Research on the Structure Design of Silicon Avalanche Photodiode with Near-Ultraviolet High Responsivity

Abstract

To improve the low responsivity of the silicon avalanche photodiode in the near-ultraviolet wavelength range, we designed a near-ultraviolet highly responsive Si-APD basic structure with a multiplication layer neighboring the photosensitive surface through the analysis of the optical absorption characteristics, junction breakdown characteristics, and avalanche multiplication characteristics. The dark current and electric field distribution of the device were investigated. Meanwhile, the structural parameters of the surface non-depleted layer, multiplication layer, and absorption layer were optimized. It was found that the breakdown voltage of the device is 21.07 V. At an applied bias voltage of 20.02 V, the device exhibits a responsivity of 6.79–14.51 A/W in the wavelength range of 300–400 nm. These results provide valuable insights for the design of silicon avalanche photodiode with high responsivity in the near-ultraviolet range.

1. Introduction

Ultraviolet detection technology displays extensive applications, such as missile warning, space exploration, fire detection, instrumental analysis, and biomedical research [1,2,3,4,5]. Traditional ultraviolet detectors contain vacuum-type ultraviolet detectors and solid-state ultraviolet detectors [6]. Among them, vacuum-type ultraviolet detectors mainly refer to photomultiplier tubes (PMTs), which could achieve large-area detection and possess the advantages of high gain, and fast response. However, PMTs suffer from drawbacks such as large size, high power consumption, and demanding operating environments, which limit their widespread applications [7,8]. Solid-state ultraviolet detectors can be broadly classified into two categories based on the different device materials, including wide-bandgap semiconductor detectors and silicon semiconductor detectors. Semiconductors with wide-bandgap include metal oxides (zinc oxide and gallium oxide), III-nitrides (gallium nitride and aluminum nitride), silicon carbide, diamond, etc. These materials, benefiting from their wide bandgap characteristics, are ideal for detecting ultraviolet light. However, semiconductors with wide bandgap merely only respond to ultraviolet light and exhibit no response to visible light. Additionally, further research on high-quality growth of substrate materials, suppression of lattice defects, and high signal-to-noise ratio detection are needed to explore. The challenges of small-scale device size and high cost exist in wide-bandgap semiconductors [9]. Silicon is an indirect bandgap semiconductor that absorbs incident light in the 300~1100 nm wavelength band and has a high ratio of electron-to-hole ionization rates. Avalanche photodiodes based on silicon, known as Silicon Avalanche Photodiodes (Si-APDs), possess high gain, low dark current, low excess noise, and fast response characteristics. They are commonly used for detecting weak light signals. However, most of the photo-generated carriers undergo surface recombination due to the limited penetration depth of ultraviolet light in silicon, resulting in low responsivity of Si-APD in the near-ultraviolet wavelength range. As a result, Si-APD is primarily applied in visible and near-infrared light detection, which is not suitable for the applications of near-ultraviolet light detection.

Recently, Scholars have conducted numerous investigations to enhance the detection capability of Si-APD for near-ultraviolet light. In 2000, avalanche photodetectors with ultraviolet light responsivity were prepared by Pauchard A et al., in which shallow p+ injection was activated by low-energy boron implantation and rapid thermal annealing. This device exhibited a peak response wavelength of 380 nm and a corresponding responsivity of 5.30 A/W at a bias voltage of 14.5 V. The maximum gain reached up to 50 within the range of 300–400 nm [10]. In 2012, Shimotori et al. utilized CMOS technology to fabricate a silicon avalanche photodiode, which exhibited a responsivity of 2.61 A/W at 405 nm and an avalanche gain of 36.8 at a bias voltage of 9.1 V [11]. In 2013, an internal quantum efficiency of approximately 60% at 400 nm was realized in Si-APD by adjusting the doping concentration in the near-surface region by Myers et al., improving the responsivity in the ultraviolet range [12]. In 2017, Napiah et al. reported the development of a p-CMOS-type Si-APD using 0.18 μm CMOS technology. This device demonstrated a responsivity of 0.20 A/W at a bias voltage of 7.0 V and a wavelength of 405 nm [13]. In the same year, Xia et al. utilized gradient boron doping technology to fabricate a highly sensitive silicon ultraviolet p+-i-n avalanche photodiode. The device exhibited an avalanche breakdown voltage of approximately 10.8 V and a responsivity of approximately 0.04–0.10 A/W in the range of 200–300 nm without external bias voltage [14]. In 2018, Iiyama et al. employed CMOS technology to fabricate a quadrant Si-APD. At a breakdown voltage near 9 V, the device showed a responsivity of approximately 1.00 A/W at a wavelength of 405 nm [15]. In 2022, Chen et al. designed a separate-absorption-charge-multiplication (SACM) type Si-APD with a breakdown voltage of approximately 34.2 V and a responsivity of 3.72 A/W at a wavelength of 400 nm [16]. Also in the same year, Sun et al. developed a lateral SAM-APD based on SOI technology, which exhibited a responsivity of 1.92 A/W at a wavelength of 300 nm near a breakdown voltage of 7.8 V [17]. The above studies have shown that the detection capability of APDs for UV light can be enhanced by optimizing the detector surface structure. However, there is relatively little research on improving the near-ultraviolet responsivity of vertical Si-APD structures, and the responsivity in the near-ultraviolet band is still relatively low in previous studies, further research on Si-APD is necessary to enhance their light detection performance in the near-ultraviolet wavelength range with the increasing demand. The focus of this study is to improve the photoresponsivity in the near-ultraviolet wavelength band (300~400 nm) through device epitaxial structure design and structure optimization, taking into account the high multiplication gain and low dark current characteristics of the device.

Based on the analysis of detector characteristics, a Si-APD structure for near-ultraviolet high sensitivity detection is proposed and optimized for the responsivity of the structure in the near-ultraviolet wavelength band, achieving highly efficient detection of Si-APD in the near-ultraviolet range with low applied bias voltage, and high avalanche multiplication gain and low dark current are achieved at relatively low applied bias voltage. The research presented in this paper serves as a valuable reference for the design and fabrication of Si-APD with enhanced responsivity in the near-ultraviolet range.

2. Design of Si-APD Structure

2.1. Analysis of the Basic Characteristics of Si-APD

The optical responsivity of APD reflects the photoelectric conversion capability of the device, which can be expressed as [18]:

$$SR=M·\frac{I_{p0}}{P_{in}}\approx M·\frac{\lambda }{1.24}·\eta =M\phi (1-R)[1-\mathit{exp}(-\alpha W_D)]\frac{\lambda }{1.24}$$

(1)

where λ, M, I_p0, η, φ, W_D, R, and α represent the wavelength of the incident light, the multiplication coefficient, the photocurrent without avalanche multiplication, the quantum efficiency, the probability of single photon excitation-producing electron-hole pairs absorbed by the silicon material, the thickness of the depletion region, the surface reflectivity of silicon material, and the optical absorption coefficient of silicon material, respectively. Here, when the incident light intensity decays to 1/e of the initial light intensity, the penetration depth of the corresponding wavelength of light in the semiconductor is d, where d = 1/α. Additionally, the relationship between R and d concerning the incident light wavelength is illustrated in Figure 1a based on the experimental values for parameters of Si material [19]. Meanwhile, it is evident that the responsivity of APD for a specific wavelength is primarily influenced by the W_D according to Formula (1). Assuming that the multiplication coefficient M = 1, φ = 100%, and all photogenerated carriers can enter the depletion region of the device, the relationship between responsivity and incident light wavelength for different W_D is depicted in Figure 1b.

As shown in Figure 1a, the penetration depth of incident light in silicon increases with the increase of the incident light wavelength. The d ≤ 0.1 μm when incident light wavelength λ ≤ 0.4 nm, indicating that most of the near-ultraviolet light is absorbed near the surface after entering the semiconductor, so the thickness of the non-depletion layer on the surface of the designed APD should be minimized to improve the collection efficiency of the photogenerated carriers. Figure 1b reveals that with the increase of W_D in the Si-APD, the responsivity improves, and the peak response wavelength shifts towards longer wavelengths. As the W_D > 0.3 μm, the absorption of near-ultraviolet light by the depletion region approaches saturation, and the number of photo-generated carriers ceases to increase. Therefore, the responsivity stabilizes in the near-ultraviolet range of 0.3~0.4 μm. Consequently, to ensure sufficient absorption of near-ultraviolet incident light by the device, it is important to design the thickness of the near-ultraviolet absorption region as not less than 0.3 μm in Si-APD.

The maximum electric field at the junction breakdown of the Si-APD is approximated using a one-sided abrupt junction model. The breakdown voltage in a one-sided abrupt junction can be expressed as [20]:

$$V_{br}=\frac{{\epsilon }_s{E_{max}}^2}{2qN}$$

(2)

Here, ε_s, N, and E_max represent the dielectric constant of the lightly doped region, the doping concentration on the lightly doped side, and the maximum electric field during p-n junction breakdown, respectively. The empirical formula for the maximum electric field at Si abrupt junctions breakdown is given by [20]:

$$E_{max}=\frac{4\times {10}^5}{1-\left(\frac{1}{3}\right){\mathit{log}}_{10}\left(\frac{N}{{10}^{16}}\right)}$$

(3)

Assuming that the doping concentration in the n⁺-region is fixed at 2 × 10¹⁷ cm⁻³, and the doping concentration in the p-region (N_p) ranges from 10¹⁴ to 10¹⁷ cm⁻³ in the n⁺-p abrupt junction model, the variation of the E_max and the V_br with the N_p during junction breakdown can be calculated according to Formulae (2) and (3), as shown in Figure 2. When the doping concentration in the n⁺-region remains constant, E_max gradually increases while V_br rapidly decreases with the increase of N_p. To obtain higher electric field strength while realizing lower breakdown voltage inside the device, when the doping concentration of the highly doped side of the silicon one-sided abrupt junction is determined, the lightly doped side should be selected with as high a doping concentration as possible. Alternatively, a reach-through avalanche photodiode (RAPD) structure can be designed to confine the high electric field strength multiplication region to a narrow portion of the depletion layer.

The multiplication coefficient M(x) of the APD represents the ratio between the output photocurrent I_M after undergoing avalanche multiplication and the initial photocurrent I₀ without multiplication. It is assumed that the thickness of the multiplication region in the APD ranges from 0 to W_m, with electron injection starting at x = 0, the multiplication coefficient M(x) is given by [20]:

$$M\left(x\right)=\frac{1}{1-{\int }_0^{W_m}{\alpha }_n\mathit{exp}\left[-{\int }_x^{W_m}\left({\alpha }_n\left(x\right)-{\alpha }_p\left(x\right)\right)d{x}^{\prime }\right]dx}$$

(4)

where α_n and α_p are the ionization rates of electrons and holes, respectively, which denote the number of electron-hole pairs generated per unit distance traveled by a single carrier. The influence of the electric field intensity E(x) on the carrier ionization rate can be expressed as [21]:

$$\begin{array}{c}\left\{\begin{array}{l}{\alpha }_n\left(x\right)=a_{n}exp\left[-\left(\frac{b_n}{E\left(x\right)}\right)\right]\\ {\alpha }_p\left(x\right)=a_{p}exp\left[-\left(\frac{b_p}{E\left(x\right)}\right)\right]\end{array}\right.\end{array}$$

(5)

where a_n, b_n, a_p, and b_p are experimental parameters representing the ionization rates of electrons and holes. By using Formula (5), the ionization rates of electrons and holes for different electric field intensities can be calculated based on the experimental parameters of a_n = 3.8 × 10⁶ cm⁻¹, b_n = 1.75 × 10⁶ V·cm⁻¹, a_p = 2.25 × 10⁶ cm⁻¹, b_p = 3.26 × 10⁶ V·cm⁻¹ [22], as shown in Figure 3a. Assuming the width of the multiplication region is approximately equal to the multiplication layer thickness and the electric field strength of the multiplication layer remains constant, the relationship between the M and the E in the multiplication region can be calculated by combining Formulas (4) and (5) for different W_m, as depicted in Figure 3b.

Figure 3a exhibits that the α_n and α_p in silicon material increase with the electric field intensity. Furthermore, the α_n is significantly higher than α_p at the same electric field intensity. Considering the shallow penetration depth of UV light in Si, in order to obtain a stronger avalanche multiplication effect of photogenerated carriers inside the device, a p-on-n type structure should be chosen for the UV-detection-enhanced Si-APD. Additionally, under the determined thickness of multiplication layer, the M sharply increases when the electric field intensity in the multiplication region reaches a specific value, as shown in Figure 3b. This indicates that the electric field intensity is close to or equal to the maximum electric field intensity corresponding to the device’s avalanche breakdown. Hence, in order to achieve a higher multiplication coefficient, the applied bias voltage (V_apd) during device operation should approximately equal the avalanche breakdown voltage (V_br-apd). The curve in Figure 3b also reveals that as the multiplication region thickness decreases, the electric field intensity corresponding to the device’s avalanche breakdown increases. This phenomenon can be attributed to the fact that higher electric field intensity results in higher ionization rates of carriers, enabling a higher multiplication coefficient to be achieved within a smaller thickness of multiplication region. However, it is important to consider the doping concentration and thickness of the multiplication region together when designing devices, as the thickness and the electric field distribution in the multiplication region are also influenced by the doping concentration.

2.2. Design and Analysis of Si-APD Structure

Based on the above analysis of detector performance parameters, a Si-APD structure for near-ultraviolet high-sensitivity detection is designed in this paper, as illustrated in Figure 4. The device structure consists of a heavily doped p⁺-type surface layer, lightly doped p-type multiplication layer, heavily doped n-type field charge, lightly doped n⁻⁻-type absorption layer, and n⁺⁺-type substrate layer from top to bottom. The Si-APD is capable of efficiently absorbing and responding to incident light in the range of 0.3 to 0.8 μm. Specifically, near-ultraviolet light is primarily absorbed in the surface non-depletion layer and multiplication layer, while visible light is mainly absorbed in the absorption layer. The thickness of the surface non-depletion layer is relatively small, which makes the depletion region closer to the photosensitive surface when the device is under a pull-through state, which reduces the recombination of photo-generated carriers in the surface non-depletion layer. Additionally, the higher ionization rate of electrons leads to avalanche multiplication, significantly improving the detection efficiency of the APD for near-ultraviolet light.

The transport behavior of carriers in Si-APD directly affects the optoelectronic performance of the device, which is influenced by the internal electric field distribution. Here, we provided a brief derivation of the internal electric field distribution of Si-APD. For a p-n abrupt junction, the electric field distribution in the depletion region can be represented as follows [20]:

$$E\left(x\right)=E_m-\frac{q{N}_m}{{\epsilon }_0{\epsilon }_m}x$$

(6)

where N_m is the doping concentration, ε₀ is the vacuum permittivity, ε_m is the relative permittivity of the doping layer, and E_m is the maximum electric field intensity within the p-n junction. The expression of the electric field distribution of the designed Si-APD, under the condition of a pull-through state (without considering the built-in potential due to the variation in doping concentrations at the heterojunction), can be derived based on Formula (6) as follows:

$$E\left(x\right)=\left\{\begin{array}{cc}{E}_M+\frac{q{N}_p}{{\epsilon }_0{\epsilon }_p}{x}_2+\frac{q{N}_{p^{+}}}{{\epsilon }_0{\epsilon }_{p^{+}}}(x_1-x)\hfill & (x_1<x<x_2)\hfill \\ E_M+\frac{q{N}_p}{{\epsilon }_0{\epsilon }_p}x\hfill & (x_2<x<0)\hfill \\ E_M-\frac{q{N}_n}{{\epsilon }_0{\epsilon }_n}x\hfill & (0<x<x_3)\hfill \\ E_M-\frac{q{N}_n}{{\epsilon }_0{\epsilon }_n}{x}_3-\frac{q{N}_{n^{-}}}{{\epsilon }_0{\epsilon }_{n^{-}}}(x_4-x)\hfill & (x_3<x<x_4)\hfill \\ E_M-\frac{q{N}_n}{{\epsilon }_0{\epsilon }_n}{x}_3-\frac{q{N}_{n^{-}}}{{\epsilon }_0{\epsilon }_{n^{-}}}(x_4-x_3)-\frac{q{N}_{n^{++}}}{{\epsilon }_0{\epsilon }_{n^{++}}}(x_5-x)\hfill & (x_4<x<x_5)\hfill \end{array}\right.$$

(7)

Here, N_p, N_p⁺, N_n, N_n⁻, N_n⁺⁺, ε_p, ε_p⁺, ε_n, ε_n⁻, and ε_n⁺⁺ represent the doping concentrations and relative permittivities of the multiplication layer, surface non-depletion layer, field charge, absorption layer, and substrate layer, respectively. E_M represents the maximum electric field intensity inside the Si-APD at device breakdown. Moreover, the E_M at the breakdown of the Si-APD can be approximated from the expression for E_max of the single-sided abrupt junction [23], which in turn allows the calculation of the V_br-apd of the device.

3. Structural Optimization and Discussion of Results

Based on the analysis of the performance parameters of Si-APD above and considering the characteristics of efficient near-ultraviolet absorption, low operating voltage, and high avalanche multiplication coefficient for the Si-APD, preliminary parameters for each layer are set as shown in

Table 1. Initial structural parameters of each layer in Si-APD.

Doping Type	Thickness/μm	Doping Concentration/cm−3
p+	0.10	1.0 × 1018
p	0.20	2.0 × 1016
n	0.15	2.0 × 1017
n−	1.00	1.0 × 1014
n++	20.00	1.0 × 1019

. Based on the parameters set in Table 1, two-dimensional simulation calculations of Si-APD were performed by the TCAD simulator to analyze the optoelectronic characteristics of the device. The simulation was performed with an incident light wavelength range of 0.3 to 0.8 μm, the power density of the incident light at each wavelength was set to 1 W/cm², and the light is vertically incident on the photosensitive surface of the Si-APD with the diameter of 10 μm. Meanwhile, the surface reflectivity is assumed to be the natural reflectivity of silicon material. To improve the accuracy of the simulation results, various physical models are employed, including the Shockley–Read–Hall recombination [24,25], Fermi–Dirac carrier distribution [26,27], Selberherr’s carrier impact ionization [28,29], and carrier mobility [30,31], etc.

3.1. Electric Field Distribution and Responsivity of Si-APD

Based on the structural parameters shown in Table 1, the internal electric field distribution curves of Si-APDs at different applied bias voltages (without considering the effect of impurity concentration on the relative permittivity of the material, the relationship between the relative permittivity of silicon and the doping concentration is given by the literature [24]) as well as the spectral response curves of Si-APD under applied bias voltages of 0.95 V_br-apd (V_br-apd ≈ 21.87 V) have been calculated, as shown in Figure 5.

As can be seen from Figure 5a, at low applied bias (V_apd < 0.5 V_br-apd) the device is not yet pulled through and the electric field strength in the depletion region is small, with further increase in applied bias (V_apd > 0.5 V_br-apd) the device is fully pulled-through and the thickness of the depletion region and the electric field strength increase, and the maximum electric field strength in the multiplier layer is 5.33 × 10⁵ V/cm when the applied bias is equal to the avalanche breakdown voltage (V_br-apd) of the device, the maximum electric field strength in the multiplication layer is 5.33 × 10⁵ V/cm. As can be seen in Figure 5b, the peak response wavelength of the APD is in the blue wavelength band (4.51 A/W@ 470 nm), but the responsivity in the UV wavelength band is still low (0.86 A/W@ 360 nm). In the following, the photoresponsivity in the near-UV band is improved by optimizing the structural parameters of the surface layer, the multiplier layer, and the absorber layer.

3.2. Optimization of Si-APD Structural Parameters

The heavily doped surface non-depletion layer is mainly used to form ohmic contacts, and the doping concentration has a minor impact on the responsivity of the Si-APD. Therefore, we only investigated the influence of the surface non-depletion layer thickness on the responsivity. Based on the parameters listed in Table 1, the spectral responsivity curves with different surface non-depletion layer thicknesses at the applied bias voltage of 0.95 V_br-apd(V_br-apd ≈ 21.87 V) are calculated, as shown in Figure 6. It can be observed that the responsivity increases in the near-ultraviolet wavelength range as the surface non-depletion layer becomes thinner. According to the relationship between incident light wavelength and penetration depth shown in Figure 1a, shorter-wavelength incident light is mainly absorbed near the shallow surface of the APD. With the increase of the surface non-depletion layer thickness, the optical absorption loss increases, resulting in a decrease in the number of optically generated carriers entering the depletion region and an increase in the number of carriers being recombined in the surface layer. So, the thickness of the surface non-depletion layer is selected as 0.05 μm.

The multiplication layer is the primary region where the carrier multiplication effect occurs. The thickness and doping concentration of the multiplication layer significantly affect the carrier avalanche multiplication effect and determine the breakdown voltage of the Si-APD to some extent. Firstly, we investigated the influence of the multiplication layer thickness on the spectral responsivity under applied bias voltages of 0.95 V_br-apd based on the optimization of the surface non-depletion layer. The V_br-apd of APDs with different multiplier layer thicknesses are shown in

Table 2. The breakdown voltage of devices with different multiplier layer thicknesses.

d/μm	0.10	0.15	0.20	0.25	0.30	0.35	0.40	0.45
Vbr-apd/V	26.53	23.60	21.87	21.12	21.01	21.36	22.08	23.00

. The influences of the thickness of the multiplication layer on the responsivity in the near-ultraviolet and visible light range are different in Figure 7a. According to Formula (7) of the internal electric field distribution within the APD, the carrier avalanche multiplication process primarily occurs in the multiplication layer. As the thickness of the multiplication layer changes, the width of the depletion region and the electric field intensity in both the surface non-depletion layer and the multiplication layer undergo significant alterations. Additionally, since the penetration depth of photons in silicon is related to the wavelength, the multiplication coefficient produced by the photo-generated carriers varies for different wavelength ranges. Figure 7b reveals that the responsivity gradually increases with the increasing thickness of the multiplication layer when the thickness of the multiplication layer is less than 0.25 μm. This phenomenon can be attributed to the insufficient absorption of 0.4 μm incident light by the surface non-depletion layer and the multiplication layer, resulting in a lower number of photo-generated carriers and an incomplete avalanche multiplication process. However, as the thickness of the multiplication layer increases beyond 0.25 μm, the responsivity gradually decreases. This results from the increasing voltage on both sides of the multiplication layer with the increasing thickness of the multiplication layer, resulting in a gradual decrease in the voltage and electric field strength across the absorption layer. Consequently, the drift velocity of photogenerated carriers in the absorption layer decreases, leading to a reduction of drift current. Therefore, a multiplication layer thickness of 0.25 μm is chosen as it exhibits higher responsivity at a wavelength of 0.4 μm.

Next, we investigated the impact of multiplication layer doping concentration on the spectral responsivity with the fixed thickness of the multiplication layer of 0.25 μm. The V_br-apd of APDs with different multiplier layer doping concentrations are shown in

Table 3. The breakdown voltage of devices with different multiplier layer doping concentrations.

N/cm−3	1 × 1015	2 × 1015	5 × 1015	8 × 1015	1 × 1016	2 × 1016	3 × 1016	5 × 1016
Vbr-apd/V	17.75	17.93	18.48	19.02	19.38	21.13	22.86	25.88

. Based on the spectral responsivity curve of the device at an applied bias voltage of 0.95 V_br-apd in Figure 8a, it can be observed that the smaller doping concentration of the multiplier layer could lead to the higher responsivity of the device in the near-ultraviolet wavelength range. Figure 8b shows the relationship between responsivity and multiplication layer doping concentration at a wavelength of 0.4 μm. As the doping concentration of the multiplication layer in the device increases from 1 × 10¹⁵ cm⁻³ to 5.0 × 10¹⁶ cm⁻³, the responsivity gradually decreases from 5.30 A/W to 3.70 A/W. Through the electric field distribution within the APD, as described by Formula (8), an increase in the doping concentration of the multiplication layer could lead to a decrease in the electric field strength across both the surface depletion layer and the multiplication layer, resulting in a reduction in the carrier ionization rate and a decrease in the avalanche multiplication current. As depicted in Figure 8b, a higher responsivity is observed at the doping concentration of 1.0 × 10¹⁵ cm⁻³ for an incident light wavelength of 0.4 μm. Therefore, the multiplication layer doping concentration of 1.0 × 10¹⁵ cm⁻³ is selected.

To achieve high spectral responsivity of Si-APD over a wide spectral range, the doping concentration and thickness parameters of the absorption layer are optimized. Firstly, the impact of the doping concentration of the absorption layer on the spectral responsivity under applied bias voltages of 0.95 V_br-apd is investigated based on the optimization parameters of the multiplication layer. The V_br-apd of APDs with different absorption layer doping concentrations are shown in

Table 4. The breakdown voltage of devices with different absorption layer doping concentrations.

N/cm−3	5 × 1013	1 × 1014	3 × 1014	1 × 1015	3 × 1015	5 × 1015
Vbr-apd/V	17.79	17.75	17.60	17.11	16.30	16.08

. Figure 9a reveals that the variation of spectral responsivity is minimal when the doping concentration of the absorption layer increases from 5.0 × 10¹³ cm⁻³ to 1.0 × 10¹⁵ cm⁻³. According to the electric field distribution within the APD as described by Formula (7), the absorption layer is fully depleted at an applied bias voltage of 0.95 V_br-apd. Meanwhile, due to the relatively low doping concentration of the absorption layer, the electric field intensity in both the absorption layer and the multiplication layer remains essentially unchanged with increasing the doping concentration of the absorption layer. Consequently, the responsivity remains nearly constant. However, when the doping concentration of the absorption layer continues to increase beyond 1.0 × 10¹⁵ cm⁻³, the responsivity rapidly decreases. This can be attributed to the decreasing electric field intensity of the absorption layer as the doping concentration further increases, resulting in a reduction in the drift velocity of photogenerated carriers within the absorption layer and a subsequent decrease of the drift current. The absorption layer doping concentration of 3.0 × 10¹⁴ cm⁻³ corresponds to a higher responsivity at an incident light wavelength of 0.4 μm in Figure 9b. Therefore, the doping concentration of the absorption layer is selected as 3.0 × 10¹⁴ cm⁻³.

Furthermore, the influence of the absorption layer thickness on the spectral responsivity under applied bias voltages of 0.95 V_br-apd is investigated based on the 3.0 × 10¹⁴ cm⁻³ doping concentration of the absorption layer. The V_br-apd of APDs with different absorption layer thicknesses are shown in

Table 5. The breakdown voltage of devices with different absorption layer thicknesses.

d/μm	0.5	1.0	2.0	3.0	4.0	5.0	6.0	7.0
Vbr-apd/V	16.71	17.60	19.16	20.23	20.85	21.07	21.09	21.09

. The spectral responsivity of the device in the near-ultraviolet spectral range steadily increases as the thickness of the absorption layer increases from 0.5 μm to 5.0 μm in Figure 10a. Since the larger breakdown voltage in the device and higher electric field intensity of the multiplication layer as the absorption layer thickness increases. Consequently, the carrier ionization rate becomes large, leading to a larger multiplication current. However, as the absorption layer thickness continues to increase beyond 5.0 μm, the responsivity in the near-ultraviolet spectral range gradually decreases. The reason is that the device is under a non-pull-through state at an applied bias voltage of 0.95 V_br-apd, and the breakdown voltage reaches a stable value, leading to the decrease of the drift current of photogenerated carriers in the absorption layer. Figure 10b, the absorption layer thickness of 5.0 μm corresponds to a higher responsivity at an incident light wavelength of 0.4 μm. Therefore, the thickness of the absorption layer is chosen as 5.0 μm.

Based on the mentioned optimization results, the final structural parameters for the Si-APD are summarized in

Table 6. Optimized structural parameters of each layer in Si-APD.

Doping Type	Thickness/μm	Doping Concentration/cm−3
p+	0.05	1.0 × 1018
p	0.25	1.0 × 1015
n	0.15	2.0 × 1017
n−	5.00	3.0 × 1014
n++	20.00	1.0 × 1019

. The calculated breakdown voltage V_br-apd for the device under these parameters is 21.07 V. Figure 11a illustrates the spectral responsivity curve of the APD at an applied bias voltage of 0.95 V_br-apd. It can be observed that the device exhibits a spectral responsivity ranging from 6.79 A/W to 14.51 A/W in the wavelength range of 0.3 μm to 0.4 μm, the responsivity is significantly improved compared to the pre-optimized structure. The device also has a high responsivity in the visible light band, especially in the blue light band with a peak photoresponsivity (14.91 A/W@ 0.47 μm), which is attributed to the wide depletion region thickness after the device is pulled through as shown in Figure 11b so that high-efficiency absorption of visible light can be realized.

3.3. I-V and Avalanche Multiplication Characteristics of Si-APD

The dark current of the Si-APD primarily consists of the diffusion current of minority carriers (I_diff), the generation-recombination current of carriers within the depletion region (I_g,r), and the avalanche multiplication current (I_m) [32]. The expressions for these currents are as follows:

$$E\left(x\right)\left\{\begin{array}{l}{I}_{diff}=q{n_i}^{2}A\left(\sqrt{\frac{D_n}{{\tau }_n}}\frac{1}{N_A}+\sqrt{\frac{D_p}{{\tau }_p}}\frac{1}{N_D}\right)\left(\mathit{exp}\left(\frac{qV}{kT}\right)-1\right)\\ I_{g,r}=\frac{q{n}_{i}A{W}_D}{{\tau }_{eff}}\left(\mathit{exp}\left(\frac{qV}{2kT}\right)-1\right)\\ I_m={\int }_0^{W_m}A\left({\alpha }_n\left|J_n\right|+{\alpha }_p\left|J_p\right|\right)dx\end{array}\right.$$

(8)

Here, D_n and D_p represent the diffusion coefficients of p-region electrons and n-region holes, respectively, n_i represents the intrinsic carrier concentration, τ_n, and τ_p represent the diffusion lifetimes of p-region electrons and n-region holes, respectively, τ_eff represents the lifetime of the effective carrier, N_A and N_D represent the doping concentrations in the p-region and n-region, respectively, T, A and V represent the lattice temperature, the area of the depletion region boundary, the applied bias voltage, respectively, J_n and J_p represent the current densities of electrons and holes, respectively. Considering the parameters provided in Table 6, the I-V characteristic curve can be calculated by Equation (8). The calculated results of Figure 5a are performed using the values given in reference [28], where n_i = 1.5 × 10¹⁰ cm⁻³, D_n = 25 cm²s⁻¹, D_p = 10 cm²s⁻¹, τ_n = τ_p = 5 × 10⁻⁷ s, τ_eff ≈ 2 × 10⁻⁷ s, T = 300 K, kT/q ≈ 0.026 V, and the wavelength of incident light for calculating photocurrent is set to 400 nm. Furthermore, the internal multiplication coefficient curves with different applied bias voltages are calculated and shown in Figure 12b.

As shown in Figure 12a, the dark current (I_d) increases with the V_apd of the Si-APD. When the V_apd is relatively small, the Id is low (part I in Figure 12a), and the dark current is mainly formed by the generation–recombination current and the lower diffusion current. With the further increase of the applied bias voltage, the device is fully pulled-through and the thickness of the depletion region and the electric field strength of the multiplication region increase, more carriers generate avalanche multiplication effect in the multiplication region and are rapidly separated under the action of the electric field in the depletion region, and the dark current is increased (corresponding to part II in Figure 12a). At this time, the multiplication coefficient is increased, as shown in Figure 12b, and the dark current is mainly formed by the higher avalanche multiplication current and the generation-recombination current. When the applied bias voltage is close to the avalanche breakdown voltage of the APD, the dark current increases sharply (corresponding to part III in Figure 12a), and the ionization rate of the carriers increases rapidly with the increase of the electric field strength in the multiplication region at this time, resulting in a drastic increase in the dark current and the multiplication coefficient. From Figure 12, it can also be seen that the device has a high avalanche multiplication gain (≈50) and low dark current (<0.1 nA) at a relatively low applied bias voltage (0.95 V_br-apd), which also indicates the advantages of the device structure in terms of electrical characteristics.

4. Conclusions

To enhance the responsivity of Si-APD in the near-ultraviolet wavelength range, this paper proposed and optimized a near-ultraviolet highly responsive Si-APD basic structure with a multiplication layer neighboring the photosensitive surface. Under the optimized parameters, which include a surface non-depletion layer thickness of 0.05 μm with a doping concentration of 1.0 × 10¹⁸ cm⁻³, a multiplication layer thickness of 0.25 μm with a doping concentration of 1 × 10¹⁵ cm⁻³, an absorption layer thickness of 5.0 μm with a doping concentration of 3.0 × 10¹⁴ cm⁻³, and a field charge thickness of 0.20 μm with a doping concentration of 2.0 × 10¹⁷ cm⁻³, the device exhibits a V_br-apd of 21.07 V. At an applied bias voltage of 0.95 V_br-apd (i.e., 20.02 V), the device demonstrates a high responsivity ranging from 6.79 A/W to 14.51 A/W in the near-ultraviolet wavelength range of 300 to 400 nm, and high avalanche multiplication gain and low dark current are achieved at relatively low applied bias voltage. The device also has a high responsivity in the visible light band (14.91 A/W@ 0.47 μm). The above results show that this APD structure can realize high-efficiency detection in the near-ultraviolet to visible wavelength bands, which is of reference significance for applications in near-ultraviolet high-sensitivity detection, underwater visible light communication, and other fields.