Introduction
Avalanche photodiodes (APDs) are crucial components for long wavelength optical communication systems (OCS). In the past decade, the performance of APDs has been improved by amending the quality of applied materials and improvement of device structure [1]. In contrast to the positive-intrinsic-negativeβ(PIN) photodiodes, APDs have an internal gain which causes higher detection sensitivity. For this reason, APD has become an efficient device with broad applications in long distance fiber OCS [2]. The gain-bandwidth product (GBP) is a key parameter. The large quantities of GBP enable APDs to work in high bit rates and provide them further future development. But, the randomness of the multiplication process produces excess noise and decreases device bandwidth. High performance APDs can be achieved by using separated absorption, grading, charge and multiplication (SAGCM) layers [3]. The APDs fabricated in this structure exhibit lower noise and higher bandwidth in comparison to other structures.
El-Batawy and Deen [10,11] respectively introduced one of the earliest circuit models for SAGCM- APDs. But, the utilized transfer function for the gain computation of this model was difficult to be applied in opto-electronic integrated circuit (OEIC) software and a uniform electric field was considered within the devices regions.
Banoushi et al. [12] presented an alternative model for SAGCM-APDS that included dead space effect but ignored the non-uniformity of the electric field within the device regions. Wu and Wang [13,14] introduced circuit models of SAGCM-APD based on small signal and circuit elements. The models incorporated main bandwidth-limiting factors, such as carrier transit time, avalanche buildup time and external parasitic elements. But these two models also involved uniform electric field in the different regions of structures. Zhao and Mo [15] proposed an equivalent circuit model for resonant cavity enhanced-separated absorption grading charge multiplication avalanche photodiode (RCE-SAGCM-APD). They also conducted a detailed comparison among RCE-SAGCM-APDs with different materials. But this model ignores the dead space effect and assumed uniformity of electric field in devices.
In this work, utilizing a basic high quality SAGCM structure, it is tried to improve its performance by adding a thin charge layer between absorption and grading layers in order to obtain a new structure. To properly model the device, the nonuniform electric field is assumed based on real inherent nonuniformity of the structure in different regions. Then a circuit model is extracted wherein, different aspects like, proper transfer function, dead space effect, carrier transit time, avalanche buildup time, external parasitic elements are considered. By simulating the model and analyzing different aspects influential on the device performance, it is tried to achieve the best widths of new charge layer and multiplication layer.
In the following sections, the details of the work are represented. The structure and the electric field profile, the carrier rate of different layers and extracted circuit model of the proposed SAGCM structure are presented in Sections 2, 3 and 4 respectively. Simulation results and drawn comparisons with other conventional SAGCM structures are shown in Section 5 and the concluded remarks are presented in Section 6.
Structure and its electric field profile
A schematic structure of the APD under a typical illumination through p+ side and its related electric field throughout the device are illustrated in Fig. 1. In this work, it is supposed that adding the new charge layer can cause an increase in primary transport speed of generating optical carriers from absorption layer (A) to multiplication layer (M) so that can improve the device performance compared to its predecessor. The new charge layer is referred to as (C1) and the charge layer between grading and multiplication layer as (C2).
In APDs, the primary carriers are produced by light absorption and then the secondary carriers are produced by the impact ionization effect. Both carriers contribute to the photocurrent. The electric field in absorption, first charge layer and grading regions are considered to be non-uniform. Second charge region and multiplication region are assumed to be fully depleted and the electric field of them is modeled by consecutive progressive steps. This assumption can simultaneously provide nonuniformity of the field, simplify the equation solution and make circuit model extraction easier. Impact ionization phenomena are considered to happen in multiplication and second charge layers due to their strong electric fields. The electric field profile, based on structural parameters and length of different layers can be described by following equations where q is the electron charge, ϵ is the permittivity and NX is the doping concentration in X region, in which X can be M, A, C1, G, C2.
To consider the spatial dependence of the electric field in an equivalent circuit model, a staircase approximate model, as shown in Fig. 2, can be beneficial. The electric field in multiplication region and the second charge region are modeled by consecutive progressive steps. To proceed, one needs to know the exact profile of the electric field in all regions. The electric field profile in the second charge region and multiplication region are supposed to be divided into four constant sections with equal steps.
Carrier rate equations
For developing a circuit model, we must deduce the carrier rate equations in the different regions. These equations for this approximate model in various regions arewhere and are the total numbers of excess minority carriers and recombination lifetimes in the p+ and n+ regions, and are the total numbers of holes and their corresponding recombination lifetimes and transit time in M or A or C1 or G or C2 region respectively. Rates of the electron–hole pair photo-generation in these regions are shown by. Also, In, Ip are the minority electron and hole currents in p+ and n+ regions, and are the electron and hole drift velocities in the M and C2 regions respectively. The dependence of the carrier drift velocities into field is given in Ref. [9]. and are the electron and hole impact ionization rates, respectively. To take the effects of dead spaces for carriers in our circuit modeling, the simple method introduced in Ref. [7] is used. The dead space of carriers is defined as below, where Eth;e(h) indicates the ionization threshold energy of the electron (hole).
The first formula for dead space is
But by considering E0 (initial energy before starting dead space), the dead space formulas are
of electron and hole are defined as below, where is the initial energy of the carrier.
Circuit model
To achieve an equivalent circuit model for the device, first, the physical quantities should be converted to the corresponding circuit quantities. In this regard, a constant capacitor value, C0, is used to convert the charge into corresponding voltage. By dividing the carrier charge of each region into C0, the equivalent voltage of the carriers in each region can be obtained [13]. The equivalent resistors of each region can be calculated by considering the different voltages, the carrier’s combination process and also the photo generation rate in the different regions. The resistor values can be obtained from Eqs. (34) to (38). Obtained circuit model of this structure is shown in Fig. 3.
The current components shown in Fig. 3 can be written as below:where
Photo-generation rates are defined as below:where Pin is the optical power, R is the reflectivity, and is the photon energy. is the absorption coefficient and is the width of the X (M or A or C1 or G or C2) region.
Simulation result, comparison and discussion
To verify the accuracy of the model, the InP/InGaAs APD of Ref. [12] has been improved by additional charge layer and then the results of the proposed model have been compared with its conventional predecessor. The parameters for simulation have been taken from Refs. [20-22] and some of them listed in Table 1.
Tab.1 Some parameters of APD |
| parameter | value | parameter | value |
|---|---|---|---|
| Nn/cm-3 | 1.5×1017 | ap | 2.1×106 |
| Nm/cm-3 | 7×1014 | bp | 1.77 |
| Np/cm-3 | 1×1018 | cp | 1.15 |
| Wn/nm | 50 | Ethp/eV | 3 |
| Wm/nm | 200 | Ethe/eV | 2.8 |
| Wp/nm | 50 | vsp/(cm∙s-1) | 0.33×107 |
| αn/cm-1 | 3.5×104 | vsn/(cm∙s-1) | 0.67×107 |
| αm/cm-1 | 1×104 | Cs/pF | 0.31 |
| αp/cm-1 | 3.5×104 | Rs/Ω | 20 |
To examine the response speed of the device, some simulations have been performed. The response to a Gaussian pulse with 10 ps width and 100 μW power is shown in Fig. 4. This curve is compared with different probability functions, such as Lognormal, Rayleigh, Maxwell, Gamma (Erlang). Finally, it was found that, the curve has been mostly compatible with the Lognormal probability distribution function. The property of Lognormal function has been employed to reach the highest peak with the lowest rising time. Fulfilling this criterion, has given us the optimum value for wc1 = 39.8 nm.
In this figure, a comparison between the proposed structure time response with different new charge layer widths and the conventional one with wc1 = 0 has been drawn. It is shown that the rising time will decrease with the growth of wc1 until a certain value, where afterwards the trend is inverse. As it can be easily seen, the device performance has improved due to additional layer and the best performance has been achieved in 39.8 nm thickness.
In addition to the effect of wc1 on rise time decreasing, Fig. 4 shows that, the output current has the largest amplitude in optimum value of wc1. By increasing the width of the C1 layer up to 39.8 nm, gain increases and afterwards has a falling trend.
Figure 5 shows the detector response to step pulse with 1 μW input power in various thickness of the C1 layer in order to examine the device slew rate. In fact, slew rate is the ratio of output changes to the time changes and mainly obtained from step response of the device.
Figure 6 is an inset of the curves in the zoomed region of Fig. 5. The zoomed region depicts 14 percent of the slew rate increment at the optimum thickness comparing to conventional SAGCM.
It can be seen in Fig. 6 that, the thicker C1 layer is, the more output current we have, which means higher gain. Also in higher widths of added layer, the output current has faster response due to more photo carrier’s generation in a specific time span that can be explained by slew rate. It should mention that the same optimum value is repeated here because after this value, slew rate decreases.
To show the effect of the new charge layer on the gain-bandwidth characteristics of the proposed structure, the device is simulated in different first charge layer widths (wc1) from 0 to 60 nm, in constant thickness of 200 nm for multiplication layer and 60 nm for the second charge layer. The result is plotted in Fig. 7, which illustrates the maximum gain-bandwidth product occurs in wc1 = 39.8 nm with a growth of about 11% in comparison with wc1 = 0 nm.
In fact, the control of the layer thickness, which in turn would result in corresponding changes in electric field, can lead to this result. It is obvious that the higher thickness can increase transit time and the higher electric field can accelerate the carrier. Accordingly, there is interaction between thickness and electric field. This interaction for thicknesses up to 39.8 nm is in a way that GBP has upwards trend and afterwards the trend is downwards.
Since, the role of the additional charge layer has been proven in the improvement of the bandwidth characteristics of the APD, a natural question comes to mind; whether this proposed structure can exhibit an improvement in breakdown characteristic or not.
As multiplication is the cause of breakdown phenomenon, the effect of the M layer has been investigated in breakdown voltage performance. The results are presented in Fig. 8. It can be easily inferred that the breakdown voltage is in direct proportion with multiplication layer thickness.
To investigate the effect of wc1 presence and its changes on breakdown voltage, some simulations have been done that is presented in Fig. 9. In this regard, to the SAGCM with 400 nm multiplication layer thickness that is introduced in Ref. [12] with a breakdown voltage of about 48.3 V, a C1 layer with thickness of 39.8 nm has been added and a significant improvement achieved.
The breakdown voltage has been around 36.3 V in comparison with 48.3 V. It also shows that by changing the width of C1 from 5 to 39.8 nm, the breakdown voltage has remained clearly unchanged. As a result, it can be said that the presence of first charge layer is very important to improve breakdown voltage but its variation has negligible effect on its value.
Finally, all the presented results show that the simulation of optimized proposed structure has provided better performance in comparison with the conventional SAGCM.
Conclusions
In this paper, the advantages of adding a thin charge layer in a non-uniform electric field SAGCM-APD structure has been investigated in order to achieve a high performance structure. Also, using carrier rate equations, a circuit model has been extracted. Then, the effects of additional layer on transient criterion, such as slew-rate, rising and falling times, have been examined. It has been shown that the time response curve is more compatible with the Lognormal probability distribution function. To achieve optimum values of the layer thicknesses, that are influential on band width, GBP and breakdown voltage of the proposed structure, some tradeoffs have been done based on performed simulations. In this regard, it has been shown that controlling the widths of new additional layer beside multiplication layer can cause a significant improvement in breakdown voltage and GBP. Finally, all results show that the proposed structure exhibits a superior performance in comparison with the other conventional SAGCMs.