PRELIMINARY STUDY TO DETERMINE THE DOPING

PROFILE OF LGAD DETECTOR

1

Marco Ferrero

With Nicolo’ Cartiglia, Francesca Cenna, Fabio Ravera,

Universita’ degli Studi di Torino & INFN

TREDI2015 WORKSHOP - TRENTO

OUTLINE

• 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 GOALS2

Mar

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FN, T

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2015

Measuring doping profile of a pn junction using the Capacitance-Voltage Curve

p type n+ typeD

eple

ted

Zone

Depleted zone can be considered as a

Parallel Plate Capacitor

Case of NA << NDCapacitance depends upon the area and

width of depleted zone

Width of depleted zone depends upon Voltage bias and doping concentration

3

Mar

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FN, T

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Detector as a Trapeziodal Parallel Plate Capacitor

x

Plate A

Plate B

Plate A

Plate B

Parallel plate capacitor

Trapezoidal parallel plate

capacitor

Plate A ≠ Plate B

n++ impiantation

p substrate

Detector CNMRun 6474

W9B6-Gain 1

4

Mar

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FN, T

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2015

Capacitance of a Trapezoidal parallel plate capacitor

a side of n-implantationb side of b substrated width of detector

By the Gauss’ Theorem

Additional contributionconstant that depends upon the geometry of the detector

parallel plate capacitor

5

x

Plate A

Plate B

Mar

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2015

Capacitance-Voltage Curve Setup

Device

Laboratory PC

Power supplyKeithley 2410

LCR MeterAgilent E4980A

6

Mar

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Setup test: measurement of a known capacitor

RESONANCEVerify the setup using a

known capacitor

Good frequency range of measurement [10 kHz ; 2 MHz]

CORRECT Value

(~ 34pF)

Scan in frequency from

50 Hz to 2 MHz

34 pF

7

Mar

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FN, T

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2015

By scanning in frequency at fixed Voltage, a variation of the detector’s capacitance

is observed

Capacitance-Frequency curve

Capacitance-frequency curve shows a variation of

detector’s area

The sensor acts as a low pass RC filter

The detector is an extended network of resistors and capacitors

Due to a smaller effective Area

8

Mar

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FN, T

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2015

Capacitance-Frequency curves at different Voltage

C-f (2 Volt)

C-f (25 Volt)

C-f (36 Volt)

We need to find a frequency that works well at every bias voltage.The measurements should follow the known relation between C and V.

9

Mar

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FN, T

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2015

Fit Equation

30kHz is a good frequency to work

Fit to the C-V curves with the expected dependencyto select the good working frequency

Voltage [V]

Capa

cita

nce

[F]

0 10 20 30 40 50 60 700

1E-11

2E-11

3E-11

4E-11

5E-11

6E-11

7E-11

f(x) = 3.10648070008886E-11 x^-0.275762571429319

f(x) = 5.03967362522733E-11 x^-0.392076898306343

f(x) = 8.8015913525478E-11 x^-0.518119141651436

Frequency of 30kHzFrequency of 30kHzFrequancy of 500kHzFrequency of 500kHzFrequancy of 1MHzFrequency of 1MHz

10

Mar

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FN, T

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2015

Effect of the Trapezoidal correction

0 20 40 60 80 100 120 140 160 1800

5E+021

1E+022

1.5E+022

2E+022

2.5E+022

No Cg correctionCg correction

Voltage Bias [V]

1/C2 [

F-2]

For a parallel plate capacitor:1/C2 vs Vbias should be a straight line

11

Mar

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FN, T

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2015

For detector W9B6-Gain 1Cg is about 4,69 pF

Parallel plate

Trapezoidal plate

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

12

Mar

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FN, T

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2015

Width of the depleted zone

Note: 360 um is too large

It’s necessary improve the absolute

scale, i.e. precise knowledge of the Cg

correction

0 20 40 60 80 100 120 140-20

30

80

130

180

230

280

330

380f(x) = 36.9236595482781 x^0.502534631985136

Fit Equation:

Wid

th o

f dep

lete

d zo

ne [u

m]

Voltage Bias [V]

Respected the relationship between width of depleted zone and Voltage bias

13

Mar

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FN, T

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2015

Extraction of the Doping profileN

A [c

m-3

]

w [um]

To extrapolate the doping profile: calculate the derivative of 1/(C2)-V curve

8.98134439052327

9.74682860025615

13.2389244704591

19.0830722845919

24.9675892540797

31.3157837860146

38.1323733264888

45.5555147206352

48.4120125393613

55.2540970739535

62.7938868820074

70.7943118760032

79.0653147844596

88.2621182301991

97.2175237857759

107.421349587852

117.937277643519

128.3458738289450.00E+005.00E+111.00E+121.50E+122.00E+122.50E+123.00E+123.50E+124.00E+12

Due to the Built-in Voltage, the depth is already 9 microns at Voltage Bias=0 14

Mar

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2015

VALUE CONSISTENT WITH EXPECTATIONS

Study of LGAD Detector

0 20 40 60 80 100 1200

2E-11

4E-11

6E-11

8E-11

1E-10

1.2E-10

1.4E-10

1.6E-10

1.8E-10

2E-10

Capa

cita

nce

[F]

Voltage [V]

In LGAD detectors, the value of capacitance is increasing with Voltage.

Why??

It’s necessary to study and better understand the Capacitance-Voltage

curve of a Detector with gain.

15

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p

n++p+

SUMMARY

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

16

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FN, T

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2015