Channel length dependence of the formation of quantum dots in GaN/AlGaN FETs

Quantum dots can be formed in simple GaN/AlGaN field-effect-transistors (FETs) by disordered potential induced by impurities and defects. Here, we investigate the channel length dependence of the formation of quantum dots. We observe decrease of the number of formed quantum dots with decrease of the FET channel length. A few quantum dots are formed in the case with the gate length of 0.05~$\mu $m and we evaluate the dot parameters and the disordered potential. We also investigate the effects of a thermal cycle and illumination of light, and reveal the change of the disordered potential.

Semiconductor quantum dots confine electron in small regions and the quantum nature of electrons appears. The confinement potential can be formed artificially by etching or gating of semiconductor nanostructures. From the viewpoint of fundamental physics, the inner electronic states in quantum dots have been investigated [1][2][3][4] and physics in combined systems were explored [5][6][7][8]. Also, the quantum dots have applications in low-power devices including single-electron transistors [9,10] and devices for quantum information processing [11,12]. Especially for semiconductor spin qubits, readout [13,14] and control [15][16][17][18][19][20] of the spin quantum states have been demonstrated and intensively studied in GaAs and Si-based deices.
Quantum dots can also be formed in simple FET structures by intrinsic disordered potential induced by impurities and defects. Formation of quantum dots in FET have been reported and high temperature qubit operation have been demonstrated [21][22][23][24][25]. Such quantum transport in FET structures have been reported mainly in Si-based devices. On the other hand, high-mobility transistors based on GaN/AlGaN heterostructures [26,27] will be another possible material. New quantum devices can be expected by utilizing the wide and direct band gap in GaN which work at higher temperatures and couple with light. Also, the quantum transport will be useful to understand the actural potential formed in GaN/AlGaN FETs and improve the performance. Previously, we investigated the formation of multiple quantum dots in GaN/AlGaN FETs near the pinch-off condition by the disordered potential near the FET conduction channel [28].
In this paper, we investigate the channel length dependence of the formation of quantum dots in GaN/AlGaN FETs. By decreasing the channel length, there are fewer impurities and defects which contribute to quantum dot formation, and the number of quantum dots can be reduced.
A few quantum dots are formed in a device with the short gate length and we evaluate the dot parameters and the potential. We also evaluate effects of a thermal cycle and illumination of light, and reveal change of the disordered potential.
The layer structure of the device is shown in Fig. 1  The source-drain current I sd are measured as a function of the source-drain voltage V sd and the gate voltage V g . The devices are cooled down to 2.3 K or 0.5 K using a helium depressurization refrigerator to measure the electronic transport at low temperature. Figure 1(c) shows a typical result of the measurement near the pinch-off voltage of the FET device with 1.4 µm gate length at 2.3 K. The differential conductance dI sd /dV sd are plotted as a function of V sd and V g . The current changes non-monotonically with V sd and V g and Coulomb diamonds due to formation of quantum dots in the conduction channel are observed. This formation is induced by disordered potential by impurities or defects, which creates potential minima confining electrons near the depletion condition of the two-dimensional electron gas [28].
Next, we investigate the channel length dependence of the formation of quantum dots.  In the case of the 1.4 µm gate length device, this corresponds to the area enclosed by the dashed lines in Fig. 1(c). With the decrease of the channel length, the overlap of the multiple Coulomb diamonds at zero bias tends to decrease and the shape of the diamonds becomes clearer. Especially   Coulomb peaks in the direction of V g at zero bias, the capacitance between the quantum dot and the gate electrode is obtained as C g 2.7 aF. The slope of the edge of the Coulomb diamond can be expressed as C g /C s and C g /(C d + C g ). The capacitances between the quantum dot and the source electrode and the drain electrode are evaluated as C s 15 aF and C d 12 aF, respectively.
The lever arm for converting the gate voltage to the electrostatic potential in the quantum dot becomes α = C g /C 0.09. By assuming that the shape of the quantum dot is a disk, the size of the quantum dot is estimated from the value of C g as 15 nm (see Supplementary Material).
We can also observe excited-state lines in Fig. 3, which are parallel to the edge of the diamond. From the distance between the edge of the diamond and the excitation line, the discrete energy level spacing of ∆ε =2.9 meV is obtained. Since the measurement temperature of 0.5 K is corresponding to an energy of 0.05 meV, it is reasonable to observe the discrete level spacing.
Assuming the confinement potential as a harmonic oscillator, the size of the confinement is evaluated as 22 nm. This value is consistent with the size evaluated from the capacitance between the quantum dot and the gate electrode. Note that the larger value evaluated from the excited state might be reflecting the asymmetry of the confinement potential in which lowers the orbital energy in the loose confinement direction.
Next, we investigate the dependence of the quantum dot formation on a thermal cycle. Because the quantum dots are induced by the disordered potential by impurities or defects, the spatial distribution will be modified by the change of the charge states of those by thermal excitation like in the cases of universal conductance fluctuations [31,32]. After the first measurement at 2.3 K, the sample is heated up to 300 K by using a heater and then cooled down to 2.3 K again. To avoid the effect of photo-excitation, the sample is kept in dark condition without opening the refrigerator's cover in the thermal cycle. The measured results of Coulomb diamonds in the sample with the channel length of 1.4 µm before and after thermal cycle are shown in Fig. 4(a) and (b), respectively. Figure 4(a) is the same to Fig. 2(a). The the Coulomb diamonds becomes different by the thermal cycle. This is due to the change of the configuration of quantum dots. Redistribution of the potential minima occurs by the thermal cycle. Charge trapping sites which can be activated by the thermal energy at room temperature 26 meV contributes the redistribution.
Finally, we measured the effect of light illumination on the formation of the quantum dots. The redistribution of the potential minima will be induced also by light. After the first measurement at 2.3 K, a red LED attached near the sample is turned on for 180 seconds and then turned off with keeping the low temperature. During this illumination, V sd and V g of the sample are fixed. shows Coulomb diamonds measured in another sample with the channel length of 0.6 µm before and after LED illumination, respectively. The pinch-off voltage shifts about -0.2 V due to the persistent photo-current [33,34] and different Coulomb diamonds are observed.
Redistribution of the potential minima occurs by the illumination of light. In this case, the trapping sites in SiN or AlGaN [35] might also contribute the reconfiguration of the quantum dots.
In conclusion, we investigate channel length dependence of the formation of quantum dots in