7. Conclusion

<sup>V</sup>mode <sup>¼</sup> <sup>∭</sup> <sup>E</sup>ð<sup>r</sup>

p ). And finally, the coupling strength scales as ffiffiffiffiffiffiffi

s

Vmode

Ω <sup>2</sup> <sup>¼</sup> <sup>ℵ</sup> 2

where E !

THz.

strength (1= ffiffiffiffiffiffiffiffi

be written as:

First, it is proportional to 1= ffiffiffiffiffiffiffiffiffiffiffiffi

82 Different Types of Field-Effect Transistors - Theory and Applications

ℏωij

!Þj <sup>E</sup> ! ðr !Þj<sup>2</sup> d<sup>3</sup> r !

Figure 7. (a). Capacitance-voltage spectrum taken after illumination with the far-infrared source for 3 h, where the visible part of the beam saturates the DX centres. The shaded region in the spectrum denotes the voltage range over which the coupling experiments are performed. (b) A contour plot of the normalized transmission showing the formation of polaritonic states at the avoided crossing point. A strongly coupled system is formed with a resonance splitting of 0.47

!Þj<sup>2</sup> n o , <sup>ð</sup>24<sup>Þ</sup>

n2D

p , which is a characteristic

ð25Þ

max Ej E ! ðr

higher coupling strength. Second, the higher the transition energy, the smaller the coupling

feature of the fermionic systems. The higher the carrier density, the greater is the coupling. The voltage tuning of our device is based on the quantum-confined Stark effect. The dependence of the coupling strength, Ω=2, on the number of quantum wells as shown Gabbay et al. [52] can

where αavg is the average absorption coefficient, ℵ is a constant, which is proportional to the average light-matter interaction and ΔZ is the distance between the QWs. For a single QW, as in the present investigation, the coupling strength is proportional to the value of ℵ=2. In the theoretical studies, Gabbay et al. found the value of ℵ to be 1, which implies that for a single QW, the coupling strength is 0.5. The splitting in our experiments is found to be 0.47 THz, which agrees well with the theoretical value. It is well known that if the splitting is significantly above the sum of the full width at half maximum of both the ISR and the metamaterial resonance, then the coupling can be assigned to be in the strong coupling regime. Thus, an

is the electric field. The coupling strength depends on three important parameters.

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>e</sup>�2αavgΔZNQW <sup>1</sup> � <sup>e</sup>�2αavgΔ<sup>Z</sup> ,

<sup>p</sup> , implying that the cavity mode volume should be small for

In conclusion, we have reviewed the quantum mechanical phenomenon that governs various electrical and optical properties in the low-dimensional semiconductor nanostructures such as a HEMT. We have demonstrated how one could electrically, or in combination with magnetic fields, probe and tune the intersubband transitions in the heterojunction of a HEMT structure. Such structures primarily have a triangular confinement potential. In the presence of a magnetic field, each subband is further split into a series of Landau levels or cyclotron orbits. Upon optical excitation with an infrared source, the intersubband resonances couple to the cyclotron resonance under tilted magnetic fields. This leads to the appearance of satellite peaks at the anti-crossing point. From the values of splitting at the anti-crossing points, the spacing between the corresponding subbands can be evaluated. Experiments performed in the absence of magnetic fields demonstrated that it is also possible to directly measure and tune these spacings via density-chopped infrared transmission spectroscopy. The subband spacings are measured directly and found to be in the far-infrared region (wide electrically tunable from 6 to 12 meV) of the electromagnetic spectrum. New epitaxial, complementary-doped, semitransparent electrostatic gates that have better optical transmission are introduced [29]. The integrated device with a 2DEG in a high electron mobility transistor structure and artificial metamaterials forms a strongly coupled system that can be electrically driven from an uncoupled to a coupled and again back to the uncoupled regime. In the strongly coupled regime, a periodic exchange of energy between the two systems is observed as a splitting of 0.47 THz at the point of avoided crossing. This is a very high-energy separation, considering the fact that only one quantum well is employed and thus the achievement of a strong coupling regime can be safely claimed. The tuning mechanism is attributed to the quantumconfined Stark effect. This device architecture is particularly interesting in designing devices like modulators and detectors specifically in the THz regime. The integrated device has the high-speed dynamic characteristics of the HEMT design and the appropriate frequency-controlling ability of the metamaterials. From the design perspective of the metamaterials, they can be made particularly for the THz regime with appropriate dimensions (like the one used in this chapter). Upon excitation with a broadband source, this layer selects the desired frequency for which it is designed, and under the application of an external electrical field across the structure, the transmission of this frequency can be controlled and also modulated. This control dynamics can be very fast, simply owing to the fast dynamics of the HEMT design [52, 53]. Furthermore, this design can also be used to detect THz frequencies. Various other 2D materials (like graphene [54–56] or black phosphorous [57, 58]) are also used these days in the transistor configuration for developing THz detectors, simply utilizing the fast dynamics of the transistor design. These novel devices have thus helped to reduce the longdebated THz gap in the electromagnetic spectrum, where there is a severe lack of fast electronic devices.
