Abstract A new dielectric Fabry–Perot cavity was designed for a resonant enhancingoptical absorption by a thin absorber layer embedded into the cavity. In this cavity, the frontmirror is a subwavelength grating with ∼ 100% retroreflection. For a HgCdTe absorber ina matching cavity of the new type, the design is shown to meet the combined challengesof increasing the absorbing efficiency of the entire device up to ∼ 100 % and reducing itssize and overall complexity, compared to a conventional resonant cavity enhanced HgCdTeabsorber, while maintaining a fairly good tolerance against the grating’s fabrication errors.
It is well known, that incorporating a photosensitive or an optically active layer into aFabry–Perot (FP) cavity enhances the efficiency of detection by or emission from the layer,as a consequence of the multiple reflections that occur between the cavity’s mirrors. Theenhancement is maximized if the round-trip phase, i.e. the phase difference between eachsucceeding reflection, satisfies the resonance condition
δ0 ≡ δ (λ0) = 4πnc (λ0) tcλ0
+ ϕf (λ0) + ϕb (λ0) = 2πn. (1)
Here λ0 is a resonance wavelength nc and tc is the refractive index (RI) and length of theFP cavity, respectively, ϕf and ϕb are the reflection phase of the mirror that is further away
M. Zohar (B) · M. Auslender · S. HavaDepartment of Electrical and Computer Engineering, Ben Gurion University of the Negev,P.O. Box 653, 84105 Beer Sheva, Israele-mail: [email protected]
L. FaraoneSchool of Electrical, Electronic and Computer Engineering, The University of Western Australia,M018 35 Stirling Highway, Crawley, 6009 WA, Australia
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from and adjacent to the illuminated side (hereafter referred to as the front and back mirror,respectively), and n is an integer. Equation (1) is thumb rule accurate regardless of the typeof flat-surface mirror being employed, whether it consist of thin metallic films, or is e.g. adistributed Bragg reflector (DBR) that is a stack of quarter-wave pairs of high/low (HL) RIdielectric layers (Heavens 1991; Knittl 1976).
Optical communication, interconnection and information processing systems require high-efficiency photodetectors (PDs). In response to this demand, the field of resonant-cavity-enhanced (RCE) PDs has steadily maturated over past two decades (Ünlü and Strite 1995;El-Batawy and Deen 2003). For thermal PDs, the optical absorbance A is an accurate measureof the efficiency, while for photodiodes and photo-conductors the key figure is the quantumefficiency η. For initial design of the RCE PDs, the adoption of η ≈ A has a widespreaduse (Ünlü and Strite 1995; El-Batawy and Deen 2003) since thus the analysis is framed intooptics alone rather than being restricted to a specific PD technology. It appears (Ünlü andStrite 1995) that for obtaining η ≈ 100% it is at least necessary to have ∼ 100% resonantreflectivity from the front mirror, which is problematic for a DBR of any practical thicknessbecause of the tight material requirements for epitaxial growth. Thus, it is relevant to consideran alternative replacement for the DBR mirror by a thin dielectric micro-optical componentwhich can be ∼ 100 % reflective in a broad spectral band. A device that can exhibit such areflection anomaly with a proper design (Hava and Auslender 1995; Mateus et al. 2004) is adielectric subwavelength grating structure.
This paper presents a theoretical study to incorporate a subwavelength grating as thefront mirror in the FP cavity, for PD applications in the mid-wave infrared (MWIR) range.For a vertical-cavity surface-emitting laser, using an air-bridge subwavelength grating as asuspended top mirror, has been proposed before (Bissaillon et al. 2006; Kim et al. 2007).Only limited work on RCE PDs for operation in the MWIR range has been reported thus far.Currently this is an area of great interest due to the potential for obtaining the uncooled PDs.
2 Design considerations and simulation tools
We adopted η = A (see Sect. 1), so RCE PDs with an absorber layer characterized by acomplex RI, na + ika, were analyzed only optically. To compute the reflectance, transmit-tance and A spectra of RCE PDs including a grating, we used the rigorous coupled waveanalysis recast with an in-layer S-matrix propagation algorithm (Auslender and Hava 1996).For DBR based PDs, a limiting case at zero grating groove width, which coincides with theimpedance form (Knittl 1976) of transfer matrix method, was employed. The optical spectrawere computed in the range 4.215 ≤ λ ≤ 4.615 µm.
We put emphasis on the two issues: (i) optimizing the peak A at λ0 = 4.415 µm andλ0 = 4.500 µm, which are kept fixed, while fulfilling Eq. (1); (ii) seeking the designs with ahigh tolerance of the efficiency to errors in the grating fabrication. Interim design parameters,serving as trial ones for computer aided optimization, will be obtained using the reflectionphases [see Eq. (1)] of the stand-alone mirrors (Ünlü and Strite 1995), which are the mirrorsplaced on an infinite medium of the same material as the cavity’s (CdTe in our designs) andirradiated from the substrate.
3 Conventional RCE PD structures
The reported RCE HgCdTe-PDs (Wehner et al. 2005a,b, 2006) have a standard configurationin which the CdTe FP cavity embeds a thin Hg0.71Cd0.29Te layer between two DBR mirrors
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CdTe
HgCdTe
CdTe
Substrate/ Input mediumCdZnTe
Grating-on-layer reflector
HgCdTe
HgCdTe
CdTe
Ge
CdTe
Substrate /Input medium
CdTe
Ge
HgCdTe
CdTe
CdTe
HgCdTe
HgCdTe
SiO
SiO
CdZnTe
CdTe
HgCdTe
Ge
Ge
Λ WDBR
(HL)kH
df
db
tc ta
tCdTe
tHgCdTe
tGe
tSiOtg
HgCdTe
tGe
Ge Air
(a) (b)
DBR
(HL)mH
tc
Fig. 1 RCE HgCdTe-absorber structures with: a (HL)kH DBR and b grating front mirror; the back mirror inboth is a (HL)mH DBR; the irradiation is from a CdZnTe substrate
Table 1 The refractive indexes N = n + ik used in the simulations
Wavelengths (µm) Ge SiO CdTe Hg0.71Cd0.29Te Hg0.56Cd0.44Te CdZnTe
(see in Fig. 1a). The HgCdTe/CdTe bilayers provide good lattice matching but the smalldifference in RIs of Hg0.56Cd0.44Te and CdTe requires m = 30, i.e. ∼ 20 µm thick DBRmirror, in order to achieve the desired reflectivity (Wehner et al. 2005b). Apart from enlarg-ing the cavity, the deposition of such a thick multilayer inevitably produces growth defectswhich deteriorate the reflectance. In practice, such DBRs have been fabricated with m = 10(Kaniewski et al. 2007) and m = 7 (Wehner et al. 2005b) and optimized with m = 8 forhigh temperature-operation RCE PDs (Sioma and Piotrowski 2004) (Table 1). We adopted amid value of m = 15, while due to Wehner et al. (2005a,b, 2006) k = 2, ta = 75 nm. Fora standard placement of the absorbing layer in the middle of the cavity (df = db), combin-ing semianalytical calculation and manual optimization, we found the optimal cavity lengthfor which A = 81.9% at λ0 = 4.415 µm (RCE-S structure in Table 2). The automatic
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Table 2 The designed and simulated RCE HgCdTe-absorber structures
The dimensional parameters and λR are in microns. Lowercase a and b refers to a wavelengths of 4.415 and4.500 µm respectively
4.25 4.3 4.35 4.4 4.45 4.5 4.55 4.60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wa velength λ [µm]
Refl
ecta
nce
,R
&A
bsor
banc
e,A
[abs
.u.
]
R a
A a
R b
A b
Fig. 2 The spectra of reflectance from the front DBR mirrors and of absorbance for the RCE-Oa and RCE-Obstructures
optimization results in the same tc as obtained manually. Further optimization, allowing fordf �= db, yields RCE-Oa and RCE-Ob structures with λ0 = 4.415 and λ0 = 4.500 µm,respectively (see in Fig. 2; Table 2). Figure 2 shows the A spectra of the designed structuresalong with the reflectance (R) from the stand-alone front DBR mirror.
4 Grating mirror based RCE PD structures
Figure 1b presents a modified RCE HgCdTe-PD, in which the front mirror is replaced by aone-dimensional (1-D) dielectric grating with period �, groove width W and depth tg, whilethe absorber, back mirror and irradiation scheme remain the same as those of the structure inSect. 3. The grating is designed as the stand-alone ∼ 100 % reflectivity mirror. Our design ofthe RCE absorber as a whole is done for the backside irradiation from CdZnTe substrate and
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New RCE absorber structures 99
is not suitable for the front irradiation from air (see Fig. 1), since the grating mirror breaksdown the irradiation symmetry inherent to the DBR based FP cavities.
Earlier work (Hava and Auslender 1995) and a recent paper (Mateus et al. 2004) on designinggrating mirrors have considered optical incidence from air, but here, However, the stand-alonegrating mirror is irradiated from CdTe. To get rid of the grating reflection orders, we imposedover all the computed wavelength range the subwavelength grating restriction nCdTe� < λ,which is tighter than for the incidence from air. Because of polarization sensitivity of the 1-Dgratings, we first maximized the R for the incidence from CdTe half-space, separately forthe TE and TM polarization.
Other trial dimensions were estimated semianalytically using the ϕf and ϕb as computednumerically for the stand-alone grating and DBR, respectively, and then refined by the optimi-zation. The manual design was performed under the constraints: df = db, w = W/� = 0.5and ta = 0.075 µm, by controlling the tc which allowed us to attain the desired δ0. To remind,the optimization goal is to achieve maximal polarized A(λ0), minimal changes of which dueto variations in the grating fabrication process are being very desirable. A fully computer-aided optimization procedure easily allows for designing the structures with df �= db andw �= 0.5. The results of such an optimization are the structures RCE-TEa and RCE-TMa
(λ0 = 4.415 µm), RCE-TEb and RCE-TMb (λ0 = 4.500 µm) for operation with a TE andTM polarized radiation (see Table 2).
The TE and TM polarized R spectra from the stand-alone grating mirrors and the relatedA spectra of the RCE-TEa and RCE-TEb structures are shown in Figs. 3 and 4, respectively.The designed gratings maintain the polarized R ≥ 99% in a wide band around λ0. For theTM polarization, as seen in Fig. 4, the high-R band width greatly exceeds 0.3 µm, in a goodagreement with the paper (Mateus et al. 2004). For the TE polarization, however, this bandis narrower which does not prevent from achieving the A ≈ 100% peak (see Fig. 3) and asuperior tolerance to a variation in the grating fabrication process, as discussed in Sect. 4.2below.
4.2 Design tolerances
An important issue for the practicality of the proposed RCE HgCdTe-PDs is the sensitivityto variations in the grating fabrication process. In this paper, we report the tolerance of thevalue and position of the A peak to the grating groove duty cycle w variations. The tolerancewas found to be very good for the structures with the optimal w �= 0.5, especially in theTE case. For example, the RCE-TEa structure still maintains high values of A(λ0) = 93.8%and 98.8% with the initially prescribed λ0 and w = 0.528 and w = 0.728, respectively. Thesmall drop in A(λ0), should not be treated as a deterioration of the detection performancesince the peak A = 99% appears to be shifted by at most 3 nm from the λ0, which indicatesan excellent tolerance including a small change of the peak value and a minute shift of thepeak position. The RCE-TEb structure exhibits similar tolerance properties.
The RCE-TMa,b structures withstand errors in w of ±0.05 as related to peak A, whichindicates a lower but still practical tolerance. However, the peak wavelength shift provesnotably larger as compared to RCE-TEa,b structures. For example, as w is shifted to 0.287the RCE-TMa structure exhibits a 24 nm red shift of the absorption peak and a drop of thepeak A to 97.5%. In this case, we found numerically that the peak wavelength, within areasonable range, depends on w linearly, as shown in Fig. 5.
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4.25 4.3 4.35 4.4 4.45 4.5 4.55 4.60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength λ [µm]
Refl
ecta
nce
,R
&A
bsor
banc
e,A
[abs
. u.]
R a
A a
R b
A b
Fig. 3 The spectra of reflectance from the front grating mirrors and of absorbance for the RCE-TEa andRCE-TEb structures
4.25 4.3 4.35 4.4 4.45 4.5 4.55 4.60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Wavelength λ [µm]
Refl
ecta
nce
,R
&A
bsor
banc
e,A
[abs
.u.
]
R a
A a
R b
A b
Fig. 4 The reflectance from the stand-alone grating mirrors and the absorbance of the RCE-TMa and RCE-TMb structures
5 Conclusion
The RCE HgCdTe-PDs, including new ones in which the front mirror is a ∼ 100% reflectancegrating, for applications in MWIR range, were designed and simulated using semianalyticand computer-aided tools such as a scrutinized control of the resonant round-trip phase δ0,and the grating reflection amplitude and phase. The results show that the δ0 control is crucial
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New RCE absorber structures 101
Fig. 5 The peak absorbance and wavelength versus w for the RCE-TMb structure
for optimizing the efficiency, as was known for the conventional RCE PDs (Ünlü and Strite1995; Wehner et al. 2005a,b, 2006). In our case, na and nc differ significantly, but the reflec-tions from the absorbing layer have a relatively small effect due to ta � tc. We also provedthat a non-standard placement of the absorbing layer is capable of increasing the efficiencyof the conventional RCE HgCdTe-PDs, which still remains below 85.2%.
It was decisively shown that for a linearly polarized light, the grating mirror based RCEHgCdTe-PDs can be designed to achieve ∼ 100% efficiency, thus highly outperforming theconventional RCE HgCdTe-PDs, and simultaneously is highly tolerant to variations in thegrating groove duty cycle w. For the TM designs, a linear dependence was found betweenthe w varied around its optimal value and the peak wavelength shifting, in a response, aroundthe prescribed λ0.
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