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Some considerations on charge collection time in solid state detectors
NUCLEAR
INSTRUMENTS
AND METHODS
29 (i964) I73-I74; ©
NORTH-HOLLAND
PUBLISHING
CO.
SOME CONSIDERATIONS ON CHARGE COLLECTION TIME IN SOLID STATE DETECTORS A. A L B E R I G I Q U A R A N T A , M. M A R T I N I , G. O T T A V I A N I and G. Z A N A R I N I
LN.F.N. Centro Elettronica, Istituto di Fisica dell'UniversitY, Bologna Received 16 May 1964
Since solid state detectors first appeared, attempts have been made to calculate the collection time of carriers generated in the depletion layer. The calculations were experimentally tested measuring the rise time of the voltage pulse induced by the carriers on the capacitance of the detector and associated electronic circuitry1-3). However, the theoretical and experimental data generally agree only roughly, owing to the simplified theoretical treatment and to the systematic errors introduced by the electronic equipment. Therefore we found it interesting to perform an accurate calculation following the line of research work by Tove and Falk 4) and taking into account some remarks by Gatti et al. 5) The calculation we performed, which will be the subject of a detailed publication, gives the following expressions for the voltage pulses re(t), Vh(t) on the detector leads produced by the electrons and the holes: ve(t) _ l x w [ 1 - ( 1 - x R l 2] 2 XR XW/ J "
Q/Cto t
[.p8exp (--t/pa)_T__pe-T exp(--t/T) + 1]
Vh(t) Q/Ctot +
(1)
_ _ l X w [ ( 1 3peexp(--t/3pe)--Texp(--t/T).]+ 2 XR 3pc-- T
Xw/
(0
(,_ Xw )
RANGEOFIONIZINGPARTICLE --P-SID~f N-SIDE
x.o
*,x~
x=xw Fig.
x ]
In the derivation of pulse shape formulas several assumptions have to be made, which fix the degree of approximation of the results. These assumptions are given below: a) the mobilities of electrons and holes are independent of electric field, b) the detector is n-type and the particles enter the detector on the p-side, c) during the collection time no charge is lost by recombination or trapping, d) #e ~ 3 Ph, e) the energy lost per unit lenght is constant, f) the original charge distribution is not disturbed by diffusion, g) the motions of holes and electrons formed in the p-region are neglected.
T + 3pe (2)
Xw - - x R
where: v~(t) = voltage pulse induced by the electrons; Vh(t) = voltage pulse induced by the holes; Q = charge released by the incident particles; C t o t : detector capacitance plus amplifier input capacitance; x w = depletion layer width (fig. 1); x R = incident particle range (fig. 1); p = silicon resistivity; e = silicon dielectric constant; T = integral time constant of electronic circuitry; po = mobility of electrons; Ph = mobility of holes.
Fig. 2
173
174
A. ALBERIGI QUARANTA et al.
The voltage pulse rise time (which can be calculated from the preceding formulae) depends on both the charge collection time and the integral time constant of the associated electronic circuitry; therefore, if we want to experimentally measure the charge collection time from the voltage pulse rise time, the integral time constant has to be much smaller than the charge collection time itself. Fig. 2 shows the voltage pulse obtained exposing to ~-particles from Pu 238 a surface barrier detector* whose resistivity was 1700 ohm. cm, thickness 400 -- 430 # and bias voltage 180 V. The photo was taken on the screen of a 661 Tek sampling 'scope triggered by a suitable electronic chain6). The pulse rise time, as can be seen in fig. 2, is 5 -- 6 nsec, this value agrees well with the corresponding * Supplied by CISE, Centro Informazioni Studi Esperienze, Milano, Italy.
theoretical expectation (5 nsec) obtained by means of the preceding formulae. The signal "dribble u p " is probably a result 7) of reduced high frequency response due to conductor skin effect resistence of a cable used in electronic equipment6). Using (1) and (2) it is also possible to evaluate how the pulse rise time varies in function of the particle incidence angle, a fact which we are now testing experimentally. References 1) C. T. Raymo, J. W. Mayer, I.R.E. Trans. N.S., 8 (1961) 157. 2) G. L. Miller, BNL Report 4662 (1960). 3) W. L. Brown, I.R.E. Trans. N.S., 8 (1961) 2. 4) p. A. Tove and K. Falk, Nucl. Instr. and Meth., 12 (1961) 278. 5) G. Cavalleri, G. Fabri, E. Gatti and V. Svelto, Nucl. Instr. and Meth., 21 0963) 177. 6) M. Martini and G. Zanarini, Nucl. Instr. and Meth. (to be published). 7) Tektronix, Type 4SI Plug-in Instruction Manual, p. 2-17.
INSTRUMENTS
AND METHODS
29 (i964) I73-I74; ©
NORTH-HOLLAND
PUBLISHING
CO.
SOME CONSIDERATIONS ON CHARGE COLLECTION TIME IN SOLID STATE DETECTORS A. A L B E R I G I Q U A R A N T A , M. M A R T I N I , G. O T T A V I A N I and G. Z A N A R I N I
LN.F.N. Centro Elettronica, Istituto di Fisica dell'UniversitY, Bologna Received 16 May 1964
Since solid state detectors first appeared, attempts have been made to calculate the collection time of carriers generated in the depletion layer. The calculations were experimentally tested measuring the rise time of the voltage pulse induced by the carriers on the capacitance of the detector and associated electronic circuitry1-3). However, the theoretical and experimental data generally agree only roughly, owing to the simplified theoretical treatment and to the systematic errors introduced by the electronic equipment. Therefore we found it interesting to perform an accurate calculation following the line of research work by Tove and Falk 4) and taking into account some remarks by Gatti et al. 5) The calculation we performed, which will be the subject of a detailed publication, gives the following expressions for the voltage pulses re(t), Vh(t) on the detector leads produced by the electrons and the holes: ve(t) _ l x w [ 1 - ( 1 - x R l 2] 2 XR XW/ J "
Q/Cto t
[.p8exp (--t/pa)_T__pe-T exp(--t/T) + 1]
Vh(t) Q/Ctot +
(1)
_ _ l X w [ ( 1 3peexp(--t/3pe)--Texp(--t/T).]+ 2 XR 3pc-- T
Xw/
(0
(,_ Xw )
RANGEOFIONIZINGPARTICLE --P-SID~f N-SIDE
x.o
*,x~
x=xw Fig.
x ]
In the derivation of pulse shape formulas several assumptions have to be made, which fix the degree of approximation of the results. These assumptions are given below: a) the mobilities of electrons and holes are independent of electric field, b) the detector is n-type and the particles enter the detector on the p-side, c) during the collection time no charge is lost by recombination or trapping, d) #e ~ 3 Ph, e) the energy lost per unit lenght is constant, f) the original charge distribution is not disturbed by diffusion, g) the motions of holes and electrons formed in the p-region are neglected.
T + 3pe (2)
Xw - - x R
where: v~(t) = voltage pulse induced by the electrons; Vh(t) = voltage pulse induced by the holes; Q = charge released by the incident particles; C t o t : detector capacitance plus amplifier input capacitance; x w = depletion layer width (fig. 1); x R = incident particle range (fig. 1); p = silicon resistivity; e = silicon dielectric constant; T = integral time constant of electronic circuitry; po = mobility of electrons; Ph = mobility of holes.
Fig. 2
173
174
A. ALBERIGI QUARANTA et al.
The voltage pulse rise time (which can be calculated from the preceding formulae) depends on both the charge collection time and the integral time constant of the associated electronic circuitry; therefore, if we want to experimentally measure the charge collection time from the voltage pulse rise time, the integral time constant has to be much smaller than the charge collection time itself. Fig. 2 shows the voltage pulse obtained exposing to ~-particles from Pu 238 a surface barrier detector* whose resistivity was 1700 ohm. cm, thickness 400 -- 430 # and bias voltage 180 V. The photo was taken on the screen of a 661 Tek sampling 'scope triggered by a suitable electronic chain6). The pulse rise time, as can be seen in fig. 2, is 5 -- 6 nsec, this value agrees well with the corresponding * Supplied by CISE, Centro Informazioni Studi Esperienze, Milano, Italy.
theoretical expectation (5 nsec) obtained by means of the preceding formulae. The signal "dribble u p " is probably a result 7) of reduced high frequency response due to conductor skin effect resistence of a cable used in electronic equipment6). Using (1) and (2) it is also possible to evaluate how the pulse rise time varies in function of the particle incidence angle, a fact which we are now testing experimentally. References 1) C. T. Raymo, J. W. Mayer, I.R.E. Trans. N.S., 8 (1961) 157. 2) G. L. Miller, BNL Report 4662 (1960). 3) W. L. Brown, I.R.E. Trans. N.S., 8 (1961) 2. 4) p. A. Tove and K. Falk, Nucl. Instr. and Meth., 12 (1961) 278. 5) G. Cavalleri, G. Fabri, E. Gatti and V. Svelto, Nucl. Instr. and Meth., 21 0963) 177. 6) M. Martini and G. Zanarini, Nucl. Instr. and Meth. (to be published). 7) Tektronix, Type 4SI Plug-in Instruction Manual, p. 2-17.