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Development of a Tabletop Setup for the Transient Current Technique Using Two Photon Absorption in Silicon Particle Detectors

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The Transient Current Technique (TCT) is widely used in the field of silicon particle detector development. So far, only laser wavelengths with a photon energy larger than or similar to the silicon band-gap (single photon absorption) were used. Recently, measurements using two photon absorption for silicon detector testing have been carried out for the first time. Excess carriers are only created at the focal point of the laser beam and thus, resolution in all three spatial directions could be achieved. The resolution perpendicular to the incident laser beam could be increased roughly by a factor of ten. First measurements using this new method were performed at the Singular Laser Facility of UPV/EHU. Following the initial success of the method, a compact Two Photon Absorption -Transient Current Technique (TPA-TCT) setup is under development. A first description of the setup and laser system is presented in this article.
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Development of a Tabletop Setup for the
Transient Current Technique Using
Two Photon Absorption in Silicon Particle Detectors
Moritz Wiehe, Marcos Fernández García, Michael Moll, Raúl Montero, F.R.Palomo, Ivan Vila,
Héctor Muñoz-Marco, Viorel Otgon, Pere Pérez-Millán
Abstract—The Transient Current Technique (TCT) is widely
used in the field of silicon particle detector development. So
far, only laser wavelengths with a photon energy larger than
or similar to the silicon band-gap (single photon absorption)
were used. Recently, measurements using two photon absorption
for silicon detector testing have been carried out for the first
time. Excess carriers are only created at the focal point of the
laser beam and thus, resolution in all three spatial directions
could be achieved. The resolution perpendicular to the incident
laser beam could be increased roughly by a factor of ten. First
measurements using this new method were performed at the
Singular Laser Facility of UPV/EHU. Following the initial success
of the method, a compact Two Photon Absorption - Transient
Current Technique (TPA-TCT) setup is under development. A
first description of the setup and laser system is presented in this
article.
Index Terms—Silicon Detector, Radiation Hardness, Two-
Photon-Absorption, Transient-Current-Technique, Femtosecond
Laser
I. INTROD UC TI ON
The Transient Current Technique (TCT) has been estab-
lished as a standard tool for the characterization of unirradiated
and irradiated silicon particle detectors [1], [2]. In laser-TCT,
laser light in the visible or near infrared range is used to
generate electron hole pairs inside the detector material. The
drift current, resulting from the movement of the generated
charge carriers in the biased silicon detector, is measured. The
light can be injected from the top or bottom of the device under
test, as well as from the edge (edge-TCT [3]). The wavelength
of the light can be tuned such that charge is created only in a
localized volume at the surface of the detector (visible light,
Manuscript submitted 21 September 2020; revised 11 November 2020
This work was performed in the framework of the RD50 collaboration
and has been partly supported by the Spanish Ministry of Economy and
Competitiveness (MINECO) under grant number FPA2013-48387-C6-1-P
and the Wolfgang Gentner Programme of the German Federal Ministry of
Education and Research (grant no. 05E15CHA).
Moritz Wiehe, Marcos Fernández García and Michael Moll are with CERN,
Route du Meyrin 285, CH-1211 Genève 23, Switzerland
Moritz Wiehe is with Albert-Ludwigs-Universität Freiburg, Physikalisches
Institut, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
Marcos Fernández García and Ivan Vila are with the Instituto de Física de
Cantabria (CSIC-UC), Avda. los Castros s/n, E-39005 Santander, Spain
Raúl Montero is with the SGIker Laser Facility, UPV/EHU, Sarriena, s/n-
48940 Leioa-Bizkaia, Spain
F.R.Palomo is with the Escuela Técnica Superior de Ingenieros, US, Avda.
de los Descubrimientos s/n, 41092, Isla de la Cartuja, Sevilla, Spain
Héctor Muñoz-Marco, Viorel Otgon and Pere Pérez-Millán are with FYLA
LASER S.L., Ronda Guglielmo Marconi 12, 46980, Paterna, Valencia, Spain
We thank Isidre Mateu for his work on the data acquisition software.
e.g. 660 nm wavelength) or along the laser beam throughout
the bulk of the device (near infrared, NIR, e.g. 1064 nm
wavelength). In any case, conventional TCT, based on single
photon absorption (SPA), results in a two dimensional spatial
resolution, since the measurement is insensitive to a change
of the position of the device under test along the beam axis.
To achieve a fully three dimensional characterization of silicon
detectors, nonlinear absorption of light can be used. The first
description of two photon absorption (TPA) can be found in
[4]. The first experimental confirmation of the process [5],
[6] was only possible, after the invention of the laser. Two
photon absorption has a large variety of applications in many
research fields and has already been used to simulate single
event upsets in electronic devices (see e.g. [7], [8]). For silicon
detector testing a wavelength of the light is chosen such that
linear absorption is negligible. In this case a single photon does
not have enough energy to create an electron hole pair and the
detector is transparent for the injected light. Only with a high
enough intensity at the focal point of the laser, charge carriers
can be created by the absorption of two photons. The focal
point of the laser can be moved inside the silicon detector re-
sulting in a three dimensional resolution. In addition, due to the
use of strong focusing optics, the beam width is significantly
smaller than in current conventional TCT setups, resulting in
an improved spatial resolution transverse to the beam prop-
agation direction. This development is especially important,
following the trend of ever thinner detectors, detectors with
implemented read-out circuitry (CMOS) and smaller read-
out electrodes and inter-pixel isolation structures. TPA-TCT
measurements at the UPV/EHU laser facility [9] have shown
the potential of this new method [10]–[12]. TPA-TCT will
prove useful in in-depth silicon sensor characterization and
will complement the existing and well established techniques
(TCT, edge-TCT). The first compact TPA-TCT setup, using a
tabletop femtosecond laser source is under development at the
Solid State Detector laboratory at CERN and is presented in
this article.
II. THEORY
In this section the mechanism of charge generation via
two-photon absorption is briefly discussed. A laser pulse
propagating through a semiconductor device will be absorbed,
depending on the material properties and wavelength of the
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laser. The change of pulse irradiance Iand phase Φalong the
propagation direction zare described by
dI(r, z, t)
dz =αI(r, z, t)β2I2(r, z, t)σexN I (r, z, t)
(1)
dΦ(r, z, t)
dz =β1I(r, z, t)γ1N(r, z, t),(2)
with rbeing the distance to the beam axis [8]. αand β2are
the linear (SPA) and non-linear (TPA) absorption coefficients.
β1and β2are proportional to the real and imaginary part
of the absorbing materials third order susceptibility χ(3).σex
and Nare the cross section for free-carrier-absorption and
the number of free charge carriers. The second term in eq. 2
describes the refraction due to free carriers. The wavelength
Fig. 1. Room temperature absorption spectrum of silicon in the visible and
near-infrared region. Data from [13].
dependent absorption spectrum of silicon is shown in fig.
1. The absorption of photons with a wavelength larger than
the silicon band-gap, Eγ(1.1µm) = hc/λ 1.12 eV,
is strongly suppressed. For light with longer wavelengths
(Eγ<1.12 eV), the first term in eq. 1 can be neglected. For
short pulses also the contribution from free-carrier absorption
can be neglected [14]. The remaining second term in eq. 1
describes the two-photon absorption process we are interested
in. The solution to this differential equation is
I(z) = I0
1 + β2I0z,(3)
which describes the depletion of the beam due to two-photon
absorption after traversing the distance z in the material with
respect to the incidence irradiance I0. The radial and time
dependence was omitted here and thus eq. 3 is not describing
the change of irradiance due to a non planar beam. Due to
the strong focusing of the laser beam to achieve two-photon
absorption, the Gaussian shape of the beam dominates the
spatial dependence of the irradiance and in fact beam depletion
due to generating charge carriers in the small volume around
the focal point can be neglected under the given experimental
conditions. The irradiance of a Gaussian beam in both space
and time (see e.g. [15]), can be written as
I(r, z, t) = Ep
τ
4ln 2
π3
2w2(z)exp 2r2
w2(z)exp 4 ln 2 t2
τ2
(4)
w(z) = w0s1 + λz
πw2
0n2
.(5)
τis the full width at half maximum (FWHM) of the beam
temporal profile. The beam radius w(z)is the two-sigma
radius of the beam intensity profile and is related to the FWHM
of the beam by w(z) = 2σ(z) = F W H M(z)/2 ln 2. The
beam radius at the waist (z= 0) is w0λ/πN A, with the
numerical aperture NA =nsin θ.nis the refractive index
of the material in which the beam propagates and θis the
opening angle of the beam with respect to the beam axis. The
numerical aperture is a constant and used to characterize the
focusing optics. Here and in the following λrefers to the laser
wavelength in vacuum. The Rayleigh length of a Gaussian
beam can be expressed as z0=πw2
0n/λ. At one Rayleigh
length away from the focal point the beam radius has increased
to w(z0) = 2w0. The Rayleigh length and the beam waist
define the volume in which charge carriers are produced and,
for a given material, solely depend on the laser wavelength
and the focusing optics. For a 1.55 µmlaser pulse in silicon,
using an objective with NA = 0.5, values of w0= 1 µm
and z0= 6.9µmcan be achieved. The energy per pulse Ep
is obtained by integrating the irradiance over time and polar
coordinates:
Ep=Z
−∞ Z2π
0Z
0
I(r, z, t)rdr dφ dt (6)
The charge carrier density due to two-photon absorption,
described by the second term of eq. 1, is [8]
dn(r, z, t)
dt =β2
2~ωI2(r, z, t).(7)
The factor of two in the denominator accounts for the fact that
two photons need to be absorbed for one electron-hole pair.
Integrating this equation over time results in the charge carrier
density
ntpa(r, z) = E2
pβ24 ln 2
τ~ω π 5
2w4(z)ln 4 exp 4r2
w2(z),(8)
with ω= 2πc/λ. The charge carrier density is shown as a
function of the distance to the beam axis rand longitudinal
distance from the focal point zin fig. 2. The used beam
parameters are shown in the figure. One can see that charge
carriers are only created in close vicinity to the focal point.
Since absorption is negligible at some distance from the focus,
the volume in which charge is created can be moved arbitrarily
inside the device under test. The spatial resolution using this
method is largest in the direction perpendicular to the beam
axis. Often it is desirable to measure the electric field profile as
a function of depth inside the silicon bulk. To exploit the high
resolution perpendicular to the beam it is possible to inject the
light from the edge of a device (edge-TCT configuration). Us-
ing TPA-TCT this approach has the limitation that, especially
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for thin devices, the beam can be clipped at the top or bottom
surfaces due to the large numerical aperture. For example, as
follows from eq. 5 for the given beam parameters, the beam
diameter is as large as 2w= 87 µmfor a penetration depth of
z= 300 µm. Since both visible and infrared light are reflected
on metallic surfaces, the sensor area where the beam enters the
silicon has to be free of metallic structures for SPA- and TPA-
TCT. Metallic structures on the sensor surfaces, especially
on the back side, can reflect the beam back into the active
volume and result in artifacts in the measurement. In SPA-
TCT measurements the reflected beam will inevitably lead to
additional charge carriers. In TPA-TCT this effect, although
still possible, is reduced because only focused reflections
lead to unwanted absorption of light. Diffuse scattering or a
divergent reflection will not lead to the creation of additional
charge carriers.
Fig. 2. Density of charge carriers created by TPA in silicon, calculated with
eq. 8. The vertical axis is parallel to the beam propagation direction with
(z= 0) at the position of the focal point. A value of β2= 1.5 cm/GW
[16] was used for the calculation.
The total number of created charge carriers is obtained from
integrating the charge carrier density over the full volume:
Ntpa =ZV
ntpa(r, z)dV =E2
p2ln 4
4~π.(9)
Inserting values of Ep= 50 pJ,τ= 60 fs and β2=
1.5 cm/GW [16] yields a value of Ntpa = 11 ·106. In
a volume of approximately V=4
3πw2
0z030 µm3, this
corresponds to an average charge carrier density of about
neh = 4 ·1017 cm3.
For irradiated detectors the SPA contribution to the signal is
not negligible anymore. The ratio of the TPA signal (I2) to
the transient SPA contribution (I) increases linearly with the
pulse irradiance. To increase the TPA/SPA ratio, it is therefore
desirable to use ultra-short laser pulses. The lower limit of the
pulse duration is given by dispersion, as is described in the
next section. The total pulse energy on the other hand can
only be increased up to an upper limit due to the threshold
for plasma creation [17].
A. Dispersion in Silicon
The pulse temporal width is restricted by dispersion, which
is very significant if the pulse is too short. In fig. 3 the pulse
width τout after passing through 300 µmof silicon is shown
as a function of the initial pulse width τin.τin and τout are
the FWHM of the pulse temporal profile. Dispersion effects
are negligible for initial pulses longer than 60 fs but lead to
a significant elongation of the pulses at shorter initial pulse
widths. The reason for this is that shorter pulses have a larger
bandwidth and are therefore more affected by dispersion. The
effect of dispersion on the pulse width can be calculated with
[18]
τout =τins1 + 16(ln 2)2GDD2
τ4
in
.(10)
GDD is the group delay dispersion, which is calculated for
a material with thickness Laccording to GDD =GV D ·L.
The group velocity dispersion GV D can be calculated with
GV D =λ3
2πc22n
∂λ2,(11)
where the value for 2n/∂λ2can be obtained using the
Sellmeier equation
n(λ) = v
u
u
t1 +
3
X
i=1
Aiλ2
λ2B2
i
.(12)
The parameters Aiand Bifor silicon at room temperature,
taken from [19], result in a value of GV D = 1119.4 fs2/mm
for a wavelength of 1.55 µm.
Fig. 3. Pulse length τout of a 1550nm laser pulse after traveling through
300 µmsilicon as a function of initial pulse length τin.
B. Elongation of a Laser Beam in Silicon
The position of the crossing point of two light rays, that
enter a medium at a certain angle, depends on the refractive
index of the medium. As a consequence, a laser beam will
appear to be elongated if traveling through a medium with
higher refractive index. The Rayleigh length z0of the beam
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spot is different in silicon and air. Following from Snell’s law
and the definition of the numerical aperture of a microscope
objective NA =nsin θ, the distance from the surface of the
material with refractive index nto the focal point z0of a
focused laser beam inside the material is
z0=zrn2NA2
1NA2.(13)
zis the respective distance for n= 1. An equivalent term can
be derived directly from Snell’s law and the relation of the
opening angle, the beam radius and Rayleigh-length tan θ0=
w0/z0, with z0=πnw2
0:
z0=zsz0πn3
z0πn λn2+λ(14)
z0is the Rayleigh length in silicon. The meaning of variables z
and z0is depicted in figure 4. It is also important to realize that
the position of the focal point in the laboratory frame changes,
if the surface of the silicon sensor is moved. A movement
of the silicon surface in the direction of the beam by z
results in a movement of the focal point by Fin the opposite
direction, so that the distance of the sensor surface to the focal
point changes by z0= ∆z+ ∆F. Either way, the scaling
factor is identical so that z0/z=z0/z. For example, for
silicon at room temperature (n= 3.4757 for T= 293 K [20]),
λ= 1.55 µmand a microscope objective with NA = 0.5the
elongation factor is z0/z = 3.97. For focusing optics with
smaller numerical aperture the scaling factor converges to the
material’s refractive index. In TPA-TCT measurements, the
position of the focal point inside the silicon sensor is important
and the elongation factor has to be taken into account.
Fig. 4. Elongation of a laser beam, when entering from air into a material
with refractive index n. A movement of the sensor surface by zresults in a
shift of the focal point in the opposite direction leading to a total displacement
of z0.
III. EXPERIMENTAL SET UP
A. Laser System
The most important difference to a conventional TCT setup
is the laser source. In TCT setups, based on single photon
absorption, usually laser wavelengths in the visible spectrum
or near-infrared are used. To exploit the process of two photon
absorption, a laser with a photon energy significantly below
the band-gap energy in silicon has to be used. For the setup
described here a wavelength of 1550 nm was chosen. The laser
LFC1500X was custom developed by the company Fyla [21]
to meet the requirements for TPA-TCT. LFC1500X is a laser
system that allows for full pulse control and measurement.
The system is contained in three different modules: The laser
module, pulse management module and a pulse compressor.
The laser module contains the oscillator, amplifiers and a
pulse picker. The pulse frequency can be changed from about
6.8 MHz down to single shot. A TTL trigger output is obtained
directly from the photo detected signal of the laser oscillator
and can be used to acquire information about the frequency
in real time. From the laser module the pulse is fed into
the pulse management module with an optical fiber. From
here, the beam is propagating in free space. In the pulse
management module the optical output pulse energy can be
adjusted from 10 nJ down to 100 pJ, using a variable neutral
density filter. A direct photo detected signal, obtained by
redirecting part of the beam to an InGaAs-photo-sensor, can be
used to relate the peak-to-peak voltage with the pulse energy.
This reference signal is used to correct measurements for
fluctuations in the output power of the laser on a pulse-to-
pulse basis. The laser management module also contains the
automatic output shutter. The laser system is controlled with a
LabView software, which was integrated into a common data-
acquisition software.
The figures 5 and 6 show the optical spectrum of the laser
and an intensity autocorrelation measurement, respectively.
The spectrum shows a pronounced peak around 1550 nm
with a central bandwidth of 40 nm. The tails of the
spectrum range from about 1500 to 1750 nm. The intensity
autocorrelation trace has a width of 120 fs, which corresponds
to about 85 fs laser pulse width, assuming a Gaussian pulse.
Fig. 5. Optical spectrum measured with OSA YOKOGAMA AQ-6375
(1200-2400nm) at collimated output, 2 nm resolution, LFC1500X Factory
Acceptance Test. [21]
The laser LFC1500X, which was used for the measurements
presented in this article, was a prototype, specifically designed
for the application in a TPA-TCT setup. Early measurements
showed an instability over time of the TPA signal, which
was not reflected in the SPA reference signal and was thus
difficult to correct for. The reason for the TPA-instability is
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Fig. 6. Intensity autocorrelation trace at the laser output, width 120 fs,
10 fs resolution, LFC1500X Factory Acceptance Test. [21]
believed to originate from spectral instabilities in the output
of the laser, which result in fluctuations in the pulse temporal
profile, thus affecting the two-photon absorption process. The
laser source is under development and technical improvements
are planned to address this issue. Therefore the pulse spectrum
and temporal profile are subject to change in future versions
of the laser.
B. Optical Components and Mechanics
The laser system, all optical components and a Faraday
cage, in which the device under test (DUT) is placed during
measurements, are mounted on a 2.5 m ×1 m Nexus passive
isolation optical table. For routing the laser beam to the
DUT Low Group Delay Dispersion (GDD) mirrors (Thorlabs
UM10-45C) are used. The laser beam is focused onto the
DUT with a 100x NIR Mitutoyo microscope objective (M
Plan Apo NIR 100x, NA = 0.5). For precise positioning of
the DUT and to perform spatial scans with high resolution a
Newport hexapod (HXP50HA-MECA) is used. A hexapod has
six degrees of freedom (3x translation, 3x rotation), which can
be used to ensure that the sensor has the correct orientation
with respect to the laser beam. The hexapod is able to perform
fine scans with a minimum incremental movement of 50 to
100 nm with a travel range of about 1to 2 cm. The hexapod
itself is mounted on a stack of two long-travel Newport linear
stages to be able to easily adjust the DUT position with respect
to the microscope objective prior to the start of a measurement.
The linear stages are usually not moved during a running
measurement. To facilitate correct DUT positioning a custom
microscope setup is installed: A CMOS camera with a white
light source and a laser pointer for alignment are used to create
an image, showing where the light will be injected in the DUT.
C. Sample and Data Acquisition
Two n-in-p deep diffused FZ-silicon sensors (unirradi-
ated/irradiated) from Hamamatsu Photonics were used for the
measurements presented in this article. The unirradiated sensor
(FZ200P_05_DiodeL_9) has an active thickness of 209 µm.
The second sensor has a thickness of about 120 µmand was
irradiated with neutrons to a fluence of 1.6×1016 neq/cm2.
Both sensors have an active area of 5×5 mm2. The respective
DUT is glued to a PCB which is equipped with SMA-
connectors for the bias voltage supply, read-out and optional
guard-ring connection. The glue is conductive and establishes
the back side connection. The read-out electrode and guard
ring on the front side of the sensor are connected to the PCB
with wire-bonds. A PT1000 temperature sensor is attached to
the PCB close to the DUT. The DUT signal is amplified by a
Cividec 2 GHz/40 dB amplifier and displayed on an Agilent
Technologies DSO9254A digital oscilloscope. To monitor the
power of the laser, part of the beam is directed onto a reference
diode inside the laser pulse management module. Its signal
is recorded with the DUT data and used in the analysis to
normalize the signal to account for fluctuations in the laser
output.
Fig. 7 shows a schematic view of the TPA-TCT experimental
setup. All important components of the optical and data
acquisition setup are shown. The Pulse management module
was simplified and includes only the components that are of
direct relevance to the user.
Fig. 7. Schematic view of the TPA-TCT experimental setup. The setup
consists of three main parts: (1) Fyla laser system comprised of the laser
module, pulse management module and pulse compressor, (2) Faraday cage
with DUT/amplifier and hexapod, focusing optics and microscope setup, (3)
voltage supply and data acquisition.
IV. MEA SU RE ME NT S ON A N UNI RR AD IATE D DET EC TOR
In this section first measurements with the new setup are
shown to demonstrate the feasibility of the method and the
tabletop laser system.
A. Z-Scan
One of the benefits of TPA-TCT is the true three dimen-
sional resolution for testing silicon detectors. With conven-
tional TCT with red, or near infra-red (<1200 nm) light,
it is only possible to fully resolve the device under test by
changing the illumination direction in different measurement
configurations. TPA-TCT provides resolution along the beam
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propagation direction and thus allows for a three dimensional
scan of the device in a single measurement setup. Fig. 8
shows a measurement of the signal, integrated over 10 ns, as
a function of the sensor position along the beam propagation
direction (z-axis). The DUT is a Hamamatsu Photonics deep
Fig. 8. Integrated signal in 10 ns as a function of z-position of the hexapod.
The sensor bias voltage is constant at 200 V. The z-axis is anti-parallel to
the beam propagation direction.
diffused diode. An active thickness of 209 µm[22] was
measured independently by using a capacitance-voltage scan.
The zero value on the horizontal axis is arbitrarily set to the
rising edge of the graph. The sensor is illuminated from the
top, whereas the z-value indicates the position of the motion
stage. Therefore, moving from z= 0 to higher values, the
focal point of the laser moves from the top of the device to
the back side. The width of the graph is thus a measure of
the width of the depleted region of the sensor. In this case, a
bias voltage of 200 V ensures that the sensor is fully depleted.
For every recorded waveform a baseline subtraction is done.
Except this, no background correction is performed. The signal
vanishes quickly when the focal point of the laser beam is not
anymore inside the detector. This indicates that no contribution
of single photon absorption is measured. It is important to
note, that no resolution could be obtained in this way for
conventional TCT. For a point like charge generation at the
focal point a box-function would be expected. The width of
the rising and falling edge are a result of the extended volume,
in which charge carriers are generated, due to the Gaussian
shape of the beam. The data is fitted with a volume integral
of the charge carrier distribution:
Nd
tpa(z)=2πZz
zdZ
0
ntpa(r, z0)rdr dz0
=E2
pn β2ln 4
4c~π3
2τtan1dz
z0+ tan1z
z0 (15)
The integration volume extends into infinity perpendicular to
the beam and has a thickness of din the direction of the
beam. Since the charge is measured only in arbitrary units, the
absolute scale of the function is absorbed by a single prefactor.
An absolute measurement of the collected charge would allow
to constrain the factor E2
pβ2, of which the pulse energy Ep
and the pulse duration τcan be measured independently. The
measured hexapod z-position, shown on the horizontal axis, is
multiplied with the scaling factor for the effect of refraction
according to eq. 14, prior to evaluating the fit function. The
fit parameters dand z0describe the thickness of the sensor
and the Rayleigh length of the beam in silicon. The measured
thickness of the device of d= 207 µmis close to the expected
value of 209 µm, obtained from a CV-measurement. The
Rayleigh length z0= 15.7µmis larger than expected. For
a numerical aperture of NA = 0.5a Rayleigh length in the
order of 7µmis expected. The discrepancy is further discussed
in the following section.
B. Knife-edge Scan
The knife-edge technique is a common method for mea-
suring the profile of a laser beam. A device (’knife’) is used
that can be moved across the laser beam to partially block it.
The intensity of the beam is measured while moving the knife
across the beam. The measured intensity as a function of the
knife position can then be used to calculate the beam intensity
profile. The spatial resolution of the TPA-TCT setup is given
by the size of the volume in which charge is generated. To
measure the resolution a knife-edge scan was carried out on a
Hamamatsu Photonics deep diffused diode at a constant bias
voltage of 300 V. The sensor sample features a metal cover
directly on top of the active volume with a cut-out to be able
to perform laser-TCT measurements. This metal cover is used
as a knife-edge to partially block the laser beam. While this
method is easy to set up, since no additional materials are
required, spatial inhomogeneities of the detector, a slight tilt
of the detector with respect to the beam and the unknown
thickness of the metal cover could have negative effects on
the measurement. Fig. 9 shows a measurement of the sensor
signal as a function of x- and z-coordinates of the hexapod.
Incremental steps of 200 nm and 1µmwere used in x- and
z-direction, respectively. The z-axis of the hexapod is anti-
parallel to the beam propagation direction. In the right half
of the figure, at x > 1.13 mm, the beam is blocked by the
metal cover of the active area. In the top left quadrant of
the figure (maximum signal) the focal point of the beam is
fully inside the silicon sensor. In the bottom left quadrant the
focal point is mostly outside of (above) the sensor. Due to the
strong focusing optics, the beam widens significantly when
moving away from the focal point. Therefore the resolution
perpendicular to the beam direction depends on where it is
measured along the beam. Away from the focal point in z-
direction, the metal-silicon transition in x-direction is less well
resolved, resulting in the cone in the top half of the figure.
To obtain the beam radius w(z)as a function of the distance
along the beam axis z, for every hexapod position in z, the
measured charge is fitted with a two dimensional integral of the
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Fig. 9. Integrated signal in 20 ns as a function of x- and z-position. The
z-axis is anti-parallel to the beam propagation direction.
charge carrier distribution, replacing r=px2+y2in eq. 8:
Zx
−∞ Z
−∞
ntpa(x0, y, z)dy dx0
=E2
pβ2λln 2
4ln 4 c~π5
2τ w2(z)1 + erf 2x
w(z) (16)
The input variable x is corrected for the offset of the hexapod
stage and, as before, the prefactor is absorbed in an arbitrary
scaling parameter. Remaining as a fit parameter is the beam
radius w. One such fit is shown as an example in fig. 10. The
Fig. 10. Integrated signal in 20ns as a function of the x-position of the
hexapod for z= 0.7 mm.
obtained beam radius as a function of zis shown in fig. 11.
The figure shows the waist of the beam and the larger beam
Fig. 11. Beam radius as a function of z-position of the hexapod. The data
and fit are restricted to measurements around the beam waist. Obtained fit
parameters w0and z0are shown.
radius before and after the focal point. For low values of z the
focal point is barely inside the active volume, resulting in a
low signal amplitude and therefore a slightly larger fluctuation
of the obtained value of the beam radius. The beam profile is
fitted with the function
w(z) = w0s1 + z
z02
,(17)
to obtain the beam parameters z0and w0. The input variable
zto the fit function is corrected for the hexapod offset and
multiplied by the scaling factor for correcting the effect of
refraction, according to eq. 14. The resulting beam parameters
are w0= 1.7µmand z0= 17.8µm. These values correspond
to a numerical aperture of about 0.3. The nominal numerical
aperture of the focusing objective is 0.5. The discrepancy of
the measured beam parameters near the focal point to the
nominal numerical aperture can be a result of insufficient
coupling of the beam to the objective (clipped beam, non-
parallel beam) or of non-Gaussian components in the output
of the laser. Further away from the focal point in the range of
0.71 mm < z < 0.75 mm, which is not shown in the figure,
a linear increase of the beam radius with z is observed. The
slope of this linear increase indicates a value of NA = 0.5
which is in agreement with the expected value. The quality of
the focusing depends largely on the optical setup and will be
further improved.
C. Intensity Scan
The amount of charge generated by two photon absorption
depends quadratically on the beam irradiance (eq. 7). Fig. 12
shows a measurement of the integrated signal as a function of
the energy per laser pulse (laser intensity). The pulse energy
is varied by changing the orientation of a neutral density
filter inside the laser power management module. For this
measurement the sensor was biased at 200 V. The focal point
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remained at a constant position in the center of the detector.
The measured values are fitted with the function Q=p0I2.
The data is compatible with a purely quadratic function,
indicating that no contribution from single photon absorption
can be observed. The last three data points at high intensities
were excluded from the fit because for these measurements
an increase of the charge collection time was observed. The
collection time should only depend on the electric field inside
the device and therefore stay constant. An increase of the
collection time hints at the formation of an electron-hole
plasma inside the sensor. This impacts the collection time and
can also alter the amount of induced charge [17].
Fig. 12. Integrated signal as a function of the laser pulse energy. The energy is
varied with a neutral density filter inside the laser power management module.
The data was fitted with a quadratic function. Three data points at high
energies were excluded from the fit due to electron-hole-plasma formation.
V. ME AS UR EM EN TS O N AN IR RA DI ATED DE TE CTOR
A. Intensity Scan
Irradiation introduces shallow and deep level defects in the
band gap of silicon, which lead to absorption of sub-band
gap photons through non-TPA processes. Especially deep level
defects enhance the possibility of single-photon absorption and
resonant two-photon absorption. As presented in the previous
sections an intensity scan of an unirradiated sensor shows a
purely quadratic dependence of the collected charge on the
laser power and in addition no signal can be measured if the
focal point is not inside the active volume of the detector
although the (unfocused) beam still traverses the sensor. This
changes in the case of an irradiated detector. Fig. 13 shows
an intensity scan of an irradiated detector for two different
positions of the focal point. The detector is a FZ-silicon
sensor with a thickness of about 120 µm. The sensor was
irradiated with neutrons to a fluence of 1.6×1016 neq/cm2.
When this measurement was taken the cooling system was
not yet in place, therefore the sensor was kept at a rather
low bias voltage of 20 V at room temperature. One intensity
scan was performed with the focal point mostly outside of
the silicon sensor (red markers) and repeated with the focal
point inside the silicon (black markers). Both data sets are
fitted with a second degree polynomial: Q=p0I+p1I2. The
measurement with the focal point outside the silicon results
in a mostly linear curve, which is expected for defect induced
single-photon absorption. The non-zero quadratic contribution
can be explained by the fact that the sensor position differs
by only 30 µmto the measurement with the focal point inside
the active volume. Therefore it is assumed that part of the
focal point is still inside the sensor and produces TPA. The
scan at which the focal point is fully contained inside the
sensor (black markers) shows a stronger quadratic dependence
on the laser power because the contribution of TPA to the total
signal is larger. The linear contribution is unchanged, which
is also expected because the defect-induced SPA contribution
is independent from the position of the focal point.
Fig. 13. Integrated signal as a function of the laser pulse energy for two
different positions of the focal point. The focal point is located outside (red)
and inside (black) of the sensor. Both data sets are fitted with a second degree
polynomial (p0: linear term, p1: quadratic term). The sensor was irradiated
with neutrons to a fluence of 1.6×1016 neq/cm2and biased with 20 V at
room temperature.
B. Z-Scan
An additional z-scan was performed on the same sample
(FZ-silicon, 120 µmthickness, neutron irradiated to 1.6×
1016 neq/cm2) at a constant laser power, again at a bias voltage
of 20 V. Fig. 14 shows a comparison of the waveforms
obtained at different positions of the focal point. The red line
shows the signal when the focal point is outside the sensor and
thus is produced by SPA due to irradiation induced defects.
The black line shows the signal with the focal point inside the
sensor and is thus produced by the constant SPA contribution
and the additional TPA at the focal point. The difference of
the two signals, which is therefore assumed to be the TPA
contribution to the overall signal, is shown as a dotted line.
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Fig. 14. Waveform for two different focal point positions and their difference.
The red/black lines show the recorded waveform with the focal point out-
side/inside the active volume. The dotted line shows the difference of the two.
When the focal point is outside of the sensor (red line) the beam still traverses
the sensor. The sensor was irradiated with neutrons to 1.6×1016 neq/cm2
and biased at 20 V during the measurement.
Fig. 15 shows the integrated TPA signal, obtained as the
difference of the total signal and the SPA contribution mea-
sured outside the active volume (red curve in fig. 14). The
horizontal axis shows the position along the z-axis of the
hexapod and is thus not corrected for refraction. Lower z-
values correspond to the front side of the device. When the
focal point is outside of the sensor, no signal is visible due
to the subtraction of the SPA contribution. Moving the sensor
through the focal point one can see that the highest TPA signal
is collected near the back side of the sensor. This is expected
due to the formation of a double junction in this device due
to irradiation. With measuring the SPA contribution with the
focal point outside of the sensor and subtracting this signal
from the total signal, when the focal point is inside the sensor,
it is possible to remove the SPA offset from the data and
perform TPA-measurements on irradiated devices.
VI. SUMMARY
Two Photon Absorption - TCT has proven to be a very
precise characterization tool for silicon particle detectors. In
the future it will complement the existing methods for sensor
characterization. In this article the first development of a
tabletop TPA-TCT setup was presented. Measurements on an
unirradiated and an irradiated detector as well as a preliminary
characterization of the spatial resolution of the setup were
presented. First results obtained with the TPA-TCT are very
promising and show that the technique is suitable to perform
high resolution measurements of unirradiated and irradiated
samples. Work to improve the resolution and stability of the
setup is ongoing.
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Fig. 15. Integrated TPA signal in 15 ns as a function of z-position of
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irradiated with neutrons to 1.6×1016 neq/cm2. The z-axis is anti-parallel to
the beam propagation direction. The lower z-values correspond to the front
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