PULSE RISE TIME FOR CHARGED PARTICLES IN p-n JUNCTIONS* H. M. Mann, J. W. Haslett,t G. P. Lietzt Electronics Division Argonne National Laboratory Argonne, Illinois The rise time of pulses from charged parti- cles entering p-n junctions is of importance in the use of these devices for fast counting. For this application coincidence resolving times of the order of 10 n6ec are presently useful. Meas- urements of rise time for alpha particles at energy 6 Mev have been made using a system with limiting rise time 7.5 nsec. Surface barrier and diffused junction detectors show a dependence of rise time t upon reverse bias V of the form t vC l/Vx where 0.4 5 x :SO.9. The rise time was determined by the lifetime of minority carriers for some detectors, and for others, by the base resistivity. The results show no limitation in application of these detectors to 10 nsec coin- cidence resolving times, since the depletion layer can be extended to reduce the effective RC time constant of the detector below 10 nsec. Introduction The pulse observed when a charged particle loses energy in a p-n junction detector is deter- mined by drift and diffusion of minority carriers. The collection processes have been largely explored using radiation at optical wavelengths for carrier generation. The possibility of changes in the charge collection time due to the types of radiation employed has been suggested by Miller, et all in an observation with Cf252 fission fragments. The observed voltage pulse rise time was 10 nsec, whereas the expected rise time was 2 nsec. The formation of a plasma by high specific ionization particles was suggested to explain the difference. Other factors which will lengthen the pulse ris'e can be grouped under "detector-circuit" RC time constant limitations. Briefly, this in- volves consideration of the series resistance of the detector, and its capacitance, together with that of the input circuitry. Raymo and Mayer (see paper, these proceedings) have developed a model, in terms of an equivalent circuit for the detector, to account for observed rise and decay times when the detector-circuit RC time constant determines the shape of the observed pulse. The present experiments were undertaken to obtain quantitative information on the pulse rise time for some detectors obtained commercially and others made at this Laboratory. It was of interest to determine any departure from the expected behavior outlined in the following section. Charge Collection The simplest picture for charge collection is the following: 1. Charge generated within the depletion region is collected in a drift time t equal to the distance traveled divided by_the average velocity. The average velocity v is CIE = UV/2d, where E is the electric intensity. Thus t = 2d2 V = Va + VO t=-.- V- + (1) where d = depletion layer thickness = mobility of the slower charge carrier V = applied reverse bias Va plus the junction potential VO at zero reverse bias 2. Charge generated outside the depletion region is collected from a distance L in a diffusion time t according to t = L2/D (2) Equation (2) defines the diffusion length L for minority carriers in terms of the minority carrier diffusion coefficient D when t = "I, the minority carrier lifetime. If charge is generated over a known fraction of the distance L, then the time for collection may be calculated from (2). Collection of charge is inherently faster when confined to the electric field within the depletion region. Both holes and electrons are collected. For p-type silicon, the distance d in microns is given approximately by (see e.g. paper by W. Brown) d = 1/3 4 'V (3) where p = resistivity in Qlcm, and V is in volts. Combining (1) and (3), t (nsec) = 2.2 P/h (4) where L has units cm2/volt - sec. Equation (4) gives the drift collection time for high energy 151
Transcript
PULSE RISE TIME FOR CHARGED PARTICLES IN p-n JUNCTIONS*
H. M. Mann, J. W. Haslett,t G. P. LietztElectronics Division
Argonne National LaboratoryArgonne, Illinois
The rise time of pulses from charged parti-cles entering p-n junctions is of importance inthe use of these devices for fast counting. Forthis application coincidence resolving times ofthe order of 10 n6ec are presently useful. Meas-urements of rise time for alpha particles atenergy 6 Mev have been made using a system withlimiting rise time 7.5 nsec. Surface barrier anddiffused junction detectors show a dependence ofrise time t upon reverse bias V of the formt vC l/Vx where 0.4 5 x :SO.9. The rise time wasdetermined by the lifetime of minority carriersfor some detectors, and for others, by the baseresistivity. The results show no limitation inapplication of these detectors to 10 nsec coin-cidence resolving times, since the depletionlayer can be extended to reduce the effective RCtime constant of the detector below 10 nsec.
Introduction
The pulse observed when a charged particleloses energy in a p-n junction detector is deter-mined by drift and diffusion of minority carriers.The collection processes have been largelyexplored using radiation at optical wavelengthsfor carrier generation. The possibility ofchanges in the charge collection time due to thetypes of radiation employed has been suggested byMiller, et all in an observation with Cf252fission fragments. The observed voltage pulserise time was 10 nsec, whereas the expected risetime was 2 nsec. The formation of a plasma byhigh specific ionization particles was suggestedto explain the difference.
Other factors which will lengthen the pulseris'e can be grouped under "detector-circuit" RCtime constant limitations. Briefly, this in-volves consideration of the series resistance ofthe detector, and its capacitance, together withthat of the input circuitry. Raymo and Mayer(see paper, these proceedings) have developed amodel, in terms of an equivalent circuit for thedetector, to account for observed rise and decaytimes when the detector-circuit RC time constantdetermines the shape of the observed pulse.
The present experiments were undertaken toobtain quantitative information on the pulse risetime for some detectors obtained commercially andothers made at this Laboratory. It was ofinterest to determine any departure from the
expected behavior outlined in the followingsection.
Charge Collection
The simplest picture for charge collectionis the following:
1. Charge generated within the depletionregion is collected in a drift time t equal tothe distance traveled divided by_the averagevelocity. The average velocity v is CIE = UV/2d,where E is the electric intensity. Thus
t = 2d2 V = Va + VOt=-.- V- + (1)
whered = depletion layer thickness
= mobility of the slower charge carrierV = applied reverse bias Va plus the
junction potential VO at zero reversebias
2. Charge generated outside the depletionregion is collected from a distance L in adiffusion time t according to
t = L2/D (2)
Equation (2) defines the diffusion length L forminority carriers in terms of the minoritycarrier diffusion coefficient D when t = "I, theminority carrier lifetime. If charge isgenerated over a known fraction of the distanceL, then the time for collection may be calculatedfrom (2).
Collection of charge is inherently fasterwhen confined to the electric field within thedepletion region. Both holes and electrons arecollected. For p-type silicon, the distance din microns is given approximately by (see e.g.paper by W. Brown)
d = 1/3 4'V (3)
where p = resistivity in Qlcm, and V is in volts.Combining (1) and (3),
t (nsec) = 2.2 P/h (4)
where L has units cm2/volt - sec. Equation (4)gives the drift collection time for high energy
151
events as well as for any particles entering thedetector through an n-type region. In terms ofresistivity for silicon
t (nsec) = 5 x 10-3 lp (5)
which shows t C0.5 nsec for P C 100 ncm, pre-sently beyond or on the limit of experimentaldetermination in the best equipment. For P10,000 Qcm, presently under consideration for usein high energy detection, this collection time isnearly 50 nsec.
When charge is produced outside the deple-tion region, the charge collection is governed bydiffusion of minority carriers as shown in equa-tion (2). The controlling time is the larger ofeither the diffusion time tDn for electrons
2
tDn= i , Dn = 35 cm2/sec (6)Dn
with diffusion length Lp in p-type material ortDp for holes L2
tDpn
Dp = 13 cm2/sec (7)
with diffusion length Ln in n-type material. Thediffusion coefficients are for intrinsic siliconat room temperature.2
Experimental Apparatus
A block diagram of the system used for risetime measurements is shown in Fig. 1. The systemlimit of 7.5 nsec was observed using an SKL No.503 pulse generator with 0.5 nsec rise time. Acathode follower preamplifier, Fig. 2, provideda decay time constant not less than 10 times thelongest observed rise time.
The pulse rise time recorded was the timebetween 10% and 90% of maximum pulse height.These values were read from the calibrated scaleof a Tektronix Type 585 oscilloscope, adjustabledown to.10 nsec/cm. The observed rise time Tobswas corrected for the system rise time Tsystemaccording to
The -detectors examined ranged in resistiv-ity from 300 to 6000 0cm p-type and from 100 to3000 ncm n-type. They were all made from silicon.Typical data for diffused junctions are shown inFig. 3. The rise time t is clearly voltagedependent, obeying 1
where for the detectors in Fig. 3, 0.68 x0.70. For two (6R and D7a) of.the detectors,the observed rise times are apparently limited bythe detector base resistance coupled with thetotal input capacitance. This is shown, forNo. 6R (1000 0cm (p)), in Table I. For each
reverse bias, colum 1, the junction capacitanceis given in column 2. The base resistance,calculated from the base resistivity, was 8 kQand was not significantly altered over thevoltage range employed. The calculated rise timesin column 3 are simply the product of baseresistance and junction capacitance. These agreeto within 107. with the observed values, correctedfor the system rise time, shown in column 4.Similar agreement was obtained for detector D7a,also made from 1000 0cm p-type silicon.
Detector No. 179, made from 300 0cm p-typesilicon, showed rise times which agreed towithin 207. or less with the time for collectionof electrons by diffusion. The data are plottedin Fig. 1 and given in Table II. The capacitancevalues, column 2, were measured with a Tektronixtype 130 L-C meter and are accurate to within*37. Area and thickness measurements, made witha microscope (40 times magnification) areaccurate to within 2% and 4X respectively. Thealpha particle range is assumed to be 28 micronsand its penetration R into the base is 28 micronsminus the depletion layer thickness, column 3,calculated from measured capacitance.
The maximum RC time constant for thisdetector, estimated from initial resistivity, is26 nsec at 0.5 volts. The circuit external tothe detector introduced an additional 4 pf overthe device capacitance of 21 pf at 0.5 volts,increasing the detector-circuit RC time constantto 31 nsec at this bias.
The observed rise times (corrected for 7.5nsec system limit) and those calculated fordiffusion are shown in column 5.
Data on surface barriers are shown inFigures 4 and 5. These were made from n-typesilicon. Uncertainties in the measuredcapacitance limit the accuracy of the calculatedtime for collection of holes, which is estiffiatedas described earlier from the depletion layerthickness. Although further capacitance measure-ments are necessary, depletion layer thicknesseswere calculated from the data at hand, and arebelieved accurate to within tO1.. On the basisof these measurements, for detectors withresistivity 200 0cm or less, the correctedexperimental rise times agree to within 207%with the times for collection of holes bydiffusion. At higher resistivity the rise timewas limited by base resistance.
Fig. 5 demonstrates the reproducibility ofrise time measurements on nearly identicaldetectors. All of the detectors in this figurewere made from 3000 ncm material, usingtechniques developed by Blankenship at Oak RidgeNational Laboratory. The rise tii measurementswere reproducible to within *10% for the fivedetectors.
Conc lusion
Additional data are needed to correlate
152
satisfactorily the observed rise times withdetector properties when the detector-circuit RCtime constant is not a limiting factor. Thosemeasurements from a few nsec to approximately100 nsec are useful for studying collection ofcharge generated beyond the depletion region.For accurate measurement of collection timeacross the depletion region, measurements downto a few tenths of a nsec are necessary. Suchmeasurements can be made with equipment currentlyused in studies of pulses in scintillators.3,4
Limits on rise time imposed by base resis-tance and collection by diffusion can be avoidedby either extension of the depletion region, orby reduction of the thickness of the detectorbase.
Acknowledgments
We wish to acknowledge the assistance,through consultation and earlier rise time
measurements, of R. J. Epstein of this Laboratory.The preamplifier used was designed by I. S.Sherman, also of this Laboratory. The surfacebarrier detectors were made at Argonne by D. M.Sparlin of Northwestern University.
*Work performed under the auspices of theU. S. Atomic Energy Commission.
tSumner employees of ANL, 1960 .1G. L. Miller, W. L. Brown, P. F. Donovan
and I. M. Mackintosh, "Silicon p-n JunctionRadiation Detectors", BNL 4662; also IRE Trans.Nuclear Science NS-7, No. 2-3, pp. 185-189(June - Sept. 1960)
2G. W. Ludwig and R. L. Watters, Phys. Rev.101, S. 1699 (1956)
R. K. Swank, R. B. Phillips, W. L. Buck andL. J. Basile, IRE Trans. PGNS-5, No. 3, pp. 183-187 (Dec. 1958)
4Robert K. Swank and Eugene A. Mroz, Rev.Sci. Instr. 30, pp. 880-884 (Oct. 1959)
Table I. Rise Time Limited by Base Resistance. Detector: Hughes #6R.
Base Resistance = 8 ksl (approximately constant from 0 to 7 volts)
p = 1000 Qcm Area = 0 8 =n2 Thickness = 1
(1)Reverse Bias
Volts
0.71'.01.52357
(2)Capacitance
pf
6.95.54.23.62.82.01.6
(3)Rise Time, nsec
Calculated, RC Observed
55443429221613
60483024211712
Table II. Rise Time Limited by Diffusion of Electrons. Detector: Hughes #179.
Area = 1.2 m2 Thickness = .05 mm
(1)Reverse Bias
Volts
0.50.71.01.5
(2)Capacitance
pf
2119.816.814.7
(3)Depletion LayerThickness, micronssA = 2.85 x 10-16 mks
