Mapping the depleted area of silicon diodes using a micro-focused X-ray beam

For the Phase-II Upgrade of the ATLAS Detector [1], its current Inner Detector will be replaced by the ATLAS Inner Tracker (ITk), which will consist of a pixel tracker and a strip tracker [2]. Silicon sensors for the future ATLAS strip tracker have been developed ([3], [4]) to meet the challenging requirements of the sensor characteristics and stability in a high radiation environment. In order to achieve a low depletion voltage and thereby increase the readout signal, the wafer material used for silicon strip sensors is required to have a high bulk resistivity.

Simulations of the electric field inside a biased sensor have shown that the combination of the foreseen sensor parameters:

• high resistivity material

• sensor doping profile

• dicing edges close to the active sensor area

• high bias voltage

could potentially lead to a breakdown in leakage current if it extends too far towards the dicing edge (see figure 1).

The simulation shows the edge region of a sensor (p-doped bulk) with a grounded bias ring (connected to an n-doped implant), guard ring (connected to an n-doped implant), edge ring (connected to a p-type implant) and a highly p-doped layer covering the sensor backside. The dicing edge of a sensor is a highly degraded silicon surface with a sufficiently large concentration of free charge carriers to be electrically conductive. This conductive edge can lead to a short circuit between the sensor backside (to which high voltage is applied) and free charge carriers accumulating beneath the bias ring (grounded) and guard ring (floating), resulting in a significant increase of the leakage current. A highly p-doped edge ring is added to the sensor to prevent the formation of a conductive path between free charge carriers under the bias and guard ring and the dicing edge. The presence of a highly p-doped edge ring reduces the extension of the space charge region and the electric field towards the dicing edge.

Monitoring diodes were added to prototype wafer layouts which, despite different geometries and sizes compared to the full scale sensor, were designed to have edge regions representative of full size sensor edges. For this study, the electric field inside diodes from prototype wafers was studied by mapping their depleted areas.

The diodes used for these measurements were included in wafer layouts for silicon strip sensors as test structures. Their wafer related characteristics (thickness of $310\pm 10\text{upmu}\text{m}$, p-doping concentration in bulk and high resistivity bulk material) are the same as for full size ATLAS silicon strip sensors.

Three diodes from two different wafers, produced by Hamamatsu Photonics K.K. (HPK) and Infineon Technologies (IFX), were studied (see figure 2). Diode HPK MD was on a wafer with a bulk resistivity of 3.0 $k$Ω⋅$cm$, diodes IFX MD2 and IFX TD3 were on a wafer with a bulk resistivity of 3.5 $k$Ω⋅$cm$. Depletion voltages for devices from the same wafers were measured to be about -300 $V$.

In addition to two $2\times 2{\text{mm}}^2$ diodes with a comparable layout of bias and guard rings (HPK MD and IFX MD2), a diode with a smaller active area, but larger distance to the dicing edge was chosen (IFX TD3) for comparison. While all diodes under investigation had a bias ring and guard ring similar to full size sensors, their edge rings vary in shape and position with respect to the active diode area (see figures 2(a) to 2(c)).

The aim of this study was to map the depleted area inside biased diodes with respect to the positions of field shaping design features (bias ring, guard ring, edge ring) and study its extension toward the dicing edges. Since the field shape in different depths of the diodes was of less interest than its extension in the sensor plane, this measurement was not set up to map the diode edge (e.g. by performing an edge-TCT measurement), but the field distribution with respect to the sensor plane: a micro-focused 15 $keV$ X-ray beam was arranged normal to the diode surface and the response at different diode positions measured.

Each 15 $keV$ photon has a 51 $\%$ chance to interact within silicon with a thickness of 300 μ$m$. An interaction produces one 15 $keV$ electron, which travels up to 20 μ$m$ in silicon and produces about 4,200 electron-hole-pairs.

The Diamond Light Source provides photons in intervals of 2 $ns$, which the process of producing a micro-focused, monochromatic beam reduces to a photon flux of about $4.7\pm 0.8$ $photons$ per 10 $ns$. Given the integration time used for current measurements (20 $ms$, see section 4), variations on the time scale of 10 $ns$ can be neglected.

While in the absence of an electric field, electrons and holes recombine, the presenceof an electric field leads to the free charge carriers moving towards the sensor surface and back plane. They thereby cause an increase in the measured leakage current due to induced ionisation produced by electrons from interactions with X-ray photons.

It should be mentioned that due to the unknown interaction depth of each X-ray photon, the current measured for each diode position is integrated over the full sensor depth. This measurement therefore does not provide information about the field distribution in different diode depths, as e.g. a Two-Photon-Absorption (TPA)-TCT measurement would.

Each diode under investigation was moved with respect to the beam using precision translation stages. By measuring the resulting current for each position, the electric field inside the diode was mapped. In these measurements, all diodes were mounted on circuit boards designed for beam tests of test structures. High voltage was applied to the diode back plane using silver conductive paint (LS 200 N) and its surface was grounded using a wire bond (see figures 1(a) to 1(c)).

Guard rings were floating during the performed measurements as is foreseen for the operation of sensors in the ATLAS ITk. The impact of a floating guard ring was previously studied in probe station measurements of a full-size ATLAS12 sensor, which was operated with both a floating guard ring (only the bias ring was connected to ground) and grounded guard ring (bias ring and guard ring were connected to the same ground). No difference was found in the sensor leakage current for measurements with a grounded or floating guard ring.

Each diode was cooled to 0 ^∘$C$ and kept at below 1 $\%$ humidity in a light-tight box during the measurements.

For these measurements, a monochromatic 15 $keV$ X-ray beam, micro-focused to a size (FWHM) of $1.8\times 3.2\text{upmu}{\text{m}}^2$ using a compound refractive lens, was provided by beam line B16 at the Diamond Light Source [6].

For each diode, three scans were performed:

1. a coarse scan in large steps over the full diode area in order to map its outer edges

2. a fine scan in small steps over one or two corners of each diode

3. line scans through the centre of each diode in both horizontal and vertical direction for different bias voltages to map the dependence of the electric field on the applied bias voltage.

Line scans were set up to use large step sizes over the plateau area of the diode centre and small steps in the more interesting edge regions. Voltages were varied between -50 $V$ (corresponding to a less than half depleted sensor) and -500 $V$ (corresponding to an over-depleted sensor) to study the diode response for different depletion depths. It should be mentioned that due to absorption, the number of photons traversing the diode decreases exponentially. Since the diode was positioned facing the sensor, more photon interactions occur in the upper region of the diode than in the lower regions, where the photon beam intensity has decreased (see figure 4).

Since the sensor depletes from the surface downwards, a larger fraction of photons interacts in the upper, depleted diode volume than in the lower, un-depleted volume, which results in a non-liner current increase with increasing depletion depth. In the following, scans parallel to the dicing edges of a diode will be referred to as ”across” (horizontal/vertical) and scans through opposite corners of a diode as ”diagonal”. Table 1 summarises the positioning parameters used for the scans of each diode.

At each position, the current was measured using the power supply readout of a Keithley 2410 high voltage power supply, which was also used to bias the diode under investigation. A python script was used to read the current from the power supply after a waiting time of 3 $s$ following a stage movement, from an average calculated from 20 measurements with an integration time of 20 $ms$ each.

All results show the absolute current measured at each position and therefore include induced photo current as well as the dark current. The dark current of each diode was measured to be $\le 1\text{nA}$ for bias voltages up to -500 $V$.