The influence of charge collection characteristics on HPGe detector timing performance

NUCLEAR INSTRUMENTS

AND METHODS

169 11980) 4 6 5 - 4 6 8 ,

(~

NORTH-HOLLAND

P U B L I S H I N G CO

THE INFLUENCE OF CHARGE COLLECTION CHARACTERISTICS ON HPGe DETECTOR TIMING PERFORMANCE B C ROBERTSON

Department o/Physics, Queen's Umversay, Kingston, Ontario, Canada K7L 3N6 Received 16 August 1979 The expected response of a constant fract)on t~mlng dlscnmmator to pulse shapes from a coaxial HPGe detector has been calculated for several chotces of charge drift length and ~mpunty concentration over a range of calculated detector bins, and also for both possible electron and hole drift directions Optimum timing performance as obtained with impurity concentrations of the order of l0 l° cm -3 and when electrons drift towards the detector centre

1. Introduction Coaxial high purity germanium (HPGe) detector pulse shapes can be appreciably modified because of the ability to change the electric field profile by the combined effects of detector bias and impurity charge concentration Since the performance of timing discriminators is sensitive to the signal form, the pulse shape variability uniquely available to coaxial HPGe detectors should be reflected in their timing performance However, the range of detector characteristics potentially available is far from being spanned by existing detectors, so that it it not possible presently to experimentally determine detector parameters that will result in optimum timing performance Consequently it is desirable to study the calculated detector performance in order to ascertain what the optimum characteristics should be, or, more hkely, to serve as a guide in the choice of the most promising region of detector parameters In the following the expected timing characteristics of a coaxial HPGe detector and a standard constant fraction discriminator have been determined for a range of detector specifications Variations of detector geometry and bias, impurity concentration and charge drift direction have been considered 2. The calculation The charge induced on the terminals of a coaxial detector with a uniform space charge density by the radial displacement of a charge q0 from an lmtlal position rx to r IS given ~) by the relation q (t) = q0 In (r/rx)/ln (ro/r,) where r, and r0 are the inner and outer detector radii, respectively The time-dependence of the radial position of charge carriers can be determined

using the relation dr = oddt for both electrons and holes by assigning the relevant sign to the drift velocity, Vd The drift velocity depends explicitly on the electric field E within the detector and also on the charge sign of the carriers The electnc fielddependence of electron and hole drift velocities was fixed by Vd=a(E)E, where

~,(E) = ~o(E)/(l +L/Eo) was determined separately for holes and electrons by fitting the experimental drift velocity measurements of Ottavlam et al 2) with the empirical constants /.to and E0 The electric field distribution inside the HPGe detector was described by the relation E(r) = nr 28

I/ - ( n / 4 e ) ( r 2 - r 2) r In (ro/r,)

where n is the net ionized charge density, ~ is the dielectric constant of germanium and V is the potential difference across the detector The presence of the net ionized charge distribution produces an electric field that increases with increasing detector radius, in distinction to the electric field produced by placing a potential difference across the detector electrodes, which produces and electric field that decreases with increasing detector radius The result of combining these two field components is a normally high electric field at large detector radii, which is largely independent of bias, and an electric field at small radii that is strongly bias dependent and can be as low as zero, at depletion bias A computer program was written to determine the time development of the detector pulse shape, q(t), as a function of interaction position rx The choice of detector bias, impurity concentration, detector inner and outer radii fixed the electric field

466

B C ROBERTSON

profile and therefore the radml variation of electron and hole drift velooty The total reduced charge pulse was then determined by following the radml d~splacement of electrons and holes from the mteraction point out to the detector electrodes The resulting pulse shapes were then used to "trigger" a constant fraction d~scnmmator The tugger t~me, /trtg, for an md~wdual pulse was set by determining the t~me that the amphtude of the pulse attenuated by a factor f equalled the amphtude of the pulse delayed by a t~me td Th~s ~S equivalent to the condtt~on

q(ttng--

td) = fq(ttr,g)

The values f - - 0 3 and t -- 15 ns were used for the calculatton, and are typical of constant fraction parameters used experimentally The general nature of charge pulses m sohd state detectors (smooth curve segments broken by an abrupt change m slope due to arrival of one charge species at an electrode) allows the operation of the constant fraction d~scnmmator to be characterized Constant Modes

~ /

Fraction

Discriminator

of O p e r a t i o n

eak

i

'

(hi~ 1 I

I

,y

o~e

X

bre|k t

brtlk|

t trlllger

Fig 1 Charactenstzc shape of a trtgger walk curve for a constant fractson discriminator and sohd state detector system The trigger walk curve shown ~s for a planar detector, ~t is principally the same as for a coaxml detector

by three d~fferent modes, as dlustrated in fig 1 Electron-hole pa~rs generated near the centre of the active region produce pulses that break suffioently late so that the constant fraction dtscnmmator can fire before the pulse break has occurred In this case the trigger time is almost completely independent of interaction posmon As the mteracuon position is moved to ezther of the detector's edges, the pulse break advances far enough to occur m the attenuated signal of the discriminator before the trigger time (but not m the delayed s~gnal) Th~s results m a trigger t~me which becomes earher as the interaction posmon is advanced further out towards the detector's edges A third mode of operation occurs when the break is so early that ~t occurs m both the attenuated and delayed s~gnals before the discriminator fires In th~s case the trigger t~me becomes later as the interaction pos~t~on is advanced yet further out towards the detector's edges These three modes of operation are responsible for the trtgger walk curve shown m fig 1 wtth the characteristic tuner and outer " k n e e s " separated by a walk-free region, and will occur for any detector configuration or electric field configuration A trigger response t~me spectrum was generated from the trigger walk curve by weighting individual points on the walk curve by the approprmte geometrical factor, assuming uniform ~rradmUon over the detector face T~mmg j~tter, due to the conversion of pulse amphtude fluctuations to timing variations, was included by folding m a Gaussmn distribution The full-width at half maximum (fwhm) of the Gaussmn distribution was set at 2 0 ns for all calculations Th~s value has been used previously 1) to fit the experimental t~mlng response of a coaxml HPGe detector It is not clear that the choice of a single value of Gaussmn fwhm describes the situation most hkely to prevad expenmentally Simple pulse rise-time arguments would suggest some systematic reduction of t~mmg no~se w~th increase of bins However the only mformat~on for HPGe detectors presently available l) shows a timing noise component that is independent of bins This points to the presence of addltzonal norse sources whtch are proportional to detector bias and can contribute s~gnlficantly to the overall t~mmg noise Consequently tt ~s not possible to predict w~th confidence what the overall vanatton of timing noise with detector bins wdl be m individual cases and the present use of a constant home figure should be viewed accordingly The overall rehablhty of the present algorithm for

CHARGE

COLLECTION

reasonably reproducing the timing performance o f detector systems has been mvestngated previously by comparing with the observed performance of timing systems for both a coaxial GE(LI) detector 3) and HPge detector I) Good agreement was obtained in both cases

3. Results and discussion The timing response function was calculated for a coaxial detector with an inner radius of 0 5 cm and outer radius of 2 25 cm The detector bias was varied from just above depletion voltage to approxImately 3 0 0 0 V for several values of Impurity charge concentrahon ranging from n = 0 - 2 × 10 j° cm-3, and for both directions of electron and hole motion The results, shown m fig 2, are charactertzed by the full width at half m a x i m u m (fwhm) and full width at tenth maximum (fwhm) of the response curve For comparison the characteristics of a G e ( L 0 detector field configuration is also shown (n = 0) As expected, the fwhm results show a much greater varmtton than the fwhm values, which do not vary strongly enough with impurity concentration m the n = 10 ~') c m - 3 r e g i o n to be d~stlngulshable on the scale shown For electrons drifting towards the outer electrode (solid curves), the fwhm versus detector bias curves show a systematically poorer performance with increasing impurity charge concentration W h e n the drift dtrec"

BIAS=1750V

BIAS=1950V

l

467

CHARACTERISTICS

FWTM

(ns)

401 22 2 I-

WH FWHM

t

J

,

I 2000

I 3000

FWHM

n=O5 I 1000

BIAS (VOLTS) F=g 2 Calculated varmtnon o f fwhm and fwtm as a functnon of detector bins, nmpunty charge densnty n, and drift d~rect~on The ]rnpurlty charge densnty is given m umts of 1 0 l ° c m - 3 The dashed curves are for electrons drifting m and the sohd curves are for electrons drifting out Deplehon bins ~s indicated by the vertical bars

tlons are reversed (dashed lines) the fwtm versus detector bias curves show a systematic improvement of fwtm with mcreastng charge concentration The source o f these effects lies m the response of the constant fraction d~scnmlnator to changes in BIAS=3250V

20

---

15

1t

!

__ ELECTRONS ~ I

II

r (cm)

10

05 I

I

I

22

I

19

f

I

21

I

18

I

I

20

I

I

22

ttr,gger (ns} Fig 3 Trigger walk curves for a HPGe detector under different bias condntlons and drift directions The nmpunty charge density is 1 5 × 101°cm - 3

468

B C ROBERTSON

22 t =1 75cm

FWHM (RS) 21

~~-~----~

t~m

DEPLETION

BIAS

20 1500 1~00 BIAS (VOLTS)

23OO

F~g 4 Variation o f f w h m w~th charge drift length t and d~rectlon T h e curves for t = 1 75 and 1 95 have an tuner detector radms of 0 5 c m , the curve for t = 1 30 cm has an tuner detector radms o f 0 6 c m T h e dashed curves are for electrons drifting m and the sohd curves are for electrons drifting out

the detector pulse break time due to drift velocity effects Th~s is shown up m the trigger walk curves dlustrated m fig 3 for the two drift directions, where the extent of the outer knee ~s sigmficantly reduced when holes rather than electrons drift outwards When the slower-moving charge species moves outwards their drift time to the termmal for any gwen pulse ongm increases, so that the break in the pulse occurs later This allows the walk-free region of the trigger curve to extend out to larger rad. Because the outer knee region includes a larger fraction of the detector's actwe volume, effects due to trigger walk changes at the outer edge outweigh those at the inner edge for the coaxial configuration, so that a net reduction m the fwtm occurs Similarly, the reduction of the relatwe field strength at outer rad. ts responsible for the improved performance for the Ge(Ll) field configu-

ration (n = 0 ) over comparable HPGe fields and outwards-drifting electrons The effect of impurity concentration and drift direction on fwhm is much less marked, as can be seen from the bottom part of fig 2 and fig 4 Despite the possibd~ty of ~mproved fwtm performance, the fwhm ~s systematically slightly poorer for HPGe than for Ge(L0 field configurations This is most hkely due to small residual slope changes m the "walk-free" region of the trigger walk curves The results m fig 4 also confirm an tmprovement of fwhm with increasing drift distance, as would be expected because of the corresponding reduction of the fractional volume that suffers trigger walk as the drift length is increased In summary, the results of the present calculation point out the strong sensmv~ty of the timing fwtm to the outer walk knee region For any gwen detector bias the effect of this region can be mlmlzed by a combination of moderately h~gh ~mpunty charge density (n ~ 1 × 101° cm -3) and the use of outwarddrifting holes The choice of optimum bins, however, will be controlled by the detaded relation of detector noise to bias observed for mdw~dual detectors At present ~t is not possible to predict with confidence what this will be, so that the calculated performance wtth constant noise assumption used here would have to be adapted to the noise charactenst~cs of mdwidual detectors References I) B C Robertson and H L Maim, Nucl Instr and Meth 150 (1978) 401 2) G Ottavlam, G Canah and A Albengi-Quaranta, IEEE Trans Nucl So NS-22 (1975)192 3) L L Gadeken and B C Robertson, Nucl Instr and Meth 136 (1976) 255