1. Introduction

The ability to monolithically integrate optical components with electrical components on silicon is of great interest and has many applications [1]. The metal-semiconductor-metal photodetector (MSM-PD) is a promising candidate to consider for the optical to electrical conversion stage due to its relatively low capacitance and ease of fabrication. The typical structure of a MSM-PD along with the commonly assumed but incorrect electromagnetic field profile caused by an incident optical signal is shown in Fig. 1. This structure is composed of interdigitated metal fingers that are biased with opposite polarity. When light is incident on the structure, it penetrates into the semiconductor, exciting electron-hole pairs that are swept in opposite directions to the contacts. The performance of Si MSM-PDs is poor compared to MSM-PDs fabricated from several other materials, such as InGaAs, due to the fact that Si is an indirect bandgap material in which the absorption length is long, approximately 10μm for 850nm incident light. In short pitch MSM structures with submicrometer contact separation, the static electric field produced by the applied bias at a depth of 10μm into the semiconductor is small. This applied bias is responsible for sweeping photogenerated electron-hole pairs from the interior of the Si to the electrical contacts, and its small magnitude at depths greater than 10µm causes charge carriers at these locations to take a long time to drift to the electrical contacts producing an induced photocurrent that is undesirably small-in-magnitude and long-in-duration.

There have been many techniques used to enhance the bandwidth and responsivity of Si MSM-PDs but efforts to improve one of these aspects tend to degrade the other [2]-[7]. In Ref. [8], we investigated the use of electromagnetic resonances (ER) (e.g., surface plasmons and vertical cavity modes (CM)) as well as other optical modes including Wood-Rayleigh anomalies (WR) and diffraction in lamellar grating structures, a structure almost identical to MSM-PDs, to focus, concentrate and overall control the electromagnetic field profile, produced by an incident optical signal. As an example of the use of these ER modes, [8] described how, with a careful design of the all aspects of the structure, one could use ER and optical modes to enhance the performance of MSM-PDs. However, most of the details of the electrical and optical modeling and a thorough analysis of the important aspects for the practical implementation of these MSM-PDs were left out of Ref. [8].

The purpose of this paper is to use the tools for controlling the electromagnetic field profile presented in Ref. [8], and develop the modeling techniques necessary to model MSM-PD devices with as few of assumptions as possible and at a level of sophistication such that the modeling of the response of the device to a optical signal composed of a pseudo-random 256 bit sequence (PRBS) can be performed. Up to this point in the literature on MSM-PDs, a first-principles analysis of these devices has not been done and simplistic and incorrect assumptions have been employed regarding the electromagnetic field produced by the incident beam and the resulting transient and steady-state charge concentrations. In this work, the absorption of the optical signal in all parts of the structure, the charge carrier generation and motion, photocurrent, responsivity, eye diagrams, inter-symbol interference (ISI), bit error ratio (BER), and maximum operating bit rate (dependent on the desired BER) of the device are calculated.

 

Fig. 1. Left: A top view of a typical MSM device. Right: A cross section view of a typical MSM device and the commonly assumed but incorrect electromagnetic field profile.

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To perform this detailed time dependent analysis of ER-enhanced MSM-PDs, an Integrated Electrical/Optical Response Algorithm (IEORA) was developed in C++ that includes five modeling algorithms that are integrated together in a time-dependent manner, as shown in Fig. 2 and listed below. The IEORA program allows the accurate modeling of the performance of the photodetector in a situation that more closely resembles the practical real-world implementation of these devices than has been done by in previous theoretical and modeling work on MSM-PDs.

 

Fig. 2. A schematic of the IEORA program. For each step in time (each of the 256 bits is divided into approximately 20 time steps), all five algorithms above are called on to perform their tasks as listed above.

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One example of an ER-enhanced Si MSM-PD that uses a hybrid mode (i.e., a combination of a WR, diffracted mode and a CM) will be described; however it is not the purpose of this paper to optimize one particular type of device but rather to describe the tools to model the optical and electrical characteristics of ER-enhanced MSM-PDs. These modeling tools can also be used to model a variety of other detector structures including Si APDs and MSM-PDs fabricated on silicon-on-insulator substrates [9]-[10]. Also, it is not the purpose of this paper to completely optimize the IEORA C++ code or to execute IEORA on supercomputers to eliminate minor and insignificant approximation errors produced by the authors’ limitations of computer resources. These optimization tasks can easily been done later; only the framework of IEORA and the details of each algorithm and their integration are included in this work.

2. Extended-SIBC algorithm and electromagnetic resonance/optical modes

The surface impedance boundary condition (SIBC) method has become increasingly popular for modeling lamellar grating structures in the infrared wavelength range because of its experimentally observed accuracy and because it is computationally less demanding [11]-[12]. The standard SIBC algorithm, however, is too restrictive to allow the complicated photodetecting device structures and their ER modes to be modeled. Therefore, an extended-SIBC method was developed that allow for many degrees of freedom in the design of the structure that affect the optical and electromagnetic resonance modes in ways that are controllable, allowing one to engineer the resulting optical field in the Si substrate of a MSM-PD such that it produces a high responsivity and high bandwidth device [8]. These structural degrees of freedom (SDF) include:

The various ER modes and optical modes are thoroughly described in Ref. [8] and only a brief description of their properties, as they pertain to MSM-PDs, is given here. The three different types of ER and optical modes in MSM-PDs and are Wood-Rayleigh modes (WR), horizontal surface plasmon modes (HSP), and vertical cavity modes (CM) (or vertical surface resonance in Ref. [8]). WRs occur when one diffraction order grazes the surface of the grating as it changes from an evanescently decaying surface-confining mode to a radiating diffracted mode as the wavelength of the incident beam is increased. HSPs are surface plasmons, i.e., surface charge oscillations and their associated electromagnetic fields, and usually have energies and in-plane momenta that are close in value to WR modes. Hence HSP/WR pairs exist in optical grating structures; techniques to selectively eliminate one mode of the pair are described in Refs. [8] and [14]. Typically the energy of a HSP is slightly less than the associated WR mode for a given momentum. The field distributions of HSP have high field intensities immediately below the metal contacts while WRs have high field intensities below the contact windows [8], [14]. Also, HSPs have a higher amount of electromagnetic energy density within the metal wires leading to increased absorption within the lossy metal [8]. Both WRs and HSPs have a strong wavelength, angle of incidence and grating pitch dependence and weak dependence on the thickness of the wires, and wire width [8]. The third type of ER mode is a CM that produces large electromagnetic field intensities within the grooves of the structure. CMs have a strong dependence on the thickness of the wires, the width of the grooves and the dielectric constant of the material in the grooves. We have found that the increasingly accepted view on anomalously large transmission in these structures is correct, namely, that it is a result of coupling of WR modes/propagating diffracted modes on the two sides of the contacts (i.e., air and the substrate) via a CM mode as explained in detail in Refs. [8] and [14]-[20]. In this work, an ER-enhanced Si MSM-PD will be developed that uses the light channeling and localization effects of a hybrid WR/CM mode and uses SDF 2 to minimize certain HSPs.

3. Device design and preliminary optical/electrical characteristics

In a Si MSM-PD, one wants to minimize the reflectance (R_o) in order to maximize the amount of the optical signal that remains in or near the MSM structure. However, minimizing the 0^th order transmission (T_o) is also crucial because this radiating field component propagates deep into the Si thereby reducing device speed. Techniques to simultaneously minimize R_o and T_o using HSPs, WRs and CMs, and hybrid modes (i.e., modes consisting of combinations of these HSPs, WRs, and CMs) in lamellar gratings are explained in detail in Ref. [8]. In Ref. [8], it was found that a desirable electromagnetic field profile for a Si MSM-PDs was obtained when a WR/diffracted mode is aligned with a CM mode producing a hybrid-like ER/optical mode. It was also found that the most effective way to align the WR and CM was to start with a structure where the CM mode had a slightly larger energy than the HSP/WR pair and then to increase the dielectric constant of the material in every other groove as shown in Fig. 3. This method not only allowed the alignment of the minima of R_o and T_o but also inhibited the HSP component of the HSP/WR pair because HSPs are more sensitive to local perturbation in the periodicity than are WRs. To expound on this last statement of HSPs’ sensitivity to local perturbations in the periodicity, consider the structure shown in Fig. 3, but with air in all of the grooves. In this case, there would be HSP/WR pairs in the Si at 0.77eV, 1.38eV and 1.82eV. But with a ε=2 dielectric material inserted in every other groove, the HSP at these energy values are significantly inhibited, leaving only the WRs, along with the weak and broad CM centered about 1.65eV [8]. In particular, the WR mode at 1.38eV, with its properties of enhanced transmission (via a CM) and light localization near the contact/Si interface is present without the typical accompanying HSP mode and its undesirable transmission inhibiting property and undesirable electromagnetic field profile within the Si. Again, these aspects of HSP/WR pairs and the elimination of HSPs are covered in detail in Refs. [8] and [14].

 

Fig. 3. The structural parameters for the Si MSM-PD that is analyzed in this work. One period of the structure is shown, from the MIDDLE of one contact to the MIDDLE of the next identical and identically surrounded contact.

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Figure 4 shows the optical characteristics of the structure shown in Fig. 3 for a TM polarized, normal incident plane wave of light. The minima of R_o and T_o are slightly, and purposefully, misaligned because it was found that this produced the most desirable electromagnetic field profile to produce a Si MSM-PD with simultaneously high bandwidth and high responsivity. Continued analysis will likely lead to structures where these minima are better aligned while still producing desirable electromagnetic field profiles. The Poynting vector shows that the WR/CM hybrid mode is channeling a large percentage of the incident beam around the metallic contacts and into the Si substrate; light channeling occurs through both grooves but especially through the groove with the high dielectric material. The electromagnetic field energy density shows that while the light localization near the contact/Si interface, and between the metal contacts is significant, there is still some light that propagates deep into the Si. What is envisioned is that the light channeling and localization techniques described in this work will be used in conjunction with the standard techniques to increase bandwidth in Si MSM-PDs, namely ion-induced damage in certain areas of the Si substrate to render it a non-participatory area of the device [21]. This technique involves producing damage in the Si starting at a certain depth in the Si, as determined by the energy of the incident ions, and extending several microns beyond this depth. Throughout the damaged Si layer, most electron-hole pairs that are generated by the incident optical signal will non-radiatively recombine in a short time period. The top layer of the Si will remain largely damage free because the ions initially undergo electronic scattering that does not produce damage and only after the kinetic energy of the ions have reduced to some threshold energy will damage inducing nuclear scattering commence [22]. This damage free top layer of the Si will be referred to as the active layer. Later in this work, the responsivity and BER as a function of the thickness of the active layer will be graphed to show the trade-off between these two important performance characteristics.

 

Fig. 4. Top Left: R_o and T_o for the Si-MSM-PD structure that is optimized to select a hybrid WR/CM mode. The structure is designed to have a slight misalignment of R₀ and T₀ because of the desirable field profile that is subsequently produced. Top Right: The Poynting vector showing that a large amount of energy is channeled around the electrical contacts and into the Si substrate. The groove with ε=2 shows increased energy channeling compared with the other groove with ε=1. This asymmetry of the groove dielectrics is introduced to inhibit HSPs. Bottom: Two graphs of the energy density showing a desirably high energy density between the contacts and close to the contact/Si interface. While the light localization near the contact/Si interface is significant, the expanded view shown in the bottom right plot shows that there is still some light that propagates deep into the Si that will reduce bandwidth and increase ISI and BER.

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Before the IEORA program is used, two important aspects of optical losses and capacitance are briefly analyzed to verify that they will not significantly reduce device performance. Regarding the optical losses, it is important to obtain a measure of the incident electromagnetic field intensity lost due to metal absorption (A_wire), reflection (R_o) and diffraction in the top air layer (D_±1). These three components are optical components that are entirely lost, i.e., components that do not reach or penetrate into the semiconductor. Diffracted components in the Si are certainly not loss components because these optical field components may generate electron-hole pairs within the Si leading to photocurrent. The value of I_Si = 1 - R_o - A_wire - ΣD_n represents the total electromagnetic field intensity entering Si. It is important to note the I_Si will only indicate whether or not there are excessive optical losses; I_Si is not the final indicator of a good MSM-PD device design that has high bandwidth and high responsivity! One of the reasons why efforts were employed to minimize HSPs was that they lead to increased A_wire compared to WRs, another reason is that HSPs have larger stored energies in the metals that can re-radiate thereby increasing noise and decreasing bandwidth of a MSM-PD [6], [7]. The calculation of A_wire is performed by integrating the normal component of the Poynting vector along the wire surface and using the SIBC assumption relating tangential components of the electric and magnetic fields, resulting in the equation (for TM polarization):

where all quantities are in cgs units, d is the pitch of the structure (i.e., the distance from the middle of one contact to the middle of the next identical and identically surrounded contact), θ is the angle of incidence, Z = 1/n_metal , with n_metal as the complex index of refraction of the metal contact. For any real n^th diffracted component in air, the energy transported away from the structure relative to the energy incident on the structure via the normalized incident beam is given by:

where R_n and θ_n are the amplitude and angle of the n^th diffracted component (this can include the 0^th order reflected beam). The values for all of these loss mechanisms are given in Table 1 below and show that 83.41% of the incident optical signal energy gets transmitted into the Si. This value is exceptionally large considering that 66.66% of the surface of the detector is covered with Au contacts and illustrates the dramatic light channeling capabilities of WR/CM hybrid modes.

The capacitance produced by the interdigitated contacts is always a concern because it can contribute to a RC constant that may possibly reduce f_3dB. This is exacerbated in MSM-PD studied in this work by two things. First, the use of any dielectric material with a high dielectric constant between the metal contacts (i.e., the ε=2 material in Fig. 3) can increase capacitance and second, the small cross-sectional area of the contacts may increase the R. In this work, the capacitance of each metal finger pair is calculated using two methods, one method uses the equation developed in Ref. [23] and used almost consistently in the numerical modeling of these device (for examples see [24]-[25]) and assumes infinitely thin contacts. The second method uses a finite difference Poisson’s equation solver that calculates the surface charge density as a function of applied bias. The second method is more accurate because of the non-negligible aspect ratio of the contacts and predicts a small capacitance of 3.5fF. This small capacitance is produced because the majority contributing factor to capacitance in MSM-PDs, even in these structures with relatively high aspect ratios, is the ratio between grating pitch and wire width, which is a reasonable two-thirds in the MSM-PD structure analyzed in this work. If the total device dimensions are assumed to be 50μm×50μm to match the core diameter of a multimode optical fiber, the 50μm long, 0.125μm thick, 0.150μm wide Au fingers each have a resistance of 33Ω. The resulting f_3dB value of f_3dB = 12πRC = 348GHz indicates that this aspect of the device will not limit the bandwidth. Hence we conclude that if the transimpedance amplifier (TIA) and the other components of the optical receiver system do not introduce significant noise or bandwidth limitation, the ER-enhanced MSM-PD may be capable of operating at a very high bandwidth.

Table 1. Calculated optical losses for the Si MSM-PD (Fig. 3). The incident beam is normally incident, TM polarized and has an energy (wavelength) of 1.46eV (850nm).

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4. Integrated electrical/optical response algorithms and device characterization

Once the initial qualitative aspects of the device characteristics have been analyzed, the IEORA program is used to fully characterize the performance of the device. As stated before, the IEORA program is composed of five algorithms; each algorithm will now be briefly described.

The input signal of the photodetector is modeled as a pseudo-random bit sequence (PRBS) where the bits are either periods when the normal incident, normalized, TM polarized optical signal is incident upon the detector (represented by a “1”) and periods of no optical signal (represented as a “0”). The PRBS Algorithm produces a 256 bit PRBS by using a maximum-length shift-register sequence (i.e., m-sequence). This m-sequence is generated by a m-stage shift register with linear feedback as shown in Fig. 5. The m-sequence is the most widely used technology for generating binary pseudorandom noise (PN) codes, which is used in almost every spread spectrum communication system. For example, the core of third generation (3G) wireless telecommunication system, the code-division multiple access (CDMA) technology uses PN code to identify each cell phone user. The m-sequence has three important characteristics:

Characteristic #3 is especially important because the increased concentration of charge carriers generated during a long series of 1’s can require more time to be fully swept from the Si than the small concentration of charge carriers generated by a single 1 bit preceded and followed by 0 bits. Because of this, the zero level in the eye diagram will rise resulting in the closing of the eye, increased ISI and increased BER.

 

Fig. 5. The PRBS Algorithm uses a m-stage shift register to obtain the bit sequence. The index k represents the k^th bit. After each period of time, or output of one bit, the values in the registers are modified according to the equations shown in the figure.

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In our simulation, the PRBS is obtained by a 7-stage shift register, which has a period of 127. To make the number of 0’s equal the number of 1’s, a 0 bit is patched into the m-sequence every 127 bits, resulting PRBS code has a period of 128 bits. This 128 bit sequence is then repeated to produce a 256 bit sequence. The initial value of our 7-stage shift register is: S ₁ = S ₃ = S ₅ = S ₇ = 0 and S ₂ = S ₄ = S ₆ = 1. Also in our settings, a ₁ = a ₇ = 1 and a ₂ = a ₃ = a ₄ = a ₅ = a ₆ = 0.

The second algorithm in the IEORA program is the Extended-SIBC algorithm (ExSIBCA) that calculates the interaction of the normal incident, normalized, TM polarized incident beam with the structure. This technique and algorithm have been described in detail in previous sections of this work and in our past works on lamellar gratings, surface plasmon-enhanced Si avalanche photodiodes and ER-enhanced SOI MSM-PDs [8]-[10]. Therefore, only a couple of items need to be discussed here concerning two reasonable assumptions made in this particular algorithm.

Both of these assumptions pertain to the assumption that there is no charge-carrier generation during a 0 bit. Other assumptions in the IEORA program are employed in the four other algorithms and are described in the sections describing these algorithms.

The third and fourth integrated algorithms in the IEORA program are the Monte-Carlo Algorithm (MoCA) and the Poisson’s Equation Solver Algorithm (PESA) and are extensively integrated together in a time dependent way. MoCA describes all aspects of charge-carrier generation, recombination, drift, impact ionization, and induced photocurrent in the electrical contacts. PESA calculates the quasi-static electric field produced by the time independent bias applied across the metal contacts and the time-varying charge density produced by the incident beam. The PESA algorithm by itself is not a major innovation of IEORA but its integration with PRBS, ExSIBC, MoCA and EDNA in a time-dependent manner is important. In fact, the version of PESA used in this work uses a 5-point finite difference (FD) algorithm to solve for the pseudo-static electric fields, however no significant errors are expected to be produced by using this 5-point FD algorithm. More accurate and rigorous 9-point FD or finite element algorithms can easily be implemented. In these two algorithms, the cross-section of the Si substrate is divided into an array of grid points (typically 1000 × 1000; the greater the number of grid points the more accurate the results but longer runtimes and greater computer resources are needed). MoCA tracks each charge (i.e., the charge enclosed within the area surrounding one grid point) generated or residing about every grid point at every time step (we use 20 time steps per bit). This technique is computer and memory intensive but by recording all of this information (including the magnitude of charge, position, velocity and how long it has been since it was generated), very few assumptions need to be made and many second order effects can be added to the MoCA. Each charge generated about a grid point will, both drift in response to, and affect, the quasi-static electric field calculated by PESA; hence the quasi-static electric field has to be calculated at every time step. Instead of using the typical but incorrect exponentially decaying electromagnetic field profile shown in Fig. 1 as used in many works on MSM-PDs, we use the Poynting vector (S) obtained from ExSIBCA, conservation of energy and the Divergence Theorem, leading to the correct expression for the charge carrier generation rate g_carrier:

where η^QE the internal quantum efficiency of Si. For subsequent time steps (i.e., a ∆t in time later), the new positions of the charges that have not reached the electrical contacts or recombined are calculated using the following obvious equation:

where the index i denotes the charge. A linear relationship between drift velocity v _i and electric field E is not assumed because of the large electric fields produced with these nanoscale contact geometries; rather, a full functional relationship between v _i and electric field E is used and obtained from [26]. Several charge carrier lifetimes were used to analyze the effects of recombination on the results with values ranging from 0.1μs→10ms; however, little effect was observed which was attributed to the much shorter time scales of the drifting charge carriers (in the sub-picosecond range). Two assumptions were made in MoCA:

The electron and hole charge densities about each grid point for the next time step (i.e., t + ∆t) are then easily constructed by summing the charges that have drifted into the area about the grid point or have been generated about the grid point during the preceding ∆t duration in time by the incident beam. Once the charge densities for the time t + ∆t have been calculated, PESA is then used to evaluate the quasi-static electric field. Also at each step in time, MoCA calculates the induced photocurrent in the electrical contacts by using Ramo’s Theorem [27]. Ramo’s Theorem states that moving charges within the semiconductor will induce a current within the contact fingers according to the equation:

where E _bias is the static field produced solely by the applied bias without taking into account the charge carrier concentration.

Hence, IEORA progresses in steps in time with the PRBS algorithm turning on or off the incident beam, which produces an electromagnetic field distribution in the Si that is modeled using ExSIBCA; the Poynting vector obtained then is used by MoCA and PESA to calculate the behavior of the photogenerated charge carriers and the quasi-static electric field. The final result is the current vs. time (i(t)) plot that will be used by the fifth and final integrated algorithm.

The fifth algorithm is the Eye Diagram Noise Analysis (EDNA) algorithm and takes the i(t) plot, produces a eye diagram, and calculates the quality factor (Q) and bit error rate (BER). This is a fairly simple algorithm and “folds” back the i(t) plot and puts the entire curve into a time duration of a 2 bit period, namely construction an eye diagram.. Given the eye diagram, the Q-factor at the input of a transimpedance amplifier (TIA) in an optical communication system, with the affects of closing of the eye due to ISI included, is given by [28]-[29]:

where the numerator of Eq. (7) represents the vertical extent of the eye opening and the terms in the denominator σ₀ and σ₁ represents the root mean square of the additive white noise produced by ISI (see Fig. 7 for a further explanation of these terms). The term V _ISI represents the how much the eye has closed due to inter-symbol interference (ISI) relative to the opening of the eye at low frequency operation. ISI contributes to V_ISI, σ₀ and σ₁ because of the random bit pattern in the PBRS signal; a longer continuous series of 1’s will produce more slowly migrating carriers in areas of the Si substrate where the static electric field is small resulting in a raising of the zero level and maximum level in the eye diagram. The numerator of Eq. (7), i.e., V_pp - 2V_ISI, is numerically extracted from the eye diagram by finding the average separation of the 1 and 0 bit levels at the position in the eye diagram where this value is at its maximum. The terms σ₀ and σ₁ are then determined by evaluating the top and bottom spreads in the curves in the eye diagram, modeling them as a Gaussian distribution and calculating the standard deviation (Fig. 7). Then, once Q is calculated, the BER can be easily calculated using the equation [28]-[29]:

5. Results and discussion

In this section, we discuss the results of the modeling and design efforts by analyzing several important aspects associated with the practical use of the ER-enhanced Si MSM-PDs in optical communication systems. Figure 6 shows a simplified schematic of an optical receiver that includes four components [28]-[29]. The first component is the photodetector that detects the incident light and produces a proportional photocurrent. The second component is a transimpedance amplifier (TIA) that amplifies the photocurrent from the photodetector. The third component is a limiting amplifier (LA) that serves as a decision circuit where the sampled voltage v(t) is compared with the decision threshold V_TH. The fourth component is a clock data recovery block (CDR). ISI can be produced in a number of ways in an optical receiver including: high frequency bandwidth limitation, insufficient low frequency cutoff caused by AC-coupling or DC-offset cancellation loop, inband gain flatness, or multiple reflection between the interconnection of the TIA and LA [28]-[29]. In this work, we analyze the ISI produced by the intrinsic behavior of the ER-enhanced Si MSM-PD itself i.e., we analyze the contribution to ISI caused by the drift and migration of carriers within the Si due to the randomness of the 256 bit pattern.

 

Fig. 6. A typical optical communication system including the four components: photodetector, transimpedance amplifier, limiting amplifier and clock data recovery block. The ISI will be evaluated at the input of the TIA.

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Fig. 7. Top Left: The eye diagram for a Si MSM-PD operating at 100Gb/s with an active layer depth of 0.5μm. Top Right: The dependence of responsivity and BER on the depth of the active layer. Bottom: The eye diagram for a Si MSM-PD operating at 100Gb/s with an active layer depth of 6μm. Both eye diagrams use the same y-axis units, illustrating the fact that the 6μm active layer device has higher responsivity but much increased noise and BER. For the device with 0.5μm active area thickness, the BER has a very low value of 10^-20 but with a low responsivity of 0.06A/W, whereas for the device with 6μm active area thickness, the BER is a higher value of 10^-9 but with a higher responsivity of 0.25A/W.

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There are several different ways to characterize the MSM-PDs but we approached the analysis by setting the bandwidth to a large value of 100Gb/s and evaluating the tradeoff between responsivity (ρ) and BER. The bandwidth of 100Gb/s is higher than any Si MSM-PD device reported to date but is a value that will be of interest in current and future optical communication systems. As has been stated before, different thicknesses of the top active layer Si can be chosen by inducing damage below a certain depth by ion implantation [21]. Two eye diagrams for the Si MSM-PD operating at 100Gb/s are shown in Fig. 7 for active layer thickness of 0.5μm and 6μm and represent two extremes of these high bandwidth Si MSM-PDs. The 0.5μm active layer thickness device has a low ρ (0.06A/W) and low BER (10^-20) and the 6μm active layer thickness device has a high ρ (0.25A/W) and high BER 10^-9.

One thing that should be noted is that some of the oscillations in the eye diagram for the 6μm active layer thickness device are a result of the limitations of the authors’ computing resources and not a real affect of the device. Techniques to eliminate the oscillations can be implemented but these techniques are not expected to significantly change the responsivity or BER shown in Fig. 7. Depending on the application, with its specific requirements for ρ and BER and keeping in mind that the TIA will contribute to BER, the data in Fig. 7 can be used to choose a Si MSM-PD for a particular optical communication system.

6. Conclusion

This work has shown that the metal contacts play a large role in the behavior of Si MSM-PDs because of the near field effects, electromagnetic resonances, and optical modes they produce. It was shown that ER and optical modes perform two critical roles:

Role 1 - Channeling TM polarized light around the metal contacts and into the Si.

Role 2 - Localize light near the contact/semiconductor interface.

With regard to Role 1, Fig. 4 shows that by using hybrid modes, a substantial amount of the incoming light is channeled around the metal contacts and into the semiconductor layer. In the simplified and incorrect model shown in Fig. 1, one would predict that the maximum percentage of the incident signal entering the semiconductor as equal to the ratio of the contact window width to the pitch (neglecting reflection at the air/Si interface), which is 1/3 in this work. However, it is seen that even after subtracting off the 5.09% absorption in the metal wires, the 3.85% 0^th order reflectance and the 7.92% for the diffracted modes in air (sum of the +1 and -1 diffracted modes), one gets 83.4% of the TM polarized 1.46eV incident optical signal transmitted and absorbed in the Si. This by itself would be a significant enhancement to Si-MSM-PDs because it would suggest an enhancement in responsivity by a factor of 2.5. As has been stated before however, this enhancement in responsivity would be of little use if it reduces the bandwidth or speed of the device; Role 2 deals with this problem by localizing the channeled light near the contact/Si interface. However, the light localization near the contact/Si interface is not perfect and there will be a tradeoff between responsivity and BER depending on the thickness of the active layer thickness of the Si. This tradeoff has been analyzed resulting in design parameters for various Si MSM-PD designs with low responsivity and BER to high responsivity and BER. However, at just over 5 microns of active layer depth, the device we are characterizing as having a high BER still has a BER in the range of 10^-10 to 10^-12 and a responsivity level of about 0.22 A/W. This is an acceptably low BER and a reasonable high responsivity level at this data rate of 100 Gb/sec. We believe that the Si MSM-PDs modeled in this work are the best performing devices of this type theoretically and numerically modeled to date, in terms of simultaneously having high bandwidth (100Gb/s), high responsivity (0.05→0.30A/W), and low BER (10^-20→10^-10).

There are several items that will need to be addressed for this analysis of ER-enhanced MSM-PDs to be truly complete: the TE polarization behavior, re-radiation of light by SP modes during a 0 bit, enhanced thermal effects exacerbated by the localization of light, spatial hole burning and device saturation, and additional noise added by the TIA. However, all of these items, except for the TIA (which can be analyzed separately), can be included in the algorithms and modeling and design tools developed in this work on ER-enhanced Si MSM-PDs.