Nuclear Instruments and Methods to Physics Research A 337 (1994) 362-369

NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Section A

A time-of-flight detector based on silicon avalanche diodes J.A. Hauger a, Y. Choi a, A.S. Hirsch ", R.P. Scharenberg a, B .C. Stringfellow M.L. Tincknell *,a, N.T. Porile b , G. Rai c, J. Girbarino d , R.J. McIntyre d

a,

Department of Physics, Purdue University, West Lafayette, IN 47907-1396, USA n Department of Chemistry, Purdue University, West Lafayette, IN 47907, USA Nuclear Sei. Diu, Lawrence Berkeley Laboratory, Berkeley, CA 94720, USA d Optoelectronies Div ., EG&G Canada, Vaudreud, Quebec, Canada J7V SP7

(Received 16 August 1993) We have investigated reach-through silicon avalanche diodes (AVDs) as time of flight detectors for nuclear and particle physics experiments . The signal is initiated by a minimum ionizing charged particle passing directly through the AVD We have studied the effect of pulse amplitude and noise characteristics on timing using (3 - particles. The time resolution of four AVDs has been measured with a range of standard deviations, Q = 65-87 ps . This time resolution is comparable to the best available with the conventional alternative, a plastic scintillator and photomultiplier tube . Further optimization of the AVD results appears possible . 1. Introduction Future experiments in nuclear and high energy physics will require high pixel-density detector systems able to measure time of flight (TOF) of fast charged particles with sub-100 ps precision . These detector systems should be thin so as to minimize multiple scattering and secondary interactions, capable of handling high hit densities, and inexpensive . Conventional systems made of scintillators and fast photomultiplier tubes (PMTS) often cannot meet these requirements . As a new approach to TOF technology, we have studied reach-through silicon AValanche Diodes (AVDs) for direct detection of minimum ionizing particles (MIPs). We have tested the timing characteristics of a commercially available reach-through Avalanche PhotoDiode (ÀPD), modified for our requirements, and have used it to demonstrate a proof of principle. Direct ionization in silicon can be an efficient signal for particle detection and timing because the creation of an electron-hole pair requires only 3 .6 eV on average. In comparison, creation of an optical photon in plastic scintillator requires an average of about 100 eV, and there are additional penalty factors for light collection and photocathode quantum efficiency . This implies that a silicon detector can be much thinner than plastic, and silicon will have many times the number of primary signal electrons per unit path length of a particle traversing the detector . Thus, in a silicon detector (even with a thickness of only - 100 ltm), the * Corresponding author .

intrinsic statistical fluctuations in arrival times of the primary electrons are minimal, significantly reducing one important contribution to timing resolution . Because AVDs have internal gain, they boost the signal to noise ratio prior to external amplification, which is the dominant noise source in timing applications . These characteristics suggest AVDs should have excellent timing resolution . Furthermore, small (- 3 X 3 mm z) AVD pixels can locate particle hits precisely, which can aid the accurate determination of the particles' trajectories . Since particle identification is based on the particles' velocities, both trajectory and time must be measured with comparable precision to achieve good identification . Arrays of AVDs with small pixel size will also tolerate high particle multiplicities . AVDs can be packaged with individual integrated preamplifiers, amplifiers, and discriminators, capitalizing on the economies of large scale electronic integration . Presently the cost of AVDs is prohibitive for large applications, but these costs should decrease sharply under mass production . 2. Experimental setup The four AVDs we have studied are custom modules from EG&G Optoelectronics Division, Montreal, Canada . In Table 1, the diodes are numbered and listed along with several measured parameters for each diode. These diodes are modified avalanche photodiodes (APDs) of the reach-through design ; they operate in the proportional region for a MIP at a bias voltage

0168-9002/94/$07 .00 © 1994 - Elsevier Science B.V . All rights reserved SSDI 0168-9002(93)E0848-M

JA . Hauger et al. I Nucl. Instr. and Meth . in Phys. Res. A 337 (1994) 362-369

363

Table 1 Time resolution, gain and breakdown voltage of the diode modules Diode module

fume (ps)

Gain

VBD (V)

1 2 3 4

65 66 78 87

47 31 32 49

425 409 348 404

(VBD - Vb,as =10 V)

CONTACT

of - 400 V, with an internal gain of - 45 . The sensitive area of these diodes is 5 X 5 mm 2 , with an effective thickness of 140 wm and diode capacitance of - 20 pF. The modules include a low noise transimpedance preamplifier with a GaAs FET first stage, packaged with the diode in a 3 .8 X 13 X 33 mm 3 metal enclosure (Fig. 1). The preamplifiers have a gain of - 48 . These diodes were adapted from an existing design, with the following modifications : - The glass window used in the APDs to transmit light to the diode was replaced by an opaque beryllium window 1 mil thick . - Two capacitors on opposite edges of the diode were used to buffer the high voltage ; this arrangement minimized the signal transit time variations across the diode . - A thin (opaque) metallic layer was added to the p+ side of the diode to decrease spreading resistance . A small hole was left in the layer to allow optical gain measurements. - The bandwidth of the DC coupled preamplifier was 100 MHz so as to optimize the signal-to-noise ratio . We summarize here the operation of the AVD ; a more complete description can be found in refs . [1,3] . A schematic of a typical reach-through diode is shown in Fig . 2. The AVD is operated under a bias voltage high enough to produce a depletion layer that reaches through the p and p-intrinsic (called rr) regions into

- 33 .0 mm

(common)

5 -3x10

E(x) V/cm -2x10

4

140 microns

Fig . 2. Schematic AVD profile and resulting electric field distribution . The peak field corresponds to the multiplication region.

the p+ contact layer . The signal is created in the silicon by the ionizational energy loss (dE/dx) of a fast charged particle . The deposited energy creates electron-hole pairs in the silicon . The electrons drift at nearly saturation, velocity through the depletion layer into the thin p-n+ junction where they encounter an electric field strong enough to cause avalanche multiplication . The initial gain from electron multiplication is essential because it boosts the signal prior to the inevitable addition of noise in subsequent amplification steps . The advantage of avalanche gain is clear when the noise generated by the bulk dark current and surface dark current is considered, along with other noise sources . In an AVD only the bulk dark current, Idb , about 50 pA in these diodes, undergoes multiplication . The surface dark current, Ids , about 200 nA, does not . The detector contribution to the noise current is given by 2 t nd = 2 RBn (Ids + IdbM2F ),

5.0 mm -

Case Fig . 1 . AVD package.

Electrodes

where B is the noise bandwidth and F is the excess noise factor (discussed below) . Note that at a gain of 45 (F - 3), the noise contributions from the surface and dark currents are roughly equal. Thus avalanche gain only increases the detector noise current by a factor of about V2, while the signal is boosted by a factor of 45 . The total noise current in the absence of signal, which is dominated in a wide-band system by amplifier noise,

364

J.A . Hauger et al /Nucl. Instr. and Meth. in Phys . Res. A 337 (1994) 362-369

is not increased significantly, even at gain of 45 . The amplifier noise current is given, for a two-pole filter, by cn,=

4kTB n R +64e n,CtB n f

where Rf is the feedback resistor (3000 W of the transimpedance amplifier used, B is the noise bandwidth (= 1 .22 X B), e n is the amplifier equivalent noise voltage (~ 1 nV/ Hz ) and Ct is the total input capacitance (~ 20 pF). For these parameters, the second term is the dominant noise source by a wide margin . As discussed below, the timing resolution depends on anme = anoise/(dV/dt) (with 0-noise (X tna) . Increasing the bandwidth of the preamplifier increases ano,Se as B3/2 , but only increases dV/dt proportional to Bn , and then only up to the intrinsic risetime of the signal from the AVD. Thus, it is important to limit the preamplifier bandwidth to - l/(AVD risetime) for the best timing resolution . However, higher gain would increase dV/dt, which might improve the timing resolution . For the diodes tested, the high field avalanche region is a few microns thick and the reach-through depletion region is - 140 win thick. Most holes produced by primary ionization drift away from the avalanche region and do not contribute strongly to the resulting signal . Due to their lower ionization coefficient, holes which do enter the avalanche region are much less likely to cause multiplication . The process of multiplication is a statistical one, with the result that not all primary pairs are multiplied equally. The excess noise factor F is defined as (M2)/M2' where M= (m,) is the average value of the individual gains m, experienced by a large ensemble of i primary pairs. If we consider only those primary pairs which result in an electron being multiplied, F can be shown [1] to be given by F=kM+ (1 - k)(2-1/M), where k is a properly weighted average of the ratio of the ionization coefficients of holes and electrons . For the diodes used here, the effective k factor is about 0.02. Note that both electrons and holes contribute to F, with F = 2 at high gains if a semiconductor existed in which only electrons ionized. Any ionization by holes increases F significantly at high gains, with the result that at high gains the achievable timing resolution is limited by the noise in the multiplication process . A schematic diagram of the test setup is shown in Fig. 3 . The tests consisted of exposing two AVDs in coincidence to minimum ionizing particles and recording the time differences. The time resolution was obtained directly from the standard deviation (a) of these time differences . The MIPs used were (3 - electrons from a 106Ru(106Rh) source, which was selected for its high endpoint energy of 3.5 MeV. These particles were

Scmtillator

Diode 2

Diode I

Fig. 3. Schematic of the test setup. A coincidence between diode 1, diode 2, and the scintillator is required to trigger an event. collimated, sent through the AVDs and stopped in a plastic scintillator coupled to a photomultiplier tube . A pulse height cut on the scintillator signal selected the high energy tail of the beta spectrum, and a triple coincidence was required among the AVDs and the scintillator to trigger an event. Each diode channel of the test setup used an additional fast, low-noise amplifier (Phillips 6954) [4] with gain 100. See Fig. 4. The signal was then split to Phillips 711 [4] fast Leading Edge discriminators (LE) and the linear fan in/out unit . The linear fan unit provided a signal for charge-sensitive (integrating) Analog to Digital Converters (ADCs) and a second set of discriminators used for trigger logic. The fast discriminator outputs then provided the start and stop signals for the time measurements . The start and stop were fed into an Ortec [51467 Time to Pulse Height Converter (TPHC), which then fed a shaped pulse into a LeCroy [6] 2259A peak-sensing ADC. The time calibration was determined by adding 1 ns cable lengths to increase the amount of delay, and recording the number of channels the TOF distribution peak shifted. Care was taken to keep the total number of connectors constant . The data obtained can be fit with a linear function and the slope of the added delay (ns) versus peak time position (channel) was used as the single channel time calibration . The TPHC-ADC combination achieved 5 .54 ps/channel, which is a larger dispersion than that obtained with commercial

Fig. 4. Simplified diagram of coincidence system with scintillation trigger .

JA . Hauger et al. /Nucl. Instr. and Meth. in Phys. Res. A 337 (1994) 362-369

TDCs (- 25 ps/channel) . The time calibration was linear over the range of time differences used in the experiment . The fast discriminator and TPHC-ADC system was tested with a fast pulse generator and yielded a system time resolution Full Width at Half Maximum (FWHM) of 9 ps . Both the charge-sensing and the peak-sensing ADCs were read out through a CAMAC system connected to a Macintosh IIci computer running LabView [7] data acquisition software . To facilitate mechanical positioning of the AVDs and collimators, commercial optical mounting hardware was employed . The ß - source holder mount, two AVD mounts and the scintillator/PMT mount were all aligned on three parallel optical rails attached to an aluminum base plate. Because of the high gain and sensitivity of the amplification chain used for each AVD channel, the test setup had to be carefully shielded from radiofrequency pickup noise, and protected against feedback oscillations . All detector elements and front-end electronics were enclosed in a copper screen Faraday cage to shield against pickup . A copper sheet on top of the cage acted as a ground plane. All internal and external (to the cage) signal and high voltage coaxial cables passed through bulkhead connectors grounded on this plane . In addition, wires from the DC power supplies passed through low pass LC filters on this plane to eliminate pickup . These measures succeeded in curing pickup problems in an initial, unshielded configuration . The whole Faraday cage and its contents were contained in a commercial 20 ft 3 upright freezer with heating and cooling controls to provide the temperature range between -20°C and +50°C with 0.1°C stability. The diode modules were outfitted with sen-

depletion + primary region i electrons

E

depletion region function

365

sors that provided temperature monitoring accurate to 1°C. 3. Expected AVD signals and noise The most probable energy loss of a minimum ionizing particle in 140 [Lm of Si is about 34 keV, so a typical ß - produces about 9500 electron-hole pairs along a straight-line path through the AVD. The signal is amplified by the diode avalanche gain of - 45 (c.f . Diode 1), effective preamplifier gain of - 48, amplifier gain of 100, and then split two ways (effective gain 0.5). After these amplifications, the expected output is 1 .03 X 10 9 electrons. Using a charge-sensitive ADC with 0.25 pC/channel, the expected signal for Diode 1 should peak in channel ^J 660 (plus ADC pedestal). The time development of the signal is expected to involve three time constants: - Te , the drift time of the electrons across the 140 wm of Si ; - T, the time for holes created in the avalanche region to drift back across the 140 p,m; - sac the input RC time constant of the diodepreamplifier circuit. At 400 V bias, the average electric field in the drift region of the AVD is - 2 x 10 4 V/cm . At this field strength, the drift velocity of electrons in Si is v p,e - 8 x 10 6 cm/s, and v D,h e 5 x 10 6 cm/s for holes, thus, Te - 1.75 ns, and 7 n = 3 ns . The bandwidth of the preamplifier is 100 MHz, which gives an equivalent risetime of 1 .6 ns (deliberately matched to the other time constants) . As in all parallel-plate electronic devices, the signal in the external circuit is actually in-

k secondary

depletion region junction

bq

.v x

a,

L,

Time in i°+ Tri (a)

Fig. 5. Ideal time development of the pulse: (a) The column of primary electrons drifts toward the avalanche region, while the holes produced by multiplication drift away from the junction, inducing an external current. (b) All primaries have been multiplied . A column of secondary holes drifts from the junction . (c) The last of the secondaries drift from the junction .

366

JA Hauger et al. /Nucl Instr. and Meth . m Phys. Res. A 337 (1994) 362-369

duced during the transit of internal charge across the device . The primary electron and hole currents are negligible, and only the current of secondary holes from the avalanche multiplication is observable since, in the reach-through profile the holes drift over a much larger potential difference than the electrons, thus producing a larger output signal . A MIP passes through the diode in 0.5 ps, and the column of primary electrons descends on the junction at nearly the saturation drift velocity . Almost all the primary holes drift away from the junction, and are not multiplied . A column of avalanche-multiplied holes grows from the junction, and drifts back across the reach-through region, where it is collected at the negative electrode . Since the drift velocity of the holes is only half that of the electrons, the column of secondary holes grows until the whole column of primary electrons has been multiplied, then the packet of secondary holes drifts to the negative electrode, where the column of holes shrinks to zero again as the holes recombine . In the absence of signal shaping by the preamplifier, the external signal should rise linearly as the secondary holes are produced at the junction, then the induced current should be constant while the holes drift, and finally the external signal should fall linearly to zero as the holes vanish at the electrode . The ideal pulse waveform would be a trapezoid, as depicted in Fig. 5; however the preamplifier alters the actual shape of the pulse, c.f. Fig. 6. The signal rise and fall times should be tnse = tfa -'re + ,r,, = 2.5 ns, and the FWHM should be tFWHM =Th + Tic _ 5 ns . For Diode 1, the current is expected to be - 33 mA (1 .03 x 10`' electrons in 5 ns), corresponding to an expected - 1.7 V peak output signal (into a 50 dZ load). Fluctuations in the signal amplitude are expected from four sources: AVD Pulse Shape

- intrinsic fluctuations in the primary energy loss (the Vavilov distribution of dE/dx), - diode avalanche gain nonuniformity, - diode avalanche fluctuations, and - preamplifier noise. For a thin absorber (e .g . 140 win Si), the FWHM of the Vavilov distribution for a MIP is - 25% . Superimposed on this are the path length variations of the ßdue to multiple Coulomb scattering; however these are minimal for the high energy ß- required by the experimental trigger. Gain nonuniformity across the AVD area is specified as ± 10% maximum, which is comparable to the Vavilov fluctuations . Both of these pulse height variations can be remedied by off-line amplitude walk corrections . Since the - 9500 primary electrons are expected within the 2.5 ns risetime of the pulse, primary statistical fluctuations will be negligible . The dominant uncorrectable source of signal fluctuations comes from the preamplifier noise, specified as 40 nV/ Hz at the preamplifier output . Given the preamplifier bandwidth of 10" Hz, and the effective gain of 50 in the channel following the preamplifier, the expected noise agrees with the observed noise, 20 mV RMS. This gives an expected signal-to-noise ratio of 1.7 V/ (2 x 20 mV) = 42 for Diode 1 . For a leading edge discriminator, the expected time resolution can be estimated directly from the slope of the pulse at the discriminator threshold and the RMS noise [2] . The time that a linearly-rising signal crosses a fixed threshold will vary simply as O'nme=

O'noise

(dV/dt) .

Thus, it is clear that the optimal trigger level for the LE is at the level where the pulse has a maximum slope. For Diode 1, a maximum pulse slope of - 300 mV/ns occurs at - 450 mV . With O'no,se - 20 mV, we can expect a time resolution ame = (20 mV)/(300 mV/ns) = 67 ps for this diode. 4. Experimental results - amplitude measurements

-02

-0 6 -08

0

10

20

30

Time (ns)

40

Fig. 6. Actual pulse shape as measured from incident ß particles. The circuit elements shape the pulse.

The measured pulse shape of the (3 - signal in the AVD (Diode 2) is shown in Fig. 6. The risetime from 10% to 90% is - 2.5 ns as expected, and the falltime is - 9 ns . The falling edge slope decreases from - 0.2 V/ns to - 0.1 V/ns at about the half maximum point. The maximum pulse height is - 1 V, which is lower than the previous estimate since this particular diode has lower gain . The observed pulse shape is not an ideal trapezoid because the preamplifier shapes the output . Noise measurements have been made in two ways : - observation of the preamplifier output on a fast oscilloscope, and

J.A . Hauger et al. /Nucl. Instr. and Meth. in Phys. Res. A 337 (1994) 362-369

- sampling of the preamplifier output by a charge-sensitive ADC. The raw preamplifier output (without any R_ pulses) was observed by an oscilloscope with 400 MHz bandwidth. The preamplifier noise, amplified by the downstream channel gain of 50, had an RMS deviation of 20 mV . The frequency of the fluctuations appeared consistent with the 100 MHz bandwidth of the preamplifier, and there were no correlations in the noise signals over a range from 10 ns to 1 ~Ls . A second technique was used to ascertain the spectral density of the noise fluctuations . The amplified preamplifier output (gain 50), without any (3 - pulses, was added to a DC offset, and input into a charge-sensitive ADC. The DC offset raised the noise fluctuations into the middle of the ADC range. The ADC was gated for 10, 20, 30, and 40 ns intervals to integrate the noise plus offset . The peak channel and the FWHM of the resulting ADC spectra were analyzed to determine the frequency spectrum of the noise. The FWHM is a measure of the noise fluctuations in the gate interval : the ratio (FWHM) 2/(peak channel minus pedestal) indicates the noise within a frequency range - 1/(gate interval) . This ratio was constant for the four gate intervals, showing that the noise spectrum is approximately uniform (white) over the 100 MHz bandwidth of the preamplifier. The observed preamplifier noise is fully consistent with its specifications . An ADC spectrum of the ß- pulses is shown in Fig. 7. The ADC pedestals are - 100 channels . Diode 1 in Fig. 7a has a median integrated charge signal consistent with our previous estimate (770 - 100 = 670); Diode 2 in Fig. 7b has less gain . Space charge buildup could suppress the gain of AVDs for a direct ionization signal [1]. The column of secondary holes produced by avalanche multiplication ADC Spectrum 800 600 400 200

c

0 U

0

400

600

800

1000

400

600 800 ADC Channels

1000

800 600 400 200 0

Fig. 7. ADC spectrum of (3 - pulses : (a) Diode 1 and (b) Diode 2.

367

ADC Channel versus Energy Deposited ® "Fe X-ray 600 - ® Normal Incidence r ® 20° Incidence Angle ® 40° Incidence Angle U 400 0 U Q

50 Fig. 8. ADC peak channel versus deposited energy . The approximate linearity suggests that there is no strong space charge saturation at these levels of energy deposition. The line is a best fit constrained to pass through the origin. has a very high space charge density because of its small transverse area . The avalanche gain depends exponentially on the voltage at the junction, and the space charge might reduce the voltage enough to diminish the gain . To see whether this occurs, we deposited a variable amount of ionization into the diode, and checked the linearity of the integrated output charge . We used four cases, a 5.9 keV X-ray from 55 Fe, and the most probable energies from three different trajectories of ß- through the diode. The ß - path length was changed by varying the angle of incidence from the normal (and most probable energy deposition) from 0° (34 keV), to 20° (36 keV), and 40° (44 keV). The results of this comparison using Diode 2 are shown in Fig. 8. The pedestal-subtracted peak ADC signal does vary linearly with deposited energy, so there is no evidence of a strong space charge suppression of the avalanche gain . The FWHM of these distributions is - 35-40% . The FWHM of the Vavilov distribution for a thin absorber is - 25%. In order to account for this discrepancy, gain nonuniformity across the sensitive area of the diode was investigated . Following the example of ref. [1], the diode was used to measure the ADC spectrum of a monoenergetic SS Fe 5.9 keV X-ray source. The width of the spectrum is a combination of dispersions due to gain nonuniformity and noise. To extract the contribution from gain nonuniformity, the FWHM of the gain variation was calculated by subtracting in quadrature the FWHM due to the noise from the actual FWHM of the X-ray ADC spectrum . The resulting FWHM due to gain nonuniformity was 30% at high Vb,as . This implies an RMS gain variation of - 13% .

368

J.A . Hauger et al /Nucl. Instr and Meth . i n Phys . Res. A 337 (1994) 362-369

This analysis was used to estimate the FWHM of the R - ADC spectrum . The expected variance without gain nonuniformity is given by Petrillo et al . [31 as : o-2(NM) =M20-2 (N) +NM 2(F- 1), where N is the mean number of primary charges deposited, M is the average gain, o, 2(NM) is the variance in the diode signal, o- 2(N) is the variance in the number of primary charges produced and F is the excess noise factor . For the diodes tested, k - 0.02 and M - 45 giving an excess noise factor F - 2.8 . Using the expected mean number of primary electron-hole pairs of 13 600 and an expected RMS fluctuation of - 1700 pairs due to the Vavilov distribution, we calculate o-(NM)-77000 electrons. Thus, the FWHM of the ADC spectrum due to the excess noise factor and fluctuations in energy deposition is - 30%. This width is dominated by the width of the Vavilov distribution, Q(N) . Adding this width in quadrature with the gain nonuniformity spread gives a FWHM - 43%, which is slightly higher than the observed widths of the ADC spectra. We have measured the influence of temperature on the breakdown voltage VBD. In Fig. 9, VBD for Diode 1 is shown to increase with temperature . Since the device gain is roughly proportional to 1/(VBD - V,,,,), the gain at a constant bias voltage will also be a function of temperature . Thus, in order to maintain a constant gain, the difference VBD - Vb,as must remain nearly constant . The multiplication of the AVD has been measured versus Vbias at a temperature of 25°C . In Fig. 10, these measurements on Diode 1 are shown superimposed with optical gain measurements performed by EG&G using optical stimulation at a wavelength of 900 nm .

Reduced Veo versus Temperature

it Y

Vap = 425 V

LI

1

CD O M

09 08

D

n

D

C

D 07

Fig.

9.

260

280

300

Temperature (K)

320

Reduced breakdown voltage versus temperature .

Diode Gain versus Bias Voltage , , . . . . ~ _ 50

40

D3 Particle Data Optical Test Data

20

rl o 200

ql@

C@

1

300 Bias Voltage (V)

4C0

Fig. 10 . Multiplication versus bias voltage . The (3 - particle gain results are comparable to the gain measurements obtained from optical input.

The measurements show comparable gains for energy deposited either by a MIP or photons. The difference may be due to space charge saturation effects and/or gain variations across the diode surface . 5. Experimental results - time resolution Our major result is the diode timing resolution . For all diodes a 450 mV LE discriminator threshold was selected to optimize dV/dt. The amplitudes of both diodes in coincidence were recorded for each event with a charge-integrating ADC; the ADC gate was 40 ns wide in time to accept the whole diode pulse. Amplitude walk correction was performed off-line . First, this analysis corrected the start signal amplitude walk using third order polynomial fits of the time measurements versus individual ADC readings . Then, this process was repeated to correct the stop signal amplitude walk . The effect of the complete correction routine can be seen in Fig. 11, where scatter plots of time versus individual ADCs are shown for each diode, both before and after corrections are made . Only minor cuts were made on the amplitudes to eliminate ADC overflows and small pulses . The resulting histogram of corrected time measurements was fitted with a Gaussian (see Fig. 12). Since the time measurements are made with two diodes, the variance of this distribution is the sum of the variances of the individual diodes . Individual time dispersions were found by timing the four diodes against one another in all combinations of pairs. Table 7 lists the results. The range of individual Q's is 65-87 ps for the four diodes tested . Fig. 12 shows a histogram taken with Diodes 1 and 2,

J.A . Hauger et al. / Nucl . Instr. and Meth . in Phys. Res. A 337 (1994) 362-369 Amplitude Walk Corrections 1600

1600

1500

1500

1 400

1400

1300

1300

1200

1200

1100

1100 500

0

U

750

1000

6. Conclusions and future prospects A set of four reach-through AVDs operated in the

proportional mode have delivered a range of timing resolutions a" = 65-87 ps when bombarded with mini-

750

500

1000

mum ionizing ß - particles to demonstrate a proof of principle. The diodes tested were 5 X 5 mm2 with k - 0 .02 and have an internal gain of - 45 . The observed signals are consistent with those measured with

1600

optical input. The time resolution measurements agree with estimates made by dividing the RMS noise by the

,400

slope of the rising edge of the pulse according to the equation 0"t,n,e-tTnolse/(dV/dt) . Significant further development of an AVD system for timing applications

1200

,000

369

(c) Diode 2 Uncorrected

should be possible . For the diodes tested, the risetime

ADC Channels Fig. 11 . Time versus ADC for diodes both before and after stewing corrections are made .

seems to be RC limited. Lower input RC should be possible. Larger AVDs can be divided into several

small pixels per chip that have lower capacitance and

should have faster rise times, offering the potential of improved time resolution . For example, AVD arrays

which had approximately equal time dispersions. The

with pixel sizes of ^ 0.1 cm 2 are technically feasible .

two dispersions contribute equally to the variance, or 2 = = 65 ps for each + Un21 So , ODt = ffD2 91 .8/ individual diode. The time resolution does not vary

These diode arrays and electronics could be packaged

a temperature range of - 20°C to 40°C, holding the

mass production of AVD arrays becomes economically

V

aDl

strongly as a function of temperature or voltage. Over

as a low mass unit to minimize scattering and backgrounds in a large detector system . Detectors of total area _ 1 m2, with - 10 5 channels, could be possible if

difference VBD - V1,as constant at 10 V, the time resolution varied only - 6% .

feasible . Progress toward these goals will require the development of high volume, low cost manufacturing

Amplitude Corrected TOF 10 3

X'= 3_07 a = 91 .8 Fsea

of AVDs and the associated integrated electronics .

Acknowledgements The authors would like to thank D.S . Kottick for

useful discussions. We would like to acknowledge the generous support of this generic research and develop-

ment work by the Heavy Ion Nuclear Physics Division of the Department of Energy under contract number DOE-FG02-88ER4041213 .

10 2 0 U

10

References

-500

0 500 1000 Time (ps) Fig. 12. Time coincidence spectrum after stewing corrections. This histogram was taken with two diodes which have approximately equal time dispersions. The two dispersions contribute equally to the variance so aD1 = aD2 = 91 .8/ = 65 ps for each individual diode.

[1] P.P. Webb, R.J . McIntyre and J. Conradi, RCA Rev. 35 (2) (1974) 234. [2] H. Spieler, IEEE Trans. Nucl . Sci . NS-29 (3) (1982) 1142 . [3] G.A . Petrillo, R.J. McIntyre, R. Lecomte, G. Lamoureux and G. Schmitt, IEEE Trans. Nuc. Sci. NS-31 (1) (1984) 417. [4] Phillips Scientific, Mahwah, NJ 07430. [5] EG&G Ortec, Oak Ridge, TN 37831. [6] LeCroy Corp ., Chestnut Ridge, NY 10977. [7] National Instruments, Austin, TX 78730.