General Characteristics of Detectors
§ Sensitivity
capability of producing an usable signal for a given type of radiation mass of the detector, noise level, …
§ Energy resolution
§ Response Function
§ Timing
§ Efficiency
§ Dead Time
Energy Resolution
E E E
FWHM
R = / = Δ /
for E = 1 MeV
NaI R ∼ 8-9 %
HpGe R ∼ 0.1 %
• Two peaks are considered as resolved when d > FWHM
• R is a function of E: it improves with higher energy (Poisson statistics)
d
E = n w, with w = average energy per ionization, n = # ionization Partial deposition of energy Full deposition of energy
E w n n
n E
E FWHM R
n
35 . 1 2
35 . 2 35
. 2
/ 35 . 2
/
2
=
=
=
=
=
=
σ σ
E Fw n
Fn E
E FWHM R
Fn
35 . 2 35
. 2
/ 35 . 2
/
2
=
=
=
=
=
σ σ
F< 1
Fano Factor
Poisson
[independent charge carriers Formation]
Not fully Poisson
( ) ( )
2det( )
2...
2
= Δ + Δ +
Δ E E E
elect F ≡ observed variance in nPoisson predicted variance
Detector Response
HpGe NaI
Eγ = 661 keV
DETECTOR response function Best Response:
f ( E , E ' ) = δ ( E − E ' )
' )
' , ( ) ' ( )
( E S E f E E dE S = ∫
Compton Edge only !
Response Time
Dead Time:
it is strongly related to the efficiency Time taken to form the signal after arrival of radiation
GOOD timing: signal quickly formed in a sharp pulse
almost vertical rising flank ⇒ precise moment in time marked by the signal Duration of the signal: No second event can be fully accepted
(insensitive detector or pile up)
Methods to estimate dead time
Methods to estimate dead time
m = true count rate
K = number o counts registered in interval T τ = dead time due to a single event
à mkτ = lost counts
à mT = true number of counts
More Difficult
only counts arriving at t > τ are recorded
Distribution of time interval
between events decaying at a rate m
Efficiency
ε π ε
ε ε
ε
4
int
int
= Ω
=
×
=
=
d
impinging events
registered events
source by
emitted events
registered events
geom
geom TOT
depends on radiation, material, …
fraction of solid angle: pure geometry
2
2 2 2
1 2
cos
d A
a d
d r dA
d
=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
+
−
=
=
Ω
∫
π θ
A a
for d >> a
MonteCarlo simulations are needed for complex geometry …
Simplified Detector Model
R=input resistance C=input capacitance+
detector capacitance + cables …
τ = RC
operation mode
for time information, high rates, …
operation mode
for energy information
tc
charge collection time ~100 ns
τ =RC
decay time
~ 50 µs
mainly due to preamplifier
Current output
τ = RC << tc
τ = RC >> tc
Ge
Vmax ~ Q
⇒ output is a string of pulses
each one resulting from interaction of single quantum of radiation
Current flowing through the load resistance R
is equal to
current flowing in detector
Little Current flowing through the load resistance R
during collection time Detector Current à
momentarily integrated on C
Preamplifier
R=input resistance C=input capacitance+
detector capacitance + cables …
τ = RC
operation mode
for time information, high rates, …
operation mode
for energy information
tc
charge collection time ~100 ns
τ =RC
decay time
~ 50 µs
Amplifier
(RC-CR shaping)
RC-integrator (low-pass filter)
) 1
( ...
/τ t out
out in
e E E
E iR E
− −
= +
=
CR-differentiator (high-pass filter)
/τ
...
t out
out in
Ee E
C E E Q
= −
+
=
for Ge
Pulse shaping (in Ge)
true pulses
from preamp
τ ~ 50µs
after shaping FET
Preamplifier :
FET (at 130 K,to minimize noise) Amplifier: CR-RC shaping circuit
pile-up energy
time
τ
τ
t
out t e
E
E = −
if C1R1=C2R2=τ
τ ~ 15 µs
τ ~ 15 µs is a good compromise between reduced pile-up and good energy resolution
(depending on large charge collection)
mV
V
