CHEN Wei-shuai，WANG Hao-bing，TAO Jin，Gao Dan，LV Jin-guang，QIN Yu-xin，GUO Guang-tong,2，LI Xiang-lan,2，WANG Qiang，ZHANG Jun，LIANG Jing-qiu，WANG Wei-biao

（1.State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics,Chinese Academy of Sciences, Changchun 130033, China；2.University of Chinese Academy of Sciences, Beijing 100049, China；3.Collage of Science & Engineering, Jinan University, Guangzhou Key Laboratory of Visible Light Communication Engineering Technology, Guangzhou 510632, China）

Abstract:In order to achieve high spectral responsivity of the silicon avalanche photodiode in blue band(400?500 nm),Separated Absorption Control Multiplication (SACM) basic device structure was designed.Based on multiple physical models,the effect of the thickness on the avalanche breakdown voltage and the photocurrent gain of the device and the effect of the doping concentration of the multiplication layer on the optical responsivity were investigated.Comprehensively considering the factors of light responsivity and breakdown voltage,the results show that the device has a low breakdown voltageVbr-apd=34.2 V when the doping concentration of the surface non-depleted layer is 1.0×1018 cm?3,and the thickness is 0.03 μm;the doping concentration of absorption layer is 1.0×1015 cm?3,the thickness is 1.3 μm,the doping concentration of field control layer is 8.0×1016 cm?3,the thickness is 0.2 μm and the doping concentration of double layer is 1.8×1016 cm?3 and the thickness is 0.5 μm.WhenVapd=0.95Vbr-apd,it has higher optical responsivity in blue band,i.e.SR is 3.72～6.08 A·W?1.The above research results provide certain theoretical reference for the preparation of practical Si-APD devices with high blue light detection responsivity.

Key words:avalanche photodiode;silicon;spectral response

1 Introduction

With the development and wide application of short-wavelength visible light sources (such as blue LEDs,blue semiconductor lasers),the application requirements of short-wavelength visible light efficient detection technology are also increasing.Especially with the rapid development of visible light communication technology[1],biomedical engineering,underwater optical communication[2]and other fields,there is an urgent need for visible light detectors with high bandwidth,high gain,wide spectrum and high optical response[3].White LEDs are an important light source for visible light communication[4].Currently,commonly used white LEDs mainly include fluorescent white LEDs (white light is formed by mixing phosphors excited by blue LEDs to form white light[5]);red,green and blue white LEDs (RGB-LED)[6].For the above two white LEDs,blue light is the main working band,so photodetectors with high blue light response are of great significance to further promote the development and application of the integration of lighting and communication[7].Currently commonly used photodetectors are mainly PIN photodiode (PIN-PD),Photo Multiplier Tube (PMT) and Avalanche Photodiode(APD).However,PIN has low optical responsivity,short detection distance,and high light source power requirements,which limit its further application in visible light communication[8].PMTs can detect short wavelengths,but the disadvantages of high voltage and sensitivity to magnetic fields limit their application in visible light communication[9].Avalanche photodetector (APD) is a semiconductor detector with high internal gain and high photoresponsivity[10],and does not have the above-mentioned disadvantages of PMT,so it has attracted extensive attention in the research of visible light detectors.

Silicon (Si) can absorb incident light in the 380–1 100 nm band,which is a good material for the preparation of wide-spectrum detectors[11].In addition,the preparation process of Si semiconductor devices is mature[12]and the impact ionization rate of electrons to holes is high and the tunnel current is low in silicon materials[13].Therefore,the siliconbased avalanche photodiode (Si-APD) has the advantages of high gain,low noise and good stability.However,due to the high absorption coefficient of blue light in silicon,the penetration depth of blue light in silicon is relatively shallow,and most of the photo-generated carriers are located in the shallow surface layer.Therefore,it is easy to cause some carriers to recombine on the shallow surface,resulting in a small number of photogenerated carriers entering the absorption layer and low photoelectric conversion efficiency in the blue light band.This brings great difficulty to the design and fabrication of Si-APD device with high blue light responsivity.In order to improve the detection efficiency of silicon for blue light and to improve the performance of Si-APD in the blue light band,researchers have carried out the following related studies:in 2010,Catherine M.Pepinet al.of Excelitas Company prepared a UV-enhanced Si-based APD by "buried junction" on an epitaxial wafer with an avalanche breakdown voltage of 400 V and a responsivity of 39 A/W (M=150) at a wavelength of 430 nm[14].In 2015,Othmanet al.highly integrated Si-based APDs through a CMOS process with an avalanche breakdown voltage of 10 V and a gain of 100 at 405 nm wavelength[15].In the same year,Wang Xudonget al.optimized the structural parameters of the device based on Separated Absorption Control Multiplication (SACM) type Si-APD (n-p-p+-p-p+type doped structure,light incident from the surface of the N type layer),and an antireflective film structure with alternating high and low refractive index was designed on the device surface.With the structure of antireflection coating,the optimized device has a peak response wavelength of 406 nm,avalanche breakdown voltage of 105.9 V,and optical responsivity at the peak wavelength of 250 A/W[16].In 2015,Huo Linzhanget al.proposed a SiPM detector with a deep trench isolation structure,which improved the detection efficiency in the blue-violet region (360～420 nm) with about 90 V of the breakdown voltage[17].In 2019,Lu Huanhuanet al.designed a SAM-type Si-APD.The multiplication layer of the device is closer to the photosensitive layer,which can effectively reduce the recombination loss of photogenerated carriers.The device has a breakdown voltage of about 50 V and a photoresponsivity of 31.1 A/W at 450 nm[18].In the above studies,the blue light detection efficiency of Si-APD devices was improved.With the increasing demand,it is necessary to further study Si-APD devices to improve their blue light detection performance.Conventional Si-APD devices generally have a higher avalanche breakdown voltageVbr(150～500 V)which makes the device power consumption larger and the stability worse.In order to obtain high blue light responsivity and low avalanche breakdown voltage of Si-APD devices in blue light band,based on the traditional Si-APD structure,according to the transport characteristics of photogenerated carriers,a structure in which the positions of the absorption layer and the avalanche layer are interchanged is designed,and the structure is optimized in the blue light band.The relationship between the doping concentration and thickness of the device multiplication layer and the avalanche breakdown voltage and spectral responsivity is also studied.This paper provides a basic reference for the design and fabrication of practical high blue light responsivity silicon-based avalanche photodetector chips.

2 Epitaxial structure design

2.1 SACM type Si-APD

According to the analysis of the visible light absorption characteristics of Si (The material parameters of Si used in this paper are from the experimental measurements of Schinkeet al[19]) and that of the working principle of the Si avalanche photodetector,a SACM device structure is adopted,that is,the absorption layer and the multiplication layer are separated,a field control layer is added between them,and the multiplication layer is placed behind[20-21].The basic epitaxial structure of SACM type Si-APD is shown in Fig.1 (color online) from top to bottom,the device is a p++type heavily doped surface non-depletion layer,a π type absorption layer,a p+field control layer,a p type multiplication layer and an n++type substrate.Light is incident from the surface of the p++non-depletion layer.The absorption layer can absorb incident light with a wavelength of 0.3 to 1.1 μm,covering the visible light band,the field control layer is used to modulate the electric field between the multiplication layer and the absorption layer in the device to achieve a good transition between the low electric field intensity of the absorption layer and the high electric field intensity of the multiplication layer.Under the premise of ensuring that the photogenerated carriers can be transported to the avalanche layer,the noise carriers can be suppressed[22].The multiplication layer is used to achieve the number gain of the initial photogenerated carriers;the surface non-depletion layer and the heavily doped substrate act as conductive electrode.When the applied bias voltage is high enough,the device will be in a pull-through state,that is,from the PN junction to the surface non-depletion layer,the depletion region not only ensures the avalanche breakdown of the multiplication layer,but also ensures that the electric field of the absorption layer is high enough,so that the photogenerated carriers can reach the saturation drift velocity and move to the multiplication layer.

Fig.1 The basic epitaxial structure of SACM type Si-APD圖1 SACM-APD 基本外延結構

2.2 Electric field distribution in Si-APD

The electric field distribution of the PN junction depletion layer can be expressed as

whereqis the single charge,Nmis the impurity concentration,εmis the relative permittivity of the doping material,ε0is the vacuum permittivity,EMis the maximum electric field strength in the PN junction,andEMis related on the doping concentration on both sides of the multiplication layer and the applied bias voltageVm,expressed as

whereNDis the donor impurity concentration,NAis the acceptor impurity concentration,andVbiis the built-in potential of the multiplication layer,expressed as:

whereKis the Boltzmann constant,Tis the Kelvin temperature (T=300 K),andniis the intrinsic carrier concentration (ni=1.02×1010cm?3[23]).

According to formula (1),the expression of electric field of each layer of the device in Fig.2(color online) is deduced (the built-in potential of homogeneous junction due to different doping concentration is not considered in this paper).

Fig.2 The distribution of electric field in Si-APD圖2 Si 基APD 內部電場分布

when 0

whenx1

whenx2

whereNp,Np+,NπandNp++are the doping concentrations of the multiplication layer,field control layer,absorption layer and surface non-depletion layer,respectively.By modulating the doping concentration and thickness of each layer,the electric field distribution and corresponding voltage in each layer can be designed and modulated;EMis the electric field strength at the position ofx=0 in Fig.2,which is also the maximum electric field strength in the device;εp,εp+,επandεp++represent the relative permittivity of the multiplication layer,field control layer,absorption layer and surface non-depletion layer.The relative permittivity of doped silicon[24]can be expressed as:

N-type doped silicon:

If the thickness and doping concentration of each layer are determined,according to the electric field distribution in the device defined by Equations(4)?(7),the voltageVapdon the Si-APD device in Fig.1 can be expressed as:

whereVcandVaare the voltages on both sides of the field control layer and the absorption layer,respectively.IfEMreaches the maximum valueEbrduring the avalanche multiplication breakdown,the voltage applied across the device at this time is the avalanche breakdown voltageVbr-apd.

2.3 Quantum efficiency and photoresponsivity

Quantum efficiencyQEis the number of electron-hole pairs generated inside a semiconductor by a single incident photon[25],which is defined as:

whereIphis the photocurrent,Poptis the incident light power,hνis the single-photon energy,andqis the charge of the electron.Assuming that all the carriers generated by the incident illumination of Si-APD under the action of working bias enter the depletion region,the quantum efficiencyQErelation can be expressed as:

whereφis the probability that a single photon absorbed by the material excites a hole-electron pair;Ris the reflectivity of the silicon surface,αis the light absorption coefficient of the material,and the relation ofRandαon the wavelength is shown in Fig.3 (color online);WDis the depletion layer thickness.Equation (12) shows that the excitation probabilityφof photogenerated carriers is fixed,and under the action of incident light of a certain wavelength,the quantum efficiency of APD is mainly affected by the surface reflectivityRand the thickness of the depletion layerWD.For the convenience of calculation,assuming thatφ=100%,and all the excited hole-electron pairs can enter the depletion layer,the relation between the quantum efficiency of Si-APD blue light band and the thickness of the depletion layer is calculated by formula (12).The results are shown in Fig.4 (color online),that is,when the depletion layer thicknessesWDare 1.0 μm,2.0 μm,3.0 μm,4.0 μm and 5.0 μm,the corresponding peak quantum efficienciesQEpeakare about 55.03%,58.23%,59.83%,60.99% and 61.72%,and the corresponding incident wavelengthsλpeakare 0.43 μm,0.47 μm,0.49 μm,0.51 μm and 0.52 μm,respectively.

Fig.3 The surface reflectance and absorption coefficient of the silicon vary with different incident wavelengthes圖3 硅表面反射率及吸收系數(shù)隨入射波長的變化情況

Fig.4 The relationship between quantum efficient and incident wavelength under different depletion layer thicknesses圖4 不同入射波長的量子效率與耗盡層厚度的關系

The above calculation curve results show the variation of quantum efficiency with incident wavelength under different depletion layer thicknessWD.It can be seen from the figure that the quantum efficiency increases with the increase of the depletion layer thicknessWD.The analysis shows that with the increase of the incident wavelength,the corresponding absorption coefficientαdecreases.The increase in the thickness of the depletion layer can improve the light absorption rate of Si-APD,and correspondingly increase the number of photogenerated electron-hole pairs in the depletion layer.The peak quantum efficiencyQEpeakred-shifts with the increase of the corresponding incident wavelength and the thickness of the depletion layer.It can be found from the curve in the figure that under the excitation of a specific incident wavelength,theQEpeak of the Si-APD quantum efficiency does not increase with the increase of the thickness of the depletion layer.This is because the light absorption of the depletion layer to the incident wavelength is saturated,making the number of photogenerated carriers constant,for example,when the depletion layer thicknessWD≥2.0 μm,the quantum efficiency at the incident wavelength λ=0.45 μm is fixed atQE=57.58%.

The photoresponsivitySRis a measure of the photoelectric conversion capability of the photodetector on the macroscopic scale,which is defined as the ratio of the photocurrentIphto the incident optical powerPopt,and the expression isSR=Iph/Popt.The relationship between optical responsivity and quantum efficiency is[26]:

whereMis the gain coefficient.According to the quantum efficiencyQEdefined by Eq.(12),the above equation can be rewritten as:

Assuming that the gain coefficientM=1 andφ=100%,the relationship between the optical responsivitySRin the visible light band and the thicknessWDof the depletion layer is calculated according to Eq.(14),as shown in Fig.5 (color online).

Fig.5 The relationship between spectral response and incident wavelength under different depletion layer thicknesses圖5 在不同耗盡層厚度下，光響應度與入射波長的關系

The curves in Fig.5 show that when the depletion layer thicknessWDare 1.0 μm,2.0 μm,3.0 μm,4.0 μm or 5.0 μm,the corresponding peak photoresponsivitySRpeakare about 0.196 A·W?1,0.226 A·W?1,0.246 A·W?1,0.261 A·W?1,or 0.272 A·W?1,and the corresponding incident wavelength λ are 0.44 μm,0.50 μm,0.52 μm,0.56 μm,or 0.57 μm,respectively,which are consistent with the incident wavelength corresponding to the peak quantum efficiency.

2.4 Effect of multiplication layer parameters on gain

The photocurrent gain is the most important characteristic of APD,and its underlying physical mechanism is the impact ionization effect of carriers,which is usually expressed by a multiplication factor.Assuming that the avalanche effect only occurs in the multiplication layer,the multiplication factorM(x)[27]defined by Eq.(15) shows that the avalanche multiplication is mainly depended on the width of the depletion layer,the electric field strength,the collision ionization coefficient of carriers,etc.In the case of electron-induced avalanches,the multiplication factorM(x)is:

whereα(x) andβ(x) are the collisional ionization coefficients of electrons and holes,respectively,andWmis the thickness of the multiplication region.Chynoweths describes the effect of electric field strengthEon the collisional ionization of carriers as[28]:

wherean，bn，apandbpare the experimental parameters of the collision ionization rate of electrons and holes,respectively,andE(x) is the electric field strength in the multiplication region,which is a function of the distancex.The numerical calculation in this paper adopts Lee’s experimental fitting coefficients[29]:an=3.8×106cm?1,bn=1.75×106V·cm?1;ap=2.25×106cm?1,bp=3.26×106V·cm?1.

Consider the relationship among the thickness of the multiplication layer in the PN junction,the applied bias voltageVmon both sides of the multiplication layer,and the multiplication coefficientMunder a certain doping concentration.Assuming that the doping concentration of theN-type substrate isND=1.0×1019cm?3,and the doping concentration of theP-type multiplication layer isNA=1.0×1016cm?3,combined with Eqs.(1),(2),and (16),in order to simplify the calculation,perform the third-order Taylor expansion ofα(x) andβ(x),and substitute them into Eq.(15) to calculate the relationship between the applied bias voltageVmof the multiplication layer and the multiplication coefficientM,the result is shown in Fig.6 (color online).

Fig.6 The relationship between the thickness of multiplication layer and multiplication factorM圖6 倍增層厚度與倍增系數(shù)M 的關系

The curves in the above figure show thatMincreases sharply when the applied bias voltageVmon both sides of the multiplication layer increases to a specific value,and Equation (15) shows thatVmis close to or equal to the voltageVbr-mon both sides of the multiplication layer at the time of avalanche breakdown.Therefore,in order to obtain a higher gain for the APD,the applied bias voltageVapdacting on the device needs to approximate the avalanche breakdown voltageVbr-apdof the device.The curves in the figure shows that as the thickness of the multiplication layer increases,the voltage to obtain the same multiplication factor decreases.That is,at small multiplication layer thickness,the voltage needs to be increased so that the carriers have a higher ionization rate in order to obtain a higher gain.However,the increase of the thickness of the multiplication layer is affected by the doping concentration and the applied bias voltage at both ends of the PN junction,and the selection of the thickness is also based on the electric field distribution,which is related to the doping concentration,so the thickness of the multiplication layer needs to be comprehensively considered with its doping concentration.

For silicon,the carrier energy is completely lost in the collisional ionization only when the electron energy isEele≥6.5 eV[30].From the perspective of energy,it is assumed that the collision ionization effect occurs only in the multiplier layer,the influence of field control layer on electron energy is not considered,and the hole electron recombination mechanism and scattering energy loss are ignored.It can be seen from formula (4),that let the carrier obtain energy under the action of the electric field of the multiplication layerΔEis:

For the convenience of calculation,the critical breakdown electric field intensityEMis substituted into the above formula ΔE,and we have:

The doping concentration of the substrate is set toNn++=1.0×1019cm?3,the doping concentration of the multiplication layerNpis 1.0×1015～1.0×1017cm?3,and the PN junction is set as a unilateral mutation junction.According to Eq.(18),the numerical relationship between the doping concentration and the carrier energyΔEunder different multiplication layer thicknesses was calculated,and the results are shown in Fig.7 (color online).When the thickness of the fixed multiplication layer isWm=0.5 μm,the curves in the figure show that when the doping concentrationsNpis 1.2×1016cm?3,1.8×1016cm?3or 2.4×1016cm?3,the energyΔEis 18.22 eV,18.39 eV or 18.26 eV,respectively.Therefore,when the doping concentration of the multiplication layer is 1.8×1016cm?3,the carriers obtain a higher energyΔE=18.39 eV in the multiplication layer,which can theoretically generate a higher gain coefficientM.

Fig.7 Relationship between carrier energy ΔE and multiplication layer doping concentration圖7 載流子獲得能量ΔE 與倍增層摻雜濃度的關系

2.5 Influence of field control layer

The doping concentration (Np+) and the thickness (Wc) of the field control layer are important for adjusting the electric field intensity between the multiplication layer and the absorption layer.The field control layer is located between the absorption layer and the multiplication layer,and reduces the tunneling probability of the device by reducing the electric field strength of the absorption layer.However,the thickness of the field control layer should not be too large.The reasons are as follows:when the applied bias voltage and the doping concentration of the field control layer are fixed,increasing the thickness of the field control layer will reduce the electric field strength of the absorption layer,and affect the drift velocity of photogenerated carriers in the absorption layer;if the thickness is too small,it will increase the electric field strength of the absorption layer,induce carrier ionization,and increase unnecessary noise current.According to Eq.(5),under the condition of ensuring the carrier saturation drift velocity,the appropriate doping concentration and thickness is beneficial to the modulation and transition of the electric field between the multiplication layer and the absorption layer.In general,compared with multiplication.a smaller thickness and a higher doping concentration should be chosen to ensure the least effect on the multiplication layer variation.

2.6 Design of absorption layer

Due to the absorption characteristics of Si material itself[31],the blue light band in the wavelength range of 0.4～ 0.5 μm has a high absorption coefficient (as shown in Fig.3),which leads to a shallow penetration depth of light in the blue light band,about 0.098～0.82 μm in silicon.In order to fully absorb the blue light by the absorption layer,the thickness of the absorption layerWa=1.3 μm is selected in combination with the relationship between the quantum efficiency and the thickness of the depletion layer shown in Fig.4.In silicon,when the electric field strengthE>1.0×104V·cm?1,the velocity of electrons tend to the saturation drift velocity,that is,vs（Si）≈107cm·s?1.In order to keep the high bandwidth of the device,the carriers should move at the saturation velocity in the device.When the doping concentration and thickness of the multiplication layer and the field control layer are fixed (Wm=0.5 μm,Np=1.8×1016cm?3;Wc=0.2 μm,Np+=8.0×1016cm?3),and the mutation PN junction is close to breakdown,the field strength distribution of the absorption layer under different doping concentrations is drawn according to Eq.(6),as shown in Fig.8(color online).It can be seen from the figure that the field strength of the absorption layer gradually decreases with the increase of the doping concentration.When the doping concentration of the absorption layer isNπ=1.0×1016cm?3and 5.0×1015cm?3,the field strength has been exhausted before reaching the surface non-depletion region,and at this time,the blue-light excited carriers enter the absorption layer and are dominated by diffusion motion,which increases the carrier transit time and reduces the device bandwidth.WhenNπis1.0×1014cm?3,5.0×1014cm?3or 1.0×1015cm?3,respectively,the edge field strength of the absorption layer isE>104V·cm?1,the device is in the pull-through state,and the carriers drift at the saturation velocity in the whole device.Therefore,the doping concentration and thickness of the absorption layer should be selected so that the absorption layer have a good electric field distribution and the carriers move in this layer at a saturated drift velocity,and that the red and green light has a certain absorption rate at the same time.

Fig.8 Field intensity distribution of the absorption layer under different doping concentrations圖8 不同吸收層摻雜濃度下吸收層的場強分布

2.7 Si-APD initial structural parameters

Assuming that the layers are uniformly doped,the incident light is absorbed only in the absorption layer,and under reverse bias voltage,the avalanche effect occurs only in the multiplication layer.Based on the relationship among the gain coefficient,the applied bias voltage and the thickness of the multiplication layer,the relationship among the quantum efficiency,the photoresponsivity and the thickness of the depletion layer,the selected parameters of each layer are shown in Table 1,whereWs,Wa,Wc,WmandWsubare the thicknesses of the surface nondepletion layer,absorption layer,field control layer,multiplication layer and substrate,respectively.

Tab.1 Parameters of Si-APD layers表1 Si-APD 各層參數(shù)

3 Si-APD numerical calculation

The basic equations of semiconductor device operation include electrostatic equation,current density equation and continuity equation.The generation and recombination mechanism of carriers is the key to the performance of semiconductor photodetectors.In the two-dimensional simulation of the device characteristics of Si-APD,the diameter of the photosensitive surface of the Si-APD used in the calculation is 10 μm.In order to improve the accuracy of the calculation results,physical models such as Selberherr's ionization[32,33],Shockley-Read-Hall recombination[34, 35]and carrier mobility[36-38]are used in the calculation.

3.1 The relationship between the field strength distribution of Si-APD and the applied bias voltage

According to the parameters in Table 1,when theVapdin the device is 0 V,0.5Vbr-apd,0.7Vbr-apdorVbr-apdrespectively (the correspondingVapdis 0 V,17.1 V,23.9 V,34.2 V),the field strength distribution inside the Si-APD as shown in Fig.9 (color online).It can be seen from the figure that the electric field strength inside the Si-APD increases with the increase of the bias voltageVapdapplied to the device.WhenVapdis small,the device is in a nonpull-through state,and the carriers begin to diffuse in the device.With the increase of the applied bias voltage,the device is pulled through as a whole,at this time,the carriers are dominated by drift motion.As the applied bias voltage is continuously increased,the carriers will eventually move in the device at the saturation drift velocity.

Fig.9 The field strength distribution of Si-APD under different applied bias voltages圖9 不同外加偏壓下Si-APD 的場強分布

3.2 Further optimization of the thickness of non-depletion layer on the surface

Generally,the surface of the semiconductor photodetector has a certain thickness of the surface heavily doped non-depletion layer (also act as an electrode layer),and the penetration depth of light in the blue light band in silicon is relatively small.When light passes through the non-depleted layer at the top of the device,most of the blue light energy is absorbed by this layer to generate hole-electron pairs,so it is necessary to optimize the thickness of the surface non-depleted layer.On the basis of the parameters in Table 1,the impurity concentration of the surface layer and the structural parameters of other doped layers are fixed,the incident light is vertically irradiated on the surface layer of the detector,and the spectral response curves of different surface non-depleted layer thicknesses are obtained whenR≠0,which are shown in Fig.10 (color online).

Fig.10 Effect of thickness of surface layers of Si-APD on spectral responsivity圖10 不同表面層厚度Si-APD 的光譜響應曲線

The curve in the figure shows the spectral responsivity under the applied bias voltage of 0.95Vbr-apd(M≈26) when the thickness of the surface non-depletion layer isWs=0.03 μm,0.06 μm and 0.10 μm.WhenWs=0.03 μm,the photoresponsivity of the blue bandSRis 3.71～6.08 A·W?1;whenWs=0.06 μm,the photoresponsivitySRof the blue band is 3.15～5.94 A·W?1;whenWs=0.10 μm,the photoresponsivitySRin the blue band is 2.57～5.75 A·W?1,indicating that the smaller the thickness of the surface non-depletion layer is,the smaller the inhibitory effect on the photoresponsivity of blue light will be.It is also found from the curve that the change ofWshas little effect on the optical responsivity of the device in the long wavelength band.The analysis shows that according to the transmission characteristics of light in the medium,the light absorption lossAsof the incident light in the surface non-depletion layer with a thickness ofWsis

whereRis the surface reflectance,andαis the light absorption coefficient of Si.The drift current density formed by photogenerated carriers in the depletion region of widthWDis:

For the fixed incident optical powerPoptin the visible light band,the first half of Eq.(20) represents the number of photons that penetrate to the edge of the depletion layer of the detector at a specific wavelength,and the second half represents the absorption rate of the incident photons by the depletion layer with a thickness ofWD.Ignoring the recombination mechanism of carriers,set the quantum efficiencyQE=100% in the depletion region.According to the material characteristics of Si,the intensity of long-band incident light absorbed by the material is small,so the light absorption loss generated by the surface non-depletion layer has little effect on the light energy transmitted to the depletion layer.Therefore,the long wave band light response is basically stable in the process of adjustingWs.However,on the short-wave side,the thickness of the surface non-depletion layer has a great influence on the optical responsivity.

3.3 Effect of doping concentration of multiplication layer on optical responsivity

According to the calculation results in Fig.10 and the calculation results of the surface non-depletion layer thickness above,take the surface non-depletion layer thicknessWs=0.03 μm,the surface reflectivityR≠0,and other parameters are based on the data in Table 1 to obtain that whenVapd=0.95Vbr-apd,the photoresponsivity of Si-APD in the visible light band is shown in the red curve in Fig.11 (color online),and the corresponding photoresponsivitySRin the blue light band is divided into 3.72～6.08 A·W?1.

Fig.11 Effect of doping concentration of multiplication layer on spectral responsivity圖11 倍增層摻雜濃度對光響應度的影響

For comparison,when other parameters remain unchanged,the doping concentrations of the multiplication layerNPare calculated as 1.2×1016cm?3,2.4×1016cm?3(the corresponding breakdown voltageVbr-apdis 39.2 V and 30 V respectively).The photoresponsivity atVapd=0.95Vbr-apdare shown in the blue and black lines in Fig.11(color online).The corresponding photoresponsivity in the blue light bandSRare divided into 3.02～4.93 A·W?1and 2.83～4.68 A·W?1.In both cases,the photoresponsivity is lower than theSRvalue forNp=1.8×1016cm?3doping indicated by the red line.

This phenomenon can be attributed to the fact that at this doping concentration,the carriers can gain higher energy in the multiplication layer (as shown in Fig.7),resulting in a greater photocurrent gain.Based on the above results,the basic epitaxial structure parameters of the Si photodetector were finally determined as shown in Table 2.

Tab.2 Parameters of Si-APD layers表2 Si-APD 各層參數(shù)

3.4 I-V characteristics of Si-APD dark current

Assuming that each layer is uniformly doped,the I-V relationship characteristics of the Si-APD in the dark environment can reflect the electrical parameters such as the avalanche breakdown voltageVbr-apdand the current gain coefficientMof the device.The I-V characteristic curves are calculated qualitatively according to the parameters in Table 2 and the current density equation defined in Equation (21).The current density magnitude is mainly influenced by the carrier transport behavior and is expressed in the numerical relationship as the sum of electron current density and hole current density,i.e.:

whereJnis the electron current density,Jpis the hole current density,Jcondis the conduction current density,μnis the electron mobility,μpis the hole mobility,Dnis the electron diffusion coefficient,Dpis the hole diffusion coefficient,?nand ?pare the excess carrier concentration gradients.The curve in Fig.12 (color online) shows the calculated reverse current as a function of the applied bias voltageVapd.It can be seen from the figure that the magnitude of the current increases with the increase ofVapd,but the change trend of the current is different.According to different current formation mechanisms,it is s ummarized as parts (i)-(iv) in Fig.12.

Fig.12 The dark current I-V curve of Si-APD圖12 Si-APD 暗電流的 I-V 曲線

The dark current density of avalanche photodiode includes[39]recombination current densityJr,minority carrier diffusion current densityJdiff,carrier drift current densityJdrof depletion layer and avalanche current densityJm.The recombination current density is expressed asJr=qniWD/2τD.τD=1/Rec·Nis the carrier lifetime,Rec≈10?15cm3s?1is the indirect band gap semiconductor recombination coefficient[27],andNis the doping concentration.Jdiff=(qDpni2/LpND)+(qDnni2/LnNA),Dp=kTμp/qandDn=kTμn/qare the diffusion coefficient of hole and electron respectively,LpandLnare the diffusion length of hole and electron respectively.WhenT=300 K,kT/q=0.025 9 V,Dp=12.95 cm2·s?1,Dn=37.56 cm2·s?1.For simple calculation,combined with the doping concentration of π absorption layer,p+type field control layer and p type multiplication layer in the APD structure designed above,the three regions are regarded as p type silicon materials with doping concentrationand carrier life

whereτsc(p),τsc(p+)andτsc(π)are the carrier lifetimes of the multiplication layer,the field control layer and the absorption layer,respectively.

When the applied bias voltageVapdis small,the Si-APD current is dominated by the diffusion and recombination currents.Substituting the above data into equation (24) to calculate the diffusion and recombination currents of the device,the results correspond to part (i) in Fig.12.

When increasing the applied bias voltageVapd,the number of carriers subjected to the internal electric field increases and the drift current accounts for the major part of the current.According to equation(21),the drift current density of the device is expressed asJdr=qnμnE+qpμpE,whereEis the electric field strength of the depletion layer defined by equations (4) to (7).Substituting the calculatedJdrinto the following equation,the result corresponds to part (ii) in Fig.12.

If the applied bias voltageVapdcontinues to increase,the carriers collide and ionize under the action of strong electric field.The high-energy initial carriers collide with the internal lattice to produce secondary carriers,and then continue to collide with the lattice to produce new carriers to form avalanche current densityJm=αnJn+αpJp,JnandJpare electron and hole current densities,αn,αpare the ionization coefficient of electrons and holes,respectively.The collision effect continues under the working bias voltage and the number of carriers is doubled.Assuming that the avalanche effect only occurs in the multiplication layer,the avalanche dark currentIdgenerated in the multiplication layer with a thickness ofWmcan be expressed as:

As shown in part (iii) of Fig.12.

Generally,the gain coefficientMof the device can be obtained from the following empirical relation

whereIdis the dark current generated based on the impact ionization of the carriers,Id0is the initial dark current,the constantnis affected by the device structure,doping distribution and other factors,usually thenof the Si material is 1.5?4.0.When the applied bias voltageVapdis close to the avalanche breakdown voltageVbr-apd,the current will increase with the sharp increase of the multiplication factorM,as shown in the area (iv) in Fig.12.

The dark current I-V curve in Fig.12 shows that when the APD device is at a low applied bias voltage,the diffusion current accounts for most of the total current;after that,the internal electric field strength will increase with the increase ofVapd,and the width of the depletion region will increase too.More carriers enter the depletion region to form a drift current under the action of the electric field,which becomes the main part of the total current;whenVapdcontinues to increase,due to the impact ionization of carriers,there will be a current gain phenomenon,but the effect is not obvious;ifVapdis close to the device avalanche breakdown voltageVbr-apd,and there will be a sharp increase in current.

By comparing the variation trend of current with voltage in parts (iii) and (iv),it can be found that APD can produce a higher current gainMwhen the bias voltage is higher than the avalanche breakdown voltage.According to the analysis,the ionization rate of the carrier is an important indicator to measure the avalanche multiplication effect,which is closely related to the electric field strength associated with the device bias voltage[40],and the ionization rate increases with the increase of the bias voltage.Taking the carriers in the multiplication layer as an example,the impact ionization rate distributions of electrons and holes under different bias voltages are calculated according to Equation(16),Lee's carrier ionization parameter and the electric field distribution of Equation (4),Figs.13 (a)and 13(b) (color online) clearly show that the collision ionization coefficient increases with the increase of the voltageVmon both sides of the multiplication layer,so whenVapdapproachesVbr-apd,there will be a high current gain,and the electron gain is dominant.

Fig.13 (a) Electron ionization coefficients in the multiplication layer under different bias voltages;(b)hole ionization coefficients in the multiplication layer under different bias voltages.圖13 (a) 不同倍增層偏壓下倍增層內電子離化系數(shù);(b)不同倍增層偏壓下倍增層內空穴離化系數(shù)

4 Conclusion

In order to meet the urgent demand for blue light high response photodetectors in optical communication systems,a SACM type Si-APD structure with interchangeable positions of absorption layer and multiplication layer is designed and the relationship between multiplication layer thickness and device gain,absorption layer doping concentration and absorption layer field strength distribution,external bias and internal field strength distribution,surface non-depletion layer thickness and spectral response,and multiplication layer concentration and spectral response are studied.After comprehensive consideration,the structural parameters of the device are selected as follows:the thickness of the surface non-depletion layer is 0.03 μm,the doping concentration is 1.0×1018cm?3;the thickness of absorption layer is 1.3 μm,the doping concentration is 1.0×1015cm?3;the thickness of field control layer is 0.2 μm,the doping concentration is 8.0×1016cm?3;the thickness of multiplication layer is 0.5 μm,the doping concentration is 1.8×1016cm?3.The device has a low breakdown voltageVbr-apd=34.2 V.WhenVapd=0.95Vbr-apd,it has a high optical responsivity of 3.72～ 6.08 A·W?1in the blue band.The results of this paper have a certain reference value for the preparation of actual devices.

——中文對照版——

1 引言

隨著短波長可見光光源（如藍光LED、藍光半導體激光器等）的發(fā)展和廣泛應用，短波長可見光高效探測技術的應用越來越廣泛。尤其是可見光通信技術[1]、生物醫(yī)學工程、水下光通信[2]等領域的快速發(fā)展，迫切需要具有高帶寬、高增益、寬光譜、高光響應的可見光探測器[3]。白光LED 是可見光通信的重要光源[4]，目前常用的白光LED 主要有熒光型白光LED(通過藍光LED激發(fā)熒光粉混合形成白光[5])、紅藍綠型白光LED（RGB-LED）[6]，上述兩種白光LED，藍光都是主要的工作波段，因此具有藍光高響應的光電探測器對進一步促進照明通訊一體化的發(fā)展應用具有重要意義[7]。目前常用的光電探測器主要為：PIN 光電二極管（PIN-PD）、光電倍增管（Photo Multiplier Tube,PMT）和雪崩光電二極管（Avalanche Photodiode,APD）。然而，PIN 光響應度低、探測距離短，對光源功率要求高，限制了其在可見光通信中的進一步應用[8]。光電倍增管（PMT）可以探測短波長，然而電壓高、對磁場敏感等缺點限制了其在可見光通信方面的應用[9]。雪崩光電探測器（APD）是一種具有較高的內部增益和高光響應度的半導體探測器[10]，并且沒有PMT 的上述缺點，在可見光探測器的研究中引起了廣泛關注。

硅（Si）對于380～ 1100 nm 波段的入射光均有吸收能力，是制備寬光譜探測器的良好材料[11]，且Si 半導體器件制備工藝成熟[12]，同時硅材料中電子與空穴的碰撞電離率比值高、隧道電流低[13]，使得硅基雪崩光電二極管（Si -APD）具有增益高，噪聲低，穩(wěn)定性好等優(yōu)點。然而由于藍光在硅中的高吸收系數(shù)特性使得藍光在硅中的透入深度較低，大部分的光生載流子位于淺表層，易導致部分載流子在淺表面復合，進入吸收層的光生載流子數(shù)量較少，降低了藍光波段的光電轉換效率，這給藍光高響應度的Si-APD 的器件設計和制備帶來較大難度。為了提高硅對藍光的探測效率，改善Si-APD 在藍光波段的性能，研究人員進行了相關的研究：2010 年，Excelitas 公司的Catherine M.Pepin 等人通過在外延片上“埋結”，制備了一種紫外增強型Si 基APD，該器件的雪崩擊穿電壓為400 V，在430 nm 波長處的響應度為39 A/W（M=150）[14]。2015 年，Othman 等人通過CMOS工藝將Si 基APD 高度集成，雪崩擊穿電壓為10 V，在405 nm 波長處的增益為100[15]。同年，王旭東等人基于吸收場控倍增分離(SACM)型Si-APD（n-p-p+-p-p+型摻雜結構，光從N 型層表面入射）優(yōu)化了器件結構參數(shù)，同時在器件表面設計了折射率高低交替分布的增透膜結構，優(yōu)化后器件的峰值響應波長為406 nm，雪崩擊穿電壓為105.9 V，峰值波長處的光響應度為250 A/W[16]。2015 年，霍林章等人提出了一種深槽隔離結構的SiPM 探測器，提高了在藍紫光區(qū)（360～420 nm）的探測效率，該器件的擊穿電壓約為90V[17]。2019年，魯歡歡等人設計了一種SAM 型Si-APD，該器件的倍增層更靠近光敏層，能夠有效降低光生載流子的復合損耗，該器件的擊穿電壓約為50 V，450 nm 處的光響應度為31.1 A/W[18]。上述研究改善了所設計的Si-APD 器件的藍光探測效率。隨著需求的日益增長，有必要對Si-APD 器件作進一步研究，以提高其藍光探測性能。傳統(tǒng)的Si-APD 器件雪崩擊穿電壓Vbr較高（150～500 V），而高的雪崩擊穿電壓使得器件功率變大，穩(wěn)定性變差。為獲得在藍光波段的硅基APD 器件的高藍光響應度和較低的雪崩擊穿電壓，本文在傳統(tǒng)的Si-APD 結構基礎上，根據(jù)光激發(fā)載流子的輸運特征，優(yōu)化設計了一種吸收層與雪崩層位置互換的結構，并對結構在藍光波段進行了優(yōu)化。對器件倍增層的摻雜濃度及厚度與雪崩擊穿電壓和光譜響應度的關系進行了研究。本文為設計與制備實際高藍光響應度硅基雪崩光電探測器芯片提供參考。

2 器件外延結構設計

2.1 SACM 型Si-APD

根據(jù)對Si 吸收可見光特性（本文所使用的Si 材料參數(shù)來自于Schinke 等人的實驗測量值[19]）和Si 雪崩光探測器工作原理的分析，本文采用一種SACM 型器件結構，即：吸收層和倍增層分離，并在二者之間加入場控層，將倍增層后置[20-21]。SACM 型Si-APD 基本外延結構如圖1（彩圖見期刊電子版）所示。器件自上而下分別為p++型重摻雜表面非耗盡層、π 型吸收層、p+場控層、p 型倍增層以及n++型襯底，光從p++非耗盡層表面入射。吸收層可吸收波長為0.3～1.1 μm的入射光，覆蓋可見光波段；場控層用于調制器件中倍增層與吸收層的電場，實現(xiàn)吸收層的低電場強度和倍增層的高電場強度良好過渡，在保證光生載流子能輸運到雪崩層的前提下，抑制噪聲載流子[22]；倍增層用于實現(xiàn)初始光生載流子的數(shù)量增益；表面非耗盡層和重摻雜襯底兼具導電電極作用。當外加偏壓足夠高時，器件將處于拉通狀態(tài)，即耗盡區(qū)從PN 結直到表面非耗盡層，在保證倍增層的雪崩擊穿的同時，也保證吸收層電場足夠高，使光生載流子能夠達到飽和漂移速度從而運動到倍增層。

2.2 Si-APD 電場分布

PN 結耗盡層的電場分布可以表示為：

式中，q為單電荷量，Nm為雜質濃度，εm為摻雜材料的相對介電常數(shù)，ε0為真空介電常數(shù),EM為PN 結內最大電場強度,EM由倍增層兩側的摻雜濃度及外加偏壓Vm決定,表示為，

其中ND為施主雜質濃度，NA為受主雜質濃度，Vbi為倍增層的內建電勢，Vm為倍增區(qū)兩側的電壓，表示為：

式中，K為玻爾茲曼常數(shù)，T為開爾文溫度（T=300 K），ni為本征載流子濃度（ni=1.02×1010cm?3[23]）。

根據(jù)公式（1），推導求出圖2（彩圖見期刊電子版）中器件各層電場表達式（本文中沒有考慮同質結因摻雜濃度不同產(chǎn)生的內建電勢）。

當0

當x1

當x2

當x3

式中，Np、Np+、Nπ和Np++分別為倍增層、場控層、吸收層和表面非耗盡層的摻雜濃度，通過調整各層摻雜濃度和厚度，可以設計和調整各層中的電場分布及相應的電壓；Em為圖2 中，x=0 位置處的電場強度，也為器件中的電場強度最大值；εp、εp+、επ與εp++表示倍增層、場控層、吸收層與表面非耗盡層的相對介電常數(shù)。摻雜硅的相對介電常數(shù)[24]表達式分別為：

N 型摻雜硅：

P 型摻雜硅：

如果確定了各層厚度和摻雜濃度，根據(jù)公式（4）?（7）定義的器件內部電場分布，圖1 中Si-APD 器件上的電壓Vapd的表達式為：

Vc和Va分別為場控層、吸收層兩側的電壓。如果EM達到雪崩倍增擊穿時的最大值Ebr，那么，此時器件兩端所加的電壓則為雪崩擊穿電壓Vbr-apd。

2.3 量子效率與光響應度

量子效率QE為單入射光子在半導體內部產(chǎn)生電子-空穴對的數(shù)目[25]，定義式為：

式中，Iph表示光電流，Popt表示入射光功率，hν為單光子能量，q為電子的電荷量。假設Si-APD 在工作偏壓作用下入射光照產(chǎn)生的載流子全部進入耗盡區(qū)，量子效率QE關系式可表達為：

式中，φ為被材料吸收的單光子激發(fā)空穴-電子對的概率；R為硅表面反射率，α為材料的光吸收系數(shù)，R、α對波長的依賴關系如圖3（彩圖見期刊電子版）所示；WD為耗盡層厚度。式（12）表明，光生載流子的激發(fā)概率φ固定，在一定波長的入射光作用下，APD 的量子效率主要受表面反射率R與耗盡層厚度WD的影響。為計算方便，假設φ=100%，且激發(fā)空穴-電子對都可以進入耗盡層，通過式（12）計算得出Si-APD 藍光波段的量子效率與耗盡層厚度的關系，結果如圖4（彩圖見期刊電子版）所示。圖4 中曲線展示了耗盡層厚度WD分別為1.0、2.0、3.0、4.0 與5.0 μm 時，所對應的峰值量子效率QEpeak分別為55.03%、58.23%、59.83%、60.99%和61.72%，相應的入射波長λpeak分別為0.43 μm、0.47 μm、0.49 μm、0.51 μm 和0.52 μm。

圖4 給出了不同耗盡層厚度WD時量子效率隨入射波長的變化情況。從圖中可以看出：量子效率隨耗盡層厚度WD的增加而提高。分析認為，隨著入射波長的增加，相應的吸收系數(shù)α減小，而耗盡層厚度增大可提高Si-APD 的光吸收率，相應地增加耗盡層內光生電子-空穴對的數(shù)量，峰值量子效率QEpeak隨相應入射波長、耗盡層厚度的增加而紅移。通過圖中曲線可以發(fā)現(xiàn)，Si-APD 在特定入射波長的激勵下，量子效率QE峰值不隨耗盡層厚度的增加而提高，這是由于耗盡層對該入射波長的光吸收飽和，使光生載流子數(shù)量恒定，因此出現(xiàn)量子效率穩(wěn)定現(xiàn)象，例如當耗盡層厚度WD≥2.0 μm 時，入射波長λ=0.45 μm 的量子效率固定為QE=57.58%。

光響應度SR是衡量光電探測器在宏觀上的光電轉換的能力，定義為光電流Iph與入射光功率Popt的比值，表達式為SR=Iph/Popt。光響應度與量子效率關系式為[26]：

式中，M為增益系數(shù)。根據(jù)式（12）定義的量子效率QE，上式改寫為：

假設增益系數(shù)M=1，φ=100%，根據(jù)式（14）計算得到可見光波段光響應度SR隨耗盡層厚度WD的變化關系，如圖5 所示。

圖5 中曲線表明，耗盡層厚度WD分別為1.0、2.0、3.0、4.0 與5.0 μm 時，所對應的峰值光響應度SR分別約為0.196、0.226、0.246、0.261和0.272 A·W?1，相應的入射波長λ分別為0.44、0.50、0.52、0.56 和0.57 μm，與峰值量子效率所對應的入射波長相一致。

2.4 倍增層參數(shù)對增益的影響

光電流增益是APD 最重要的特性，其根本物理機制是載流子的碰撞電離效應，通常用倍增系數(shù)表示。假設雪崩效應僅發(fā)生在倍增層，則在電子引發(fā)的雪崩情況下，倍增系數(shù)M(x)如式（15）所示[27]。由式（15）可知，雪崩倍增主要由耗盡層寬度、電場強度、載流子的碰撞離化系數(shù)等決定。

式中，α(x)和β(x)分別為電子和空穴的碰撞離化系數(shù)，Wm為倍增區(qū)厚度，Chynoweths 描述了電場強度E對載流子碰撞離化的影響，關系式為[28]：

式中，an，bn，ap，bp分別為電子和空穴的碰撞離化率的實驗參數(shù)，E(x) 是倍增區(qū)中電場強度，為距離x的函數(shù)。本文的數(shù)值計算采用Lee 的實驗擬合系數(shù)[29]：an=3.8×106cm?1，bn=1.75×106V·cm?1；ap=2.25×106cm?1，bp=3.26×106V·cm?1。

考慮在一定摻雜濃度下，PN 結內倍增層的厚度、倍增層兩側的外加偏壓Vm及倍增系數(shù)M三者之間的關系。假設N型襯底摻雜濃度為ND=1.0×1019cm?3，P型倍增層摻雜濃度為NA=1.0×1016cm?3，結合公式（1）、（2）、（16），為簡化運算，將α(x) 和β(x) 進行3 階泰勒展開，代入式(15)中，計算倍增層外加偏壓Vm與倍增系數(shù)M的關系，結果如圖6（彩圖見期刊電子版）所示。

圖中曲線表明當倍增層兩側的外加偏壓Vm增加至特定值時，M急劇增加，公式（15）表明此時Vm大小接近或等于雪崩擊穿時倍增層兩側的電壓Vbr-m，因此，為了使APD 獲得較高增益，作用在器件的外加偏壓Vapd大小需近似于器件的雪崩擊穿電壓Vbr-apd。圖中曲線表明隨著倍增層厚度的增加，獲得相同倍增系數(shù)時的電壓降低。即，在小的倍增層厚度下，需要提高電壓，使載流子具有更高的電離率，才能獲得較高的增益。但是倍增層厚度的增加受摻雜濃度和PN 結兩端外加偏壓的影響，其厚度的選擇還要依據(jù)電場分布選擇，而電場分布又與摻雜濃度相關，因此倍增層的厚度需要與其摻雜濃度綜合考慮。

對于硅，僅當電子能量Eele≥6.5 eV，載流子能量才完全損耗在碰撞電離過程中[30]，從能量角度分析，假設僅在倍增層發(fā)生碰撞電離效應，不考慮場控層對電子能量的影響，忽略空穴-電子復合機制及散射能量損耗，通過公式（4）可知，設載流子在倍增層的電場作用下獲得能量ΔE為：

為簡便計算，將PN 突變結擊穿臨近電場Em代入上式整理得ΔE：

設定襯底的摻雜濃度Nn++=1.0×1019cm?3，倍增層的摻雜濃度Np為1.0×1015～1.0×1017cm?3，PN結設為單邊突變結，根據(jù)公式（18）計算不同倍增層厚度下?lián)诫s濃度與載流子獲得能量ΔE的數(shù)值關系，結果如圖7 所示。當倍增層厚度Wm固定為0.5 μm 時，由圖5 曲線可知，摻雜濃度Np分別為1.2×1016、1.8×1016與2.4×1016cm?3時，能量ΔE分別為18.22、18.39 與18.26 eV。因此，當倍增層摻雜濃度為1.8×1016cm?3時，載流子在倍增層獲得較高能量ΔE=18.39 eV，理論上可產(chǎn)生較高的增益系數(shù)M。

2.5 場控層的影響

場控層的摻雜濃度（Np+）和厚度（Wc）是調節(jié)倍增層與吸收層電場過渡的重要參數(shù)，場控層位于吸收層與倍增層之間，通過降低吸收層的電場強度，減少器件的隧穿幾率。然而場控層厚度不宜過大，原因如下：當外加偏壓與場控層摻雜濃度固定時，增加場控層厚度會將減小吸收層的電場強度，會影響吸收層光生載流子的漂移速度；而厚度過小，又會增加吸收層電場強度，誘發(fā)載流子電離，增加不必要的噪聲電流。根據(jù)公式（5），在保證載流子飽和漂移速度下，選擇合適的摻雜濃度和厚度，有利于倍增層和吸收層之間電場的調節(jié)和過渡。一般地，選擇比倍增層小的厚度和比倍增層高的摻雜濃度，可以保證對倍增層變化的影響最小。

2.6 吸收層設計

由于Si 材料自身的吸收特性[31]，對波長為0.4～ 0.5 μm 的藍光波段具有較高的吸收系數(shù)（如圖3 所示），導致藍光波段的光在硅中的穿透深度較淺，約為0.098～0.82 μm。為了使藍光被吸收層充分吸收，結合圖4 所示的量子效率與耗盡層厚度的關系，選取吸收層厚度Wa=1.3 μm。在硅中，當電場強度E>1.0×104V·cm?1時，電子會趨于飽和漂移速度，vs（Si）≈107cm·s?1。為了使器件保持較高的帶寬，載流子在器件中應以飽和速度運動。倍增層、場控層的摻雜濃度和厚度固定時（Wm=0.5 μm,Np=1.8×1016cm-3;Wc=0.2 μm,Np+=8.0×1016cm?3），當突變PN 結臨近擊穿時，根據(jù)式（6）繪制了不同摻雜濃度下吸收層的場強分布，如圖8（彩圖見期刊電子版）所示。從圖中可以看出，吸收層的場強隨著摻雜濃度的增加逐漸減小，當吸收層的摻雜濃度為Nπ=1.0×1016cm?3和5.0×1015cm?3時，場強在到達表面非耗盡區(qū)以前已經(jīng)耗盡，此時藍光激發(fā)的載流子進入吸收層以擴散運動為主，增加了載流子的渡越時間，降低了器件帶寬。當Nπ分別為：1.0×1014cm?3、5.0×1014cm?3和1.0×1015cm?3時，吸收層的邊緣場強E>104V·cm?1，器件處于拉通工作狀態(tài)，載流子在整個器件中以飽和速度漂移運動。所以吸收層的摻雜濃度和厚度選取需保證吸收層內載流子有良好的電場分布，保證載流子的飽和漂移速度，同時還要滿足紅綠光有一定的吸收率。

2.7 Si-APD 初始結構參數(shù)

假設各層摻雜均勻，入射光僅在吸收層被吸收，在反偏電壓下，雪崩效應只發(fā)生在倍增層?；谏衔年P于增益系數(shù)與外加偏壓、倍增層厚度的關系、量子效率及光響應度與耗盡層厚度的關系，選取的各層的參數(shù)如表1 所示，其中Ws、Wa、Wc、Wm和Wsub分別為表面非耗盡層、吸收層、場控層、倍增層和襯底的厚度。

3 Si-APD 數(shù)值計算

描述半導體器件工作的基本方程有：靜電方程、電流密度方程和連續(xù)性方程。載流子的產(chǎn)生與復合機制是影響半導體光電探測器性能的關鍵。對Si-APD 的器件特性進行二維模擬，計算采用的Si-APD 的光敏面直徑為10 μm，為了提高計算結果的準確性，計算過程中采用了Selberherr's離化[32-33]、Shockley-Read-Hall 復合[34-35]及載流子遷移率[36-38]等物理模型。

3.1 Si-APD 的場強分布與外加偏壓的關系

根據(jù)表1 中的參數(shù)，研究了器件中Vapd分別為：0 V、0.5Vbr-apd、0.7Vbr-apd、Vbr-apd（所對應的Vapd分別為：0 V、17.1 V、23.9 V、34.2 V），Si-APD 內部的場強分布，如圖9（彩圖見期刊電子版）所示。從圖中可以看出，Si-APD 內部的電場強度隨著器件外加偏壓Vapd的增加而提高。當Vapd較小時，器件處于非拉通工作狀態(tài)，載流子在器件中，開始以擴散運動為主，隨著外加偏壓的增加，器件整體被拉通，此時載流子以漂移運動為主，隨著外加偏壓的不斷增加，載流子最終將以飽和漂移速度在器件中運動。

3.2 表面非耗盡層厚度進一步優(yōu)化設計

通常半導體光電探測器表面具有一定厚度的表面重摻雜非耗盡層（兼作電極層），藍光波段的光在硅中的穿透深度較淺，當光經(jīng)過器件頂部的非耗盡層時，大部分藍光能量被該層吸收產(chǎn)生空穴—電子對，因此有必要對表面非耗盡層的厚度進行優(yōu)化。在表1 參數(shù)基礎上，固定表面層的雜質濃度及其它摻雜層的結構參數(shù)，入射光垂直照射在探測器表面層，得到R≠0 時，不同表面非耗盡層厚度的光譜響應曲線，結果如圖10（彩圖見期刊電子版）所示。圖中曲線展示了當表面非耗盡層厚度Ws分別為0.03、0.06 和0.10 μm 時，外加偏壓為0.95Vbr-apd（M≈26）下的光譜響應度，其中當Ws=0.03 μm 時藍光波段的光響應度SR為3.71～ 6.08 A·W?1；當Ws=0.06 μm 時藍光波段的光響應度為SR為3.15～5.94 A·W?1；當Ws=0.10 μm時藍光波段光響應度為SR為2.57～5.75 A·W?1，表明表面非耗盡層越薄，對藍光光響應度的抑制作用會越小。通過曲線也發(fā)現(xiàn)，Ws的變化對器件在長波段入射光的光響應度的影響較小，分析認為根據(jù)光在介質中的傳輸特性，入射光在厚度為Ws的表面非耗盡層光吸收損耗As為：

式中，R為表面反射率，α為Si 的光吸收系數(shù)。寬度為WD的耗盡區(qū)內光生載流子形成的漂移電流密度為：

可見光波段入射光功率Popt固定，公式（20）的前半部分表示特定波長光透射至探測器的耗盡層邊緣的光子數(shù)量，后半部分表征厚度為WD的耗盡層對入射光子的吸收率，忽略載流子的復合機制，設耗盡區(qū)量子效率QE=100%。根據(jù)Si 的材料特性可知，長波段入射光被材料吸收的強度較小，因此表面非耗盡層產(chǎn)生的光吸收損耗對透射至耗盡層的光能量影響較小，因此調節(jié)Ws的過程中長波段光響應度基本穩(wěn)定。但在短波一側，表面非耗盡層厚度對光響應度有較大的影響。

3.3 倍增層的摻雜濃度對光響應度的影響

根據(jù)圖10 的計算結果，結合上面非表面耗盡層厚度計算結果，取表面非耗盡層厚度Ws=0.03 μm，表面反射率R≠0，其它參數(shù)依據(jù)表1 中數(shù)據(jù)，得到Vapd=0.95Vbr-apd時，Si-APD 在可見光波段的光響應度如圖11（彩圖見期刊電子版）紅色曲線所示，所對應的藍光波段的光響應度分為SR=3.72～6.08 A·W?1。

作為比較，在其他參數(shù)不變的情況下，還分別計算了倍增層摻雜濃度Np分別為1.2×1016cm?3、2.4×1016cm?3（所對應的擊穿電壓Vbr-apd分別為39.2 V、30 V），Vapd=0.95Vbr-apd時的光響應度，如圖11 中藍線和黑線所示，所對應的藍光波段的光響應度SR分別為3.02～4.93 A·W?1、2.83～4.68 A·W?1。這兩種情況下，光響應度均低于紅線所示的Np=1.8×1016cm?3摻雜時的SR值。

這種現(xiàn)象可以歸因于在該摻雜濃度下，載流子在倍增層可以獲得更高的能量（如圖7 所示），產(chǎn)生更大的光電流增益。根據(jù)上述的研究結果，最終確定Si 光探測器的基本外延結構參數(shù)如表2 所示。

3.4 Si-APD 暗電流的I-V 特性

假定每一層都是均勻摻雜的，Si-APD 在暗環(huán)境中的I-V 關系特性可以反映器件的雪崩擊穿電壓Vbr-apd、電流增益系數(shù)M等電學參數(shù)。根據(jù)表2 中參數(shù)及公式（21）定義的電流密度方程定性計算I-V 特性曲線。電流密度大小主要受載流子輸運行為的影響，在數(shù)值關系上表示為電子電流密度和空穴電流密度之和，即：

式中Jn為電子電流密度，Jp為空穴電流密度，Jcond為傳導電流密度，μn為電子遷移率，μp為空穴遷移率，Dn為電子擴散系數(shù)，Dp為空穴擴散系數(shù)，?n、?p為過剩載流子濃度梯度。圖12 中曲線展示了計算得到的反向電流與外加偏壓Vapd的變化關系。從圖中可以看出電流大小隨Vapd的增加而不斷提高，但電流的變化趨勢不同，根據(jù)不同的電流形成機理，總結為圖12 中(i)?(iv)部分。

雪崩光電二極管的暗電流密度包括[39]復合電流密度Jr，少子擴散電流密度Jdiff，耗盡層的載流子漂移電流密度Jdr與雪崩電流密度Jm。復合電流密度表示為Jr=qniWD/2τD。τD=1/Rec·N，為載流子壽命，Rec≈10?15cm3s?1，為間接帶隙半導體復合系數(shù)[27]，N為摻雜濃度。Jdiff=(qDpni2/LpND) +(qDnni2/LnNA)，Dp=kTμp/q與Dn=kTμn/q分別為空穴與電子擴散系數(shù)，Lp和Ln分別為空穴與電子的擴散長度。當T=300 K 時，kT/q=0.025 9 V，Dp=12.95 cm2·s?1，Dn=37.56 cm2·s?1。為簡便計算，結合上文設計的APD 結構中π 吸收層、p+型場控層與p 型倍增層的摻雜濃度，將該3 個區(qū)域視為摻雜濃度、載流子壽命的P 型硅材料：

τsc(p)，τsc(p+)與τsc(π)分別為倍增層、場控層與吸收層的載流子壽命。

當外加偏壓Vapd較小時，Si-APD 電流以擴散電流和復合電流為主。將上述數(shù)據(jù)代式（24）計算器件的擴散與復合電流，結果對應于圖12 的(i)部分。

增加外加偏壓Vapd，受內部電場作用的載流子數(shù)量增多，漂移電流為電流的主要部分，根據(jù)式（21），器件的漂移電流密度表示為：Jdr=qnμnE+qpμpE，其中E為式（4）～（7）定義的耗盡層電場強度，將計算結果Jdr代入下式（25），結果對應于圖12 中(ii)部分。

若外加偏壓Vapd持續(xù)增加，載流子在強電場作用下發(fā)生碰撞電離，高能初始載流子撞擊內部晶格產(chǎn)生次生載流子，之后繼續(xù)碰撞晶格產(chǎn)生新的載流子，形成雪崩電流密度Jm=(αnJn+αpJp)，Jn與Jp為電子與空穴電流密度，αn、αp分別為電子和空穴的離化系數(shù)。該碰撞效應在工作偏壓下持續(xù)進行，載流子數(shù)量倍增，假設雪崩效應僅在倍增層內發(fā)生，則厚度為Wm的倍增層內產(chǎn)生的雪崩暗電流Id可以表示為：

如圖12 的第（iii）部分所示。

通常，器件的增益系數(shù)M可根據(jù)經(jīng)驗關系式(27)得出

式中，Id為基于載流子激發(fā)碰撞電離作用下產(chǎn)生的電流，Id0為初始暗電流，常量n大小受器件結構、摻雜分布等因素影響，通常Si 材料的n為1.5～4.0。當外加偏壓Vapd接近雪崩擊穿電壓Vbr-apd時，則此時電流會隨倍增因子M急劇增加而提高，如圖12 中區(qū)域(iv)所示。

圖12 的暗電流I-V 關系曲線表明：APD 器件處于低外加偏壓時，擴散電流占總電流的主要部分；之后內部電場強度隨Vapd增加而提高，耗盡區(qū)寬度增大，更多的載流子進入耗盡區(qū)，在電場作用下形成漂移電流，其成為總電流的主要部分；當Vapd持續(xù)增加，由于載流子碰撞電離作用，出現(xiàn)電流增益現(xiàn)象但效果不明顯；若Vapd接近器件雪崩擊穿電壓Vbr-apd，則出現(xiàn)電流急劇增加現(xiàn)象。

通過對比（iii）與（iv）部分中的電流隨電壓的變化趨勢發(fā)現(xiàn)，APD 處于相對雪崩擊穿電壓較高的偏壓時可產(chǎn)生較高的電流增益M。分析認為載流子的離化率是衡量雪崩倍增效應的重要指標，其與器件偏壓相關聯(lián)的電場強度聯(lián)系緊密[40]，離化率隨偏壓提高而增大。以在倍增層內的電子為例，根據(jù)（16）式并按照Lee的載流子電離參數(shù)與（4）式的電場分布計算電子、空穴在不同偏壓下的碰撞電離率分布，圖13（a）和圖13（b）（彩圖見期刊電子版）清楚表明碰撞離化系數(shù)隨倍增層兩側電壓Vm的增加而提高，因此在Vapd接近Vbr-apd時會出現(xiàn)電流高增益現(xiàn)象，并且以電子增益為主。

4 結論

為了解決光通信系統(tǒng)對藍光高響應光電探測器的迫切需求，本文設計了一種吸收層與倍增層互換位置SACM 型Si-APD 結構，研究了倍增層厚度與器件增益、吸收層摻雜濃度與吸收層場強分布、外加偏壓與器件內部場強分布、表面非耗盡層厚度與光譜響應度以及倍增層濃度與光譜響應的關系，綜合考慮，選取器件的結構參數(shù)為：表面非耗盡層厚度為0.03 μm，摻雜濃度1.0×1018cm?3；吸收層厚度為1.3 μm，摻雜濃度為1.0×1015cm?3；場控層厚度為0.2 μm，摻雜濃度8.0×1016cm?3；倍增層厚度為0.5 μm，摻雜濃度為1.8×1016cm?3。該器件具有較低的擊穿電壓Vbr-apd=34.2 V,當Vapd=0.95Vbr-apd在藍光波段有較高的光響應度SR=3.72～6.08 A·W?1。本文的研究結果對實際器件的制備具有一定參考價值。