The measurement of the pixel capacitance of the silicon planar sensor is not as straightforward as it was sketched in the previous section. Therefore, first the sensor itself and the effects influencing the capacitance measurement will be introduced. The measured sensor is n+on n type and its cross section is shown in Figure3.15. The sensor has been fabricated on a high resistive n-type silicon wafer. The collection electrodes (pixels) are the n+type regions. The sensor backplane is formed by highly doped p+region. The sensor operates with a negative high voltage connected to the backplane. The depletion region grows from the backplane towards the n+collection electrodes. The total pixel capacitance Ctot
3.5 PixCap
thickness of the measured sensor is 230µm and the spacing between pixel regions is 20 µm. The in- terpixel capacitance is assumed to be the dominant part of the total pixel capacitance due to the closely spaced n+charge collection regions (see Figure3.15).
The collection electrodes are separated by shallow p-regions (p-spray), preventing the pixels from an ohmic short connection. If the sensor is not fully depleted, all the pixels are effectively shorted and the capacitance measurement is not possible.
Figure 3.15: Cross section of the silicon planar sensor and its capacitance components.
The interpixel current has been studied experimentally with the PixCap by measuring the DC current between two adjacent pixels at a potential difference of 1.8 V as a function of a sensor bias voltage Vbias.
This IV characteristic is shown in Figure3.16. In the Vbiasrange from 0 to -25 V, the sensor is not fully
depleted and a large current (tens ofµA) between the pixels is observed. The pinch-off effect occures at the voltage of about -25 V. Adjusting the Vbias to the more negative values, the interpixel current
drops significantly below 1 nA. Taking into account the pixel to pixel variations, the capacitance can be measured from -35 V towards the more negative voltage.
Another restriction for the capacitance measurement with the PixCap arises from a bias grid of the sensor. A schematic of the sensor bias grid is shown in Figure3.17. The original purpose of the bias grid is the measurement of the leakage current of the sensor. The bias grid establishes the same potential at all pixels during the measurement of the leakage current, which is a direct indicator of the sensor quality and is evaluated during sensor production. However, in case of a capacitance measurement with PixCap, the bias grid is rather an obstacle. In the default capacitance measurement configuration, all pixels are grounded by the PixCap and only one is pulsed between 0 and 1.8 V. At the phase when M1 is ON, the pixel is at 1.8 V and the leakage current of all 26880 pixels flows into the Vin terminal through
the bias grid and spoils the capacitance measurement. To avoid this effect, during the capacitance meas- urement all pixels must be kept at 1.8 V and the measured pixel is switched between 0 and 1.8 V. For design reasons, the switching voltage swing was reduced down to 1.1 V to achieve the correct switching. As we have shown, the capacitance measurement works only for the sensor bias voltage above the pinch-off region. In a real pixel detector, the sensors are usually operated in a full depletion mode and at this mode, the capacitance should be measured. The depletion voltage has been determined by the measurement of the CV characteristic of the sensor. The CV characteristic of a single pixel measured with the PixCap chip is shown in Figure3.18(a). The total pixel capacitance is inversely proportional to the width of the depletion region. Referring to Equation2.13, the depletion width is proportional to
Figure 3.16: The interpixel current as a function of the bias voltage of the silicon planar sensor.
Figure 3.17: A schematic view of the pixel layout with the bias grid.
square root of the bias voltage. If the sensor is not fully depleted, the quantity 1/C2tot is directly pro-
portional to the bias voltage. As the full depletion is achieved, the depletion width is constant and the capacitance does not change. This behavior of the sensor capacitance has been experimentally observed and is shown in Figure3.18(b). Full depletion voltage can be found in the transition region between the linear dependence of 1/C2toton Vbiasand the region where this quantity is constant. In our case, the full
depletion voltage is about -75 V.
In silicon, pairs of electrons and holes are continuously created by thermal excitations causing a leak- age current in the pixels. This current adds up with the switching current generated by PixCap and influences the capacitance measurement. The influence of leakage current is more significant at small switching frequencies. Before each capacitance measurement, the leakage current of the pixel has been measured and the pixel capacitance has been corrected accordingly. For illustration, the leakage current map of the measured silicon sensor is shown in Figure3.19. The leakage current in most of the pixels is below 2 nA. However, the top row of the pixel matrix exhibits higher leakage current, by an order of magnitude, probably due to the high electric field on the edge of the sensor.
3.5 PixCap
Figure 3.18: The CV characteristic of the silicon planar sensor (a). By expressing the capacitance in the form of 1/C2
tot, the full depletion voltage of -70 V can be extracted (b).
Figure 3.19: A leakage current map of the silicon planar sensor.
During the capacitance measurement, the sensor has been operated slightly over-depleted at -80 V, the switching frequency was 4 MHz, the voltage at the switching pixel has been alternated from 0 to 1.1 V and the remaining pixels have been connected to 1.8 V. A capacitance map of the silicon planar sensor obtained at these conditions is shown in Figure 3.20. The capacitance of the pixels is not perfectly homogeneous across the pixel array. Capacitance gradients and pixels with a capacitance significantly larger than the average are present. This observation can be explained by fabrication process variations of the sensor and also by the non-uniformity of bump-bonding of this particularly small assembly. Therefore, a cut has been made on the homogeneous pixel region (dotted line in Figure3.20) and the mean capacitance in this region is (105.5 ± 1.8) fF. The measurement error has been calculated from an error of the voltage measurement, an error of the current to voltage conversion, an error of the bare PixCap capacitance and an error of the leakage current determination. The capacitance measurement of a second PixCap assembly gives an average pixel capacitance of (111.7 ± 3.8) fF.
Figure 3.20: A capacitance map of the silicon planar sensor.