THE SPICE MODEL
The model described here is intended only for low frequency,
quasi-dc applications. The model does not include temperature
effects that can lead to changes in the VCSEL output over
time. The thermal relaxation time constant for the VCSEL and
submount is on the order of 10ยตs, and, depending on current,
application and assembly, may lead to slight output power
variations during the first millisecond of operation. The optical
rise and fall time of the VCSEL is much less than 10ns, and this
model is appropriate for signals having time bandwidth less
than 200MHz. Typical packaging used for VCSELs, including
TO type headers, surface mount products, and most leadframes
have intrinsic bandwidth greater than one gigahertz. For a
detailed description of the VCSEL and package high frequency
characteristics, the reader is referred to the application note
titled Modulating VCSELs.
Figure 1 is a schematic of the circuit used to describe the low
frequency characteristics of VCSELs. There are two input
nodes, Anode and Cathode, and two output nodes, OP and
ON. The low frequency electrical properties of the VCSEL are
modeled as a temperature dependent resistor in series with a
temperature dependent voltage source. The optical output of
the VCSEL is modeled as a current dependent current source.
The light output is defined as the current flowing from ON
to OP (1mA=1mW). The VCSEL threshold current and slope
efficiency are included in the model through the transfer
function of the current dependent current source.
The adjustable parameters in the model are the series resistance,
threshold current and slope efficiency. The bandgap voltage
variation is hard coded into the model. The equations that
govern the electrical and optical properties of the VCSEL are
given below.
In the above equations the series resistance (RS) and slope
efficiency (SE) are assumed to be linear; RSO is the room
temperature series resistance, RST is the temperature
coefficient of S, SE0 is the room temperature slope efficiency,
and SET is the temperature coefficient of SE. The threshold
current is parabolic with temperature, reaching a minimum
value of I0 at the temperature T0. For purposes of simulation,
the minimum, typical, and maximum values of each of the six
adjustable parameters are summarized in table one. Refer to
data sheets for actual limits.
Figure 1. Schematic of the circuit used to describe the electrical properties of a VCSEL