# photoelectric detectors

```PHOTODETECTORS
References
Hans Kuzmany : Solid State Spectroscopy
(Springer) Chap 5
S.M. Sze
Physics of semiconductor devices
(Wiley) Chap 13
Detection of Electromagnetic
•Signal and Noise
•Photomultipliers
•Photoelectric Detectors
Signal and Noise for photon counting
Scattering experiment
S= signal
N = noise
B = background
D = dark level
Low signal/noise ratio
23/4 = 6.5
Origin of Noise
at detector
Signal and Noise
Scattering
Probability = q =1-p
Signal = photon absorption
Absorption
Probability of absorption,
i.e. contribution to signal= p
For coins p=q=1/2
For photons……. p <<q
Low probability event
Signal and Noise
Signal = photon absorption
n incident photons
Probability of 1 photon absorption = p
Probability of no absorption q =1-p
Or no contribution to signal
Probability absorption of k photons
n!
P (k ,n , p, q ) 
p k q n k
k ! (n  k )!
Binomial distribution
Signal and Noise
n!
P (k ,n , p, q ) 
p k q n k
k ! (n  k )!
For photons……. p <<q
Poisson distribution
(np )k np
P (k ,n ) 
e
k!
np = expected value
0.14
n = 200
p = 0.05
k = 10
0.12
0.10
Pnk
0.08
0.06
0.04
k = mean value of k
0.02
(np )
k   kP (k ,n )dk  
e np dk
(k  1)!
k
0.00
-0.02
0
5
10
15
20
K
25
30
35
40
45
For large n, np  k
If I have 200 photons every sec, for every second the absorbed photon number might be
7,9,10,15, depending on the probability distribution, but on average I have 10 photons
absorbed per sec.
So <k> is the average magnitude of the signal
The noise intensity is defined as the variance
 of the Poisson distribution
 
k
So the signal is on average 10  
By increasing the measuring time (or equivalently increasing
the number of incident photons ) the magnitude increases
linearly, and the noise increases as square root, so the signal
to noise ration gets better as T
PHOTOMULTIPLIERS
Elements:
e-
Photocathode
Dynodes
Anode
Operation:
•
•
•
•
•
Photon in Photocathode
e- emission
e- on dynode
Secondary e- emission
Current on Anode
Photocathode
animation
http://micro.magnet.fsu.edu/primer/java/digitalimaging/photomultiplier/sideonpmt/index.html
Photocathode
Material to emit electrons by photoelectric effect
Key property: low work function to allow extraction of e-
The photon absorption depend on the material
Hence the photocathodes are sensible to
some part of the light spectrum
ne

nph

Quantum efficiency
Ic= current at photocathode
P = incident light power
Typical 80 mA/W
Ic e  
E   

P

A 


W 
Dark current
Due to thermal emission of electrons
J T   M A0T e
2
A0 
4mk e
2
h
3
 1.2x106 Am-2K -2
20
W
KT
1.5 eV
1.6 eV
1.7 eV
1.8 eV
15
e/s*cm2
M = material dependent factor (0.5)
T = temperature
W = material work function (1.5-3 eV)

10
5
0
200
250
300
T (K)
J(T) increases rapidly with T,
so photocathode needs to be cooled
if you need to observe few e/s
350
400
Dynodes
The dynodes work by employing
secondary electron emission (SEE)
SEE:
When a primary beam hits a surface,
then it generates electrons that are either emitted either travel
into the solid and generate more electrons
Secondary Electron Eemission
Physical principle: ionization of a solid (atom) by
an electron with kinetic energy E0
E0 =[1 106 eV]
Each scattering event might generate one or more e-
Is
 
I0
Secondary Electron Yield
I0 = incident beam current
IS = secondary current
(I emitted from surface)
Secondary Electron Eemission
Contributions
E0 =[1 106 eV]
Ie = elastically scattered eIr = rediffused eIts = true secondary e-
  e   r  ts
I0 = incident beam current
IS = secondary current
(I emitted from surface)
Collect the current by applying a voltage V
so that only e- with EK  E = eV arrives at detector
The signal is the sum (integral) over the electrons up to the maximum EK
Is (E )
S (E 0 , E ) 

I0
Ep
E N (E )d (E )
0
I0
Usually we are interested in the value of S for a range of energy
and to get N(E) we must differentiate the signal
dS (E 0 , E ) d

 N (E )
dE
dE
N(E)
E0
E0 + ΔE
Electron Energy (eV)
For dynodes all the current originated from secondary emission is used
Is
 
I0
The number of dynodes n provides the
multiplication factor G (gain) of the photomultiplier
G  n
Typical values
 = 5, n = 10
G = 510  107
G depends on the voltage because the voltage
sets the primary energy of the incident egenerated in the dynode
PHOTOELECTRIC DETECTORS
Slab of semiconductor between
two electrodes
Generation of carriers: intrinsic
  q nn  p p 
cutoff
Generation of carriers: extrinsic
The cutoff is determined by the energy
of donor and acceptor states
 = mobility
n,p = concentration
q = charge
hc
1.24


( m)
E g E g (eV )
Performance detemined by:
gain, response time, sensitivity
PHOTOELECTRIC DETECTORS
Principle of operation
n0 = density of carriers generated by a photon flux at t=0
Recombination processes
n(t) = density of carriers at time t
n (t )  n0e
t


1/ = recombination rate
Steady, uniform photon flux on A=wL
P = optical power
Total number of photons impinging on the surface/unit time is P/h
At steady state, the carrier generation rate is equal to recombination rate
Generation rate
P

G  h
WLD
 = quantum efficiency
The current due to photon absorbption
I p WD WDqnnE
 P  n E 
I p  q 


 h  L 
Defining primary photocurrent as
Ip
n E

gain 

 
I ph
L
tr
nE  vd
The gain of the device depends on
Carrier
Transit
time
P
n  h
WLD

I ph
 P 
 q 

 h 
PHOTODIODES
Depleted semiconductor
High E to separate photogenerated e--h pairs
Depletion region small to reduce tr
Depletion region large to increase 
Reverse bias to reduce tr
I ph
 P 
 q 

 h 
 I ph
  
 q
  P 
 /
  h 

 depends on absorption coefficient
R
I ph
P

q
h
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