Marco Ferrero
With
Nicolo’ Cartiglia, Francesca Cenna, Fabio Ravera,
Universita’ degli Studi di Torino & INFN
1
Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
• THEORY OF EXTRAPOLATION OF DOPING PROFILE
FROM CAPACITANCE-VOLTAGE CURVES
• LABORATORY SETUP
• DESCRIPTION OF THE METHOD FOR DETECTORS
WITHOUT GAIN
• PRESENTATION OF THE RESULTS
• FUTURE GOALS
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p type
Depleted
Zone
Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Measuring doping profile of a pn junction using
the Capacitance-Voltage Curve
n+ type
Capacitance depends upon the area and
width of depleted zone
Depleted zone can be
considered as a
Parallel Plate Capacitor
Case of NA << ND
Width of depleted zone depends upon Voltage
bias and doping concentration
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Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Detector as a Trapeziodal Parallel Plate Capacitor
n++ impiantation
Detector CNM
Run 6474
W9B6-Gain 1
Plate A
Parallel plate
capacitor
p substrate
Trapezoidal
parallel plate
capacitor
Plate A
x
Plate A ≠ Plate B
Plate B
Plate B
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Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Capacitance of a Trapezoidal parallel plate
capacitor
By the Gauss’ Theorem
Plate A
x
Plate B
parallel plate capacitor
Additional contribution
constant that depends upon
the geometry of the detector
a side of n-implantation
b side of b substrate
d width of detector
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Capacitance-Voltage Curve Setup
Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Laboratory PC
Power supply
Keithley 2410
LCR Meter
Agilent E4980A
Device
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Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Setup test: measurement of a known capacitor
RESONANCE
CORRECT
Value
(~ 34pF)
Verify the setup using a
known capacitor
34 pF
Scan in frequency
from
50 Hz to 2 MHz
Good frequency range of measurement [10 kHz ; 2 MHz]
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Capacitance-Frequency curve
Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
The detector is an extended
network of resistors and capacitors
The sensor acts as a low pass RC
filter
By scanning in frequency at
fixed Voltage, a variation of
the detector’s capacitance
is observed
Due to a smaller
effective Area
Capacitance-frequency
curve shows a variation of
detector’s area
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Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Capacitance-Frequency curves at different Voltage
We need to find a frequency that works
well at every bias voltage.
The measurements should follow the
known relation between C and V.
C-f (2 Volt)
C-f (25 Volt)
C-f (36 Volt)
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dependency
Fit Equation
7E-11
30kHz is a good
frequency to work
y = 9E-11x-0.518
6E-11
Capacitance [F]
Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Fit to the C-V curves with the expected
to select the good working frequency
y = 5E-11x-0.392
5E-11
y = 3E-11x-0.276
Frequency of 30kHz
4E-11
Frequancy of 500kHz
Frequancy of 1MHz
3E-11
Frequency of 30kHz
Frequency of 500kHz
2E-11
Frequency of 1MHz
1E-11
0
0
20
40
60
Voltage [V]
80
10
Effect of the Trapezoidal correction
2.5E+22
Parallel plate
No Cg correction
Cg correction
2E+22
1/C2 [F-2]
Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
For a parallel plate capacitor:
1/C2 vs Vbias should be a straight line
1.5E+22
For detector W9B6-Gain 1
Cg is about 4,69 pF
1E+22
Trapezoidal plate
5E+21
0
0
50
100
Voltage Bias [V]
150
200
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Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Capacitance-Voltage and 1/(C2)-Voltage curve
1/(C2)-V Curve acquired at 30 kHz
(Cg Corrected)
Above 120 V the
measurement is
hard to
understand
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Width of depleted zone [um]
Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Width of the depleted zone
380
330
280
Note:
360 um is too large
230
Fit Equation:
180
It’s necessary
improve the absolute
scale, i.e. precise
knowledge of the Cg
correction
y = 36.924x0.5025
130
80
30
-20 0
20
40
60
80
100
120
140
Voltage Bias [V]
Respected the relationship between width
of depleted zone and Voltage bias
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Extraction of the Doping profile
4.00E+12
3.50E+12
NA [cm-3]
Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
To extrapolate the doping profile:
calculate the derivative of 1/(C2)-V curve
3.00E+12
2.50E+12
VALUE CONSISTENT WITH
EXPECTATIONS
2.00E+12
1.50E+12
1.00E+12
5.00E+11
0.00E+00
9
11
19
28
38
45
55
67
79
92
107 122
w [um]
Due to the Built-in Voltage, the depth is already 9 microns at Voltage Bias=0
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n++
p+
p
2E-10
1.8E-10
In LGAD detectors, the value of
capacitance is increasing with Voltage.
Why??
1.6E-10
Capacitance [F]
Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
Study of LGAD Detector
1.4E-10
It’s necessary to study and better
understand the Capacitance-Voltage
curve of a Detector with gain.
1.2E-10
1E-10
8E-11
6E-11
4E-11
2E-11
0
0
20
40
60
80
100
120
Voltage [V]
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Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015
The CV method illustrated allows the measurement of
the doping profile in silicon sensors.
The method gives the correct doping concentration for
standard pin diods
Application of the method on LGAD sensors under
study
Need to improve the Cg correction to the capacitance
for a better width absolute scale
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