## Voltage dependence of the rise and fall times

The measurement of the rise time and fall time of an LED is shown in Fig. 24.2 (Schubert et al., 1996). As indicated in the figure, the rise and fall times are measured from the 10-90% values of the optical signal. The photocurrent of a p-n junction photodetector is used in the measurement. It must be ensured in the measurement that the rise and fall time of both the pulse generator and the photodiode are much faster than the LED rise and fall time. The measured rise and fall times include the time constant of the pulse generator, the LED, the detector, detector amplifier circuit, and the oscilloscope. However, the time constant of the LED is the longest and hence the dominant time constant. The time constants shown in Fig. 24.2 are upper limits to the true time constants of the LED.

Inspection of Fig. 24.2 reveals that the rise time is much longer than the fall time. The large difference between the rise and the fall times displayed in Fig. 24.2 is not expected based on the theoretical model discussed above.

To gain a better understanding of the difference between the rise time and the fall time, the times have been measured as a function of the diode bias conditions. In the “on” state, the diode is biased with a voltage of 1.4 V. However, a range of voltages can be chosen for the “off” state, since a p-n junction diode does not emit light for voltages even slightly below the turn-on voltage.

 Fig. 24.3. Rise time and fall time as a function of the volt­age swing. The fall time of the diode decreases with increas­ing voltage swing due to sweep-out of carriers out of the active region.

 0 0.5 1.0 1.5 Diode voltage swing V — V _ (V) on off

The experimental results are shown in Fig. 24.3. Whereas the “on” voltage is kept constant at Von = 14 V, the “off’ voltage is varied from 0 to 1.0 V. Inspection of Fig. 24.3 reveals a strong voltage dependence of the fall time. The voltage dependence is caused by carrier sweep-out of the active region. In contrast, the rise time is practically independent of voltage.

24.4 Carrier sweep-out of the active region The voltage dependence of the fall time shown in Fig. 24.3 can be explained by voltage- dependent carrier sweep-out of the active region. Figure 24.4 shows the active region band diagram in the “off’ state for small (a) and large (b) voltage swings. For the case of a small voltage swing, carriers essentially remain in the active region until they recombine. As a result, it will take the spontaneous lifetime for the carriers to recombine and the light intensity to decay.

 Fig. 24.4. Illustration of two mechanisms determining the fall time, (a) Return to zero bias results in carrier sweep-out of the active region. The sweep-out time can be very short, « 1 ns. (b) If the modulating voltage amplitude is smaller, carriers are not swept out of the active region, so that the intensity decay is determined by the spontaneous re­combination lifetime.

The situation is quite different for large voltage swings. At zero bias, the band diagram of the active region is highly sloped due to the built-in electric field of the p-n junction. As a result, free carriers are swept out of the active region into the neutral n - and p-type confinement regions of the semiconductor. The carrier sweep-out is most efficient for large voltage swings, i. e. when a high electric field is created in the space-charge region of the p-n junction. The sweep-out time can be much shorter than the spontaneous lifetime. Thus, the fall time is determined not by the spontaneous recombination lifetime but by the shorter sweep-out time. Considering the magnitude of the built-in electric field and the carrier mobility, the sweep-out time is estimated to be in the picosecond range.

Exercise: Calculation of carrier sweep-out time. Calculate the carrier sweep-out time for typical values of the electric field in the p-n junction depletion region, typical carrier velocity, and an active region thickness of 0.1-1 pm.

Solution: The carrier sweep-out time can be very short. For typical diode parameters, the carrier sweep-out time is about 1-100 ps, i. e. much shorter than the spontaneous recombination time.

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