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