Studies have been carried out to assess the influence of radiation damage on a variety of silicon devices within fields like particle and astroparticle physics, aerospace engineering, and radiation monitoring, etc. The damage caused by radiation to silicon devices can be categorized into two primary types: bulk damage and surface damage.

Ionization occurring in the silicon bulk is a reversible process and, consequently, does not result in any damage within the silicon bulk. On the other hand, non-ionizing energy loss (NIEL) induces atomic displacement damage in the silicon bulk. The effects of this displacement damage in the silicon bulk include (1) modifications to the effective doping concentration of the bulk, potentially leading to a type inversion of the original silicon, (2) a decrease in the generation lifetime, causing an elevation in the leakage current, and (3) the capture of signal charge, ultimately resulting in signal loss[1, 2].

In the majority of silicon devices, the combined components of the metal layer, silicon dioxide layer, interface connecting the silicon bulk and silicon dioxide, and implant structure constructed on the silicon bulk are collectively referred to as the surface of the device. Non-ionizing energy loss (NIEL) has minimal impact on silicon dioxide since silicon dioxide inherently possesses a highly irregular atomic structure, especially at the interface of the silicon bulk and silicon dioxide. Although ionization does not induce damage in the silicon bulk, it does result in damage to the surface of silicon devices. Some holes generated through ionization become trapped in silicon dioxide, with trapping being more probable in the silicon dioxide region near the interface of silicon and silicon dioxide due to the highly irregular atomic structure of that region. The consequences of the damage caused by trapped holes include (1) an elevation in the oxide charge and (2) the introduction of surface generation centers, leading to an increased leakage current[1, 2].

The increase in leakage current results in the sensor effectively operating at a lower bias voltage. The signal from a silicon sensor (for example, a PIN diode sensor) is directly proportional to the effective thickness, also known as the depletion depth, determined by the bias voltage. Consequently, it is crucial to examine how the sensor signal depends on the bias voltage.

A PIN diode consists of p-type, intrinsic or lightly doped, and n-type silicon regions.

When it is reverse biased, there is a depletion region formed where there are no free charge carriers in the intrinsic or lightly doped region.

As the reverse bias voltage increases, the depletion region increases.

When a minimum ionizing charged particle travels through the depletion region in the PIN diode, it produces ∼10,000 electron-hole pairs per a travel distance of 100 μm[3].

The depletion depth of the PIN diode is express as

where ε is the permittivity of the silicon, μ and

ρ are the major carrier mobility and the resistivity of the intrinsic or lightly doped region, respectively, and V is the reverse bias voltage applied on the PIN diode[4].

For this study, we utilized a silicon pixel sensor identical to the ones employed for detecting high-energy charged particles in the International Space Station[5].

The silicon pixel sensor was manufactured on a silicon wafer with a thickness of 525 μm as shown in Fig. 1. The silicon sensor comprises 16 pixels arranged in a 4 × 4 array, and each individual pixel occupies an area of 1.55 × 1.38 cm​2. The sensor is affixed to a flexible printed circuit board for the purpose of signal readout interconnection as shown in Fig. 2. The detailed procedure for fabricating these silicon sensors and establishing the signal readout interconnection is provided elsewhere[6].

Figure 1. (Color online) Schematic of the silicon PIN diode pixel sensor.

Figure 2. (Color online) Dimension of the silicon pixel sensor and its interconnection for signal readout.

We measured the electrical characteristics, specifically the capacitance and leakage current as a function of the reverse bias voltage, of a single pixel in the silicon sensors using an LCR meter and a pico-ammeter. The capacitance (C) is proportional to Ad, where A and d represent the area and depletion depth of the pixel. Therefore, the capacitance is expected to decrease as a function of 1V as the bias voltage increases until the pixel is fully depleted. Once the pixel reaches full depletion, the capacitance remains constant even as the bias voltage continues to increase. The measured capacitance of the pixel as a function of the bias voltage (C-V) agrees with the expected one. The full depletion voltage is ∼120 V.

Assuming there are no sources or effects of surface currents or damages, the leakage current (I) is expected to increase as a function of V as the bias voltage increases until the pixel is fully depleted[7]. Once the pixel reaches full depletion, the leakage current is expected to remain constant, even as the bias voltage continues to increase[7]. However, the measured leakage current of the pixel in the bias voltage (I-V) deviates from the expected behavior. This deviation can be attributed to various not well-known sources or effects of surface currents or damages. Despite this, the leakage current of ∼3.4 nA at 120 V is still very small, ensuring that it has no detrimental impact on the pixel performance.

We carried out the radiation source test for the silicon PIN diode pixel to measure the depletion depth of the pixel as a function of the reverse bias voltage. The radiation source is ​90Sr source which emits β-rays (i.e., electrons). Its β-ray energy spectrum is shown in Fig. 5[8].

Figure 3. (Color online) The capacitance of the pixel was measured as a function of the bias voltage. The vertical red line at the bias voltage of 120 V indicates the full depletion voltage, above which the capacitance remains more or less constant.

Figure 4. Measured leakage current of the pixel as a function of the bias voltage. The leakage current at the full depletion voltage of 120 V is ∼3.4 nA.

Figure 5. (Color online) The energy spectrum of the β-rays from the ​90Sr source[8].

The schematic of the experimental setup for the radiation source test is shown in Fig. 6. Electrons hit the trigger pixel and then proceed to hit the silicon pixel of interest if they have enough energy to pass the trigger pixel and reach the pixel of interest. When the trigger pixel is hit, it issues a trigger signal, which tracks and holds the signal from the pixel of interest. Subsequently, the signal is fed to external analog electronics and finally to an Analog to Digital Converter (ADC) for signal readout.

Figure 6. (Color online) Schematic of the setup for the radiation source test.
The track and hold method is employed in the electronics for signal readout.

We collected the pixel responses to the β-rays from the ​90Sr source using the experimental setup depicted in Fig. 6 for 9 different bias voltages. The distributions of the pixel responses for the bias voltages of 21, 60, and 167 V are illustrated in Fig. 7. Each distribution comprises two components: pedestal events and signal events. Pedestal events represent the pixel responses when the β-rays hit the trigger pixel but do not reach the pixel of interest, while signal events correspond to the pixel responses when the β-rays pass the trigger pixel and reach the pixel of interest.

Figure 7. (Color online) Distributions of the pixel response for the bias voltages of 21, 60, and 167 V. Each curve is the fit of the associated distribution to the two separate Gaussian functions, one for pedestal events and the other for signal events.

We performed a fitting process on each distribution acquired with the 9 distinct bias voltages. This fitting involves the use of two Gaussian functions—one for pedestal events and the other for signal events.

The results obtained are listed in Table 1, where ped and sig represent the means of the two Gaussians, while σped and σsig represent the standard deviations of the two Gaussians. Also listed are S(≡sig-ped) and Sσped. The latter is the signal-to-noise ratio (SN), which measures the separation of signal from noise. Shown in Fig. 8 is S as a function of the bias voltage. S is equivalent to the depletion depth and, therefore, it increases as the bias voltage increases and then remains constant once the PIN diode pixel is fully depleted. The vertical red line in Fig. 8 indicates the full depletion voltage of 120 V, beyond which S remains constant. The full depletion voltage determined with the S measurement from the radiation source test is consistent with the one determined with the C-V measurement from the electrical characterization. Finally, the measured SN values indicate that effective separation between the signal and noise is achievable even at low bias voltages with the silicon PIN diode pixel.

Figure 8. (Color online) S, which is equivalent to the depletion depth, as a function of the bias voltage. The vertical red line at the bias voltage of 120 V indicates the full depletion voltage, above which S remains more or less constant.

Table 1 . Fit results where ped and sig are the means of the two Gaussians, σped and σsig are the standard deviations of the two Gaussians, and S≡sig-ped.

V	ped	σped	sig	σsig	S	Sσped
12	5745.0	6.5	5774.7	8.6	29.7	4.6
21	5743.2	8.9	5782.5	8.6	39.3	4.4
37	5743.7	7.8	5789.7	10.4	46.0	5.9
60	5745.0	10.1	5797.5	11.4	52.5	5.2
80	5744.3	11.0	5800.9	15.5	56.6	5.2
100	5744.6	6.6	5802.7	10.6	58.0	8.8
127	5743.1	8.8	5805.5	12.1	62.4	7.1
150	5744.0	9.3	5806.5	13.1	62.5	6.7
167	5744.1	6.7	5806.5	11.8	62.4	9.3

The full depletion voltage of a silicon PIN diode sensor was determined by (1) the electrical C-V test and (2) analyzing the signal response to β-rays at various reverse bias voltages, with both measurements showing excellent agreement.

The signal response of the PIN diode, observed as a function of reverse bias voltage, could serve as a pre-calibration for the depletion depth (the effective thickness), especially when the PIN diode is operating in a severe radiation environment.

Although Silicon PIN diode sensors are recognized for their ability to withstand radiation levels in space environments, showing no observable signs of functional degradation even after extended exposure spanning many years, they do have a radiation exposure limit in harsh environments such as collider experiments. Beyond this limit, sensors may lose functionality due to damage or degradation caused by radiation. Hence, having prior knowledge of the effective thickness (i.e., depletion depth) as a function of the bias voltage is crucial in case the sensor is not fully depleted due to increased leakage current caused by radiation damage.

This research was supported by Kyungpook National University Development Project Research Fund, 2022.