The pump pulses generate carriers through interband transition in semiconductors can be probed by the time-resolved photoreflectance. After pumping, the various carrier relaxation and decay mechanisms inside semiconductors cause the change of complex refractive index. This brings about the change in reflectivity of probe beam.
So from detecting the intensity change of the reflected probe beam, we can get the status of carrier decaying. The reflectivity change can be modeled by the absorption change due to band filling (BF) effect, band gap renormalization (BGR), plasma screening effect, enhancement of absorption, and interband absorption of photons by free carriers (FCA).
The change of reflectivity (ΔR) is because of the change of complex refractive
index (n + iκ). The major contribution to the change of n + iκis written as Δn =ΔnBF+BGR +ΔnFCA. ΔR is the difference between the reflectivity R with and
without pumping, which is calculated as ΔR(hν) = R(n’,κ’;hν) – R(n,κ;hν). The reflectivity R is given by
)
the absorption coefficient by ( ) ) 4
and κ’ are the modified real and imaginary parts of refractive index with pumping (under the presence of the carrier density N), respectively.
We have measured InGaAs1-xNx SQWs with x = 0 and 0.02 at 820 and 880 nm, separately. Since the band gap energy of the GaAs confining layer corresponds to the wavelength of 870 nm, tuning the pumping photon wavelength to 880 nm is enough to avoid absorption of the GaAs confining layer. The bandgap of In0.4Ga0.6As and In0.4Ga0.6As0.98N0.02 SQW are 1.2 µm and 1.45 µm, respectively.
The absorption curve of GaAs is presented in Figure 4-1, the absorption coefficient
decreases immediately in photon wavelength from 870 to 1000 nm, and its value at 870 nm is far more than that at 880 nm [29]. We have reduced the absorption of GaAs effectively when tuning the pumping wavelength to 880 nm. The definition of penetration depth is the reciprocal of absorption coefficient. From Figure 4-1, we can extract the penetration depth of GaAs at 800 and 880 nm. They are 1.43 µm and 1000 µm, respectively. As we know, the thickness of confining layer GaAs is 0.3 µm, so the intensity of the laser beam which is incident into the quantum well remains 0.81Io at 800 nm and 0.9997Io at 880nm, where Io is the incident intensity of the beam.
Therefore, the single quantum well can efficiently absorb the pumping laser beam.
Notice that the exciton resonances are very weak in bulk GaAs and thus can only be observed at very low temperature [30].
Fig. 4-1 Absorption curve of GaAs (Ref. [29]).
We extract the data from 10 to 50 mW and obstruct the laser beam between every measuring to reduce the thermal effect. Therefore, the thermal effect is not
4-1 Ultrafast Time-Resolved Photoreflectance of
In
0.4Ga
0.6As
1-xN
xSQW
In order to describe a complete sketch of the optical properties of In0.4Ga0.6As1-xNx, we review some results of Y. H. Lin in 2005 [31]. Keeping the pumping wavelength at 800 or 820 nm, whose corresponding energies are both above the bandgap of GaAs, Figure 4-2 shows the results of time-resolved photoreflectance of bulk GaAs and In0.4Ga0.6As1-xNx (x = 0 and 0.02) SQW with pumping power varying from 10 to 100 mW, respectively. The fast rising and decaying responses in Figure 4-2(a), (b), and (c) are because the generation of carriers occupies the optical-coupled transition states. After the absorption, the carriers scatter out of their initial states and subsequent relax toward the band edges through carrier-carrier and carrier-phonon scattering. In bulk GaAs, there is a positive ∆R/R, however, In0.4Ga0.6As1-xNx SQWs have the opposite behavior with GaAs with negative ∆R/R.
It is amazing to find that the thickness of these quantum wells is only 60 Å, we still can distinguish the huge differences of carrier dynamics between bulk GaAs and In0.4Ga0.6As1-xNx SQWs. The positive ∆R so as positive index change is mainly due to band filling effect because the pumping photon energy is above the bandgap of bulk GaAs. On the other hand, the negative change of transient reflectance of In0.4Ga0.6As1-xNx SQWs corresponds to a negative index change. The exact mechanism of negative index change is very complicated and still not fully understood. Because the thickness of these quantum wells is only 60 Å and the pumping photon energy is above the bandgap of the GaAs confining layer, we speculate that the carriers are mainly excited in the confining layer then quickly trapped into the quantum wells of both InGaAs and InGaAsN SQW samples. Due to
the much smaller bandgap, the band filling would not contribute to index change that results in negative change of transient reflectance from the band gap renormalization and the free-carrier absorption (FCA) or re-excitation of trapped carriers into the conduction band [32].
0 2000 4000 6000 8000
0.000
0 2000 4000 6000 8000 10000 -0.006
-2500 0 2500 5000 7500 10000 12500
Fig. 4-2 The pump-intensity dependent time-resolved photoreflectance of (a) bulk GaAs, (b) In0.4Ga0.6As SQW pumped at 800 nm from [31], and (c)
In0.4Ga0.6As0.98N0.02 SQW pumped at 820 nm.
Although the mechanism of carrier relaxation in In0.4Ga0.6As1-xNx SQWs is distinct from that in bulk GaAs, the GaAs confining layer whose bandgap is 870 nm makes the carrier relaxation complicated when pumping wavelength is at 800 or 820 nm. It can truly avoid the absorption of GaAs confining layer by adjusting the pumping wavelength to 880 nm. Shown in Figure 4-3 are the results of time-resolved photoreflectance of In0.4Ga0.6As1-xNx (x = 0 and 0.02) SQWs with pumping power varying from 10 to 60 mW at 880 nm. It reveals a contrary result comparing to the previous measured results in Figure 4-2. The measured reflectance turned to be positive at 880 nm. The positive change of transient reflectance is due to the band filling effect, indicating a positive change of refractive index (∆n > 0) [24].
The opposite phenomenon may result from different initial occupied states of the photo-excited carriers for two pump wavelengths. With pumping wavelength < 820 nm, the carriers are generated in confining layer GaAs during pumping, and then the
quantum well capture those carriers in a short time. After carriers are trapped in In0.4Ga0.6As1-xNx SQWs, there will be no band filling effect but the increase of carriers in the well could cause bandgap shirinkage and therefore leads to negative index change so as the negative ∆R.
Locations of the peaks in Figure 4-3(a) are a little different with various pumping power, the reason might be fluctuation of our laser or vibration of the step-motor.
Besides, we have adjusted the polarization of pumped and probe beam perpendicular to each other, the interference caused by overlapping of pumped and probe beam occurs around the zero delay point which is clearly seen in Figure 4-3(b). We extract every peak at different pumping power and sketch them in Figure 4-4 to expose the tendency.
-2000 0 2000 4000 6000 8000
-2500 0 2500 5000 7500 10000 12500 -0.00005
Fig. 4-3 The pump-intensity dependent time-resolved photoreflectance of (a) In0.4Ga0.6As SQW and (b) In0.4Ga0.6As0.98N0.02 SQW pumped at 880 nm.
Due to the interference of pumped and probe beams nearby the zero time delay, it is hard to find the exact location of peaks with pumping wavelength at 880 nm in Figure 4-3(d). By fitting the curves with a Lorentzian and a biexponential function to all of the photoreflectance curves, the measured peak amplitude of ∆R versus pumping
power density of In0.4Ga0.6As SQW is displayed in Figure 4-4. The magnitude of ∆R peak is proportional to the density of carriers accumulated in the allowed optical transition states after photoexcitation. The carrier density N can be calculated using the relation mentioned in Section 3-1 based on the Drude model: n
n R
R ∆
= −
∆
1 4
2 ,
where ∆n=−Ne2/2nω2m*εo. The estimated carrier densities are listed in Table 4-1.
Due to absorption by the GaAs confining layer, the carrier densities with pumping wavelength < 820 nm are an order of magnitude larger than those of pumped at 880 nm for both samples but the larger carrier density for InGaAs SQW than for InGaAsN SQW. It is worth to note that when pumped at 880 nm, whose photon energy is below GaAs bandgap but above those of both samples, the carrier densities are nearly the same at the lowest pumping; whereas, with increasing pumping power density, the carrier density increases faster than that of InGaAsN SQW.
Table 4-1. List of carrier densities of In0.4Ga0.6As, In0.4Ga0.6As0.98N0.02 with various pumping power.
In0.4Ga0.6As In0.4Ga0.6As0.98N0.02
N (1018 cm-3) N (1018 cm-3) Power density
(MW/cm2)
800 nm 880 nm 820 nm 880 nm
184.6 6.19 0.11 0.83 0.12
369.2 6.95 0.78 1.31 0.30
553.8 8.87 1.36 1.70 0.39
738.4 10.07 1.82 2.07 0.46
923 11.76 2.12 2.21 0.51
1107.6 -- 2.19 -- --
After being pumped to the higher states, carriers can diffuse in the 3000Å GaAs confining layer or be trapped into the quantum well. The band filling effect will not be obvious, so all of the carrier densities basically linearly increase with the pumping power for those pumping at wavelength < 820 nm in Figures 4-4(a) and (b). On the other hand, when pumping at 880 nm, carriers will localize in InGaAs1-xNx single quantum well. The band filling effect dominates positive ∆n and it will saturate at high pumping, that is because ∆α is nonlinear, the relation of power density versus peak amplitude in Figure 4-4(c) and (d) is also nonlinear.
200 400 600 800 1000
2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0
power density (MW/cm2) Peak amplitude (10-3 )
(a) InGaAs SQW at 800nm
200 400 600 800 1000
0.3 0.4 0.5 0.6 0.7 0.8 0.9
Power density (MW/cm2) - Peak amplitude (10-3 )
(b) InGaAsN SQW at 820nm
200 400 600 800 1000 1200
-0.2
(c) InGaAs SQW at 880nm
200 400 600 800 1000
0.04
(d) InGaAsN SQW at 880nm
Fig. 4-4 The measured ∆R peak amplitude versus pumping power with pumping wavelength at 800/820 nm in (a) In0.4Ga0.6As (b) In0.4Ga0.6As0.98N0.02 SQW and at 880
nm in (c) In0.4Ga0.6As (d) In0.4Ga0.6As0.98N0.02 SQW.
4-2 Carrier Relaxation Time of InGaAs
1-xN
xSQW
We extract the relaxation time of carriers by fitting the experimental ∆R traces by using a double exponential decay function, A exp(-t/τ1) + B exp(-t/τ2). We obtain the carrier decay time which is exhibited in Figure 4-5. The profile shows an initial fast decay followed by a slower relaxation [33]. The fast component of carrier lifetime approximates 2-3 ps with pumping wavelength at 800 nm and 1-2.5 ps at 880 nm. It does not change much with increasing pumping power. It is attributed to the carrier-carrier scattering. Because the pumping energy remains still, the rate of carrier-carrier scattering will basically not change even if the pumping power is already different. The later component of relaxation time is about several tens ps with pumping wavelength at 800 nm and 2-8 ps at 880 nm. As we know, τ2
increases with increasing pumping power. The reason of these results is the appearance of hot phonons [24]. After receiving the energy from pumping beam, the carriers transfer their additional kinetic energy to phonons. Those phonons become hot phonons, and then transfer the energy back to carriers. Carriers which have more kinetic energy also take more time to relax to thermalization. As a result, it takes longer to decay when pumping power is rising. On the other hand, we could not judge the trend in Figure 4-5(a) due to the lack of statistics.
300 450 600 750 900
400 600 800 1000 1200
0
Fig. 4-5 The carrier lifetime versus pumping power in In0.4Ga0.6As SQW with pump wavelength at (a) 800 (b) 880 nm.
Figure 4-6 presents the carrier relaxation time fitted from Figure 4-3, and the illustrations represent In0.4Ga0.6As0.98N0.02 SQW with the pumping wavelength at 820 and 880nm, respectively. In In0.4Ga0.6As0.98N0.02 SQW, the photo-excited carrier could quickly and efficiently be trapped by the local defects (alloy fluctuation) due to
N-incorporation during or after they experienced electron-hole scattering to lose their excess kinetic energy. In Figure 4-6(a), the observed short relaxation time of ~1-2 ps is attributed to the carrier-carrier scattering; τ1 is almost constant for various power densities. The longer decay time of 5-8 ps increases with the pumping power that is attributed to hot phonon decay. The mechanism of hot phonon has already reported in Section 4-1. After adjusting the pumping wavelength to 880 nm, we discover that the behavior of τ2 is contrary to the second decay time at 820nm. Originally it takes 0.3-0.8 ps to relax in Figure 4-6(b), carrier-carrier scattering occurs at this moment.
Then it takes 2-4.5 ps to accomplish the later relaxation process, which decreases when the pumping power increases. As we know, the sample has lasing characteristics [34], stimulated emission decay times faster than 10 ps have been noticed. The stronger of the pumping intensity, the more carriers will be in the upper state, and then the carrier decaying will also be faster [35]. Moreover, we can only see an exponential decay time with pump power in 10mW through large fluctuation at low pumping.
200 400 600 800 1000
200 400 600 800 1000
0.0
Fig. 4-6 The carrier lifetime versus pumping power in In0.4Ga0.6As0.98N0.02 SQW with pump wavelength at (a) 820 (b) 880 nm.
Comparing In0.4Ga0.6As SQW with In0.4Ga0.6As0.98N0.02 SQW, it clearly reveals that In0.4Ga0.6As SQW shows not only an order of magnitude ∆R/R larger than that of In0.4Ga0.6As0.98N0.02 SQW, but also a longer relaxation time. It is consistent with the time-resolved PL measurements which were done by Lifang et al. [19] and the below threshold modulation frequency response measurements which were studied by
Anton et al. [36]. This phenomenon can be explained by presence of defects after nitrogen incorporation. Some trap states are formed within the bandgap by defects, and they will capture excited carriers efficiently. The trap states act like nonradiative recombination centers. This process lasts a shorter time than the intraband relaxation, and that is why carrier lifetime in In0.4Ga0.6As0.98N0.02 is shorter. Besides, carriers in excited states above the conduction band minimum can also be trapped due to the localization of these trap states. Furthermore, the carrier density of In0.4Ga0.6As0.98N0.02 SQW is an order of magnitude smaller than that of In0.4Ga0.6As SQW, which is mainly due to the bandgap of In0.4Ga0.6As0.98N0.02 being farther from the excited photon energy of 1.55eV.