1 Marco Ferrero With Nicolo’ Cartiglia, Francesca Cenna, Fabio Ravera, Universita’ degli Studi di Torino & INFN

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 2 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

Measuring doping profile of a pn junction using the Capacitance-Voltage Curve p typen+ type Depleted Zone Depleted zone can be considered as a Parallel Plate Capacitor Case of N A << N D Capacitance depends upon the area and width of depleted zone Width of depleted zone depends upon Voltage bias and doping concentration 3 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

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 CNM Run 6474 W9B6-Gain 1 4 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

Capacitance of a Trapezoidal parallel plate capacitor a side of n-implantation b side of b substrate d width of detector By the Gauss’ Theorem Additional contribution constant that depends upon the geometry of the detector parallel plate capacitor 5 x Plate A Plate B Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

Capacitance-Voltage Curve Setup Device Laboratory PC Power supply Keithley 2410 LCR Meter Agilent E4980A 6 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

Setup test: measurement of a known capacitor RESONANCE Verify 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 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

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 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

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 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

Fit Equation 30kHz is a good frequency to work Fit to the C-V curves with the expected dependency to select the good working frequency Voltage [V] Capacitance [F] 10 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

Effect of the Trapezoidal correction Voltage Bias [V] 1/C 2 [F -2 ] For a parallel plate capacitor: 1/C 2 vs V bias should be a straight line 11 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015 For detector W9B6-Gain 1 Cg is about 4,69 pF Parallel plate Trapezoidal plate

Capacitance-Voltage and 1/(C 2 )-Voltage curve 1/(C 2 )-V Curve acquired at 30 kHz (Cg Corrected) Above 120 V the measurement is hard to understand 12 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

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 Width of depleted zone [um] Voltage Bias [V] Respected the relationship between width of depleted zone and Voltage bias 13 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015

Extraction of the Doping profile NA [cm -3 ] w [um] To extrapolate the doping profile: calculate the derivative of 1/(C 2 )-V curve Due to the Built-in Voltage, the depth is already 9 microns at Voltage Bias=0 14 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015 VALUE CONSISTENT WITH EXPECTATIONS

Study of LGAD Detector Capacitance [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 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015 p p n++ p+

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 Marco Ferrero, Universita’ Di Torino, INFN, Tredi2015