Effect of bias conditions on transient anode current for quasi-double-sided silicon drift detector with high energy resolution

doi:10.21203/rs.3.rs-2503413/v1

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Effect of bias conditions on transient anode current for quasi-double-sided silicon drift detector with high energy resolution

https://doi.org/10.21203/rs.3.rs-2503413/v1

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published 01 Jun, 2023

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Silicon drift detectors (SDDs) are widely applied for x-ray detection due to their remarkable energy resolution. The main contribution to energy resolution is the electrical noise of measurement system. In addition, other factors, including imperfect charge collection and ballistic deficit, can deteriorate the energy resolution. Those factors are closely related to the bias conditions of the device. However, the effect of bias conditions on device energy resolution has rarely been reported, primarily because the applied bias of classical SDDs is limited by twice the depletion voltage and little attention is focused on bias conditions. In order to enhance the flexibility of bias conditions and investigate the effect of bias conditions on energy resolution, we proposed a novel quasi-double-sided silicon drift detector (QD-SDD) with a drift ring structure designed on the back side. Device simulations of SDD and QD-SDD under different bias conditions were performed to obtain the transient current response of the anode. It was found that the QD-SDD has greater flexibility in bias conditions, and then better electron collection efficiency and shorter electron collection time can be realized at higher bias voltage (> 200 V). Finally, the fabricated QD-SDD was characterized using a ⁵⁵Fe radioactive source. The experiment results showed that the energy resolution of QD-SDD varies with different bias conditions. The optimal energy resolution is 170 eV under the optimized bias conditions.

The concept of silicon drift detector (SDD) was introduced by Gatti and Rehak in 1983[1, 2]. A chief feature of a silicon drift detector is its unique small capacitance, which is independent of the detector’s active area [3, 4]. As a result, SDDs have better energy resolution compared with other x-ray detectors [4]. The energy resolution is primarily dependent on the noise level [5–7]. The total noise includes the Fano noise and the electric noise. The first term depends on the material properties; therefore, the main factor affecting the full width at half maximum (FWHM) is the electric noise, which is closely related to the leakage current of the detector and the total capacitance [5–7]. Moreover, additional factors can broaden the peak and worsen the energy resolution; those include ballistic deficit [6], imperfect charge collection [8], and various other factors. Those factors are susceptible to the bias conditions of the device. While the energy resolution of SDD has been studied extensively [9–11], in literature, a limited number of articles have reported the study of bias conditions on energy resolution. The charge collection of the SDD was measured using a ⁵⁵Fe radioactive source, and an improvement of the peak-to-background ratio of up to 20% was achieved by optimizing biasing voltages [9]. Another research reported that the energy resolution varies with the different bias voltages on the back contact [10]. The charge collection efficiency and carrier collection time are closely related to the bias conditions since the transport characteristics are susceptible to the bias conditions of the device. In addition, for classical SDDs, the flexibility of bias conditions is limited because its maximum applied voltage is not allowed to exceed twice the depletion voltage [12], resulting in fewer studies on the bias conditions. Therefore, we proposed a quasi-double-sided silicon detector to analyze and verify the effect of bias conditions on energy resolution.

In this paper, a quasi-double-sided silicon detector (QD-SDD) was proposed to enhance the flexibility of bias conditions and investigate the effect of bias conditions. Then, simulations were performed to obtain the transient response current of the anode under different bias conditions. Modeling is critical for accurate inference and analysis. Therefore, the parameters used in the model are authentic and reliable. Devices operating at different bias conditions and irradiated by an incident x-ray were simulated. The electrical properties under those conditions were also compared and analyzed. and, the electron collection efficiency of the QD-SDD at different operating conditions was calculated. The magnitude of the electric field at different bias conditions was extracted, which is essential for the analysis of the carrier transport process. Thus, from the analysis of the simulation results, it is clear that better electron collection efficiency and shorter collection time are achieved due to optimized bias conditions. Finally, the fabricated QD-SDD was characterized using a ⁵⁵Fe radiation source and better energy resolution of QD-SDD was realized by optimizing the bias conditions. Energy resolution down to 170 eV was obtained.

2.1. Design and Parameters in simulation

For a conventional SDD, its maximum applied bias voltage is not allowed to exceed twice the depletion voltage, otherwise large hole currents will appear between the drift rings [12]. In order to enhance the flexibility of device bias conditions and investigate the effect of bias conditions on device performance, a novel quasi-double-sided silicon drift detector, shown in Fig. 1b, was proposed. Silicon drift detectors are devices that require bias voltages applied on both sides to achieve sideward depletion [2]. For a quasi-double-sided silicon drift detector, the drift path for transporting and collecting electrons is established by applying bias voltages to the four electrodes of the device. On the anode side (front side), a circular n⁺ region is located in the center, which acts as an anode (V_a) to collect electrons, and a large amount of concentric p⁺ rings surround the anode [13]. The innermost concentric p⁺ ring (V₁) close to the anode and the outermost concentric p⁺ ring (V_n) near the guard ring area, as the front electrodes, are biased to build the electron drift path. On the other side (back side), the large circular p⁺ ring in the center (V_b) and the outermost concentric p⁺ ring (V_bn), as back side electrodes, are also biased to drive electrons toward the anode. In addition, to create a potential gradient that forces electrons to drift toward the anode, different negative voltages are biased at the innermost p⁺ ring near the anode and the outermost p⁺ ring on the front side, respectively. The negative bias gradually decreases from the outermost drift ring to the innermost drift ring. The condition of the back side electrodes is similar to that of the front side. Once the electron-hole pairs are created by an incident x-ray, electrons drift toward the anode while holes are driven to the neighboring p⁺ drift rings [13]. The disad

To illustrate the great flexibility of a quasi-double-sided silicon drift detector in terms of bias conditions, the TCAD was used to simulate the transient anode current of SDDs. The current response of a silicon drift detector consists of two processes: the generation process of carriers in silicon substrate from an incident x-ray event; and the transport process of carriers in the device. During the simulation, only the carrier transport process is considered to simplify the model and reduce the computation time. The parameters in the model are realistic, and those parameters are used in experiments. An n-type high-ohmic wafer with a thickness of 525 µm (≥ 10 kΩcm, a depletion voltage close to -40 V) was introduced as substrate in the simulation. Table 1 shows the parameters of SDDs used in the simulations. The pitch of drift rings and guard rings are 100 µm and 65 µm, respectively. In addition, the numbers of drift rings and guard rings are 20 and 10, respectively.

Table 1

Parameters used to simulate QD-SDD and classical SDD.
Radius of anode (µm)	Width of drift ring (µm)	Gap of drift ring (µm)	Width of guard ring (µm)	Gap of guard ring (µm)	Width of ground ring (µm)
50	75	25	40	30	150

2.2. The simulation results of QD-SDD and single-sided SDD at different V_n voltages.

Carrier collection efficiency and carrier collection time are related to the bias conditions, and shorter collection time [9] and better collection efficiency [10] imply better device performance. In order to investigate how the bias conditions of the QD-SDD affect the transport characteristics and energy resolution, the simulations of the device under different bias conditions were performed and the simulation results were analyzed.

Firstly, the QD-SDD and classical SDD at different V_n voltages have been simulated with: (1) the innermost drift ring (V₁) has been biased at -10 V; (2) the center drift ring on the back (V_b) has been kept at -40 V; (3) the assumption that electrons are generated by x-rays is introduced into the model, and an energy of 3.6 eV is required to generate an electron-hole pair. The bias conditions of QD-SDD are shown in Fig. 2. X-rays are incident vertically on the detector with a distance of 1500 µm from the anode. The pulse signal is obtained by extracting the instantaneous current response of the anode. In addition, by processing and analyzing the date of the transient anode current, the electron collection efficiency and electron collection time have been plotted as a function of the bias voltages on the outermost drift rings (V_n and V_bn).

The QD-SDD depicted in Fig. 2 has been simulated and the transient anode current from x-ray events has been extracted. In addition, the simulation of a single-sided SDD at different V_n voltages has been performed with the same bias conditions. Figure 3 shows the transient anode current evolution after the electron-hole pairs generated by x-rays for a QD-SDD and a single-sided SDD at different V_n voltages. The simulation results show that the transient anode current is composed of a fast ramp and a slow decay component. For a single-sided SDD, the transient anode current is shown in Fig. 1a and it is distorted with increasing V_n voltage at reverse bias voltage greater than − 80 V. At reverse bias voltage less than − 80 V, the peak of the pulse current is reduced with decreasing V_n voltage. This result indicates that the maximum voltage applied to classical SDD in simulation is -80 V, which is close to twice the depletion voltage of the device. Due to the presence of the maximum bias voltage, the flexibility of the bias conditions for a single-sided SDD is definite. However, for a QD-SDD, as the bias voltages (V_n and V_bn) on outermost drift rings increase, the change in the transient anode current shown in Fig. 1b is considered in these two aspects: the collection time of electrons becomes shorter; the width of pulse current becomes narrower (pulse peak becomes higher), respectively. The difference in anode pulse current originates from the different bias conditions. It is clear that the transport characteristics have been changed due to the variable V_n voltages and the great flexibility of bias conditions is achieved for the QD-SDD. Lastly, both the rise time and the fall time (time required for the current to rise/fall from 10%/90% of its peak to 90%/10%) are reduced due to the increased V_n voltages. The reduction in the rise time or the fall time is mainly due to the larger V_n voltages.

In order to clarify the effect of V_n voltage on the transient anode current, the analyze of the electric field has been performed. The electron concentration in the detector is shown in Fig. 4a, and the drift path of electrons is clearly visible. The transport path of electrons is away from the front surface. A safe distance between the electron drift trajectory and the anode is crucial to avoid trapping electrons at the Si-SiO₂ interface [14]. A cutline along with the drift trajectory has been used to extract the electric field intensity. In order to observe the change in the electric field as accurately as possible, the line from (0, 160) to (2000,250) is chosen as the cutline. As shown in Fig. 4b, the variation of electric field intensity at different V_n voltages has been extracted. The electric field intensity is closely related to the potential difference. As the voltage on the outermost drift rings increases, it can be noticed that the electric field also increases, and the increment below the drift ring region is greater than that below the anode region. A stronger electric field means higher electron drift velocity and shorter collection time.

The charge collection time is defined as the time required to collect (1–1/e) of the total charge [15]. As shown in Fig. 5a, the electron collection time at different V_n voltages is plotted as a function of the bias voltages of the outermost drift rings. As the bias voltages on the outermost drift rings on both sides increases, the electron collection time to the anode is reduced. The higher potential difference between the innermost drift ring and the outermost drift ring on both sides results in a stronger electric field in bulk. As a result, the collection time of electrons drifting toward the anode is reduced. Once the electrons are generated by x-rays in the detector, those electrons are driven toward the anode and collected. The collection time is inversely proportional to the electron drift velocity and the time for electrons to reach the anode is shorter for the detector operating at higher V_n voltages. At higher bias voltages, the shorter electron collection time is realized due to stronger electric field in bulk and reduces the effect of ballistic deficit, resulting in a better energy resolution [17].

For the silicon radiation detector system, the pulse height spectrum is related to the charge collection efficiency [8], therefore energy resolution of the detector is affected by carrier collection efficiency. In order to clarify the relationship between V_n voltage and the electron collection efficiency (ƞ), which has been extracted by processing the transient anode current. It is defined as the ratio of the number of electrons collected by the anode to the total number of free electrons created by the x-ray event [18]. The electron collection efficiency is shown in Fig. 5b. The electron collection efficiency of the anode is related to the bias voltage on the outermost drift rings and electron collection efficiency is improved by increasing the V_n voltage. The better collection efficiency is mainly due to the stronger electric field.

2.3. The simulation results of V_b voltage

In order to investigate the effect of V_b voltage on the anode current, the QD-SDD at different V_b voltages has been simulated with 1) the innermost drift ring (V₁) has been biased at a fixed voltage of -10 V, and 2) the outermost drift rings on both sides (V_n and V_bn) has been biased to -130 V, and 3) the assumption that electrons are generated by x-rays and that the energy of 3.6 eV is required to generate an electron-hole pair is used into the model. The QD-SDD shown in Fig. 6 was simulated. The variation of anode pulse current at different V_b voltages is shown in Fig. 7a. The change in instantaneous anode current for the QD-SDD at different V_b voltages is mainly concentrated on the pulse width of the anode current. This phenomenon implies that the change in V_b voltage is different from the change in V_n voltage.

In order to analyze the electric field changes of QD-SDD at different V_b voltages, simulations have been carried out. The cutline along with the electron drift trajectory is drawn. The electric field at different bias voltages is shown in Fig. 8. The change in the electric field due to V_b voltage is different from the change due to V_n voltage. It is worthwhile to note that the effect of V_b voltage is not unidirectional. In the horizontal direction, the potential difference between the V_bn electrode and the V_b electrode is reduced as the V_b bias voltage increases, therefore the electric field (horizontal electric field) below the drift area decreases. In the vertical direction, the electric field (vertical electric field) below the anode area is enhanced for the increased potential difference between the V_b electrode and the V₁ electrode. The phenomenon is shown in Fig. 8b. When the distance is less than 500 µm, the electric field increases. However, when the distance is greater than 500 µm, the electric field decreases.

The electron collection time is mainly controlled by the electric field strength due to the linear relationship between electron drift velocity and the electric field strength. It is clear that the electron collection time varies with the distribution of the electric field. The electron collection time of the QD-SDD at different V_b voltages is shown in Fig. 7b. For QD-SDD at higher V_b voltage, the collection time is reduced due to the stronger electric field below the anode region. It is also important to note that although the electric field below the drift rings area decreases, the electric field below the anode area increases with increasing V_b voltage, so the collection time is still reduced because the vertical electric field is more dominant.

The drift path is closely related to the electric field distribution. The drift trajectory is different due to different bias conditions. Figure 9 displays the drift trajectory of the QD-SDD at different V_b voltages. Therefore, the larger the voltage on the V_b electrode, the closer the electron drift trajectory is to the front surface. To accurately analyze the effect of the V_b voltage, the electron concentration and potential distribution along with the cutline at X = 40 µm are shown in Fig. 10. From the potential distribution in Fig. 10a, it can be observed that the difference in the potential distribution has emerged at different V_b voltages. The detector with a thickness of 525 µm is not fully depleted when the bias voltage of the V_b electrode is less than 40 V and the depletion region depends on the V_b bias voltage. The comparison of the electric field (Fig. 8) and the potential distribution (Fig. 10) shows that the lower V_b voltage implies a larger non-depletion region below the anode with a smaller electric field. The electron concentration in Fig. 10b changes due to the increase of V_b voltage. It can be seen that the drift path is closer to the surface when the V_b voltage increases.

QD-SDDs shown in Fig. 1 were fabricated on a 4-inch n-type wafer with a thickness of 525 µm and a resistivity of over 10 kΩ·cm. The diameter of a QD-SDD is 3.2 mm. In order to verify the effect of the bias conditions on the device performance, the experiments of the QD-SDD under a ⁵⁵Fe radiative source were measured with: (1) The innermost drift ring (V₁) was biased to a fixed voltage of -10 V, and the center ring (V_b) on the back was biased at -44 V. (2) The outermost drift rings (V_n and V_bn) on both sides were connected and biased to the same voltage. This measurement was carried out at 213K with a shaping time of 2 µs. The x-ray spectrum at different V_n voltages is shown in Fig. 11. The QD-SDD at different bias voltages shows different energy resolutions. The detector shows an energy resolution of 210 eV with the V_n bias voltage at -80 V, which is improved to 170 eV with a bias at -130 V or -100 V [13]. The experiment results indicate that the energy resolution is affected by the V_n voltage.

The establishment of the electron drift trajectory is also controlled by the bias voltage of the center drift ring on the back side (V_b). The transport characteristics are altered due to the different V_b voltages. The energy resolution of the QD-SDD at different V_b voltages was measured. The innermost drift ring (V₁) was biased to a fixed voltage of -10 V. The outermost drift rings (V_n and V_bn) on both sides were connected and biased at -130 V. Figure 11b shows the pulse height spectrum at the different V_b voltages. The energy resolution deteriorates as the bias voltage of the back center drift ring increases. The experiment results show that the energy resolution is related to the bias voltage of the V_b electrode.

QD-SDD used for x-ray detection has two advantages: Firstly, the QD-SDD can be biased at a voltage higher than twice the depletion voltage without the reach-through effect. The electric field in bulk is enhanced with the increasing potential difference between p⁺\(\)drift rings. As a result, the electron collection time to the anode is reduced. Second, the electron drift path of QD-SDD differs from that of the classical silicon drift detector and is safer for the signal electrons during the drift process because it is farther away from the surface. Therefore, the fewer electrons trapped on the surface, the higher the electron collection efficiency. The better electron collection efficiency and shorter collection time is helpful to achieve a better energy resolution.

In this work, a novel silicon drift detector, quasi-double-sided SDD (QD-SDD), is proposed to improve the flexibility of bias conditions and investigate the effect of bias conditions on energy resolution. Simulations of QD-SDD under irradiated x-rays were performed and the transient current of the anode was obtained. The electrical of the QD-SDD at different bias conditions were analyzed and compared by dealing with the date of the anode current.

From the simulation results, it can be seen that the electric field in the bulk increases with increasing V_n voltage. A stronger electric field means a greater electron drift velocity, resulting in shorter drift time and better collection efficiency. The effects of the increasing V_b voltage are considered to be mixed. On the one hand, a larger V_b voltage enhances the vertical electric field and reduces collection time, on the other hand, a larger V_b voltage leads to a deterioration of the energy resolution. As the V_b voltage increases, the transverse electric field below the drift region is decreasing, while the longitudinal electric field below the anode region is increasing. Due to the higher V_b voltage, the collection time is reduced, however, the drift path moves upward, closer to the front surface. The upward shift of the electron drift path results in electrons being trapped at the front surface and the energy resolution decreases.

Compared with the classical SDD, the QD-SDD has great flexibility of bias conditions, and the better electron collection efficiency and shorter drift time is realized when the QD-SDD is under optimized bias conditions. The measurement results also show that better energy resolution of the QD-SDD is realized at optimized bias conditions. The measurement results agree with the device simulation of the QD-SDD.

Acknowledgement

This work was supported by the National Key Research and Development Program of China (2022YFF0709501), National Natural Science Foundation of China (NSFC, Grant Nos. 12035020,52072399,62074165,12175305,62104253 and 12105357), Natural Science Foundation of Beijing Municipality (4192064,1212015).

Credit author statement

Longjie Wang: Validation, Data Curation, Formal analysis, Investigation, Simulated Data, Writing, Original Draft, Writing- Review& Editing,

Wei Luo: Mathodology, Data Curation, WritingReview& Editing, Investigation,

Rui Jia: Conceptualization, Data Curation, WritingReview& Editing, Project administration, Investigation

Xing Li: Conceptualization, Data Curation, WritingReview& Editing

Xiaorang Tian: Conceptualization, WritingReview& Editing, Project administration,

Mingpeng Zhang: Investigation, Data Curation, Simulated Data

Shuai Jiang: Investigation,

Jiawang Chen: Investigation,

Chengjian Lin: Investigation,

Xiaoping Ouyang:Investigation

Conflicts of interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The authors have no relationship with the Editors, and reviewers of this journal.

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Journal Publication

published 01 Jun, 2023

Read the published version in Microelectronics Journal →

Version 1

posted

You are reading this latest preprint version

Effect of bias conditions on transient anode current for quasi-double-sided silicon drift detector with high energy resolution

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Simulation Of Quasi-double-sided Silicon Drift Detector

2.1. Design and Parameters in simulation

2.2. The simulation results of QD-SDD and single-sided SDD at different V_n voltages.

2.3. The simulation results of V_b voltage

3. Experiment Results Of Quasi-double-sided Silicon Drift Detector

4. Conclusion

Declarations

References

Status:

Journal Publication

Version 1

Effect of bias conditions on transient anode current for quasi-double-sided silicon drift detector with high energy resolution

Status:

Journal Publication

Version 1

Abstract

Figures

1. Introduction

2. Simulation Of Quasi-double-sided Silicon Drift Detector

2.1. Design and Parameters in simulation

2.2. The simulation results of QD-SDD and single-sided SDD at different Vn voltages.

2.3. The simulation results of Vb voltage

3. Experiment Results Of Quasi-double-sided Silicon Drift Detector

4. Conclusion

Declarations

References

Status:

Journal Publication

Version 1

2.2. The simulation results of QD-SDD and single-sided SDD at different V_n voltages.

2.3. The simulation results of V_b voltage