Hints, Tips and Solutions

 

Volume 12, Number 8, August 2002

Q. Can ATLAS reproduce basic experiments to study the transient decay of carriers ?

A. Yes, ATLAS may be used to study these effects. A standard experiment for studying recombination in silicon is the transient decay of photoexcited carriers - known as the Stephenson-Keyes method for measuring minority carrier lifetime [1]. This method has been well described in [2]. The following is a description of the implementation of this experiment using the 2D device simulator ATLAS.

In the original experiment a constant current is passed through a n-type sample and a series of light pulses are shone onto the surface. The photogeneration causes a momemtary increase in the conductivity which is observed as a voltage drop across the sample. This can be seen on an oscilloscope and used as a measure for lifetime. In this simulation a simpler method is possible. Under zero bias conditions a transient can be performed where the illumination is initially at 1 W/cm-2. At a given time the illumination is suddenly turned off and the transient is continued out to a large time value, 1 ms.

Two observations should be apparent; first the minority carrier density under illumination should be

hole density = taup * Gphoto

where Gphoto is the photogeneration rate due to the light source and taup is the minority (hole) carrier lifetime.

Second, when the light is switched off the minority carrier density should begin to fall off at a time equal to the carrier lifetime. It should decrease by a factor 1/e at that point. The simulated minority carrier density at a point in the structure can be saved during the transient analysis using the PROBE statement of ATLAS. This makes it straightforward to extract the carrier lifetimes.

Device Creation

An n-type silicon sample is created, using ATLAS/Spisces, with a heavy doping of 1e20 cm-3 n-type. The heavy doping concentration is there to ensure that the device operates only under low injection conditions ie the excess minority carrier concentration, created by photogeneration, is much less than the majority carrier density. This is in accordance with the original experimental proposal. The device structure is also made to be very tall, 1000 um, so that any effects due to recombination at the contacts or on the surface do not interfere with the measurement of the bulk lifetime.

The silicon sample is defined to be sufficiently thin, 0.1 um in this case, so as to operate similiar to a one-dimensional device. As a result the photogeneration rate is not susceptible to spatial decay and the photogeneration rate is then uniform across the sample.

Physical Models

Two fundamental models may be used to simulate carrier recombination statistics in silicon. The first is the standard Shockley-Read-Hall recombination model where the simulation is defined with constant electron and hole recombination lifetime values. The second is to simulate the presence of mid-gap states explicitly as either donor or acceptor states.

Fermi statistics have been used in this analysis to remove any effects due to the high doping concentrations used.

Finally, the carrier mobilities were made artificially low, again to ensure that no contact effects are present.

 

Simulation Results

The first simulation has invoked the standard Shockley-Read-Hall statistics for carrier recombination. Four transient simulations were performed using fixed carrier lifetimes of 1e-6, 1e-7, 1e-8 and 1e-9 sec. Figure 1 shows the results of the phototransient on the minority (hole) density for these lifetimes. The light source is on until 1e-9 sec where it is turned off.

Figure 1. Transient simulation of hole current density for varying
fixed carrier lifetimes. The Shockley-Read-Hall model was used
for carrier recombination. The light intensity was 1 W/cm
2
and switched off at time t=1e-9 sec.

 

When the light beam is on there should be constant photogeneration through the structure and hence a constant hole density. Figure 2 shows the photogeneration rate in the structure for the case of a 1e-9 s carrier lifetime. Apart from directly underneath the contacts, a uniform photogeneration rate of approx 4e21 /scm3 is observed. The hole density should therefore be 4e21 * 1e-9 = 4e12 cm-3 which is as shown in Figure 1.

Figure 2. Two-dimensional structure under analysis.
The light beam is switched on and photogeneration
is plotted on the structure.

 

To extract the lifetime from these plots is most easily done on a linear - linear scale and by extrapolating the minimum slope of the hole concentration to find the x-intercept on the time axis. This was performed using an EXTRACT statement with the results as shown below for a lifetime of 1e-9 sec.

EXTRACT> extract name="Calc. Lifetime(1e-9)= "
(xintercept(minslope(curve(abs(time),abs(probe.
"h+ conc. (per cc)")))) - $"StartTime")
Calc. Lifetime(1e-9) = 1.05045e-09

The extracted lifetime (1.05045e-09 s) compared well with the simulated lifetime (1e-9 s).

Clearly the experimental extraction technique for minority carrier lifetime has been proved correct by the simulation.

The above simulation has been repeated with mid-gap states specified in the simulation. Figure 3 shows results for a donor-like trap situated 0.504 eV above the valence band. The lifetime associated with the trap was then varied as before. Figure 4 shows results for an acceptor-like trap situated 0.504 eV below the conduction band. The lifetime associated with the trap was then varied as before.

Figure 3. Transient simulation of hole current density.
A donor-like trap was inserted into the bandgap and the
carrier recombination calculated accordingly. The light intensity
was 1 W/cm
2 and switched off at time t=1e-9 sec.

 

Figure 4. Transient simulation of hole current density.
An acceptor-like trap was inserted into the bandgap and the
carrier recombination calculated accordingly. The light intensity
was 1 W/cm
2 and switched off at time t=1e-9 sec.

 

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References

  1. D.T. Stevenson and R.J. Keyes, "Measurement of Carrier Lifetime in Germanium and Silicon", J. Appl. Phys., 26, 190 (1955).
  2. S.M. Sze, "Physics of Semiconductor Devices", Wiley, 1981, pp. 52-57.