Design of GaInAs/InP membrane p-i-n photodiodes with back-end distributed Bragg reflector

Xu Zheng; Tomohiro Amemiya; Zhichen Gu; Koichi Saito; Nobuhiko Nishiyama; Shigehisa Arai

doi:10.1364/JOSAB.36.001054

1. INTRODUCTION

The advent of Si large-scale integration (LSI) circuits based on complementary metal oxide semiconductor (CMOS) technology has made it possible to integrate a large number of components into a single circuit for computers and other applications. The development of LSI circuits has greatly improved the processing capability and reduced the total power dissipation of electronic systems. However, the physical limitations of electrical interconnections such as excessive propagation delay and Joule heat generation in metal interconnections are the limiting factors that hinder further development of LSI systems. A few innovative solutions have been proposed to interconnect the functional blocks and overcome these limiting factors, such as three-dimensional integrated circuits with through-silicon via [1,2] wireless capacitive coupling [3] and inductive coupling [4]. On-chip optical interconnections have also attracted considerable attention in recent years because these interconnections significantly improve data capacity and power savings [5]. For on-chip optical interconnections, the system energy cost should be 100 fJ/bit or less for a data rate of 10 Gb/s [6].

In order to fulfill the above demand for on-chip optical interconnections, we had proposed a hybrid optical-electrical interconnection method, where an InP-based membrane photonic integrated circuit (MPIC) is attached onto a Si LSI chip with multilevel interconnection by adhesive bonding (see Fig. 1) [7–10]. In this system, the uppermost interconnection of the LSI is optical and it is not electrical. This enables us to realize high-speed data transmission between distant circuit blocks in the Si LSI circuit. The lasers and detectors in the data-transmission circuits are connected to the driving circuits on the Si LSI circuit via through-silicon.

Fig. 1. Conceptual diagram of an MPIC bonded on Si-based CMOS LSI circuit.

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The uppermost MPIC consists of a thin semiconductor core layer sandwiched between low refractive index materials, such as ${SiO}_{2}$ and air. A strong optical confinement in the gain region can be achieved by fabricating the laser in a membrane structure and therefore, the laser can be operated at very low power consumption compared with conventional semiconductor lasers [11–18].

We had also studied a membrane photodiode (PD) with ultralow power consumption [19,20], which is another crucial element for MPICs. One of the essential requirements of a membrane PD is to achieve a suitable modulation speed that matches the laser diode, with extremely low power consumption. In order to further reduce the power consumption of the membrane PD, the transimpedance amplifiers (TIAs) and post amplifiers should be replaced with a high load resistor directly connected to the membrane PD [21–24].

In this work, we propose and investigate two types of membrane GaInAs/InP $p - i - n$ PDs integrated with a back-end distributed Bragg reflector (DBR) in order to achieve a membrane PD with shorter device length and high 3-dB bandwidth for a backreflection of $- 30 dB$ .

2. DESIGN OF THE MEMBRANE PDs WITH DBR

A. Design Guide for the Membrane PDs

Figure 2(a) shows the simplified schematic of the membrane interconnection system. It can be seen that the PD receives an input power, $P_{in}$ , from the laser transmitter, whose output power is $P_{out}$ after propagating through a membrane waveguide with a link loss (i.e., coupling loss and propagation loss).

Fig. 2. (a) Simplified schematic of the membrane interconnection system. (b) Equivalent circuit of the receiverless PD.

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Figure 2(b) shows the output voltage equivalent circuit of the membrane PD with a directly connected load resistor. Here, the photocurrent is assumed to be extremely small due to the low output power from the laser diode. The photocurrent, $I_{pd}$ , from the PD passing through the load resistor, $R_{L}$ , can produce a voltage swing ( $V_{out} = I_{pd} \times R_{L}$ ) to directly drive the standard digital static CMOS inverter. The key point is that the capacitance, $C_{j}$ , of the membrane PD must be extremely small in order to obtain a high 3-dB bandwidth.

Figure 3(a) shows the relationship between the load resistance, $R_{L}$ , and capacitance, $C_{j}$ , for various 3-dB bandwidths, $f_{3 dB} = {(2 π R_{L} C_{j})}^{- 1}$ . In order to produce several hundreds of millivolts (mV) for the output voltage of the PD, the load resistance must be several kΩ or higher because of the small photocurrent, $I_{pd}$ . For convenience, we assume that $R_{L} = 10 kΩ$ and $C_{j} < 1 fF$ for $f_{3 dB} > 10 GHz$ . This is a difficult task for conventional PDs used as optical receivers. However, we believe that this can be realized by using our membrane PDs owing to the relatively large optical confinement factor of the absorption layer.

Fig. 3. (a) Relationship between $R_{L}$ and $C_{j}$ used to determine the required bandwidth. (b) Received power requirement of the membrane PD for a data rate of 10 Gbps (indicated by the red line) and required output power of the laser (indicated by the black line) as a function of the load resistance, $R_{L}$ .

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In this work, we aim to achieve a low bit error rate (BER) and high output voltage (several mV) for our designed PDs. Thus, we determine the minimum output power required for the laser transmitter to fulfill the BER and $V_{out}$ criteria prior to discussing the design of the membrane PDs. The required power received at the PD, $P_{in}$ , was determined as a function of the load resistance, $R_{L}$ , for a data rate of 10 Gb/s. Here, we use a large value of $R_{L}$ instead of TIA to reduce the thermal noise, which will be beneficial for our MPIC. The noise generated by the circuit needs to be determined before the laser power requirement is calculated. For a receiverless PD circuit [Fig. 2(b)], the thermal noise, shot noise, and BER for the intensity modulation-direct detection method are determined using the following equations [25]:

BER = \frac{1}{2} erfc (\frac{\sqrt{SNR}}{2 \sqrt{2}}),

SNR = 4 Q^{2},

Q = \frac{I_{1} - I_{0}}{σ_{1} + σ_{0}},

where

Q

is a factor of

I_{1}

,

I_{1}

is the current signal when the corresponding bit is 1,

I_{0}

is the current signal when the corresponding bit is 0,

σ_{1}

is the noise current of

I_{1}

, and

σ_{0}

is the noise current of

I_{0}

. In this case, the

Q

factor is assumed to be 7, which means that the BER is approximately

10^{- 12}

. Without an increase in the amplifier noise, the equation for the thermal noise limited power and shot noise limited power can be expressed as

{SNR}_{thermal} = \frac{R_{L} R_{esp}^{2} P_{in}^{2}}{4 k_{B} T_{emp} f} \geq 4 Q^{2},

{SNR}_{shot} = \frac{R_{esp} P_{in}}{2 q f} \geq Q^{2},

where

R_{esp}

is the responsivity (

= η \times λ [μm] / 1.24 [A / W]

and

η

is the quantum efficiency) of the PD,

k_{B}

is the Boltzmann constant,

T_{emp}

is the operation temperature,

f

is the bandwidth,

q

is the electron charge, and

P_{in}

is the minimum received power for the thermal noise and shot noise. The thermal noise limited power and shot noise limited power are strongly restricted by the

Q

factor and therefore, they are related to the BER. The blue line in Fig. 3(c) indicates the sum of the limited minimum received power for the thermal noise and shot noise whereas the red line indicates the incident power required for a voltage output of 200 mV. It can be seen from Eq. (4) that the increase in the load resistance will reduce the thermal noise limitation and power demand of the voltage output. In other words, the received power at the PD,

P_{in}

, is inversely proportional to the square root of the load resistance,

R_{L}

. For a case where the

BER = 10^{- 12}

(

Q = 7

),

f = 10 GHz

, and

R_{L} = 10 kΩ

at room temperature, the minimum input power considering the thermal noise is equal to

- 27.5 dBm

, assuming that the responsivity is 1 A/W. The green line indicates the shot noise limited power, which is a constant value (

- 38.0 dBm

). With the demand for noise limited power, we need to consider the value of the received power for the PD,

P_{in}

, which can be determined from the following equation:

V_{out} = P_{in} \times R_{esp} \times R_{L} .

The theoretical responsivity of the PD is assumed to be 1 A/W (

η = 0.80

). The minimum input power of the PD,

P_{in}

, for an output voltage,

V_{out}

, of 200 mV is found to be

- 17.7 dBm

when the load resistance is 10 kΩ, and the required laser output power can be obtained by considering the link loss. Here, the link loss is assumed to be 3 dB, which is obtained from the coupling loss between the laser and waveguide and the coupling loss between the waveguide and PD (0.5 dB) and propagation loss (2 dB). Hence, the required output power of the laser,

P_{out}

, is

- 14.7 dBm

(34 μW) for

R_{L} = 10 kΩ

and a data rate of 10 Gb/s.

B. Two Types of Membrane PDs Integrated with Back-End DBR

Figure 4(a) shows the schematic of a membrane GaInAs $p - i - n$ PD with the back-end DBR bonded on a Si substrate through 1-μm-thick ${SiO}_{2}$ using benzocyclobutene adhesive bonding. A 120-nm-thick GaInAs absorption section is sandwiched laterally between the $n$ -InP and $p$ -InP side clads, which also forms a lateral $p - i - n$ junction. The GaInAs absorption section is sandwiched vertically between a 100-nm-thick InP clad (top) and 50-nm-thick InP clad (bottom). The absorption section is connected to a back-end DBR in order to suppress backward radiation of light. The absorption section length, $L_{abs}$ , can be reduced owing to the high-reflectivity back-end DBR and therefore, the 3-dB bandwidth can be increased while maintaining the same responsivity compared with a device without the back-end DBR [19,20].

Fig. 4. (a) Schematic of the membrane GaInAs $p - i - n$ PD with the back-end DBR. Conceptual diagrams of the membrane GaInAs $p - i - n$ PD with the back-end DBR in the (b) active region and (c) passive region.

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In this study, we analyze and investigate two types of membrane PDs: (1) membrane PD with a back-end DBR in the GaInAs absorption region [Fig. 4(b)], and (2) membrane PD with a back-end DBR in the 155-nm-thick GaInAsP passive region [Fig. 4(c)]. In the former device, the GaInAs DBR region functions simultaneously as an absorption layer and reflection layer.

We also determine the required absorption section length for both types of membrane PDs [Figs. 4(b) and 4(c)] using the transfer matrix method (TMM). Following this, we estimate the 3-dB bandwidth of these membrane PDs, which will be described in the following sections.

3. REQUIRED LENGTH OF THE MEMBRANE PDs FOR EFFICIENT ABSORPTION

In this section, we determine the optimum device length for two types of membrane PDs based on the following criteria: (1) efficient absorption and (2) low reflection power to the laser side. Figure 5 shows the numerical model used for the TMM simulations. The reflectivity ( $= E_{l} (0)$ ) and transmittivity ( $= E_{r} (L)$ ) of the membrane PD can be expressed as

[\begin{matrix} E_{r} (L) \\ E_{l} (L) \end{matrix}] = M_{ma} \cdot {(M_{sm} \cdot M_{s} \cdot M_{ms} \cdot M_{m})}^{N} \cdot M_{L} [\begin{matrix} E_{r} (0) \\ E_{l} (0) \end{matrix}] = [\begin{matrix} M_{11} & M_{12} \\ M_{21} & M_{22} \end{matrix}] [\begin{matrix} E_{r} (0) \\ E_{l} (0) \end{matrix}],

where

N

is the number of grating periods,

E_{r} (0)

and

E_{l} (0)

denote the input and output power at the left side of the device, respectively, and

E_{r} (L)

and

E_{l} (L)

denote the input and output power at the right side of the device, respectively. Assuming that the input light enters from the left side of the device,

E_{r} (0)

and

E_{l} (L)

are set as 1 and 0, respectively. The matrices

M_{m (s)}

and

M_{m s (s m)}

for the grating region are given by

M_{m (s)} = [\begin{matrix} e^{- j β_{m (s)} L_{m (s)}} & 0 \\ 0 & e^{j β_{m (s)} L_{m (s)}} \end{matrix}],

M_{ms (sm)} = \frac{1}{2 \sqrt{n_{m (s)} n_{s (m)}}} [\begin{matrix} n_{s (m)} + n_{m (s)} & n_{s (m)} - n_{m (s)} \\ n_{s (m)} - n_{m (s)} & n_{s (m)} + n_{m (s)} \end{matrix}],

where

β_{m (s)}

,

n_{m (s)}

, and

L_{m (s)}

represent the effective complex propagation constant, effective complex refractive index, and length for each part of the grating region, respectively. The matrix

M_{L}

for the absorption region is in the same form as

M_{m (s)}

and it can be written as

M_{L} = [\begin{matrix} e^{- j β_{abs} L_{abs}} & 0 \\ 0 & e^{j β_{abs} L_{abs}} \end{matrix}],

where

β_{abs}

and

L_{abs}

represent the effective complex propagation constant and length of the absorption region, respectively. The matrix

M_{ma}

for the interface between the membrane PD and air is given by

M_{ma} = \frac{1}{\sqrt{1 - R}} [\begin{matrix} 1 & \sqrt{R} \\ \sqrt{R} & 1 \end{matrix}] {R = {(\frac{n_{s} - 1}{n_{s} + 1})}^{2}} .

Based on Eq. (7), the reflectivity,

R

, and transmittivity,

T

, are given by

R = {| \frac{E_{r} (0)}{E_{l} (0)} |}^{2} = \frac{{| M_{21} |}^{2}}{{| M_{22} |}^{2}},

T = {| \frac{E_{r} (L)}{E_{r} (0)} |}^{2} = \frac{{| M_{11} M_{22} - M_{12} M_{21} |}^{2}}{{| M_{22} |}^{2}} = \frac{1}{{| M_{22} |}^{2}} .

First, we calculate the reflectivity,

R

, and transmittivity,

T

, as a function of the absorption section length,

L_{abs}

, and the DBR section length,

L_{DBR}

. In the simulations, the wavelength of the incident light is assumed to be 1.55 μm, and the grating period

Λ

, grating depth

d_{g}

, and duty ratio are set as 288 nm, 50 nm, and 50%, respectively. The refractive indices for InP, GaInAsP, and GaInAs are set as 3.17, 3.34, and 3.62, respectively. The absorption coefficient of the GaInAs is set as

5000 {cm}^{- 1}

.

Fig. 5. Numerical model of the DBR grating structure model used for the TMM simulations.

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Figure 6 shows an example of the simulation results for the device with a stripe width $W_{s}$ of 0.8 μm (grating coupling coefficient $κ = 1650 {cm}^{- 1}$ ). Figures 6(a) and 6(b) show the reflectivity, $R$ , and transmittivity, $T$ , respectively, of the membrane PD with the back-end DBR in the GaInAs absorption section (Type A device). The thick black solid lines indicate the conditions $R = - 30 dB$ and $T = - 30 dB$ in Figs. 6(a) and 6(b), respectively. These conditions are chosen to achieve efficient absorption of the input optical power and prevent instability of the laser transmitter due to the reflected light. Figures 7(a) and 7(b) represent the reflectivity, $R$ , and transmittivity, $T$ , respectively, of the membrane PD with the back-end DBR in the 155-nm-thick GaInAsP passive section (Type B device).

Fig. 6. (a) Reflectivity and (b) transmittivity as a function of the absorption section length and DBR section length for the membrane PD with DBR in the GaInAs absorption region (Type A device).

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Fig. 7. (a) Reflectivity and (b) transmittivity as a function of the absorption section length and DBR section length for the membrane PD with the back-end DBR in the GaInAsP passive section (Type B device).

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By overlaying the simulation results obtained for the reflectivity and transmittivity, we can identify the region where both $R$ and $T$ are less than $- 30 dB$ . Figure 8 shows the results for the two types of membrane PDs. The total length, $L$ , for the Type A device is given by

L = L_{abs} + L_{DBR} .

In contrast, the total length,

L

, for the Type B device is given by

L = L_{abs} .

Hence, the required device length for each membrane PD can be estimated by drawing a line given by Eq. (14) in Fig. 8(a) and a line given by Eq. (15) in Fig. 8(b) such that the line passes through the red dot. For the Type A configuration, the required length related to the capacitance,

C_{j}

, of the membrane PD is 20.8 μm (

L_{abs} = 14.2 μm

,

L_{DBR} = 6.6 μm

) whereas the required length for the Type B configuration is

L_{abs} = 11.8 μm

. Even though the total length (

L_{abs} + L_{DBR} = 26.6 μm

) for the Type B configuration is slightly longer than that for the Type A configuration, the capacitance,

C_{j}

, of the Type B device can be significantly reduced and this approach will be effective to increase the RC-limited bandwidth, which will be discussed in the next section.

Fig. 8. Optimum device length as a function of the absorption section length and DBR section length for the (a) Type A and (b) Type B devices.

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By performing the above analysis for devices with various stripe widths, the required length related to the capacitance, $C_{j}$ (denoted by the device length in Fig. 9), can be determined as a function of $W_{s}$ , as shown in Fig. 9. For the Type A configuration, the required length is almost constant, where the value is 20–21 μm for $W_{s} > 0.8 μm$ , which is $\sim 30 %$ shorter than that of the membrane PD without the DBR section. For the Type B configuration, the absorption length is 11–12 μm for $W_{s} > 0.8 μm$ , which is $\sim 60 %$ shorter than that of the membrane PD without the DBR section. Therefore, it can be deduced that the Type B configuration is more desirable as a membrane PD because it is more effective to decrease the absorption section length and increase the RC-limited bandwidth.

Fig. 9. Required device length as a function of the stripe width.

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4. ESTIMATION OF THE JUNCTION CAPACITANCE AND 3-DB BANDWIDTH

The junction capacitance, $C_{j}$ , can be roughly estimated by applying the calculated device length and stripe width into the parallel-plate model such as $C_{j} = ε_{GaInAs} h L / W_{s}$ , where $ε_{GaInAs} = 13.5$ , $ε_{0}$ is the permittivity of the GaInAs, and $h$ is the thickness of the absorption layer, which is 0.27 μm. The stripe width, $W_{s}$ , can be considered as the width of the depletion layer because of the full depletion of the absorption layer upon application of the reverse bias voltage.

Figure 10 shows the junction capacitance, $C_{j}$ , determined as a function of the stripe width, $W_{s}$ . It can be seen that the junction capacitance for each membrane PD can be significantly reduced with the back-end DBR compared with the conventional membrane PD without 0 DBR. In order to obtain $C_{j} < 1 fF$ , the stripe width must fulfill the following criteria: (1) $W_{s} > 0.7 μm$ (for Type A device) and (2) $W_{s} > 0.5 μm$ (for Type B device).

Fig. 10. Junction capacitance as a function of the stripe width for two types of membrane PDs.

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Based on the simulation results obtained for the junction capacitance, $C_{j}$ , the 3-dB bandwidth, $f_{3 dB}$ , for two types of membrane PDs is calculated by using a simple circuit model, as shown in Fig. 11. The 3-dB bandwidth can match the modulation speed of the membrane laser connected to a high load resistor in order to provide sufficient output voltage. In terms of the high-frequency response, the 3-dB bandwidth of the lateral $p - i - n$ junction PD is limited by the resistance-capacitance delay and the carrier drift time within the intrinsic region. The 3-dB bandwidth $f_{3 dB}$ can be expressed as [26]

\frac{1}{f_{3 dB}^{2}} = \frac{1}{f_{RC}^{2}} + \frac{1}{f_{TT}^{2}},

where

f_{RC}

is the RC bandwidth, and

f_{TT}

is the transit frequency.

Fig. 11. Numerical model used for the 3-dB bandwidth estimation.

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The RC bandwidth, $f_{RC}$ , can be simply estimated using the first-order RC circuit:

f_{RC} = \frac{1}{2 π (R_{L} + R_{s}) C_{j}},

where

R_{L}

and

R_{s}

represent the load resistance and sheet resistance of the PD, respectively (see Fig. 11). Here,

R_{L}

is assumed to be 10 kΩ in order to provide sufficient output voltage to the CMOS circuit.

The transit frequency, $f_{TT}$ , is given by [27]

f_{TT} = \frac{\sqrt{2}}{π} \frac{υ_{sat} \cdot \tanh (μ_{h} \cdot \frac{V_{i}}{W_{s}} \cdot \frac{1}{υ_{sat}})}{W_{s}},

where

υ_{sat}

is the hole saturation drift velocity (assuming that the absorption layer is fully depleted),

μ_{h}

is the mobility, and

V_{i}

is the bias voltage, which is applied in the intrinsic region of the PD.

We analyze the 3-dB bandwidth of the membrane PD as a function of stripe width, $W_{s}$ , by using Eqs. (16)–(18). Figures 12(a)–12(c) show the results obtained from the simulations, where the $I_{pd}$ values are 5, 20, and 80 μA, respectively. The applied bias voltage $V_{b}$ and load resistor $R_{L}$ are fixed at $- 1 V$ and 10 kΩ, respectively, for the simulations. The theoretical curves indicate that for a small stripe width, the transit frequency surpasses the RC bandwidth because the carrier drift time is short and there is a sufficiently strong electric field in the depletion region. However, for a large stripe width, the junction capacitance decreases, which in turn, increases the RC bandwidth. In addition, the electric field applied to the absorber becomes weak while the bias voltage is fixed and the drift distance increases, which explains why the 3-dB bandwidth is more dependent on the RC bandwidth in this case.

Fig. 12. Theoretical curves of the 3-dB bandwidth for different $I_{pd}$ values: (a) 5 μA, (b) 20 μA, and (c) 80 μA. Red line, PD with the back-end DBR in the GaInAsP passive region (Type B device); blue line, PD with the back-end DBR in the GaInAs absorption region (Type A device); dashed line, PD without the back-end DBR.

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It can be observed from Fig. 12 that the 3-dB bandwidth is greater than 10 GHz for both devices at an appropriate value of $W_{s}$ . Assuming that the required output voltage is 200 mV ( $I_{pd} = 20 μA$ ) for the device with the DBR in the GaInAsP passive region (Type B), the maximum 3-dB bandwidth obtained is 17.3 GHz (which is 27% higher than that of the device without the DBR) for $W_{s} = 0.7 μm$ . Even in the situation where an output voltage of 800 mV ( $I_{pd} = 80 μA$ ) is required, the maximum 3-dB bandwidth remains at 10.7 GHz for $W_{s} = 0.5 μm$ .

Figures 13(a)–13(c) show the 3-dB bandwidth, $f_{3 dB}$ , and the output voltage, $V_{out}$ ( $= R_{L} I_{pd}$ ), as a function of the photocurrent, $I_{pd}$ , for each membrane PD: (a) PD with the DBR in the GaInAs absorption region (Type A device), (b) PD with the DBR in the passive region (Type B device), and (c) PD without the DBR. The increase of photocurrent $I_{pd}$ leads to a higher output voltage $V_{out}$ ( $= R_{L} I_{pd}$ ). However, at the same time, the 3-dB bandwidth is limited due to the reduction of the bias voltage $V_{i}$ applied in the intrinsic region of the PD according to the following equation:

V_{i} = V_{b} - (R_{L} + R_{S}) \cdot I_{pd} .

In addition, the variation of the photocurrent or the bias voltage applied to the depletion region does not significantly reduce the 3-dB bandwidth for

W_{s} = 0.3 μm

because the strong electric field can be maintained. In contrast, the 3-dB bandwidth can be significantly reduced at higher values of

I_{pd}

for

W_{s} > 0.8 μm

because of the lower transit frequency. For the membrane PD with the DBR in the GaInAsP passive region (Type B device), it is estimated that the 3-dB bandwidth is higher than 15 GHz at lower

I_{pd}

(30 μA). The 3-dB is also higher than 10 GHz at higher

I_{pd}

(60 μA).

Fig. 13. Theoretical curves of the 3-dB bandwidth and output voltage $V_{out}$ as a function of the photocurrent $I_{pd}$ for different stripe widths. (a) PD with the back-end DBR in the GaInAs absorption region (Type A device); (b) PD with the back-end DBR in the GaInAsP passive region (Type B device); (c) PD without the back-end DBR.

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5. CONCLUSIONS

In this work, we proposed and investigated two types of GaInAs/InP membrane $p - i - n$ PDs with back-end DBR in which the round-trip light absorption can reduce the area and capacitance of the detecting region.

Based on the analysis using TMM, we obtained the required device length to achieve a reflectivity and transmittivity of less than $- 30 dB$ . For a stripe width of 0.8 μm, the required length was estimated to be 20.8 and 11.8 μm for the device with the DBR in the GaInAs absorption region (Type A) and the device with the DBR in the GaInAsP passive region (Type B), respectively.

Next, we analyzed the junction capacitance and 3-dB bandwidth for various stripe widths. We obtained a 3-dB bandwidth greater than 10 GHz for the appropriate value of $W_{s}$ , which is a sufficient speed for intra-chip optical interconnection. Finally, we obtained a maximum 3-dB bandwidth of 17.3 GHz with sufficient output voltage for the device with the DBR in the GaInAsP passive region.

Funding

Japan Society for the Promotion of Science (JSPS) (15H05763, 16H06082); Core Research for Evolutional Science and Technology (CREST) (JPMJCR15N6).

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Design of GaInAs/InP membrane p-i-n photodiodes with back-end distributed Bragg reflector

Abstract

1. INTRODUCTION

2. DESIGN OF THE MEMBRANE PDs WITH DBR

A. Design Guide for the Membrane PDs

B. Two Types of Membrane PDs Integrated with Back-End DBR

3. REQUIRED LENGTH OF THE MEMBRANE PDs FOR EFFICIENT ABSORPTION

4. ESTIMATION OF THE JUNCTION CAPACITANCE AND 3-DB BANDWIDTH

5. CONCLUSIONS

Funding

REFERENCES

Cited By

Figures (13)

Equations (19)

Journal of the Optical Society of America B