Electrical properties study under radiation of the 3D-open-shell-electrode detector Open Access

In extremely harsh radiation environments, such as the Large Hadron Collider (LHC) and its upgrade, namely the HL-LHC, the total radiation fluence can reach up to 1 $×$ 10¹⁶ n_eq/cm².¹ Under heavy radiation, radiation induced defects in Si will cause increases in detector leakage current and full depletion voltage, which in turn will degrade detector performance.² In addition, trapping of the electrons and holes defects induced by radiation will reduce detector’s Charge Collection Efficiency.³ 

Proposals of the conventional 3D detector (called 3D column detector here) and the 3D-Trench-Electrode Detector structures made it possible to improve silicon detector’s performances in situations of heavy radiation. This has been achieved by the separation of the detector electrode spacing from its thickness, which also makes the detector’s designing more flexible than planar detector.^4–9 Furthermore, the trench-like electrode makes the electric potential and electric field distributions more uniform and eliminates the low electric field region near the electric potential saddle point existed in the 3D-Column-Electrode detector.¹⁰ That is why the 3D-Trench-Electrode Detector draws our attention to study in recent years.^11,12 In spite of that, there is about 10% percent of the wafer thickness untouched regarding trench etching in the 3D-Trench-Electrode Detector to prevent the main detector body from falling off the wafer. The region that is not penetrated by trench etching is a region with very low electric field, giving rise to slow charge collection or even no collection in this region. This may result in a virtual dead space, as much as 10% in volume, in the detector.

To solve this dead space problem, we proposed a new type of 3D detector, namely the 3D-Open-Shell-Electrode Detector (3DOSED)¹³ to eliminate this virtual dead space, while still keep the easy one-sided detector processing and good advantages of the 3D-Trench-Electrode detector. As described in details in Ref. 13, we choose a square shape 3DOSED as shown in Fig. 1 for our simulation studies. With respect to the center column collection electrode, the square shape electrode is like a shell surrounding it, with only two narrow openings. This is the reason why we call it the open shell electrode detector. The opening gaps connect the neighboring cells, as well as cells and the wafer main body. This ensures the mechanical stability of the detector array while eliminating the virtual dead space. In this work, we choose the width of the “opening gap” to be 7 μm with a small angle crossing the shell electrode wall as a practical example for the illustration of the concept. We will investigate the detector electrical characteristics under heavy radiation fluence to investigate possible effect of the opening gap to the detector.

For high energy physics applications with radiation hardness consideration, we mainly focus on the 3D-Open-Shell-Electrode Detector (3DOSED) with p-type bulk silicon. A single cell of a square shape 3DOSED is shown in Fig. 1. It is the schematic diagram and it presents the incident particle and the path of the induced electrons in the detector. In Fig. 1, the green electrode is the shell electrode and the red electrode is the central column electrode. Drifting paths of MIP (minimum ionizing particle) induced electrons and holes are also shown. Full 3D simulations on the novel 3DOSED’s electrical characteristics have been carried out in this work using Silvaco’s TCAD simulation software.^14–16 Fig. 2 is the detector structure used in the 3D simulation with an optimized design. Through Fig. 2, we can obtain the information about the size of the detector we studied and the materials of each part of the 3DOSED.

We set all the parameters down to obtain a complete square 3DOSED with a specifically shaped opening gap that is optimum.¹³ In our simulation here, the detector thickness is 150 μm. The bulk silicon is p-type Si with a doping density of 1 $×$ 10¹⁴ cm^-3 to simulate the space charge induced by radiation effect at a radiation fluence of 1 $×$ 10¹⁶ n_eq/cm².¹⁷ The p⁺ doped square shape central column electrode has aside length of 10 μm and a depth of 150 μm. The square shell electrodes are formed by two complementary n⁺ doped silicon trenches, with a width of 10 μm and a depth of 150 μm. After etching of those electrodes, the detector main body in a unit cell will be connected to the bulk of Si wafer through the openings in the shell electrodes. The width of these openings is usually chosen to be less than the width of the shell electrode, which is set to be 7 μm in this work.

Under radiation condition, one main influence is the space charge transformation. We also use an effective doping concentration of 10¹⁴ cm^-3 to account for the space charge increase to the absolute value of a negative space charge of 10¹⁴ cm^-3 after a radiation of 10¹⁶ n_eq/cm².

When a high energy particle detector is working without heavy radiation damage, the electric field distribution is similar to that of a photon or X-ray detector. However, when it is working under high radiation situation, there are some different characteristics as we will show in the following study. Fig. 3 shows a 2D cut plane at Z=103 μm, for which we will display our 3D simulation results. Fig. 4 is the electric field distribution profile in the cut plane at Z=103 μm (Fig. 3) of the 3DOSED shown in Figs. 1 and 2. The bias voltage on cathode electrode (the central column electrode) is -150 volts.

Fig. 4 shows that the electric field value is high near the anode electrode and decreases towards the cathode electrode, which reflects the fact that the junction is at the shell electrode where the depletion of hole starts and extends towards the central column electrode. It is clear in Fig. 4 that two openings in the left and right side walls of the shell electrode cause distortions in electric filed distributions near these opening. We can compare these distorted distributions to those near the top and bottom walls that have no openings. In fact the strength of the electric field in a opening is still very high, about 2 $×$ 10⁴ V/cm to 3 $×$ 10⁴ V/cm, which is only slightly lower than that (3.6 $×$ 10⁴ V/cm) near an identical location in the top or bottom wall. In fact, due to the existence of high electric filed in the openings, the effective detector sensitive area will be increased as compared to a detector without openings. Therefore, our novel 3DOSED detector improves charge collection efficiency of the 3D-Trench-Electorde detector in two folds: 1) it eliminates about 10% dead volumes, and 2) it increases sensitive volume (in our case here this increase is about 3%). We can thus expect that our novel 3DOSED detector will bring an improvement in charge collection efficiency of about 13% with little perturbations in electric field distributions near the shell electrode openings.

Fig. 5 is a 3D plot of the electric potential distribution at z=103 μm cut plane. The bias voltage at the central collecting electrode is set at -150 volts to ensure an full depletion (we will discuss full depletion voltage later). The anode electrode is set to be zero. The shape of the electric potential profile is like a funnel, which will force holes to drift towards the central column electrode for a good charge collection. In addition, it can be observed that there are small waves of electric potential changes near the openings in the shell electrode due to our special structure design, but as a whole, the electric potential distribution is smooth and uniform. Also, the electric potential profile of the novel 3DOSED detector is much more uniform than that of the traditional 3D electrode detector and it has no saddle point.

As we know, the change of leakage current per unit volume at total depletion increases linearly with fluence.¹⁸ As Fig. 6 shows, the leakage current of our novel 3DOSED detector at full depletion is about 1 $×$ 10^-8 amperes before radiation (we set Φ_eq as 1 $×$ 10¹² n_eq/cm² to similar the environment without radiation since this value of radiation is really low.). After radiation, the change in leakage current is a function of radiation fluence Φ_eq, which is shown below:

where $α$ is a constant describing the damage rate by particle radiation (⁠$α$ was chosen to be 4 $×$10^-17 A/cm in this work). Vol in Eq. (1) is the detector depletion volume. The leakage current after radiation fluence of 1 $×$10¹⁶ n_eq/cm² can be read in Fig. 6, and the value is already close to 10^-5 amperes level, which means that the radiation damages the detector, causing an increase in detector leakage current. This can have an impact on the detector performance by increasing the detector electronic noise.

The capacitance is a sensitive parameter in the operation of a silicon tracking detector, as it directly affects the noise.¹⁹ We can first estimate the capacitance of a single cell of a 3DOSED detector using a cylindrical capacitor:

where $ε0εr$ is the product of the vacuum permittivity and relative permittivity. R and r are the outer and inner radius of the cylinder, respectively. d is the depth of the electrode. In our case d = 0.015 cm. Using Eq. (2) one can estimate that Ccyl = 41 fF. Fig. 7 is the simulated C-V characteristic of the open shell electrode detector under high radiation. The value at full depletion voltage is about 5 $×$10^-14 F = 50 fF, which is very close to our estimation before.

The induced current is caused by a minimum ionizing particle (MIP) incident through the 3DOSED detector shown in Fig. 1. Its value may depend on several factors, like the weighting-field’s profile (shown in Fig. 8), the trapping level (the charge collection distance is the carrier’s drift time multiplied by the carrier’s trapping time), the electric field’s profile (shown in Fig. 4), and the degree of contributions of both electrons and holes. There are deep level single defects and/or defect clusters (extended defect regions) for displacement radiation induced damage in silicon to different kinds of radiation like neutron radiation, gamma and electron radiation and charge particles (proton, pions, etc.).

For a non-irradiated detector, the induced current generated by a MIP can be written as:

where q is the electron or hole charge, v_dr is the drift velocity for electrons or holes, E_w is the weighting field.

The detector weighting field E_w only depends on the detector geometry, and can be simulated in the TCAD simulation using the detector geometry, setting the bulk material as insulator, the bias on the collecting electrode (central column electrode here) as 1, all other electrodes (shell electrode here) as 0. Results of such simulations are shown in Fig. 8.

The charge carrier drift velocity, taking into account the saturation velocity, can be expressed as:

where E(r) is the electric field. When the detector is working in a hard radiation situation, due to the influence of the trapping effect, the induced current will be affected:

where carrier trapping constant $τt$ is a function of radiation fluence.

In this work, we only study the charge collection near the openings in the shell electrode. We assume that the MIP is randomly hitting the detector at a location r, then the collected charge in time interval t can be written as:

In Fig. 9, simulated collected hole and electron charges and the total collected charge as a function of MIP incident position for an irradiated 3DOSED detector are shown. As we can see, the collected charge changes with the MIP incident positions. Through analyzing results of charge collection simulations, we find that the charge collection of the 3DOSED under heavy radiation is nearly not influenced by the opening gap of the shell electrode.

The calculation of full depletion voltage of a 3D trench detector is already studied in previous work, with expression shown in Ref. 9. For 3DOSED detector, the full depletion voltage is independent of the detector thickness, and that is why the value of it can be reduced compared to the planar detector. The full depletion voltage depends on electrode spacing. As for different geometry structures, the larger the electrode spacing is, the larger the full depletion voltage will be. The voltage at which the hole concentration has decreased to below the initial equilibrium value in the entire volume of the detector indicates the holes are just depleted in the whole detector. We can get the hole concentration profile at z=103 μm cut plane of the 3DOSED, as shown in Fig. 10, and cut a line from point (0,0) to (60,0) to obtain a clue of the detector full depletion voltage. For a non-irradiated detector, the full depletion voltage was found to be 2 volts.¹³ Through this way, we obtain a full depletion voltage of about 120 volts with a radiation fluence 1 $×$10¹⁶ n_eq/cm² as Fig. 11 shows.

In this work, we have studied the electrical characteristics of the novel 3DOSED detector under heavy radiation. The electric field distribution, electric potential distribution, current-voltage characteristics, capacitance-voltage characteristics, charge collection property, and full depletion voltage under radiation have been simulated using the Silvaco ATLAS tool. We have found that the structure is reasonable and flexible, with minimum perturbations near the openings in the shell electrode. Therefore we can eliminate the dead space (about 10% in total space) existed in the 3D-Trench-Electrode detectors with minimum side effects by using the novel 3DOSED structure. It is clear that this new element, namely the opening gap, of the construction does not significantly change the electric field inside the detector cell, thus affects little the detector charge collection property. This is due to fact that the width of the opening gap (7 μm here) is less than the shell electrode width (10 μm here) with a small angle crossing the shell electrode wall. Moreover, the openings in the shell electrode increase the detector effective sensitive area by about 3%. The induced current and collected charge are strongly affected by the radiation fluence, as well as by the weighting field and electric field distribution. The total collected charge also depends on the incident position of the detector.

In all, the novel 3DOSED detector eliminates the dead space existed in the 3D-Trench-Electrode detectors while retains their radiation hard properties in terms of low full depletion voltages and high charge collection efficiency.