Photodetector arrangement

According to embodiments of the present invention, a photodetector arrangement is provided. The photodetector arrangement includes a plurality of germanium-based photodetectors, each germanium-based photodetector configured to receive an optical signal and to generate an electrical signal in response to the received optical signal, and an electrode arrangement arranged to conduct the electrical signals.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority of Singapore patent application No. 201300749-7, filed 30 Jan. 2013, the content of it being hereby incorporated by reference in its entirety for all purposes.

TECHNICAL FIELD

Various embodiments relate to a photodetector arrangement.

BACKGROUND

A germanium-on silicon (Ge-on-Si) photodetector is a key building block for optical interconnect and microwave photonics. A high-power and high-speed photodetector is particularly important for analog optical link with high gain, low noise floor, and high spurious-free dynamic range. However, there is a trade-off between the photodetector operation bandwidth and its saturation power. In general, a photodetector with high speed is usually designed with a low capacitance and a small carrier transit time, thus resulting in small dimensions. This causes the saturation power to be low due to the space charge effect. For conventional photodetectors, it is difficult to work at high speed with a high saturation power. Currently, a Ge photodetector is usually provided with only ˜5 mW saturation power and ˜10 GHz bandwidth.

SUMMARY

According to an embodiment, a photodetector arrangement is provided. The photodetector arrangement may include a plurality of germanium-based photodetectors, each germanium-based photodetector configured to receive an optical signal and to generate an electrical signal in response to the received optical signal, and an electrode arrangement arranged to conduct the electrical signals.

DETAILED DESCRIPTION

Embodiments described in the context of one of the devices are analogously valid for the other devices.

In the context of various embodiments, the phrase “at least substantially” may include “exactly” and a reasonable variance.

In the context of various embodiments, the term “about” or “approximately” as applied to a numeric value encompasses the exact value and a reasonable variance.

Various embodiments may relate to fields including silicon (Si) photonics (e.g. Si nano/micro-photonics), microwave photonics, and optical communication systems.

Various embodiments may provide an approach for developing a traveling-wave photodetector array (TWPDA) with large bandwidth and high power handling capability. Various embodiments may also provide an approach for developing a cost effective photodetector for a silicon (Si) integrated circuit.

Various embodiments may provide a large-bandwidth, high-power traveling-wave photodetector array. In other words, various embodiments may provide a traveling-wave electrode photodetector array with a high operation bandwidth and a high power handling capability. The traveling-wave electrode photodetector array may be applicable for optical communication and microwave photonics.

Various embodiments may provide a traveling-wave photodetector array or arrangement (TWPDA) with a large-bandwidth and high power handling capability. Such a TWPDA may be based on a germanium-on-silicon (Ge-on-Si) substrate, which may provide the benefit of large-bandwidth operation. The TWPDA may include multiple cascaded germanium (Ge) photodetectors (PDs) with parallel feeds, which may enhance the power handling capacity of the TWPDA. The photocurrent from each Ge PD may be collected by using an impedance matched traveling-wave electrode (TWE) to maintain the operation bandwidth. The phase difference, for example corresponding to optical signals and/or electrical signals, that may be present in the TWPDA may be compensated by a design of one or more optical waveguide delay lines.

Various embodiments may provide a traveling-wave photodetector (PD) structure or arrangement with double metal layers. A velocity and impedance matched coplanar waveguide (CPW) for a traveling-wave electrode (TWE) may be employed in the photodetector arrangement of various embodiments. In various embodiments, optical waveguide delay lines may be employed in the photodetector arrangement for velocity matching between the optical signal and the electrical signal propagating in the photodetector arrangement.

Various embodiments may provide a simple design of a traveling-wave photodetector (PD) array. Various embodiments may enable a cost effective implementation and CMOS compatible fabrication of the photodetector array or arrangement of various embodiments. Further, the photodetector array of various embodiments may be ready for photonic integration for various applications.

Various embodiments may provide a traveling-wave photodetector array (TWPDA) that may be designed to be velocity and impedance matched, taking into consideration the periodic loading effect from each individual Ge photodetector. Thus, the TWPDA may feature the merits of a large operation bandwidth and a high power handling capability. Such a TWPDA may be potentially usable for microwave photonics, among other possible photonic applications.

FIG. 1shows a schematic top view of a photodetector arrangement100, according to various embodiments. The photodetector arrangement100includes a plurality of germanium-based photodetectors102, each germanium-based photodetector102configured to receive an optical signal150and to generate an electrical signal152in response to the received optical signal150, and an electrode arrangement104arranged to conduct the electrical signals152.

In other words, a photodetector arrangement100may be provided. The photodetector arrangement100may include an array of photodetectors (PDs)102, where each PD102may include a germanium (Ge)-based material. For illustration purposes, four germanium-based photodetectors (Ge PDs) are shown inFIG. 2, including a first Ge PD102a, a second Ge PD102b, a third Ge PD102cand a fourth Ge PD102d. However, it should be appreciated that the photodetector arrangement100may include two, three, four, five or any higher number of Ge photodetectors102. Each Ge PD102a,102b,102c,102dmay receive an optical signal (e.g. light)150at its input and consequently may produce an electrical signal (e.g. a photocurrent)152at its output. The germanium (Ge)-based material of each Ge PD102a,102b,102c,102dmay act as an optical or light absorbing portion. The photodetector arrangement100may further include an electrode arrangement104for conducting the electrical signals152generated by the plurality of Ge PDs102. This may mean that the electrode arrangement104may be electrically coupled to each Ge PD102a,102b,102c,102d, where the electrode arrangement104may be adapted to propagate the electrical signals152, or in other words, the electrical signals152may travel or flow through the electrode arrangement104. Further, this may mean that the plurality of Ge PDs102may be electrically coupled to each other by means of the electrode arrangement104. The electrical signal152from each Ge PD102a,102b,102c,102dmay be combined by the electrode arrangement104into a single output.

In the context of various embodiments, each germanium-based photodetector102a,102b,102c,102dmay receive the same optical signal150.

In various embodiments, the electrode arrangement104may include a traveling-wave electrode (TWE) arrangement. This may mean that the photodetector arrangement100may be a traveling-wave photodetector array or arrangement (TWPDA). The traveling-wave electrode (TWE) arrangement may act as a transmission line for the electrical signals152.

The traveling-wave electrode arrangement may include a coplanar waveguide (CPW). The coplanar waveguide may include three electrodes, in the form of a signal (S) electrode and two ground (G) electrodes arranged adjacent to the signal electrode. The two ground electrodes may be arranged on opposite sides of the signal electrode and spaced apart from the signal electrode. The signal electrode and the two ground electrodes may be located on a same plane, and hence coplanar. This may mean that the signal electrode and the two ground electrodes may be arranged on a same side, for example with reference to a substrate. In various embodiments, the signal (S) electrode and the two ground (G) electrodes may be arranged at least substantially parallel to each other.

In various embodiments, the coplanar waveguide may include a signal (S) electrode electrically coupled to the plurality of germanium-based photodetectors102to conduct the electrical signals152, and two ground (G) electrodes arranged on opposite sides of the signal (S) electrode and spaced apart from the signal (S) electrode. The signal electrode may conduct the respective electrical signals152generated by the plurality of germanium-based photodetectors102. The signal electrode may be electrically coupled to the light absorbing portion of each germanium-based photodetector102a,102b,102c,102d. The two ground electrodes may be electrically coupled to respective contact regions of each germanium-based photodetector102a,102b,102c,102d. In various embodiments, the plurality of germanium-based photodetectors102may be arranged successively or sequentially along a length of the signal electrode.

In the context of various embodiments, the signal electrode may have a width, w, of between about 2 μm and about 20 μm, for example between about 2 μm and about 10 μm, between about 2 μm and about 5 μm, between about 5 μm and about 20 μm, between about 10 μm and about 20 μm, or between about 5 μm and about 10 μm.

In the context of various embodiments, a spacing, g, between the signal electrode and each of the two ground electrodes may be between about 1 μm and about 200 μm, for example between about 1 μm and about 100 μm, between about 1 μm and about 50 μm, between about 100 μm and about 200 μm, or between about 50 μm and about 100 μm.

In the context of various embodiments, the electrode arrangement104may include a first conductive layer defined into a plurality of contacts, a respective contact being electrically coupled to a respective germanium-based photodetector102a,102b,102c,102dof the plurality of germanium-based photodetectors102and electrically isolated from the other contacts of the plurality of contacts, and a second conductive layer electrically coupled to the plurality of contacts. A respective contact may collect an electrical signal152from an associated germanium-based photodetector102a,102b,102c,102d. The second conductive layer may form a common contact or electrode to the plurality of contacts, and therefore also to the plurality of germanium-based photodetectors102. The second conductive layer may be arranged over the first conductive layer.

In various embodiments, the first conductive layer and the second conductive layer may define a traveling-wave electrode arrangement, for example in the form of a coplanar waveguide (CPW). The second conductive layer may be defined into a signal (S) electrode and two ground (G) electrodes, the signal electrode being electrically coupled to the plurality of contacts defined from the first conductive layer, while the two ground electrodes may be electrically coupled to respective contact regions of each germanium-based photodetector102a,102b,102c,102d.

Each of the first conductive layer and the second conductive layer may be a metal layer. Each of the first conductive layer and the second conductive layer may include a metal including but not limited to aluminum (Al), or copper (Cu). However, it should be appreciated that other metals may be used.

In various embodiments, the photodetector arrangement100may further include a plurality of waveguides, wherein a respective waveguide of the plurality of waveguides may be arranged to propagate the optical signal150towards or to a respective germanium-based photodetector102a,102b,102c,102dof the plurality of germanium-based photodetectors102. A respective waveguide may be optically coupled to a respective germanium-based photodetector102a,102b,102c,102d. A respective germanium-based photodetector102a,102b,102c,102dmay be formed on or over a respective waveguide. Therefore, the photodetector arrangement100may include waveguide-based Ge photodetectors. The plurality of waveguides may be on-chip waveguides, e.g. integrated in the photodetector arrangement100.

In the context of various embodiments, each waveguide may include silicon (Si). Therefore, the photodetector arrangement100may include waveguide-based Ge-on-Si photodetectors.

In various embodiments, a difference in lengths of respective waveguides corresponding to adjacent germanium-based photodetectors of the plurality of germanium-based photodetectors102may introduce an optical time delay (or propagation delay) between the adjacent germanium-based photodetectors such that the respective electrical signals152generated by the adjacent germanium-based photodetectors are at least substantially in phase (or phase-matched). Therefore, each waveguide may act as an optical delay line for the optical signal150. In this way, the optical signal delay between the adjacent germanium-based photodetectors may be at least substantially matched to an electrical signal delay between the adjacent germanium-based photodetectors. Therefore, a velocity matched electrode arrangement104may be provided.

In various embodiments, respective optical time delays between respective adjacent germanium-based photodetectors may be at least substantially the same.

In various embodiments, the electrode arrangement104may be arranged to conduct the electrical signals152in a direction at least substantially perpendicular to a direction of propagation of the optical signal150through the respective waveguide.

In the context of various embodiments, an impedance, Z, of the electrode arrangement104may be at least substantially matched to at least one electrical parameter of each germanium-based photodetector102a,102b,102c,102d. In this way, the loading effect of each germanium-based photodetector102a,102b,102c,102dmay be taken into consideration for forming an impedance matched electrode arrangement104. The at least one electrical parameter may include a resistance, Rs, and/or a capacitance, Cp, of the germanium-based photodetector102a,102b,102c,102d. Each germanium-based photodetector102a,102b,102c,102dmay have at least substantially similar resistance and/or capacitance.

In the context of various embodiments, the plurality of germanium-based photodetectors102may be arranged one after another (e.g. in series or in cascade) in a direction along the conduction of the electrical signals152through the electrode arrangement104. This may mean that the plurality of germanium-based photodetectors102may be arranged along a length of the electrode arrangement104.

In the context of various embodiments, respective electrical signals152generated by respective germanium-based photodetectors102a,102b,102c,102dof the plurality of germanium-based photodetectors102may be at least substantially in phase.

In the context of various embodiments, each germanium-based photodetector102a,102b,102c,102dmay be arranged to receive the optical signal150in parallel relative to the other germanium-based photodetectors102a,102b,102c,102d. This may mean that the plurality of germanium-based photodetectors102may be arranged with parallel feeds of the optical signal150to each germanium-based photodetector102a,102b,102c,102d.

In the context of various embodiments, the plurality of germanium-based photodetectors102may be arranged spaced apart from each other. A period or centre-to-centre spacing, Λ, between adjacent germanium-based photodetectors of the plurality of germanium-based photodetectors102may be between about a few tens of microns and about a few hundreds of microns, for example between about 20 μm and about 900 μm, between about 20 μm and about 500 μm, between about 20 μm and about 100 μm, between about 50 μm and about 100 μm, between about 500 μm and about 900 μm, or between about 100 μm and about 500 μm.

In the context of various embodiments, each germanium-based photodetector102a,102b,102c,102dmay have a length, PDl, of between about a few microns and about a few hundreds of microns, for example between about 5 μm and about 500 μm, between about 5 μm and about 300 μm, between about 5 μm and about 100 μm, between about 50 μm and about 100 μm, between about 100 μm and about 500 μm, or between about 100 μm and about 300 μm.

In the context of various embodiments, each germanium-based photodetector102a,102b,102c,102dmay have a width, PDw, of between about a few microns and about a few tens of microns, for example between about 2 μm and about 50 μm, between about 2 μm and about 30 μm, between about 2 μm and about 10 μm, between about 5 μm and about 10 μm, between about 10 μm and about 30 μm, or between about 10 μm and about 50 μm.

In the context of various embodiments, the photodetector arrangement100may further include a substrate, wherein the plurality of germanium-based photodetectors102may be formed on the substrate. The substrate may include silicon (Si), e.g. a silicon wafer or a silicon-on-insulator (SOI) wafer. Therefore, a Ge-on-Si photodetector arrangement100may be provided.

Various embodiments may provide a photodetector arrangement, e.g. a traveling-wave photodetector array (TWPDA). The traveling-wave photodetector array may include an array of high-speed Ge photodetectors. Multiple-channel optical signal or light may be separately input into each high-speed photodetector. Each high-speed photodetector may generate an electrical signal or photocurrent in response to the received light. The generated photocurrent from each of the photodetector may be collected by a traveling-wave electrode (TWE). The traveling-wave electrode may be designed with an impedance match by considering the periodic loading of the photodetectors. Waveguide delay lines may be adopted for velocity matching between the optical and the electrical signals. Further, the photodetector array may be designed with two metal layers in order to provide an easy design and layout for the traveling-wave electrode.

FIG. 2Ashows a schematic design layout of a photodetector arrangement200, according to various embodiments. The photodetector arrangement200may be a traveling-wave photodetector array (TWPDA).

The photodetector arrangement200may include an array of germanium-based photodetectors or Ge PDs. As a non-limiting example, as shown inFIG. 2A, the photodetector arrangement200may include four Ge PDs, for example a first Ge PD202a, a second Ge PD202b, a third Ge PD202cand a fourth Ge PD202d. The first Ge PD202a, the second Ge PD202b, the third Ge PD202cand the fourth Ge PD202dmay be arranged spaced apart relative to each other. Adjacent Ge PDs may be arranged with a periodicity of A. Each of the first Ge PD202a, the second Ge PD202b, the third Ge PD202cand the fourth Ge PD202dmay be at least substantially similar, for example in terms of structure and/or dimension(s) and/or material(s).

The photodetector arrangement200may further include an array of input waveguides206respectively optically coupled to the plurality of Ge PDs for conveying or guiding an optical signal (e.g. light), as represented by the arrow250, to the respective Ge PDs. For example, a first input waveguide206amay be optically coupled to the first Ge PD202a, a second input waveguide206bmay be optically coupled to the second Ge PD202b, a third input waveguide206cmay be optically coupled to the third Ge PD202c, while a fourth input waveguide206dmay be optically coupled to the fourth Ge PD202d.

Adjacent input waveguides, e.g.206aand206b, may have different lengths. As shown inFIG. 2A, a loop208may be introduced in the second input waveguide206b, thereby introducing a delay line length, and consequently a time delay, as compared to the first input waveguide206a. In this way, the optical signal250propagating through the second input waveguide206bmay arrive at the second Ge PD202bat a delayed or later time (e.g. by a time difference, tdiff) as compared to the optical signal250arriving at the first Ge PD202avia the first input waveguide206a. Further, two loops210,212may be introduced as delay line lengths in, the third input waveguide206c. Each of the loops210,212may have a length that is at least substantially similar to the length of the loop208. Therefore, the time difference for the arrival of the optical signal250at the third Ge PD202cas compared to the second Ge PD202bmay be tdiff, while the time difference for the arrival of the optical signal250at the third Ge PD202cas compared to the first Ge PD202amay be 2tdiff. Accordingly, the plurality of input waveguides206may be waveguide delay lines, acting as optical delay lines. In this way, a respective time delay for the propagation of the optical signal250to the respective Ge PDs202a,202b,202c,202dmay be introduced for successive Ge PDs202a,202b,202c,202d. The plurality of waveguide delay lines206may provide identical delay incremental between successive adjacent input waveguides, e.g. between206aand206b, between206band206cand between206cand206d.

The photodetector arrangement200may further include a plurality of output waveguides216respectively optically coupled to the plurality of Ge PDs for outputting at least a portion of the optical signal250. For example, a first output waveguide216amay be optically coupled to the first Ge PD202a.

The photodetector arrangement200may further include a coplanar waveguide (CPW) as a traveling-wave electrode204. The traveling-wave electrode204may be electrically coupled to the plurality of Ge PDs. The traveling-wave electrode204, in the form of the CPW, may include a source (S) electrode204aand a pair of ground (G) electrodes (e.g. a first ground (G) electrode204band a second ground (G) electrode204c). The first ground (G) electrode204band the second ground (G) electrode204cmay be arranged on opposite sides of the source (S) electrode204a. Each of the first ground (G) electrode204band the second ground (G) electrode204cmay be arranged spaced apart from the source (S) electrode204a. This may mean that the first ground (G) electrode204band the second ground (G) electrode204cmay be physically separated and electrically isolated from the source (S) electrode204a.

As the optical signal250is received or detected by the respective Ge PDs202a,202b,202c,202d, in response, each Ge PD202a,202b,202c,202dmay generate an electrical signal (e.g. a current, e.g. a photocurrent), as represented by the arrow252, which may be conducted via the source (S) electrode204a. Each of the first ground (G) electrode204band the second ground (G) electrode204cmay act as a common return path for an electrical current (e.g. the electrical signal252) in the CPW204. The electrical signal252may provide an indication of a parameter (e.g. intensity) associated with the optical signal250. In various embodiments, a circuit (not shown) may be provided to receive the electrical signal252. Such a circuit may be provided internally as part of the photodetector arrangement200. The electrical signal252may be processed by means of the circuit.

As a result of the time delay associated with the arrival of the optical signal250at adjacent Ge PDs, there is a corresponding time delay in the generation of the respective electrical signals252by the adjacent Ge PDs. For example, there may be a time delay in the generation of the electrical signal252by the second Ge PD202bso as to compensate for the time required for the propagation or conduction of the electrical signal252generated by the first Ge PD202afrom the first Ge PD202ato the second Ge PD202b. In this way, there may be a velocity matching between the optical250and the electrical252signals. As a result, respective electrical signals252generated by the Ge PDs202a,202b,202c,202dmay be at least substantially in phase.

In various embodiments, the traveling-wave electrode204may be designed with an impedance match by considering the periodic loading of the photodetectors (PDs)202a,202b,202c,202d. With optimization, each of the Ge PDs202a,202b,202c,202dmay operate with a bandwidth that may be larger than approximately 10 GHz. With the traveling-wave electrode design, the operation bandwidth of such TWPDA or photodetector arrangement200may maintain the operation bandwidth as that of each individual Ge PD202a,202b,202c,202d.

In order to compensate for the phase difference between each PD202a,202b,202c,202dinduced by the traveling-wave electrode204, the respective waveguide delay lines206a,206b,206c,206dfor each input channel may be suitably designed and optimized.

FIGS. 2B and 2Cshow schematic cross-sectional views of the photodetector arrangement200, illustrating the TWPDA design, taken long the lines A-A′ and B-B′ respectively indicated inFIG. 2A. As shown inFIGS. 2B and 2C, the second Ge PD202band the third Ge PD202cmay be arranged at a spacing or period indicated as Λ. Each of the second Ge PD202band the third Ge PD202cmay have a width, PDw, as illustrated inFIGS. 2B and 2C, and a length, PD1.FIGS. 2B and 2Cillustrate cross-sectional views of a design of the photodetector arrangement200with two metal layers232,246which will be described later below. In order to provide for an easy layout and impedance matching of the traveling-wave electrode204, the CPW, as the traveling-wave electrode204, may be arranged in a direction orthogonal to the input waveguides206a,206b,206c,206d, and two metal layers232,246may be introduced.

Using the second Ge PD202bas an example, although similar descriptions may apply to the other Ge PDs of the photodetector arrangement200, the second Ge PD202bmay include a germanium (Ge) material portion220on a silicon (Si) substrate222. The germanium (Ge) material portion220may be a light absorbing portion for absorbing at least a portion of the optical signal or light250. Thus, the second Ge PD202bmay be constructed using a Ge-on-Si platform. The silicon (Si) substrate222may include a core region224, and a first contact region226aand a second contact region226barranged on opposite sides of the core region224. The core region224may be a lightly doped region (e.g. a P+ doped region), while each of the first contact region226aand the second contact region226bmay be a heavily doped region (e.g. a P++ doped region). The core region224may be optically coupled to the second input waveguide206b. A contact portion228may be provided electrically coupled to the Ge material portion220. The contact portion228may be a heavily doped portion (e.g. an N++ doped portion) of a conductivity type that is opposite to that of the substrate222. In various embodiments, the plurality of Ge PDs, including the second Ge PD202band the third Ge PD202c, may be embedded in an insulating layer (e.g. an oxide layer, e.g. SiO2)230. The insulating layer230may be a buried oxide (BOX).

A first metal (M1) layer232may be provided electrically coupled to the plurality of Ge PDs, including the second Ge PD202band the third Ge PD202c, of the photodetector arrangement200, for example by means of a plurality of conductive vias (e.g. Vias1). The first metal layer232may be defined into a plurality of contacts234, where a respective contact234may be electrically coupled to a respective Ge material portion220, by means of a respective via236. Each contact234may be electrically isolated from each other.

The first metal (M) layer232may be further defined into a plurality of first contacts238, where a respective first contact238may be electrically coupled to a respective first contact region226a, by means of a respective via240. The first metal (M) layer232may be further defined into a plurality of second contacts242, where a respective second contact242may be electrically coupled to a respective second contact region226b, by means of a respective via244. The plurality of contacts234, first contacts238and second contacts242may be electrically isolated from each other.

A second metal (M2) layer246may be provided electrically coupled to the plurality of contacts234, the plurality of first contacts238and the plurality of second contacts242, for example by means of a plurality of conductive vias (e.g. Vias2). The second metal layer246may be defined into the source (S) electrode204a, the first ground (G) electrode204band the second ground (G) electrode204c. As shown inFIG. 2B, the source (S) electrode204amay be electrically coupled to the plurality of contacts234, by means of respective vias247to respective contacts234. As shown inFIG. 2C, the second ground (G) electrode204cmay be electrically coupled to the plurality of first contacts238, by means of respective vias248to respective first contacts238, and electrically coupled to the plurality of second contacts242, by means of respective vias249to respective second contacts242. It should be appreciated that the arrangement and electrical coupling related to the first ground (G) electrode204bmay be analogously based on the descriptions relating to the second ground (G) electrode204c.

As compared to prior art, various embodiments may provide at least one of the following: (1) a velocity and impedance matched traveling-wave electrode design that may allow high-speed operation. Impedance matching may be designed by considering the periodic PD loading effect, while velocity matching may be designed by introducing optical waveguide delay lines; (2) a double metal layer design which may ease the design and layout of the traveling-wave electrode.

A design of the velocity and impedance matched traveling-wave electrode will now be described by way of the following non-limiting example.FIG. 3Ashows a simplified schematic top view of a photodetector arrangement300, according to various embodiments, illustrating a traveling-wave photodetector array (TWPDA) having a photodetector (PD) array302and a traveling-wave electrode (TWE)304. For illustration purposes, as a non-limiting example as shown inFIG. 3A, the photodetector (PD) array302may include three germanium photodetectors (Ge PDs), for example a first Ge PD302a, a second Ge PD302b, and a third Ge PD302c. The first Ge PD302a, the second Ge PD302b, and the third Ge PD302cmay be arranged spaced apart from each other with a periodicity of Λ. This means that adjacent Ge PDs may have a centre-to-centre spacing defined by Λ. Each of the first Ge PD302a, the second Ge PD302b, and the third Ge PD302cmay have a width, PDw, and a length, PDl.

The traveling-wave electrode (TWE)304may be in the form of a coplanar waveguide (CPW) having a source (S) electrode304a, and a first ground (G) electrode304band a second ground (G) electrode304carranged on opposite sides of the source (S) electrode304a. Each of the first ground (G) electrode304band the second ground (G) electrode304cmay be arranged spaced apart from the source (S) electrode304a, by a distance, g. The source (S) electrode304amay have a width, w. Each of the source (S) electrode304a, the first ground (G) electrode304band the second ground (G) electrode304cmay be formed of a metal layer.

FIG. 3Bshows an equivalent circuit360of the photodetector arrangement300, taking into consideration the loading effect of the individual PD302a,302b,302c, with parasitic resistor and capacitor. Using the first Ge PD302aas an example, each Ge PD may include a parasitic resistor, Rs,362and a parasitic capacitance, Cp,364coupled in series, and a DC (direct-current) source366coupled in parallel to Rs362and Cp364.

The dispersion characteristic of the photodetector arrangement300may be modelled using the equivalent circuit360. Without considering the loading effect of the Ge PDs302a,302b,302c, the effective dielectric constant, ∈eff, of the CPW304may be expressed by Equation 1:

ɛeff=[ɛr+ɛr-ɛt1+α⁡(f⁢/⁢fcutoff)-b]2,(Equation⁢⁢1)
where ∈ris the dielectric constant of a substrate (e.g. a silicon (Si) substrate), ∈tis the effective dielectric constant of the CPW304, taking into consideration the metal thickness, f is frequency, fcutoffis the cutoff frequency of the lowest TE mode propagating through the CPW304, and α and b are constants depending on the configurations and dimensions of the CPW304.

The phase velocity, νph, of the CPW304without the loading effect may thus be expressed as Equation 2 below:

vph=cɛeff,(Equation⁢⁢2)
where c is the light speed in vacuum.

The impedance, Zo, of the CPW304may be calculated as

Zo=K′⁡(k)K⁡(k)⁢12⁢(ɛr+1)⁢ɛ0⁢vph,(Equation⁢⁢3)
where K(k) and K′(k) are the complete elliptical integrals of the first kind and ∈ois the vacuum permittivity, which equals to 8.8541878176×10−12F/m.

When considering the loading effect with the resistor Rs362and the capacitor Cp364of a PD302a,302b,302c, the phase velocity, νL, and the impedance, ZL, of the CPW304may be expressed as

vL=1CM⁡(f)+Cp,eqΛ⁢1LM⁡(f),(Equation⁢⁢4)ZL=LM⁡(f)CM⁡(f)+Cp,eqΛ,(Equation⁢⁢5)
where the parameters CM, LMare the equivalent capacitance and inductance per unit length of the CPW304, Cp,eqis the effective capacitance of the photodetector (PD)302a,302b,302crelated to Rs362and Cp364, and Λ refers to the period between adjacent PDs (e.g. between PDs302aand302b, or between PDs302band302c).

The parameter CMmay be expressed as:

The effective capacitance, Cp,eq, may be expressed as:

Based on the above described numerical model, the phase velocity and the impedance of the CPW or TWE304may be calculated and compared, depending on the structure parameters, including the RF (radio frequency) frequency, the CPW dimensions, the photodetector (PD) dimensions, and the periodicity.

FIG. 4shows plots400a,400bof modelling results of the traveling-wave electrode (TWE) phase velocity, ν, and impedance as a function of radio frequency (RF) frequency, f. The modelled results402a,402bcorrespond to a standalone CPW, without the photodetector loading effect, while the modelled results404a,404bcorrespond to a CPW with the photodetector loading effect.

FIG. 5shows plots500a,500bof modelling results of the traveling-wave electrode (TWE) phase velocity, ν, and impedance as a function of metal gap. The term “metal gap” refers to the spacing, g, between a source (S) electrode and a ground (G) electrode of the TWE. The modelled results502a,502bcorrespond to a standalone CPW, without the photodetector loading effect, while the modelled results504a,504bcorrespond to a CPW with the photodetector loading effect. The modelled results502b,504bfor the impedance are obtained for a source electrode width, w, of about 12 μm.

FIG. 6shows plots600a,600bof modelling results of the traveling-wave electrode (TWE) phase velocity, ν, and impedance as a function of photodetector length. The modelled results602a,602bcorrespond to a standalone CPW, without the photodetector loading effect, while the modelled results604a,604bcorrespond to a CPW with the photodetector loading effect.

FIG. 7shows plots700a,700bof modelling results of the traveling-wave electrode (TWE) phase velocity, ν, and impedance as a function of the periodicity, Λ, of the photodetectors. The modelled results702a,702bcorrespond to a standalone CPW, without the photodetector loading effect, while the modelled results704a,704bcorrespond to a CPW with the photodetector loading effect.

As may be observed inFIGS. 4 to 7, the photodetector loading effect may induce significant deviations or modifications from the standalone CPW. Referring toFIGS. 4 and 5, there may be a small variation of both velocity and impedance with the RF frequency, while there may be a large variation as a function of the CPW metal gap, for example when the loading effect is present. Referring toFIGS. 6 and 7, both the Ge PD length and the period, Λ, may affect the velocity and impedance significantly for a CPW with a loading effect.

As both the phase velocity and the impedance may be dependent on the design parameters, the TWPDA may be carefully designed and optimised. For example, the velocity and impedance matched traveling PD array may be designed taking into consideration one or more parameters such as the Ge photodetector width, the Ge photodetector length, the period between adjacent Ge photodetetcors and the CPW width and gap.

Based on the loading periodicity, Λ, and the phase velocity, ν, the time difference between the respective photocurrents generated from adjacent photodetectors may be calculated, and subsequently, the respective optical delay lines in each input channel may be determined in order to compensate for the time difference. Thus, the photocurrent that reaches the output point from each individual PD may have identical phases and thus may be phase matched.

Demonstration of a photodetector arrangement or TWPDA on a silicon chip will now be described. A designed TWPDA was fabricated using a CMOS-compatible fabrication process on an 8″ silicon-on-insulator (SOI) wafer. The TWPDA may be designed with velocity matching between the optical and the electrical signals. The TWPDA may be designed with impedance matching in terms of the traveling-wave electrode.

FIG. 8Ashows an optical microscope image of a fabricated 4-channel photodetector arrangement (4-channel TWPDA)800, whileFIG. 8Bshows an optical microscope image of an enlarged sectional view of the fabricated 4-channel photodetector arrangement800. The 4-channel photodetector arrangement800includes four high-speed Ge PDs802a,802b,802c,802d, two metal layers832,846, an impedance-matched traveling-wave electrode804having a source (S) electrode804a, a first ground (G) electrode804band a second ground (G) electrode804c, and balanced optical delay lines806. In such a design, the gap spacing and the strip line width corresponding to the traveling-wave electrode804may be designed freely, avoiding any layout problem.

FIG. 9shows a plot900of results of 10 Gb/s pseudo-random binary sequence (PRBS) data detection using the 4-channel photodetector arrangement800, illustrating the high-quality detection of the 10 Gb/s PRBS data. Approximately 1 ps electrical unit delay was measured for the travelling-wave electrode804.

As described above, the photodetector arrangement of various embodiments may include a cascade of N high-speed Ge photodetectors, which may be electrically connected by a coplanar waveguide (CPW) as a traveling-wave electrode arrangement. The traveling-wave electrode may be provided with velocity and impedance matchings. Two metal layers may be used in order to provide an easy design for the impedance matched traveling-wave electrode. Waveguide-based optical delay lines may be adopted for velocity matching between the optical and the electrical signals.