Frequency (Hz)
0.1 V
130K
Figure 4.6: The noise spectrum at 130K and different bias voltages.
The carrier capture probability through the QD layer changed dramatically within the temperature range. One major difference is that the gain increases without saturation even at 150 K. This shows the change of responsivity is dominated by the current gain thus the capture probability. The capture probability Pc can be calculated with the current gain g and equation 3.7.
Fig. 4.8 shows the capture probability at different temperatures and biases. With the increase in bias, the capture probability decreases rapidly, which results in a rapid increase in the current gain.
-1.0 -0.5 0.0 0.5 1.0
100 101 102 103
Curr ent gain
Bias (V)
60K 90k 120K 150K 70k 100K 130K
77k 110K 140K
Figure 4.7: The current gain of the sample at different bias and temperatures.
The capture process is influenced by the repulsive coulomb potential of the extra carriers inside the QDs. Unlike in the QWs, where carriers flow freely in the x–y direction, the isolated charge in the quantum dot could generate potential barrier to electrons passing through the QD layers. That is why such dependence was never observed in typical QWIPs. In principle, the repulsive potential is related to the capacitance of the QD and the charge number inside the QD. The capture probability Pc of the carriers passing through the QDs could be approximated with the following equation [41]: where P0 is the capture probability under neutral condition, NQD is the maximum electron number that a QD can accommodate, <N> is the average extra carrier
-1.0 -0.5 0.0 0.5 1.0
Figure 4.8: The capture probability at different bias and temperatures.
number in the QDs. C is the capacitance of the QD and aQD is area of the QD. The number of electrons inside the QD is determined by the balance of the trapped current into the QDs with the emitted current from the QDs. When the current increases with temperature and bias, the carrier number inside the QD increases. As a result, the capture probability decreases and the current gain show a dramatic increase with temperature and bias. To further verify the idea, two QDIPs with identical device structure but different QD doping density were compared.
Fig. 4.9 shows the dark current and the current gain of the two samples at 77 K.
The low doping sample showed a much lower dark current as expected. Also, the current gain of the low doping sample is much lower than that of the high doping sample. This phenomenon cannot be explained without the carrier filling process since the identical device structure should give similar transport property and the
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Figure 4.9: The dark current (solid curve) and current gain (scatter curve) curve for the two samples with different doping concentration at 77K.
current gain value should be similar for the two samples. With such a concept, the average excess carrier number can be estimated with the carrier capture probability and the device parameters. Due to the large size of our QDs, NQD is much large than
<N> and (NQD - <N>)/NQD is approximated to 1. The neutral capture probability P0 is equal to the ratio of transit time (τtd) and the capture time of the QD (τc). The transit time can be calculated with the drift velocity:
( )
where μ is the carrier mobility, vsat is the saturation velocity and h is the height of the QDs. In our calculation, the mobility value of 2000 cm2/V-s and the saturation velocity of 1×106 cm/s were used. The capture time has been reported to be in the order of pico-second by different experiments [42, 43]. Here 5ps is used in our calculation. All of the parameters in our calculation were listed in table 4.1. Fig. 4.10 shows the estimated average extra carrier number.
parameters value unit Table 4.1: The parameters used in calculation of average excess carrier in QDs.
When the temperature and bias is low, almost no extra carriers exist inside the QDs. When the device current increases with either temperature or voltage, <N>
could be more than 1 electron at 150 K. Due to the higher dark current at negative biases, the extra carrier number is higher under negative biases. Although the dark current increases exponentially with temperature, the average charge in one QD increases only linearly with temperature and bias. According to the theoretical calculation for the lens shape quantum dot, the energy difference between the ground state and the first excited state energy is around 50meV for our InAs QDs [44].
Considering the size distribution of the QDs, the density of states of the ground state and the first excited state of the QD layer could overlap and form a band. When the average carrier number increases linearly, the Fermi level of the QD layer also increases in a linear way. The emitted current is thus increases exponentially to
-1.0 -0.5 0.0 0.5 1.0
Figure 4.10: The calculated average extra carrier number <N> in one QD at different temperature and voltages.
balance the captured carriers. In order to check the reality of the calculated <N>, we tried to compare the result with the device quantum efficiency. It is well understood that the carrier number inside the QD is essential to the quantum efficiency and the performance of QDIPs. The optimized condition occurs when the ground states are fully occupied and the excited states are all empty, i.e., 2 electrons per QD. Using the measured current gain, the quantum efficiency is calculated with the responsivity and gain shown in Fig. 4.11.
Due to the increase of the escape probability of the B–B type transition, the quantum efficiency increases exponentially at low bias region in all temperature.
However, the peak quantum efficiency decreases by a factor of 10 with the increase of temperature from 70 K to 130 K. Such difference cannot be attributed to the thermal
-1.0 -0.5 0.0 0.5 1.0
10-2 10-1 100
QE (%)
Bias (V)
70K 100K 130K 77K 110K
90K 120K
Figure 4.11: The quantum efficiency of the sample at different bias and temperature.
distribution of the carriers inside the QDs which could only change for 10% in our temperature range [36]. Since the doping density of our sample is less than 2e-/QD, as the extra carrier number increases, the quantum efficiency increases and then start to drop slowly. As the temperature goes higher, <N> increases and the maximum of the quantum efficiency occurs at lower voltage. If we compare <N> with the quantum efficiency carefully as shown in Fig. 4.12, the peak quantum efficiency happened when the excess carrier number is around 0.4 independent of the temperature.
Of course, other factors such as the excited carrier life time might also induce the lower quantum efficiency at high temperature. From the discussion above, we know the change of carrier number inside the QDs plays an important role on the
-0.75 -0.50 -0.25 0.00
Figure 4.12: The quantum efficiency (solid curve) and <N> (scatter line) at different temperatures and negative voltages. The vertical lines are used to indicate the voltage of quantum efficiency peaks. The peak quantum efficiency occurs around <N>=0.4.
temperature dependence of the responsivity in QDIPs. The higher the dark current is, the more charge inside the QDs will be. This feature enhances the responsivity and the performance of the QDIPs at higher temperature. The photocurrent can be kept at a higher level with elevated temperature though the quantum efficiency decreases.
Taking the extra charge into account, it is beneficial to use smaller QDs to have a more stable responsivity. The small QDs associated with smaller capacitance could generate higher potential barrier to suppress the carrier injection into the QDs. QDIPs with smaller QDs could provide higher current gain and stable quantum efficiency.
4.4 Summary
The temperature dependence of responsivity of InAs/GaAs QDIPs has been investigated. From the measurement, we found the dramatic change of the current gain with temperature dominates the behavior of the responsivity. The increasing dark current with the temperature injects more carriers inside the QDs. The repulsive potential of the extra carriers suppress the capture process and enhance the current gain. The average extras carrier number calculated from the capture probability qualitatively explained the behavior of the quantum efficiency. From this concept, QDIPs with smaller QD and higher density is predicted to have better temperature stability and also maintain a higher current gain.