Electromagnetic Modeling of the Propagation Characteristics of Satellite Communications Through Composite Precipitation Layers


Science and Technology, 7 (2002) 101-107 
© 2002 Sultan Qaboos University 
 

101 

Design of Ultra Fast RCE Photodetectors for 
Optical Communications systems  

Joseph A. Jervase and Hadj Bourdoucen  

Department of Information Engineering, College of Engineering, Sultan Qaboos 
University, P.O. Box 33, Al Khod 123, Muscat, Sultanate of Oman.  
Email: Jervase@squ.edu.om.  

 تصميم المحسسات الضوئية لنظم االتصاالت فائقة السرعة 

 جوزيف جرفيس وحاج بوردوسن

يتمثل . التى تتحكم في نظم االتصاالت فائقة السرعة(RCE) تتناول هذه الورقة الحدان األساسيان للمحسسات الضوئية : خالصة 
م إيجاد شكل تحليلي لكفاءة الكم تتضمن الحدود الهيكلية         هـذان الحـدان في كفاءة الكم وسعة التذبذب للمحسنات المستعملة ، لقد ت             

 .واعتمادا على النتائج التمثيلية بواسطة الحاسوب،  طورت خطة للتصميم المثالي لهذه المحسسات. لتصميم المحسس الضوئي
 
ABSTRACT:  Two key parameters for RCE photodetectors that govern their suitability for ultrafast 
optical communication systems are considered. These are the quantum efficiency and the bandwidth 
efficiency product. A closed analytical form has been derived for quantum efficiency, which 
incorporates the structural parameters of the photodetector. Based on the simulation results, an 
optimization and design procedure for these photodetectors has been developed. 
 
KEYWORDS: Cavity Resonators, Photodetectors, Photodiodes, Quantum Efficiency and Resonant-
Cavity-Enhanced Photodetectors. 
 

1. Introduction  

ptical photodetectors are the key components in optical communication systems. Their 
quantum efficiency and optical bandwidth characteristics are of major importance in the 

design of fiber optic based data communication systems. A number of structures and design 
optimization techniques have been proposed in the literature to achieve high values for these 
two parameters (Kishino, 1991), (Unlu, 1992, 1995, 1998), (Tan, 1995), (Murtaza 1996), 
(Tung, 1997), (Jervase,  1998, 2000). One of the promising types is the Resonant Cavity 
Enhanced (RCE) photodetector. In the RCE, the active region is placed inside a Fabry-Perot 
cavity between two mirrors made of quarter-wave stacks (QWS) to allow the signal light to 
have more than one absorbing path inside the active region (Kishino, 1991), (Unlu, 1992, 
1995, 1998), (Tan, 1995), (Murtaza, 1996), (Tung, 1997), (Jervase, 1998, 2000), (Onat, 1998), 
(Ozbay, 1997). The resulting structure will need only a very thin absorbing intrinsic region to 
achieve high quantum efficiency as well as a high speed of response. Hence, RCE photodiodes 
with quantum efficiencies close to unity can be designed. 

In this work, the quantum efficiency is formulated in a closed analytical form. This 
includes the structural parameters of the photodetector and takes into consideration the 
wavelength dependence of the end mirrors reflectivities and the absorption coefficient of the 
intrinsic region. Using this formulation, an optimization and design procedure for RCE 
photodetectors has been developed and design charts have been generated with the quantum 
efficiency, quality factor and frequency bandwidth as input design parameters. 

O

mailto:Jervase@squ.edu.om


 JOSEPH A. JERVASE and HADJ BOURDOUCEN 
 

 102

2.   Analysis 

Figure 1 shows the integrated device of our investigation, which is based on the system of 
heterojunctions In0.53Ga0.47As/InP. The speed response for this type of PIN structure is mainly 
limited by the transit time and the diffusion time of photogenerated carriers in the space 
charge region and the neutral regions. It is also limited by the charging and discharging time 
for traps at the heterojunction interfaces and by the inherent and parasitic capacitances of the 
structure. The last two effects can be minimized by incorporating non-absorbing lateral layers 
having graded heterojunctions with the active region and to have the heterojunctions and the 
active region depleted of any trapped charges that might be stored. In addition, the 
introduction of super lattice bandgap grading layers can eliminate the interface hole trapping 
process and consequently decrease the capacitive effect on the generated carriers. To further 
improve the frequency bandwidth requirements, the active region should be shortened enough 
to minimize the transit time of the photogenerated carriers crossing it. To reduce the device 
dark current, several types of junction architectures have been proposed based on the 
enhancement of the barrier heights at the interfaces of the InGaAs active layer and the 
adjacent layers to decrease tunneling currents of minority carriers. PIN photodetectors based 
on InGaAs/InP have been analyzed by many researchers e.g. (Bottcher, 1992) and the 
references therein). In fact, the typical PIN photodiode configuration (Dentan, 1990) has been 
integrated in our proposed configuration for its simplicity and ease of fabrication as well as its 
realistic mathematical description.  
 

Si (λo/4)
SiO

2
(λo/4)

P+

InP

N-

InGaAs

N+

M

GaAs (λo/4)
AlAs ( λo/4)

GaAs (substrate)

L
1

d

L
2

x

0
Top QWS

Bottom
QWS

Refractive
index

notation

n
10

n
11

n
12

n
ex

(n
1s

)

n

n
ex

(n
20

)

n
21

n
22

n
2s

Incident Light

SiO
2

(λo /2)

AlAs (λo/4)
GaAs (λo /4)

N

InP

P+

 
 

Figure 1. The RCE photodetector model. 
 

The expression for quantum efficiency for the RCE photodetector shown in Figure 1 will 
be derived following a similar approach to that used in (Kishino, 1991) and (Jervase, 1998). 
This technique is based on finding the reflectivities of the top and bottom mirrors separately 



DESIGN OF ULTR FAST RCE PHOTODETECTORS 
 

 103

and then using their values to determine the fields inside the cavity by considering the whole 
structure of the photodetector i.e. mirrors and cavity together. 
With reference to the device model shown in Figure 1 for the RCE photodetector, the quantum 
efficiency due to the power absorbed in the i-region may be expressed as follows, 
 

( )( )( )
φ

η α
αα

coseRR1
e1eR1R1

d2
21

dd
21

−

−−

+
−+−

=                                                (1) 

where,   
[ ]{ }2121ex d)LL(2 ψψββφ ++++=                                      (2) 

λ
π

β exex
n2

=                                                          (3) 

λ
π

β
n2

=                                                        (4)  

 
In the derivation of Eq. 1, the p- and n-regions are assumed to be transparent at the design 

resonant wavelength λ0=1.3µm.Thus αex=0 for the material adopted in the model (InP) at this 
wavelength.  

It is apparent from Eq. 1 that the external quantum efficiency depends on the design of 
the top and bottom QWS's (R1, ψ1, R2, ψ2), the choice of the materials for the cavity (α, n, nex) 
and its physical dimensions (d, L1, L2) as well as the operating wavelength (λ). Within the 
range of interest in this analysis (1.2µm < λ <1.5µm), there is no much variation in refractive 
indices of the different layers of the photodetector. This does not apply, however, to the i-
region attenuation constant α. It has been shown in the literature that the absorption 
coefficient α of In0.53Ga0.47As is a function of wavelength and doping (Humphreys, 1985). 
Using the experimental results in (Humphreys, 1985), a nonlinear curve fitting technique has 
been used to obtain analytical expressions for α. 
With reference to Eq. 1, the maximum quantum efficiency occurs when 

[ ] πλψλψλβλβ 2)()(d)()LL)((2 2121ex =++++ , or multiples thereof. It then follows that (Kishino, 
1991), (Jervase,  1998), 

                         ( )( )( )
d2

21

dd
21

peak eRR1
e1eR1R1

α

αα

η
−

−−

+
−+−

=                                              (5)  

 
This expression is used in a constrained optimization procedure for the design of RCE 

photodetectors with maximum quantum efficiency. Equation 5 serves as a check on the 
optimized values (L1, L2, d) in whether they yield the maximum quantum efficiency. 
The design procedure developed is summarized below: 
Step 1: Specify the resonant wavelength λ0, the quantum efficiency η, the quality factor Q and 
the frequency bandwidth BW.  
Step 2: Select the materials for the cavity and the quarter-wave-stacks (QWS’s).  
Step 3: Design the QWS’s with the following guidelines:  
Choose the number of layers N2 to achieve a reflectivity R2 at λ0 close to unity for the bottom 
QWS. 
Choose the number of layers N1 to achieve a reflectivity 0.6<R1<0.9 at λ0 for the top QW  
Step 4: With the values of R1 and R2 now known, invoke a search and optimization program to 
determine d, L1 and L2.  
Step 5: Generate values for η for a range of wavelengths centered at λ0.  
Step 6: For each set of d, L1 and L2, deduce FWHM and compute the quality factor and the 
frequency bandwidth.  
Step 7: Select the values of d, L1 and L2 that satisfy the design criteria on Q, η and BW.  



 JOSEPH A. JERVASE and HADJ BOURDOUCEN 
 

 104

3.  Results 

The resonant wavelength used in this work is λ0=1.3µm. The refractive indices of the 
various layers of the model adopted in the analysis (Figure1), are SiO2(1.46), Si (3.46), InP 
(3.20), InAlGaAs (3.50) and InGaAs (3.73-j0.12). 

Following the design procedure outlined earlier, 42 pairs of layers were needed to 
achieve a reflectivity of 0.998 at λ0. For the top QWS, only one pair of layers is needed. This 
yields a reflectivity of 0.8. The resonance condition to achieve maximum quantum efficiency 

[ ] πλψλψλβλβ 2)()(d)()LL)((2 2121ex =++++  may thus be expressed for the adopted structure as 
 

  )2/()( 021 λMndLLnex =++                                            (5)  
where, M=1,2,3,... 
  

 

1.2 1.25 1.3 1.35 1.4 1.45 1.5
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wavelength λ (µm)  
 

Figure 2. Variation of external quantum efficiency η with wavelenghth λ.  
 
Figure 2 shows the variation of external quantum efficiency with wavelength using a set 

of generated values (d=0.1µm, L1=L2=1.465µm) in Eq.1. This Figure shows a dominant peak 
centered at λ0=1.3µm, the design wavelength. This result is physically more realistic since the 
proposed structure is acting as a resonant cavity filtering out all wavelengths other than λ0.  

The theoretical result is also in very good agreement with recently published 
experimental data on high-speed RCE Schottky photodiodes (Jervase, 2000), (Unlu, 1998), 
(Onat, 1998) and high-speed Si-based RCE photodetectors (Ozbay, 1997). With reference to 
Figure 2, the use of the free spectral range (FSR) to the wavelength full width at half 
maximum (FWHM) as a measure of wavelength selectivity of detection (Kishino, 1991) is no 
longer valid. The conventional quality factor definition used for filters design defined as the 
ratio of λ0 to the FWHM is more appropriate in this case as a measure of selectivity (Jervase, 
2000). 

It has been noticed that ignoring the variation of the attenuation constant α with λ results 
in a higher off-resonance peak for λ> λ0 and lower off-resonance peak for λ0.This is due to the 
fact that α monotonically decreases with λ.  

Following a design and optimization procedure, all the sets of values obtained previously 
for d, L1 and L2 were used to obtain the quality factor Q corresponding to every spectrum of 
quantum efficiency η. The objective is to obtain design charts relating the quality factor Q to 
the maximum achievable quantum efficiency ηmax for a given structure dimensions. The 





 JOSEPH A. JERVASE and HADJ BOURDOUCEN 
 

 106

varied, quantum efficiency increases, peaks at d=0.1µm and then decreases. Thus, there is an 
optimum value for d, which achieves maximum quantum efficiency.  The BW and BWE on 
the other hand, decrease with increasing d. Thus, for d=0.1µm, which corresponds to 
maximum quantum efficiency of 0.99 the BWE is 290GHz. It is worth pointing out here that 
the simulated values for BWE merely serve as upper limits for the bandwidth-efficiency 
product. In practice, other parasitic factors, such as the leakage RC, will lower the achievable 
values. 
 

d (µ m)  
 

Figure 4. Variation of efficiency η and bandwidth-efficiency product BWE with active region 
width d. 

4.  Conclusion 

The quantum efficiency and bandwidth-efficiency product of resonant-cavity enhanced 
photodetectors (RCE) has been formulated in closed analytical forms that incorporate device 
structural parameters. A search and optimization-based procedure has been developed with the 
quantum efficiency, quality factor and frequency bandwidth as input design parameters. Design 
charts relating the quality factor Q to the maximum achievable quantum efficiency ηmax for a given 
structure dimensions have also been generated.      

References 

BOTTCHER, E.H., KUHL, D., HIERONYMI, F., DROGE, E., WOLF, T. and BIMBERG, D. 
1992. Ultrafast semi-insulating InP:Fe-InGaAs:Fe-InP:Fe MSM photodetectors: Modeling and 
Performance, IEEE J. Quantum Electron., 28: 2343-2357. 

DENTAN, M. and CREMOUX, D.DE. 1990. Numerical solution of the nonlinear response of a p-
i-n photodiode under high illumination, J. Lightwave Technol., 8: 1137-1144. 

HUMPHREYS, D.A., KING, R.J., JENKINS, D., and MOSELEY, A.J. 1985. Measurement of 
absorption coefficients of Ga0.47In0.53As over the wavelength range 1.0-1.7µm, Electron. Lett., 
21: 1187-1189. 

JERVASE, J.A. and BOURDOUCEN, H. 2000. Design of resonant-cavity-enhanced 
photodetectors using genetic algorithms, IEEE J. Quantum Electron., 36: 325-332. 

JERVASE, J.A. and ZEBDA, Y. 1998. Characteristic analysis of resonant cavity enhanced (RCE) 
photodetectors, IEEE J. Quantum Electron., 34: 1129-1134. 



DESIGN OF ULTR FAST RCE PHOTODETECTORS 
 

 107

KATO, K. 1999. Ultrawide-Band/High-Frequency Photodetectors'', IEEE Trans. Microwave 
Theory Tech., 47: 1265-1281. 

KISHINO, K., SELIM, M.U., CHYI, REED, J.I., ARSENAULT, L., and MORKOC, H. 1991. 
Resonant cavity-enhanced (RCE) photodetectors'', IEEE J. Quantum Electron., 27: 2025-
2034. 

KOVAC, J., UHEREK, F., SATKA, A., JAKABOVIC, J., SRNANEK, R., RHEINLANDER, B., 
GOTTSCHALCH, V., HASENOHRL, S., NOVAK, J., BARNA, P., BARNA, A. and 
WOOD, J. 1996. InAlGaAs-InGaAs-InP RCE pin photodiode for 1300nm wavelength region, 
IPRM'96 Proc., Apr. 21-25, Germany, pp 219-222. 

MURTAZA, S.S., NIE, H., CAMPELL, J.C., BEAN, J.C. and PETICOLAS, L.J. 1996. Short-
wavelength, high-speed Si-based resonant-cavity photodetectors, IEEE Photon. Technol. Lett., 
8: 927-929. 

MURTAZA, S.S., TAN, I.-H., BOWERS, J.E., HU, E.L., ANSELM, K.A., ISLAM, M.R., 
CHELAKARA, R.V., DUPUIS, R.D., STREETMAN, B.G., and CAMPBELL, J.C. 1996, 
High-finesse resonant-cavity photodetectors with an adjustable resonance frequency, IEEE J. 
Lightwave Technol., 14: 1081-1089. 

ONAT, B.M., GOKKAVAS, OZBAY, M., E., ATA, E.P., TOWE, E., and UNLU, M.S. 1998. 100-
GHz resonant cavity enhanced Schottky photodiodes'', IEEE Photon. Technol. Lett., 10: 707-
709. 

OZBAY, E., SAIFUL ISLAM, M., ONAT, B., GOKKAVAS, AYTUR, M.O., TUTTLE, G., 
TOWE, E., HENDERSON, R.H., and UNLU, M.S. 1997. Fabrication of high-speed resonant-
cavity-enhanced Schottky photodiodes, IEEE Photon. Technol. Lett., 9: 672-674. 

SALEM, A.F. and BRENNAN, K.F. 1995. Theoretical study of the response of InGaAs metal-
semiconductor-metal photodetectors, IEEE J. Quantum Electron., 31: 944-953. 

TAN, I-H., HU, E.L., BOWERS, J.E., and MILLER, B.I. 1995. Modeling and performance of 
wafer-fused resonant-cavity enhanced photodetectors, IEEE J. Quantum Electron., 31: 1863-
1875. 

TUNG, H.-H. and LEE, C.-P. 1997. Design of a resonant-cavity-enhanced photodetector for high-
speed applications, IEEE J. Quantum Electron, 33: 753-760. 

UNLU, M.S. and STRITE, S. 1995. Resonant cavity enhanced photonic devices, J. Appl. Phys., 78: 
607-639. 

UNLU, M.S., GOKKAVAS, M., ONAT, B.M., ATA, E., OZBAY, E., MIRIN, R.P., KNOPP, K.J., 
BERTNESS, K.A., and CHRISTENSEN, D.H. 1998. High bandwidth-efficiency resonant 
cavity enhanced Schottky photodiodes for 800-850 nm wavelength operation, J. Appl. Lett., 
72: 2727-2729. 

UNLU, M.S., KISHINO, K., LIAW, H.J., and MORKOC, H. 1992. A theoretical study of cavity-
enhanced photodetectors with Ge and Si active regions, J. Appl. Phys., 71: 4049-4058. 

 
 
Received 23 June 2001 
Accepted 6 November 2001  


	Joseph A. Jervase and Hadj Bourdoucen
	Analysis
	Results
	References