Flat-top steep-edge photodetectorwith cascaded grating structure

Xu Zhang,* Yongqing Huang, Xiaomin Ren, Hui Huang, and Qi WangKey Laboratory of Information Photonics and Optical Communications, Ministry of Education,

Beijing University of Posts and Telecommunications, Beijing 100876, China

*Corresponding author: zhangxubetter@gmail.com

Received 6 July 2009; revised 19 October 2009; accepted 30 October 2009;posted 4 November 2009 (Doc. ID 113612); published 3 December 2009

A new type of photodetector with cascaded waveguide grating filters as a bottom reflection mirror isproposed. A greatly improved spectral response is shown to follow by the integration of a waveguidegrating into classical thin-film homogeneous layers. Calculation results for a single grating, a cas-caded-double grating, and a cascaded-triple grating structure are demonstrated. An increasing rectan-gular spectral response is obtained by cascading two or three grating filters. Compared with a traditionalphotodetector with distributed Bragg reflectors, this new type of photodetector with the same materialsrequires significantly fewer layers while maintaining narrow flattop response, high peak efficiency, andlow sideband reflectance. © 2009 Optical Society of America

OCIS codes: 230.5160, 050.2770, 230.4170.

1. Introduction

The resonant cavity enhanced (RCE) photodetectoris widely used in optical fiber communication withthe characteristics of high speed, high quantum effi-ciency, and high sensitivity [1]. To fully benefit fromthe RCE scheme in fiber communications, the peak ofquantum efficiency has to match the source wave-length. A slight fluctuation in the source wavelengthwould cause a tremendous fluctuation in the detec-tion efficiency. To overcome the disadvantages ofthe RCE photodetector mentioned above, it is quitedesirable to design a new structure of photodetectorwith a narrow spectral response linewidth and at thesame time detect all sources emitting in a particularcommunication window with a constant efficiency.The feature of a flattop and steep-edge response isrequired in order to get high detection efficiency un-der the condition of slight fluctuation in the sourcewavelength.Several methods to realize the flattop and steep-

edge response have been investigated. Design exam-ples include introducing an anomalous-dispersion

region in the reflection phase of the top mirror [2],depositing a half-wave thickness layer into the dis-tributed Bragg reflector (DBR) [3], and cascadingtwo or three Fabry–Perot (FP) cavities together [4].In [2] the experimental result of the quantum effi-ciency of the flattop steep-edge photodetector is 0.8at 1550nm, and the full width at half-maximum(FWHM) is 35:96nm. However, according to theapplicable requirements, both the theoretical simu-lation and the experimental result are not acceptableto wavelength-division multiplexing (WDM) sys-tems. In [3] a device with a wavelength of 850nmis described, but a detailed analysis and the trade-offs among the various parameters are not given.The method of achieving the flattop response in [4]is simple and easy to fabricate, but the FP cavityis so long, and precision is so difficult to control, thatthe method is hard to apply to optical electronic in-tegrated devices.

2. Design and Simulation

A stack of waveguide grating reflection elements isdemonstrated in Fig. 1. It consists of the upper layerand the substrate with reflective indices of nc and ns,respectively. A grating region of thickness dg with

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high and low indices nH and nL is sandwiched be-tween the upper layer and the homogeneous layer1. The value of grating period Λ is set according tothe rule that only the zero order and both the þ1and −1 diffracted orders are permitted to propagatein the upper layer and substrate region. All other dif-fracted orders are evanescent. The function of homo-geneous layers is to improve the symmetry of thespectral response. The response of the cascaded ele-ments can be treated in a way similar to that of thereflective feature of a dielectric homogeneous layer.The light incident to the waveguide grating structureassumes a TE-polarized, normal incident planewave, and the calculations are performed with rigor-ous coupled-wave analysis (RCWA) theory [5,6].A new type of photodetector with single waveguide

grating filters as a bottom reflection mirror is de-picted in Fig. 2, and its spectral response is sketchedin Fig. 3. The topmirror is fabricated bymeans of wetchemical etching, and the inclined mirror can beformed by depositing two periods of Si=SiO2 DBR.The reflectivity of the top mirror as a function ofthe wavelength is sketched in Fig. 4. Its spectral re-flectance is 0.87 in the range of wavelengths from1500nm to 1600nm. The top mirror reflectivityshould not be unity, as no light will be transmitted

to the cavity, and the quantum efficiency will be zero.We obtain the bottom mirror by embedding a binarygrating between two homogeneous layers. This grat-ing is called an embedded grating, and althoughmoredifficult to fabricate than a surface-relief grating, thiscascaded waveguide grating structure can be fabri-cated through amethod similar to that of the grating.The average dielectric index of the grating layer hasto be higher than the cover and substrate dielectricindices for the waveguide resonance to occur [7].The thickness of the waveguide grating is importantto determine the features of reflectance, such as side-band ripples, linewidth, and free spectral range. Thesymmetric lineshape reflection can be attained bychoosing the grating thickness and the homogeneouslayer to be multiples of quarter-wavelength, i.e.,the grating thickness dg ¼ mλgrat=4

ffiffiffiffiffiffiffiffiεequp , where

εequ ¼ ðεH þ εLÞ=2, εH and εL are the high and low re-lative permittivity of the grating, respectively, λgrat isa resonance wavelength, and m ¼ 2; 4; 6…. The

Fig. 1. (Color online) Schematic of grating structure with rectan-gular-index profile of high nH ¼ 3:4 and low nL ¼ 3:1 indices withperiod Λ ¼ 487nm and thickness d ¼ 119nm (quarter wave atλ ¼ 1550nm).

Fig. 2. Schematic diagram of a single waveguide grating photo-detector consisting of a p-i-n photodiode sandwiched between theDBR mirrors and a waveguide grating filter.

Fig. 3. Quantumefficiency of a singlewaveguide grating photode-tector centered at 1550nm,Δλ0:9=Δλ0:1 ¼ 0:12, FWHM ¼ 1:26nm.

Fig. 4. Top mirror reflectivity as a function of the wavelength.

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thickness of the homogeneous d1 ¼ λgrat=4ffiffiffiffiffiε1

p,

d2 ¼ λgrat=4ffiffiffiffiffiε2

p, where ε1 and ε2 are the relative per-

mittivities of layers 1 and 2, respectively [8]. The re-sonance wavelength is set by the value of the gratingperiod, and the waveguide geometry is symmetricwith the relative permittivity of the cover equal tothat of the substrate.Two methods exist to calculate the quantum effi-

ciency of the photodetector: one is an analytical for-mulation presented by Unlu et al. in 1991 [1], and theother is the transfer matrix method (TMM). The topmirror and the bottom grating filters reflectivitiesand phase angles are calculated by TMM. The mirrorreflectivities and reflectance phases are used to de-termine the light-field distribution inside the lossycavity considering the whole RCE structurefollowing the approach present by [1]. The quantumefficiency is the ratio of the absorbed power to the in-cident optical power, and can be written

η ¼½1þR2expð−αdÞ�

1−2ffiffiffiffiffiffiffiffiffiffiffiffiR1R2

pexpð−αdÞcosð2βþψ1þψ2ÞþR1R2expð−αdÞ

×ð1−R1Þ×½1−expð−αdÞ�; ð1Þ

where R1 and R2 denote the power reflectivity of thetop mirror and grating filters, respectively, and ψ1and ψ2 are phase shifts due to light penetration intothe mirror. α is the absorption coefficient, and d is thethickness of the active layer. The propagation con-stant β (β ¼ 2nπ=λ0, where λ0 is the vacuum wave-length and n is the refractive index) has awavelength dependence.The enhancement of optical power can be calcu-

lated by the internal optical power to the incidentpower. The quantum efficiency of the photodetectoris obtained by multiplying the internal optical powerenhancement factor by 1 − expð−αdÞ [1]. As αd in-creases, the enhancement of optical power falls off ra-pidly, as shown in Fig. 5. This is because most of thelight is absorbed in the active layer before it reachesthe grating filters, preventing the optical feedbackmechanism necessary for detection. The value ofthe active layer should be chosen properly. Too thinan active layer is not desirable because of the reduc-tion in bandwidth due to RC constant limitations.However, too thick an active layer will reduce thespeed of the response and result in poor quantum ef-ficiency. For a given value ofR1 and ofR2, there existsone value of d that maximizes the quantum effi-ciency. As shown in Fig. 6, for a given value of topmirror reflectivity, the maximum quantum efficiencycan be determined as a function of αd. A detailed ana-lysis has been discussed by Unlu et al. [1].The materials used in the design of the grating

photodetector are described as follows:

1. The top mirror of the photodetector is made ofthree pairs of Si=SiO2 with thicknesses of 112nmand 263nm, respectively.

2. The thickness of the waveguide grating struc-ture is d ¼ 119nm, the grating period isΛ ¼ 487nm,the refractive indices are nH ¼ 3:4 and nL ¼ 3:1, andthe fill factor is 0.5.

3. The materials of the homogeneous layers aremade of Ga0:47In0:53As0:68P0:32 and Ga0:47In0:53As0:33P0:67, and their optical thicknesses are λ=4 − λ=4 at1550nm, with the refractive indices are 3.4145and 3.2535, respectively.

4. The thickness of a separation layer (InP) is λ ×1:77 with a refractive index of 3.1.

5. The substrate is InP.

3. Results and Discussion

The refractive indices used in the design of the photo-detectorcorrespondtomaterialscommonlyusedinthefabricationofthesemiconductordevices.Theresponseof the photodetector can be attributed to both wave-guide grating resonance and thin-film interference

Fig. 5. (Color online) Power enhancement factor as a functionof αd.

Fig. 6. Quantum efficiency as a function of αd at the condition ofthe grating filter reflectivity R2 ¼ 0:99 and as a function of topmirror reflectivity R1.

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effects. There is a strong coupling effect between theexternal propagating wave and adjacent evanescentwaves,andthisaffectsrapidvariationinthereflection.The ratio of the spectral bandpass is a feature to gaugethe flatness of a response and is defined as the ratio ofthe linewidth at an efficiency of 90% (Δλ0:9) to the line-width at an efficiency of 10% (Δλ0:1). Cascading two orthreewaveguide grating structures in thismanner re-

sults in, respectively, an increase in the spectral re-sponse bandpass ratio of three times and more thanfive times that of a single grating photodetector.

As can be seen from Figs. 2, 3, and 7–10, comparedwith the traditional photodetector with DBRs, signif-icantly fewer layers are required to achieve the samespectral linewidth at peak quantum efficiency. Thegrating combined with the thin-film coating canreduce the reflectance in the sidebands to arbitrarilylow values and extend over a large wavelengthrange.

Fig. 7. (Color online) Structure of a cascaded double waveguidegrating photodetector consisting of a p-i-n photodiode sandwichedbetween the DBR mirrors and a waveguide grating filter.

Fig. 8. Quantum efficiency of a cascaded double waveguide grat-ing photodetector centered at 1550nm, Δλ0:9=Δλ0:1 ¼ 0:34, andFWHM ¼ 1:729nm.

Fig. 9. (Color online) Structure of a cascaded triple waveguidegrating photodetector consisting of a p-i-n photodiode sandwichedbetween the DBR mirrors and a waveguide grating filter.

Fig. 10. Quantum efficiency of a cascaded triple waveguidegrating photodetector centered at 1550nm, Δλ0:9=Δλ0:1 ¼ 0:63,FWHM ¼ 1:591nm.

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The requirement of ε2equε22=ε21 ¼ εcεs must be satis-fied in order to obtain an ideal reflection response,where εc and εs are the relative permittivities ofthe cover and substrate, respectively. From the aboveanalysis, we know that the thickness of the gratinglayer and the thickness of the homogeneous layerobey the condition that with any shift from the setvalue, the output efficiency deteriorates rapidly.We determine the response of the system by sum-ming the external field contributions resulting fromthe multiple reflections between the grating struc-ture elements. The sum of phase shifts as the inci-dent wave propagates through the grating region,and the homogeneous layer is [9]

δ ¼ 2ðδgrat þ δn1 þ δn2 þ δsepÞ; ð2Þ

where

δgrat;n1;n2;sep ¼ 2πλ ngrat;n1;n2;sepdgrat;n1;n2;sep: ð3Þ

When δ ¼ 2mπ (m is an integer), the bottom elementsof the photodetector are in phase, whereas on thecondition of δ ¼ ð2mþ 1Þπ, the bottom elements ofthe photodetector are out of phase. The simulationshows that the out of phase layout produces a profileof linewidth exhibiting broadened peak efficiencyand narrower base as compared with the in phasegrating elements. The thickness of the separationlayer should be on the order of incident wavelengthso that the fields propagating within each part of thebottom elements of the photodetector are considereduncoupled. It also indicates that the cascaded grat-ing elements result in suppressed reflection of theoff-resonance wavelength. This result is expected, be-cause the response of two or three cascaded gratingelements is approximately equal to the sum of theindividual responses, which Figs. 8 and 10 confirm.

4. Conclusion

The proposed RCE photodetector is wavelength se-lective due to the nature of grating filters. The stop-band width of the grating filters plays an importantrole in selecting different channels in WDM applica-

tions. The advantages of this design method overother schemes are that it can obtain a narrower spec-tral linewidth and a steep-edge response. Due to thereduced thickness, a simple design, and mature fab-rication techniques, this type of photodetector can bea good candidate in WDM systems.

This work was supported by the Program forChangjiang Scholars and Innovative Research Teamin University ( IRT0609), the 111 Project ( B07005),the National High Technology R&D Program ofChina ( 2007AA03Z418), and the Program of KeyInternational Science and Technology CooperationProjects (2006DFB11110).

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