## Abstract

Separate absorption grading charge multiplication avalanche photodiodes (SAGCM APDs) are widely accepted in photon starved optical communication systems due to the presence of large photocurrent gain. In this work, we present a detailed analysis of dark currents of planar-type SAGCM InGaAs–InP APDs with different thicknesses of multiplication layer. The effect of the diffusion process, the generation-recombination process, the tunneling process and the multiplication process on the total leakage current is discussed. A new empirical formula has been established to predict the optimal multiplication layer thickness of SAGCM APDs with dark current limited by generation-recombination at multiplication gain of 8.

© 2011 OSA

## 1. Introduction

There continues to be a strong interest in the use of avalanche photodiodes (APDs) in the fields of quantum key distribution, national defense, astrosurveillance and other photon starved optical communication [1–6]. For their high sensitivity and high multiplication gain (M), separate absorption grading charge multiplication avalanche photodiodes (SAGCM APDs) have drawn more and more attentions. As APDs are operated at low optical power levels, the noise is mainly attributed to dark current. This dark current was found to increase with the increase of applied bias, thereby limiting device performance. The primary concern is that the increased dark current value constrains the useful gain of the device to a low value. Compared with a mesa-type APD, APDs with a planar structure have shown an overwhelming advantage, which have been adopted widely to reduce dark current and solve the reliability issue [7,8]. It is well known that the APD performance can be influenced not only by device's fabrication process, but also by the epitaxial structure. It is important to optimize the internal electric field distribution of SAGCM APDs for dark current reduction. For practical applications, it is thought that “useful gain” of APDs is an effective parameter, considering a trade-off between the requirements of a high gain and a low dark current value of APDs. In this work, we present a detailed analysis of dark currents of planar-type SAGCM InGaAs–InP APDs with different thicknesses of multiplication layer with M in the range of 4-10. The effect of the diffusion process, the generation-recombination process, the tunneling process and the multiplication process on the total dark current is discussed and included in the analysis. Temperature coefficient of the optimized APDs is as low as 90 mV/K. To predict the optimal thickness of the multiplication layer of SAGCM APDs, a new empirical formula has been established in our work.

## 2. Experiments

A schematic cross-section of the InGaAs–InP APD with a floating guard ring (FGR) is shown in Fig. 1
. The APD wafer epitaxial structures were grown in a single reactor growth cycle using metal organic chemical vapor deposition (MOCVD) process. The 2.0 μm thick undoped InGaAs layer is the absorption layer where the primary photo-generated carriers are generated. The generated electrons are swept by electric field to the n-contact, and generated holes travel to the undoped InP multiplication layer, i.e. nearly pure injection of photo-generated holes into the gain region is obtained, which gives the most advantageous structure for low-noise operation. The n^{+}-InP charge sheet layer is highly doped to decrease the electric field in the absorption layer. The undoped InGaAsP with graded composition was inserted to avoid hole accumulation in heterointerface between InP charge layer and the InGaAs absorption layer, i.e. the InGaAsP layer was used to match the energy band gaps of materials in multiplication and absorption layers. An effective active surface area is 50 μm in diameter, above which is coated with an antireflection SiN* _{x}* layer. More details of the measured device structure parameters are tabulated in Table 1
. Six samples were prepared in our experiment, and the only difference among them was the change in thickness of the multiplication layer. The MOCVD diffusion process has been adopted using Dimethylzinc (DMZn) as Zn source. Two-step diffusion process has been used for edge pre-breakdown suppression in our experiments. The diameter of the larger Zn diffusion window is 70 μm, while the diameter of the smaller Zn diffusion window is 50 μm. The diffusion depth can be well controlled by diffusion time, temperature, gas flowing rate and pressure. The optimized process parameters in this work include the temperature of 500 °C, pressure of 400 Torr, flow rate of DMZn of 5 sccm for the first Zn diffusion; 10 sccm for the second diffusion, and 50 min. of the diffusion duration for both diffusion processes. Our experiment shows that the higher flow rate of DMZn for the second diffusion than that of the first one is very important for the formation of an abrupt p–n junction central region. FGR window was formed in the same photolithographic step as the first diffusion window. The ring window is 1.5 μm wide, and the shortest spacing between the FGR and the edge of central junction is 4 μm. The p

^{+}central junction was formed in the n

^{-}InP cap layer by Zn first diffusion and following second diffusion, while FGR was formed in the n

^{-}InP cap layer by the only Zn first diffusion at the same time during the first diffusion of p

^{+}central junction. P-Side electrode and n-side electrode were made by metallization process using Ti–Pt–Au and Au–Sn alloys, respectively. The thickness of InP multiplication layer (

*X*) has been optimized for dark current reduction. Six kinds of APDs with different

_{d}*X*(0.2, 0.35, 0.48, 0.53, 0.75 and 0.96 μm) were prepared, which are named as APD I-VI respectively in the following parts of this work.

_{d}For dc photocurrent measurements, 1.31 μm light (1 μW) was generated and transmitted over a monomode optical fiber to APD. A negative biased voltage in the range of 0 to –*V _{bd}* (breakdown voltage) was provided to APDs with a step of −0.2

*V*, and the currents flowing through APDs during the change of voltage with and without light incidence were recorded automatically with a program-controlled Keithley voltmeter. For measurement of temperature-dependent

*V*, the APDs were fixed in an aging oven and were first cooled down from room temperature. Then the measurements were taken while APDs were heating in the temperature range of −40 −100 °C.

_{bd}## 3. Results and discussion

The measured dark current of APDs can be viewed as the superposition of two main current components, i.e. the surface current component and the bulk current component [9]. In ideal APDs, the total dark current *I _{dT}* can be expressed as a function of the multiplication factor

*M*

*I*and

_{dM}× M*I*denote multiplied and unmultiplied dark current, respectively. The

_{d0}*I*is a volume contribution coming from the absorption and grading regions. It is produced by generated carriers that flow through the multiplication region under the p-n junction central region (50 μm in diameter) where the avalanche electric field is the maximum and impact ionization happens. The unmultiplied dark current

_{dM}× M*I*is identified as a combination of surface contribution as well as the contribution from the peripherical edge of the active region, where the electric field is lower than the central region of the junction and the multiplication is not expected to be built due to the suppression of edge pre-breakdown with the two-step Zn diffusion.

_{d0}The *I _{dM}* deduced from the volume contribution of

*I*(i.e.

_{dT}*I*) can be quantitatively described by the sum of the three independent current sources: generation recombination of electron-hole pairs via traps in the depletion region (

_{dM}× M*I*), tunneling of carriers across the bandgap (

_{gr}*I*), and the diffusion current due to thermally generated minority carriers diffusing into the depletion region (

_{tun}*I*) [10]. In our analysis, the tunneling via Shockley-Read-Hall (

_{diff}*SRH*) centers located within the bandgap was ignored since the measurement in our work was performed under relatively low reverse bias at room temperature [11]. For the sake of simplicity, the shunt current was also neglected.

Therefore, the theoretical components of the reverse dark current were proposed as below [12,13]

*q*is electronic charge,

*n*is the intrinsic carrier concentration,

_{i}*A*is the area of the active region,

*w*is the depletion region width,

*τ*is the effective carrier lifetime,

_{eff}*V*is applied voltage,

*k*is Boltzmann’s constant,

*T*is the temperature in Kelvin. In Eq. (3),

*m*is the free-electron mass,

_{0}*E*is the maximum junction electric field,

_{m}*ℏ*is Planck’s constant divided by 2π, and

*ε*is the energy gap. Other parameters, such as γ and

_{g}*θ*are explained in [12] in detail. In Eq. (4),

*I*is the saturation current.

_{s}In a SAGCM APD, punch-through of the depletion region from InP multiplication region into the charge layer, grading layer, InGaAs absorption layer and highly doped InP buffer-layer occurs with the increase of the bias [14]. A *p ^{+}ν* -APD is defined which consists of a highly doped p

^{+}- InP layer forming an abrupt, one-sided junction with an intrinsic absorption

*ν*(or

*n*) layer of InGaAs. When APD is biased with a voltage higher than a critical value above which the depletion region expands away from InGaAs layer to the InP buffer layer, it is defined that the APD works under the punch-through configuration (

*PT*-APD). In this work, a series of values of critical voltage have been defined as

*V*,

_{on}*V*,

_{diff}*V*and

_{M = 8}*V*. Among them

_{bd}*V*denotes the critical voltage of onset of photo-response, and

_{on}*V*is the critical voltage where a transition happens from

_{diff}*p*to

^{+}ν*PT*-APD. Also

*V*denotes the voltage of M = 8 for different APDs, and

_{M = 8}*V*is breakdown voltage, as discussed earlier.

_{bd}*V*can be calculated with a series of electric field equations [14], just sets the electric field value being zero at the interface of InGaAs/InP buffer layer, a similar procedure to the determination of

_{diff}*V*. The only difference is, in the later case, that the electric field value decreases to zero at the InGaAsP/InGaAs interface. For

_{on}*p*-APD, the saturation current should include three parts: the first one is the electron diffusion from p

^{+}ν^{+}-InP region, the second one is the hole diffusion from part of InGaAs region where it is not depleted, and the third one is the hole diffusion from intrinsic InP and InGaAs in the radial direction of central junction, as shown in the following formula

*n*(

_{i,InP}*n*) is the intrinsic carrier concentration of InP (InGaAs). τ

_{i,InGaAs}_{n,InP(p + )}is the minority carrier diffusion time in the p

^{+}-InP, τ

_{p,InGaAs}is the minority carrier diffusion time in the InGaAs undeleted part of the absorption layer, and

*A*(

_{p,InP}*A*) is the area of the depletion region boundary in the

_{n,InGaAs}*p*(

^{+}*n*) material. Also,

*N*and

_{A,InP}*N*are the doping densities, and

_{D,InGaAs}*D*and

_{n,InP}*D*are the minority carrier diffusion constants in the

_{p,InGaAs}*p*and

^{+}*n*regions, respectively. The diffusion constants are obtained from appropriate carrier mobility

*μ*using the Einstein relation

*D/μ = kT/q*.

While for *PT* -APD, the saturation current should also include three parts, as shown as follows

The first part of the right side of Eq. (6) is the electron diffusion from p^{+}-InP region, the second one is the hole diffusion from n^{+}-InP buffer layer, and the third one is the hole diffusion from intrinsic InP and InGaAs in the radial direction of central junction. We only consider the bias being a little less or larger than the critical voltage value of *V _{diff}*, which means the depletion region (

*w*) is adjacent from both sides to the InGaAs/InP buffer layer heterointerface. To a first approximation, it is reasonable to assume that

*w*is same for

*p*and

^{+}ν*PT*-APD, and therefore it is thought that the radial component of the saturation current for

*p*and

^{+}ν*PT*-APD is equal, i.e.

*I*. Then difference between formula (5) and formula (6) is determined by the second term. Since${I}_{diff}\propto {n}_{i}{}^{2}\propto {e}^{-{\epsilon}_{g}/kT}$, where${\epsilon}_{g}$is the energy gap, the diffusion current in InP is approximately 10

_{s,p + ν,radial}≈I_{s,PT,radial}^{−11}times

*I*of the InGaAs at

_{diff}*T*= 300 K [13]. Considering the structural parameters and the electric constants of InP and InGaAs, it is not difficult to understand that when the APD changes from the

*p*to

^{+}ν*PT*configuration as the bias increases to a critical bias, the

*I*will decrease abruptly, which is proved by our experiment. The punch-through configuration is useful in reducing the total reverse-bias dark current when diffusion is a significant source of the leakage.

_{diff}Figure 2(a)
shows the change of dark current (*I _{dT}*), photocurrent (

*I*) and M with bias for APD II.

_{L}*I*,,

_{dT}*I*and M were found to increase with the increase of applied voltage. The maximal value of M as high as 10

_{L}^{4}can be defined from the plot. However, the bias supporting so high M is too close to

*V*, and

_{bd}*I*becomes so huge that makes the APD useless. At the M of 8, the dark current decreases to 2.8 nA. Decrease of dark current is strongly desired for practical applications.

_{dT}To shed light on the mechanism of dark current, the change of *I _{dT}* with M derived from Fig. 2(a) is reploted, and the result is shown in Fig. 2(b), as denoted by a series of open circles. The solid line in Fig. 2(b) is a linear fit of the experimental data. It is found that the linear relationship between

*I*and the M keeps in the range of M = 2 to 8. The inset of Fig. 2(b) is an enlargement of the rectangular region which is close to the (0,0) position of the main body, and an intercept can be easily found after the enlargement, which shows that

_{dM}*I*equals to 0.012 nA, while

_{d0}*I*equals to 0.32 nA.

_{dM}*I*is only about 4% of

_{d0}*I*. It is addressed here that the multiplied and unmultiplied commponents of

_{dM}*I*are both expected to change with bias. However, the linear relationship of

_{dT}*I*vs. M reveals that in this range

_{dT}*I*is dominated by the volume contribution, which can be used for optimization of APD epitaxial structure. In the range of high values of M, it is shown the deviation from linearity in Fig. 2(b). To avoid errors caused by nonlinear effects, such as heating, only the linear region is included in our analysis.

_{dT}Reduction of *I _{dM}* is important for achieving a high-performance APD with dark current dominated by volume contribution. It is revealed in Fig. 3(a)
that

*I*increases with the reverse bias in the range of 24-40 V. Here,

_{dM}*I*is simply derived from (

_{dM}*I*-

_{dT}*I*) /M. An obvious transition point at about 33 V is also found in Fig. 3(a). On basis of the previous discussion, the theoretical value of

_{d0}*V*for APD II is 33.2 V, which is very close to the obvious transition point at about 33 V, as shown in Fig. 3(a). In Fig. 3(b)-(d) we show the measured and theoretical current-voltage characteristic under different bias. In the lower voltage part (33.0 V and lower), it is found that the combination of

_{diff}*I*with

_{diff}*I*can account for the experimental data very well, as shown in Fig. 3(b). Under bias of 33.0 V,

_{gr}*I*is about 0.195 nA, while

_{diff}*I*is 0.137 nA. The values of

_{gr}*I*is about one third lower than that of the

_{gr}*I*. In our analysis, the value of

_{diff}*I*is assumed to be consecutive in the whole bias range of 24-40 V. In the higher bias part (higher than 33.0 V), besides

_{gr}*I*and

_{diff}*I*,

_{gr}*I*has to be considered to account for the experimental data satisfactorily. In the high bias part,

_{tun}*I*decreases to a value as low as 1.0 × 10

_{diff}^{−3}nA (not included in the figure), which is so small that it can be ignored in the following analysis. It is noted that at M = 8,

*I*equals to 0.146 nA, while

_{gr}*I*equals to 0.214 nA. As we discussed early, when the bias is greater than a critical value (

_{tun}*V*), above which the APD works under

_{diff}*PT*configuration, the

*I*decreases abruptly. The theoretical prediction of

_{diff}*V*is 33.2 V, which is very close to the experimental transition point at about 33 V, as shown in Fig. 3(a). Comparison of Fig. 3(b) with (c) reveals that the value of the

_{diff}*I*of the

_{diff}*PT*-APD is about two orders of magnitude smaller than that of the

*p*APD, which is consistent with the theory predication, as we discussed before. Above 33.0 V,

^{+}ν*I*increases rapidly with the increase of bias, which means that

_{dM}*I*becomes dominant in the dark current of the

_{tun}*PT-*APD.

For practical application, it is important to keep the dark current in APD as low as possible at a fixed M (usually in the range of 5-8), which can usually be utilized by keeping APD free from *I _{tun}*. The internal electric distribution can be optimized by adjusting the thickness of InP multiplication layer and the charge doping level of the charge layer. In Fig. 3(d) we show the measured and theoretical current-voltage characteristic for APD IV under different bias (41.8-47 V) within the multiplication gain range of 4-10. The only difference of this sample from APD II is the thickness of multiplication layer. The calculation shows

*V*of APD IV is about 41.8 V, which corresponds to the M value of 4. As expected,

_{diff}*I*for the

_{diff}*PT*-APD is as low as 0.9 × 10

^{−3}nA, which is a little less than that of APD II. And the value of

*I*is two orders of magnitude smaller than that of

_{diff}*I*. No crossover in dark current with the increase of the bias is observed, which could mean that the APD is free from

_{gr}*I*. In Fig. 3(d), at the whole range of M = 4-10, the dark current can be quantitatively described by the only origin of

_{tun}*I*. Our result suggests that the tunneling current can be suppressed and InGaAs–InP avalanche photodiodes with dark current limited by generation-recombination can be realized in the multiplication gain range of 4-10 simply by adjusting the thickness of the InP multiplication layer.

_{gr}In Fig. 4(a)
we show the ratio of *I _{gr}* to (

*I*+

_{gr}*I*) at M = 8, and in (b) it is shown the change of

_{tun}*I*with the multiplication layer thickness. For APD I-VI,

_{dT}*I*at M = 8 is 100, 2.8, 0.25, 0.50, 3.1, and 33.3 nA, respectively, while the ratio of

_{dT}*I*to (

_{gr}*I*+

_{gr}*I*) for APD I-VI changes from 20%, 41%, 100%, 100%, 86% to 82.2%.

_{tun}*I*of both APD III and IV are free from tunneling and only dominated by

_{dM}*I*. However, APD III has a lower dark current than that of APD IV. The trend of

_{gr}*I*changing with

_{dT}*X*is basically consistent with that of

_{d}*I*/ (

_{gr}*I*+

_{gr}*I*), which reveals that the suppression of tunneling current is very important for

_{tun}*I*reduction. An optimum thickness of InP multiplication layer can be defined from Fig. 4. The optimized APD (APD III) with the total dark current as low as 0.25 nA at M = 8 was achieved.

_{dT}A trade-off exists between the requirements of a high gain and a low dark current value. The thickness of the InP multiplication layer and charge doping level of the SAGCM APD are adjusted to give fields high enough for photocurrent gain at the *p-n* junction (*E _{m}* = (4.5-5.0) × 10

^{5}

*V/cm*) while the field of InGaAs layer keeping small enough (

*E*<1.5 × 10

^{5}

*V/cm*) to minimize the dark current due to tunneling widely observed in this material system [15,16]. It is noted that the reported data on optimization of electric field distribution are scattered, which could originate from different quality of materials grown by different groups. In this work, electric field parameters of the home-made APD (APD III) with optimized thickness of multiplication layer have been extracted. The maximum applied field on InGaAs layer is given to an optimal value (

*E*= 1.2 × 10

^{5}

*V/cm*), which makes APDs free from tunneling dark current. On basis of the optimal electric field, a series of optimized values of InP multiplication layer thickness for SAGCM APDs with different charge doping levels have been derived at M = 8, as shown in Fig. 5 . The method for calculation of M can be easily found from previous reports [14]. For simplicity, the dead space effect is ignored in our calculation. In Fig. 5, the solid squares denote the calculated data, the open circle denotes the data from our experimental work (from APD III), and solid line denotes a fit of the calculated data with an empirical formula, which is shown as follows

*y*denotes the charge doping level, while

*x*denotes the optimized thickness of the multiplication layer. The empirical formula (7) can be used to predict the optimized thickness of the InP multiplication layer of APDs with different charge doping levels. It is no doubt that the empirical formula will be helpful to the design and fabrication of SAGCM APDs. Our work is performed based on the InGaAs-InP materials. However, the methodology can be easily applied to other material systems, such as Ge-Si [17], InGaAs-InAlAs [6], III-Nitride [18], HgCdTe [19] and SiC [20] based-SAM APDs, which are widely used in optical communication, single-photon detection, infrared detection and violet detection and so on.

In Fig. 6
we summarize the voltage characteristic for the optimized APDs with different integrated charge densities. For the integrated charge density changes from 3.11, 3.21, 3.33, 3.41, 3.51, to 3.61 × 10^{12} /cm^{2}, *V _{on}* equals to 33.2, 28.9, 25.1, 22.8, 20.5 and 18.4 V, respectively; also

*V*equals to 50.7, 44.7, 39.4, 36.3, 33.1 and 30.3 V, respectively; also

_{diff}*V*equals to 56.4, 50.0, 44.6, 41.4, 38.0 and 35.1 V, respectively; and

_{M = 8}*V*equals to 60.0, 55.0, 49.0, 46.0, 42.6 and 40.0 V. As shown in Fig. 6(a),

_{bd}*V*,

_{on}*V*,

_{diff}*V*and

_{M = 8}*V*decrease consecutively with the integrated charge density in the range of 3.11 to 3.61 × 10

_{bd}^{12}/cm

^{2}, which means that the increase of the charge doping level is an effective way to obtain an APD working under low bias. As shown in Fig. 6(b),the decrease of (

*V*) with integrated charge density reflects that the multiplication gain for APDs with high doping levels increases faster than that of low doping APDs. It is also found that (

_{M = 8}-V_{on}*V*) decreases with the integrated charge density. If we define an optimized APD working at

_{bd}-V_{on}*V*= 90%

_{M = 8}*V*, in our case the integrated charge density should be kept as 3.41 × 10

_{bd}^{12}/cm

^{2}.

Telecommunication APDs and single-photon avalanche photodiodes (SPADs) are strongly desired to operate over a wide temperature range. In particular SPADs are often cooled to suppress the dark counts for photon-counting applications [1–3]. It is therefore of interest to compare the avalanche breakdown temperature dependence of our optimized APD with the published work by other groups. We note that L. J. Tan et al. reported an empirical expression for breakdown voltage of SAM APDs, which can acount for the experimental work of APDs reported by different groups. Compaison of our experiments with the calculation of the empirical expression is important. The expression for InGaAs-InP based SAGCM APD is summarized as follows [21]

_{bd}/ΔΤ is the breakdown voltage temperature coefficient for a SAGCM APD with an avalanche region thickness of

*X*and

_{d}*w*is the total depletion width of the APD.

Using fomula (8), we can calculate ΔV_{bd}/ΔΤ for any SAGCM APD structure that utilizes InP multiplication region, assuming that there is no impact ionization in the absorption layer and that the electric field is uniform in the multiplication region. The calculated ΔV_{bd}/ΔΤ for APD(APD III) with the optimized structure is 131 mV/K. However, the measurement shows that ΔV_{bd}/ΔΤ is only about 90 mV/K, as shown in Fig. 7
. We also measured ΔV_{bd}/ΔΤ of APDs IV, since the APD shows a lower dark current than its counterparts, except for APD III. It is found that ΔV_{bd}/ΔΤ of APDs IV is about 94 mV/K, also showing a large deviation from the prediction (133 mV/K). It is a surprise that the value of ΔV_{bd}/ΔΤ from our experiment is one quarter lower than that of the predication from Eq. (8). Since a lot of experiments referenced by L. J. Tan et al. (see Table 2 of reference [21]]) are consistent with their calculation with the empirical equation, the difference between our measurement and the calculation with Eq. (8) may suggest that the optimization in APD structures can improve the temperature performance of APDs.

## 4. Conclusions

In this work, we present a detailed analysis of dark currents of planar-type SAGCM InGaAs–InP APDs with different thicknesses of multiplication layer within the multiplication gain range of 4-10. The effect of the diffusion process, the generation-recombination process, the tunneling process, and the multiplication process on the total dark current has been discussed and included in the analysis. Temperature coefficient of the optimized APDs is as low as 90 mV/K, which suggests that that the optimization in APD structures can improve the temperature performance of APDs. A new empirical formula has also been established to predict the optimal multiplication layer thickness of SAGCM APDs with dark current limited by generation-recombination at multiplication gain of 8. Our work is performed based on the InGaAs-InP material, however, the result can be extended to other material systems if the electric parameters for the material system are well selected.

## Acknowledgement

This work was supported by the National Hi-Tech Research and Development Program of China (No. 2008AA01Z207), 863 Natural Science Foundation of Hubei Province, China (Grant No. 2010CDB01606), and Scientific Research Foundation for the Returned Overseas Chinese Scholars.

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