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References 1 FUKUCHI, K., KASAMATSU, T., MORIE, M., OHHIRA, R., ITO, T., SEKIYA, K., ONO, T.: ‘10.92-Tb/s (273 x40-Gb/s) triple- OGASAHARA, D., and band/ultra-dense WDM optical-repeatered transmission experiment’. Optical Fiber Communication Conf. (OFC200l), Anaheim, CA, USA, March 200 I , PD24 2 OKOSHI, T., and KIKUCHI, K.: ‘Frequency stabilisation of semiconductor lasers for heterodyne-type optical communication systems’, Electron. Lett., 1980, 16, ( 5 ) , pp. 179-181 level 3 model for depletion capacitance [3]. An approximate small signal equivalent circuit was constructed for the 3 pm overlap GMAP since it had the lowest capacitance and therefore the highest bandwidth potential. The photodiode capacitance was calculated as 216.71 fF from the geometry of the device while the resistances were calculated from the geometry and the doping profiles for the photodiode. The wirebond inductance was estimated using (1) [4]: (1) 120 Small signal equivalent circuit for Geiger-mode avalanche photodiodes A.M. Moloney, A.P. Morrison, J.C. Jackson, A. Mathewson and P.J. Murphy The first small signal equivalent circuit for a Geiger-mode avalanche photodiode (GMAP) is presented. The equivalent circuit is derived from a 20 gm-diameter GMAP with 3 pm virtual guard ring overlap; the photodetector has peak responsivity at 600 nm and a calculated electrical bandwidth of 5.97 GHz. Introduction: One challenging aspect of fabricating a monolithic silicon photoreceiver is the integration of a high-speed, highsensitivity photodetector and an amplifier without adding complexity to the transistor process. The Geiger-mode avalanche photodiodes (GMAPs) reported in this Letter are compatible with a standard silicon on insulator (SOI) CMOS process, have high responsivity (0.04 A/Wat 5 V reverse bias, 0.4 A/W at 27 V reverse bias), high gain (10 at 27 V, 100 at 27.25 Vand in excess of 1000 at 27.5 V reverse bias) and low dark current ( 5 pA at 5 V reverse bias, 33 pA at 27.5 V reverse bias corresponding to 7 fA/pm2 and 47 fA/pm2, respectively). The s-parameters for a 20 pm-diameter GMAP with a 3 pm junction overlap (see Fig. 1) were used to develop a small signal equivalent circuit, from which a theoretical bandwidth of 5.97 GHz for the photodetector was calculated. These combined features suggest GMAPs as suitable candidates for use in gigabit-rate photoreceivers offering high sensitivity, monolithic integration, low cost, and high reliability. cathode Pig. 2 S,* parameters for IO, 5, 4 and 3 pm overlap GMAPs LB = 4.97nH port 1 RJ = 0.0380 anode CF02 = 5.41pF I/ I ”+ P I p+I I CJ = 550.98fF RB = 754Q I I P-epi I P+ substrate I Fig. 1 Virtual guard ring GMAP structure showing active area and overlap regions GMAP ,fabrication: The GMAPs, junction active areas and different cated. Details of the fabrication of previously [l]. The anode doping ( < 30 V) breakdown voltage. shown in Fig. 1, with 20 pm overlap dimensions were fabrithe GMAPs have been reported was tailored to provide a low Measurements and results: The photodiodes when fabricated were diced and mounted on FR4 1.6 mm PCB board for testing. The anodes were grounded while the cathodes were terminated with 2.92 mm-width 50 Q transmission lines. The microwave scattering parameter S I 1 for each photodiode reverse biased at 5 V (using the internal bias tees of the network analyser) was measured using a HP8753E network analyser (see Fig. 2). At 5 V reverse bias the multiplication gain is approximately independent of frequency since Mo < E/D (Mo= DC gain, E = electron ionisation coefficient and p =hole ionisation coefficient), and the RC time constant and transit-time determine the ultimate bandwidth achievable [2]. The GMAP capacitances were calculated using the SPICE ELECTRONICS LETTERS 14th March 2002 CFOl = 5.59pF Fig. 3 Small signal equivalent circuit for 3 pm overlap GMAP LB: wirebond inductance RJ: junction resistance CJ: junction capacitance CFO: field oxide capacitance RB: bulk resistance where L = inductance, 1=wire length (cm), p =wire radius (cm). This initial circuit model and the S I I parameters for the frequency range 40 MHz to 2 GHz were used as input for optimisation in commercial microwave simulation software to obtain the small signal equivalent circuit shown in Fig. 3. The measured and simulated SI1plots have an excellent fit (see Fig. 4) even though the calculated junction capacitance of the GMAP is almost twice that expected (the other two capacitances are due to the field oxide at the anode (Cfo,) and field oxide at the cathode (&) of the diode). The overall diode capacitance is taken to be 2.885 pF while the series resistance is 7.54 a, neglecting the junction resistance. The following expression (2) for photodiode bandwidth [ 5 ] was used to calculate the theoretical bandwidth of Vol. 38 No. 6 285 Availability of systems based on satellites with spatial diversity and HAPS 5.97 GHz for a GMAP with a 3 pm junction overlap. M.A. Vizquez-Castro, D. Belay-Zelek and A. Curieses-Guerrero A new simple analytical procedure to calculate availability of systems based either on satellites or a high altitude platform station (HAPS) is introduced. The method is based on the statistical comparison of the angles involved in the links, elevationsprovided by the system and the masking angles of the surrounding skyline. -maanitude (modelled) magnitude (measured) C 4 -50 100- -ai c .- m r 0) E $ 10-1- m a, 0, -0 -0 ._ c ';p 10-20 E U 2 .- c -angle (modelled) 0 a --50 3 angle (measured) B Introduction: Satellites and high altitude platform stations (HAPS) are the platforms appointed by WRC-2000 to access to the S-UMTS/IMT-2000 core network. The proposed air interface is code division multiple access (CDMA) which has inherent capabilities to counteract channel impairments such as shadowing of suburban and urban environments enabling spatial diversity to preserve the communication against heavy shadowing or blockage. For a system based on a satellite or HAPS, we refer to system availability as the average percentage of time the service delivering is not affected by service outage (mostly owing to the shadowing/blockage). In this Letter we introduce sub-models that yield a methodology to compute global availability for systems based both on HAPS and satellites.Physicalparameters: Analytical expressions for the distributions of physical parameters of suburban and urban environments are given in [l]. Mean ( p ) and standard deviation (u) of the heights of buildings/ structures are summarised in Table 1. It can be observed that building heights were found to follow well-known (truncated) statistical distributions and that urban and suburban environments are divided into two classes, class 1 corresponding to a lower height than class 2. Table 1: Building height distributions I Urban-2 Normal 21.5 Suburban-1 Log-normal 0.25 Suburban-2 I Normal I 13.0 1 4.0 I Channel model: For diversity modelling and availability analysis purposes we assume an on/off or LOS/NLOS channel, i.e. a satellite or HAPS link is available when there are line of sight (LOS) conditions and it is unavailable otherwise. This channel model is therefore only characterised by the geometry of the ground-terminal environment as those given in Table 1. Essentially, the use of geometry instead of electromagnetic formulations implies we disregard diffraction, which in satellite or HAPS-based systems and at high frequencies is correct to assume due to the lower margins compared to terrestrial systems. References 1 2 3 4 5 6 JACKSON, J.C., MORRISON, A T , HURLEY, P.K., . HARRELL, W.R., DAMJANOVIC, D., LANE, B., and MATHEWSON, A.: 'Process monitoring and defect characterization of single photon avalanche diodes'. Int. Conf. on Microelectronic Test Structures (ICMTS 2001), Kobe, Japan, March 2001, Vol. 14, pp. 165-170 EMMONS, R.B.: 'Avalanche photodiode frequency response', 1 Appl. Phys., 1967,38, (9), pp. 3705-3714 Avant Star-HSPICE manual. www.ece.orst.eddmoonlhspice981,1998 GROVER, F.W.: 'Inductance calculations: working formulas and tables' (Dover Publications Inc., New York, 1962) ALEXANDER, s.B.: 'Optical communication receiver design' (SPIE IEE, 1997) SZE, S.M.: 'Physics of semiconductor devices' (John Wiley and Sons Inc., Canada, 1981) 286 Diversity model: The provision of as many satellites in view as possible will increase the likelihood of having both LOS conditions so that communications can always be feasible. However, generally the number of satellites cannot be too high and actually is less than four for low orbit constellations. With two or three satellites in view at any time service availability in non-open environments can only be improved by using diversity if the signal paths are not correlated. In [ l ] it has been found that, in general, there usually exists a main lobe of positive, decreasing positive cross-correlation values for small azimuth separations, A4, typically A 4 < 45". Availability model: Let us define the masking angle, y , as the angle the ground-terminal sees the surrounding buildings and let 0 be the elevation provided by the system (Fig. 1). Availability can be computed as the probability of the system elevation to be above the masking angle: P ( ( 0 / A 4> 45") > y) for satellite and P(Q> y) for HAPS, where P means probability, y masking angle and 8 elevation provided by the system which is conditioned to A d > 4 5 " to assure uncorrelated paths. Masking angle and system elevation are independent random variables and therefore availability can be expressed by ELECTRONICS LETTERS 14th March 2002 Vol. 38 No. 6