolution depends on sampling frequency.

Results of SDD prototype tests show that we can expect the anode leakage currents to be in the range of 1 - 10 nP.. In calculations, I = 5nA has been used. The ENC of this current is equal to 33e for ct = 20ns and 47e for ut = 40ns. The elecmn drift velocity in the STAR SDDs is 6.43 mm/p. This value gives a maximum drift time of T- = 4 . 7 ~ ~ for the drift distance of 30 mm.

v. RESULTS The criterion for successful resolution of two hits is a value

of errors in reconstructed amplitudes and times. Usually, if errors are larger than 20 - 30 %, pulses are consider to be unresolved. To detennine at which minimum distance two hits could be resolved the standard deviations of amplitudes and times are calculated as a function of the spacing between hits normaIized'to the signal width.

,./'

Contributions of the leakage Current shot nobe and W i n noise are an order of magnitude less than the series noise of the input preamplifier. Moreover, the behavior of the resolution in the presensc of, for example, the shot noise or series noise only, is very similar. The standard deviations in amplitude and time determination due to d e s noise or shot noise only are shown infig2forthecaseof25000eineachpulscandENC~~. Asisseenfromfig~,ourcalculationsareinagoodagntmcnt

from the middle of the detector. O!O 20 30 4 O!O 20 30 40

Resolution vs. Samplhg frequency

a I

with results obtained in [a. Hits could be nsolved at distances cy 1.5~. "his cormponds to 300prn separation for hits drifting . . . ....

t

-*-?as- --?as- Seriesnoise .nd Motnoise at E N C d W k

20 16

f l6

k' 10 i :: r:

6 4 + 2 0

Centrohis distance t 2o

Hr - 0

2 6

16 * 14 % 12

k lo I

Drift time t O,=Op.25,,000 e

T,=2400 ns u, 9 0 ns u,p31 ns

~ t 1 8 . 6 8 ns 0 - series noise - shot noise

Fig. 2 Comparison of series noise and leakage cumnt shot noise with the ENct4ooe.

The amplitude and time resolution as a function of sampling fresuency is shown in fig3 for lu, 1.5u,2uspaCing between hits and for frequencies in the 25-67 MHz range. The resolution is rather insensitive u) the sampling kquency when the distance between hits is about 2a or more. Only when the distance is less than or equal to 1.k and the frequency is lower than 28 NHZ does resolution deteriorate.

The amplitude and coordinate resolution as a function of drift distance is shown in fig.4 and fig3 for two-hit separations of: 05, 0.75 and 1.0 mm. For minimum ionizing particles coordinate resolution is less than 20 pm and ampiitude resolution is about looOe for the whole drift length.

1

VI. SUMMARY Double hit resolution for the STAR SDD has been calculated

using the method proposed in [a. Presented results show: - two hits could be resolved at the distance of 300 pnr; - coordinate resolution of the order of 15-20 p m could be

Fig. 3 Resolution as a function of sampling bequency for two-hit separations of lu, 15o.b.

obtained for minimum ionizing panicles; - expected ampiitude resolution is about 1OOOe.

VII. ACKNOWLEDGMENTS This work was supported in part by the US Department

of Energy grant DE-ACO2-76CHOOO16, NSF grant PHY-9511850, and STAR R&D funds.

VIII. REFERENCES [I] J.W.HarriS and the STAR collaboration. Nuci. Phys. A566 (1994)

[2] RBellwied et (J, STAR SVT Group, Nucl. h r . MdMerh., A377

131 E.G& A.Longoni PXehak, MSampietm. Nucl. Imt. and Mefk

[4] P.Rehak er al.. Nucl. hut. and Meth. A248 (1986) pp. 367-378. (51 E.Ga& P.Rchak. M.Sampietm. Nwl. Zmr. d Meh. A274 (1989)

[6] H.Cramer. "Mathematical Method of Statistics" Primeton

(7 J VLRykov. STAR Note # 223 Nov.12.1995.

pp. 277c-286c.

(1996) p ~ . 387-392.

A253 (1987)~. 393-399.

pp. 469476.

University Press, I951 p. 313

. .

I - I #’,

R d u t k n vs. Drift disbnn for u, I

2u O O 10 20 10 z t t . l O O 10 Eo 10

1-1 Digitkation step: At = 37.3%~

Spacing between hits: -0.5mm

0 - 0.75 mm ~~~~ 2% O O 10 2.0 30 A - 1.Omm

rn

Fig. 4 The amplitude and coordinafe resolution for of = 2Onr for two-hit separations of 05 mm - black dots; 0.75 mm -open dots; 1.0 mm - triangles.

Resoiuthm vs. Drift distance for u, =40ns

1 Coordinate of 20 c 20

5 Centroids distsnce I I

Z Y I OigitizatIon step: At = 37.36ns

Spacing between hits: 9 -0.5mm 0 -0.75mm

~~~~ 250 O O 10 20 30 4 - 1.Omm m

..: _l: ..; I . ... . , . . . , 7 . . . . , .

Fig. 5 The amplitude and coordinate resolution for ut = e a . The same two-hit separation as m fig.4. I . . . .. .