акустика / gan_ws_acoustical_imaging_techniques_and_applications_for_en

can then be reconstructed. Here the sound velocity of GaN and SiO2 are 8 and 5.9 nm/ps, respectively. From the 1D scan, this gives the thicknesses of GaN and SiO2 layers as 86 and 36 nm, respectively.

To perform the 2D nanoimage of the scanned object, 1D scan were performed along the x-axis with a step size of 300 nm. Each trace of the 1D scan was normalized to the signal peak in the observed window. Following the thickness calculation, the 2D image of the nanostructure can then be directly reconstructed. The position zero along the z-axis was set to the interface of the OPT and the object. The 2D images of the structure of sample A and sample B reconstructed by the 2D nanoultrasonic scans are shown in Figure 13.3(b) and (d), respectively. In Figure 13.3(b), the GaN/SiO2 and SiO2/air interfaces at different depths have been resolved. Since the interval of two interfaces was only 40 nm, this image indicates the high axial resolution when imaging with NAW. It should be noted that the apparent ‘width’ of the interfaces in Figure 13.3(b) is due to the finite pulse width of the echoed NAW. The exact position of the interface can be determined by each 1D ultrasonic scan as shown in Figure 13.3(a) with an axial accuracy of 1 nm [17].

To examine the axial resolving power for two adjacent interfaces, 2D ultrasonic scan was performed on sample B with a reduced interval between two interfaces. The 2D reconstructed image is shown in Figure 13.3(d) and these two interfaces can still be distinguished. Figure 13.3(c) shows one corresponding 1D scan at x = 5.4 μm and the first and second peaks of the echoed wave packets were located at 17.4 and 22.8 ps. The interval between GaN/SiO2 and SiO2/air interfaces can then be determined to be 16 nm, implying that the system capability to resolve two adjacent axial interfaces is better than 16 nm. It is possible to further improve the axial resolving power by using shorter acoustic pulse width or if the interference of the echoed NAWs from two interfaces is to be analyzed [17].

For the 2D nanoultrasonic scans shown in Figure 13.3, an NA 0.85 objective was used. We can take the optical spot size of 350 nm as the transverse resolution of the 2D image, since the acoustic spot size is determined by the optical spot size in the OPT. However, following Rayleigh’s criterion of diffraction limit, a lateral acoustic resolution of half the acoustic wavelength (7 nm in this work) should be achievable. The transverse resolution is not limited by the acoustic spot size, but should be raised by scanning the xy plane with even smaller steps and by analyzing each 1D ultrasonic scan in the time domain.

To explore the transverse revolution of the 2D nanoultrasonic image, an NA 1.35 objective was used to perform 2D scan on sample C and compared with a result measured by an AFM. The transverse step size was 50 nm, which was much shorter than the generated acoustic spot size of 200 nm. Figure 13.4(a) shows the original acoustically reconstructed 2D image of nanostructure while different thickness of the GaN cap layer are clearly resolved. To investigate the potential lateral resolution of the system taking advantage of the patterned sharp edge, the peak position of the echo envelop in each 1D was acquired as shown in Figure 13.4(b), which was similar to a deconvoluted 2D image. A high lateral resolution can be found under a combined analysis with the axial scans. For comparison, a commercial AFM with a <10 nm transverse resolution was also utilized to measure the examined surface structure, as plotted in solid line in Figure 13.4(b). Excellent agreement was found between these two measurements. However, the subsurface information such as thickness cannot be obtained by the AFM. It is also noted that the edge obtained by the nanoultrasonic scan was sharper than that measured by the AFM due to the finite size of the AFM tip. The result here clearly provides the experimental evidence that <100-nm resolution can be achieved by using a NAW. If a step

13.5Generation and Amplification of Terahertz Acoustic Waves

There is a different method of generating terahertz acoustic waves from that of using the OPTs. This is the development of the saser, the acoustic equivalent of an optical laser. The saser would emit an intense beam of coherent sounds under electrical or optical pumping and could potentially transform the field of terahertz acoustics, just as the laser has transformed optical spectroscopy and imaging.

The operation of laser is based on the fundamental phenomenon of stimulated emission in systems having a population inversion. Stimulated emission is not restricted to photons, it is possible for any elementary excitation obeying bosonic statistics. In solids, for example, stimulated emission has been demonstrated for photons, plasmons [23] and optical phonons [24]. For high-frequency acoustic phonons, the theoretical possibility of sound amplification by stimulated emission of radiation has been discussed [25–27].

Practical demonstration of stimulated emission of acoustic phonons are few and include the case of inversely populated impurity states subject to very strong optical pumping and for acoustic frequency up to only about 50 GHz, corresponding to a wavelength of about 200 nm [24].

In 2006, Kent et al. [2] demonstrated stimulated emission of terahertz longitudinal-polarized acoustic phonons from GaAs/AIAs SLs under hopping electron transport. Here the population inversion was created between the Stark levels under electrical bias.

When considering the possibility of a saser, it is necessary to take account of the fact that in crystals, the speed of sound is about five orders of magnitude less than the speed of light. As a result, for a given frequency, acoustic phonons have a much shorter wavelength than photon. In particular, for the terahertz frequency band, the wavelength is only a few nanometres. This suggests that for a heterostructure-based saser not only the electron states, but also the phonon states and their coupling with electrons can be tailored to facilitate its operation. On the other hand, the short wavelength of terahertz sound as well as its relatively strong scattering in comparison to light [28] brings about severe requirements for design of the acoustic cavity. However, it has been demonstrated that modern epitaxial growth technologies enable the production of high-quality acoustic cavities for terahertz frequencies [29]. Glavin et al. [30] show evidence of saser action for transverse (shear) acoustic modes at 500 GHz in an optically pumped semiconductor SL without applied electrical bias. This device exploits the effect of strong enhancement of the piezoelectric electron–phonon interaction in SLs. The enhancement is due to resonance of the acoustic wavelength with the periodicity of the piezoelectric coupling constant in the SL and occurs only for transverse polarized phonons, propagating very close to the SL growth axis and having energy ω = 2πn cs/d, where d is the repeat period of the SL and cs is the velocity of sound and has an integer. One might expect such an enhanced interaction to facilitate transfer of the system into the regime of stimulated emission.

A picture of the structure of the optically pumped saser device and the calculated frequency dependence of the reflectivity of the Bragg mirror and active SLs for transverse-polarized sound is shown in Figure 13.5. The saser device was grown by molecular-beam epitaxy on a 0.38mm thick semi-insulating GaAs substrate. From top to the bottom, the structure consists of: a 40-period GaAs/AIAs SL with the QW thickness dQW = 6.3 nm and barrier layer thickness dB = 1.1 nm; a 0.5-μm thick GaAs spacer; and emitting 40-period GaAs/AIAs SL (the mirror SL) with the GaAs and AIAs layer thickness of 1.7 and 2.2 nm, respectively.

Figure 13.7 (a) Electron distribution in the photoexcited SL. (b) Illustration of the feasibility of sound amplification in SL. The black ring represents the populated electron states at particular value of kz and the grey rings inside (outside) show scattered electron states with emission (absorption) of a transverse phonon frequency ω = 2π cs/d = 470 GHz, and transferring no z component of momentum to electrons. For the lateral component of the phonon wave vector directed along the y-axis, the horizontal lines at ky = kem, kabmark the possible electron states capable of emitting (absorbing) the phonon, and their white portions show such states that are actually populated. One can see that in this case emission prevails absorption and sound amplification is theoretically possible (Walker et al. [31] © American Institute of Physics)

in the active SL by optical pumping to explain the experimental observation. Pumping of the active SL with interband light having photon energy greater than the effective bandgap, Eg , leads to the creation of nonequilibrium photoexcited electrons and holes in the QWs. In isolated QWs, the initial nonequilibrium electron distribution will relax to the bottom of the band, and due to fast scattering, inversion is lost. However, because the A/As barrier layers of the active SL are sufficiently narrow, electrons are able to tunnel through them and an extended electron miniband is formed [31]. This ensures fast escape of nonequilibrium electrons from the SL and so maintains the inversion electron distribution produced by the optical pumping. The escape time is determined by the length of the active SL and the electron velocity. For the

active SL used in Walker et al.’s [31] experiments, the electron escape time were estimated to be approximately 5 ps, which is much less than the electron-scattering time, provided that the electron energy is less than the optical phonon energy, and suggests that electron escape the SL ballistically, giving rise to the inversion.

For amplification of a particular mode to occur, the probability of emission must be greater than the probability of absorption. If this is the case, the population of the mode will become unstable and be amplified.

A qualitative illustration of the feasibility of amplification of a particular mode having frequency ω = 2π cs/d, where d is the repeat period of the SL and cs the sound velocity, and for which phonon-assisted electron transitions occur with conservation of kz, is shown in Figure 13.7(b). In this case, the electron transitions are within the planes obtained from the distribution of Figure 13.7(a) by cross sections at constant kz. Due to the isotropic electron dispersions in the xy plane, in such cross sections the populated electron states are within a ring, part of which is shown in Figure 13.7(b) by the black curve. Similarly, the scattered states after the phonon emission (absorption) must be within the rings of smaller (longer) radius.

To estimate the feasibility of stimulated emission, one has to take into account finite quality factor of the phonon cavity. Consider the active SL of length l within a Fabry–Perot cavity of length L between an SL Bragg mirror, reflectivity Rm, and the top surface of the structure, reflectivity Rs. Using the same analysis as for a laser, the round-trip gain is given by

where cs is the velocity of transverse sound and l is the phonon mean free path. The first term in the bracket accounts for growth of the acoustic intensity due to amplification and the second term accounts for losses due to scattering in the cavity. The threshold condition for saser oscillation to occur is G = 1, which gives

Substituting the values for the structure of Walker et al. [31]: cs = 3500 ms–1; l = 0.3 μm;

reasonable agreement with their experimental observation of a threshold at about 0.5 kWcm–2. Thus Walker et al. [31] have observed experimental evidence of saser action in the emission of terahertz transverse phonons from a GaAs/AIAs SL under interband optical pumping. The primary evidence for saser action was a strong increase in the transverse acoustic (TA) emission in a direction normal to the SL layers when pumping above the threshold intensity. They have shown that the important condition for saser operations are met in their device structure: formation of an inversion charge–carrier distribution in the optically pumped SL, resonantly enhanced piezoelectric electron–phonon coupling for phonons propagating close

to the SL axis and realization of Fabry–Perot phonon cavity.

in a classical system. In this technique, two initially entangled phonons incident on opposite sides of a beam splitter would be routed to two grazing incidence acoustic mirrors. One of the paths would lead directly to a target, while the other would include a phase shifter before the target. Classically speaking, sound interference in such a set-up yields an intensity pattern that varies as both a slowly and quickly varying function of phase shift. The slow variation limits the spatial resolution to the Rayleigh diffraction limit.

According to quantum mechanics, however, the set-up beats their limit. The beam splitter correlates the phonons even more. Each generates a new state with equal probability amplitudes for presence on both the upper and lower paths.

In a sense, the position-state of each phonon is linked to the other. Once one of each phonon strikes a given location on the target, the partner is constrained to move on the same path. More importantly, the resultant intensity pattern varies with only the high spatial frequency of the semiclassical solution, eliminating the lower frequency terms and then halving the minimum spot size at the target.

An acoustical imaging system based on multiple entangled phonon would be even more impressive. Essentially N phonons entangled state offers a resolution enhancement that varies with N. The challenge is to reliably generate such entangled phonon. If experimentally demonstrated, it could beat the classical diffraction limit and achieve a resolution limit of λ/2N, where N is the number of entangled phonons achieved.

13.9Applications of Quantum Acoustical Imaging

Quantum acoustical imaging has been experimentally demonstrated [16]. With a terahertz sound frequency, an imaging resolution of a few nanometres can be achieved. This will beat the resolution of optical imaging, which is a few microns. On top of that, acoustical imaging enables subsurface information where an optical imaging is limited only to the object surface.

Quantum acoustical imaging can be applied to nondestructive testing [1] imaging of nanostructures and to medical imaging, especially to imaging of cancer cells.

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