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When femtosecond laser pulses with photon energies that exceed the semiconductor band-gaps irradiate semiconductor surfaces, electron-hole pairs are generated. If a static electric field is present at the surface region, the photo-excited free charged carriers are accelerated in the direction of the field to generate fast time-varying transient current and radiate electromagnetic waves at terahertz frequencies (THz = 10¹² Hz). The amplitude or the intensity of the THz radiation is widely believed to be proportional to the time derivative of the transient current. Terahertz region of electromagnetic spectrum is loosely defined by the frequency range of 0.1 to 10 THz and is situated between infrared and microwave radiation (see Fig. 1). A widely-acknowledged “THz gap” exists between about 0.3 and 20 THz (10 – 600 cm^-1 wavenumber, 1 mm – 15 μm wavelength) usually refers to the lack of technology – especially sources and detectors of THz electromagnetic radiation – available at these frequencies relative to higher and lower frequencies. Below the THz gap, electromagnetics is the dominant paradigm for technology and scientific instrumentation. Above the gap, the paradigm is photonics.

Fig.1. THz frequency range lies in the between the infrared and microwave radiation in the electromagnetic spectrum.

The development of efficient emitters and detectors within each of the spectral regimes has resulted in the birth of numerous industries. The search for potential applications of THz radiation is steadily intensifying as materials research provides improved sources and detectors (Nature materials 1, 26 (2002)). With the special development of femtosecond pulsed laser sources over the last two decades, various techniques have been employed now in the free space generation and detection of terahertz pulsed radiation (THz, T-ray), which is a fast-growing field and possesses an extremely high potential of applications in academic research in all areas and in industry. Applications including the potential to extract material characteristics that are unavailable when using other frequency bands, semiconductor and high-temperature superconductor characterization, real-time 2D and 3D T-ray computed tomography, label-free genetic analysis, cellular level imaging and chemical, biological sensing, space and defense industries, and public and home securities. Semiconductors are materials over which most exquisite control has been developed. Bulk semiconductors have important resonances lying at THz frequencies (phonons hydrogenic states of impurities – bound carriers, internal transitions of excitons, and bulk plasmons in doped material etc.). Terahertz radiation provides a powerful probe into the fundamental excitations in semiconductors and their nanostructures.

Fig.2. (a) Photograph of the foam sample. (b) Defect map of the sample. Each void defect is marked with an “x”. (c) THz image of the sample.

Terahertz-based studies are needed not only to establish basic material parameters, they are also necessary for characterization of materials destined for various applications. Apart from providing a probe into excitations, THz radiation can used to manipulate and control quantum mechanical states in matter. Generally speaking THz technology applied to semiconductors will strongly impact the following area of science:

Fundamental properties of semiconductor nanostructures
Fundamental limits of electronic devices
Subwavelength THz spectroscope
Coherent control and nonlinear optics
Quantum optics
Quantum information science
Spintronics
High THz electric field physic and quantum nonlinear dynamics

Many nonconducting, dry materials that are opaque to infrared and visible light exhibit low absorption in the terahertz frequency range. Such materials are also transparent to the microwave and radio frequencies, but the shorter wavelength of terahertz radiation allows for higher spatial resolutions. The terahertz region of the electromagnetic spectrum thus represents an important intersection between spatial resolution and penetration depth for many applications. The technique of using continuous-wave radiation in the sub-THz band for nondestructive testing has been studied for several decades but only recently has semiconductor technology advanced to the point where a practical system, both compact and simple to operate, is possible. Recent systems have been designed for imaging in the THz region using radiation generated by a variety of methods, such as photomixing or quantum-cascade lasers and are capable of impressive results but generally are of high cost and complexity. Other recent optoelectronic systems using THz radiation as their sources have been developed that are more compact and lower in cost. Several examples of the applications in THz imaging are briefly discussed below.

Fig.3. (a) THz image of an empty leather briefcase. (b) Image of the same briefcase holding a large knife and various harmless contents such as a compact disc, a video cassette, and audio cassette and pens.

The space shuttle insulating foam, sprayed-on foam insulation (SOFI), shown in Fig. 2(a), is a good subject for THz techniques because it has a low absorption coefficient and index of refraction in this region of the electromagnetic spectrum. The samples studied are sprayed layer-by-layer onto an aluminum substrate. As in the tile sample, there are various intentional defects inside to test the systems’ abilities to find them. This sample has only void defects, which appear in the image as dark circles with light interiors, corresponding to scattering and interference at the edge of the feature and enhanced transmission due to the lack of material in the interior. Figure 2(b) is a defect map with the positions of 29 defects. The THz wave image of this sample is shown in Fig. 2(c). Of the defects shown on the measurement, all but two are visible in the images. One of the missing defects is located on a tilted surface, so that the radiation is not reflected in the direction of the detector. It can be seen in the image that SOFI makes an ideal subject for this imaging system as the foam absorbs very little radiation and defects show a high contrast with their surroundings.

Fig.4. Schematic diagrams of the SIN⁺ structure, (a) charged carrier and field distribution, and (b) the directions of the motion and acceleration of the electrons induced by the electric field.

Figure 3 shows a THz scan of a standard size leather briefcase, both empty and containing benign and suspicious items. The strengths of the system can be immediately seen: objects can be recognized fairly easily, and since the radiation involved is nonionizing, it poses little threat to human beings. The primary limitations are also clear. Metal objects are shown only as silhouettes since unlike the case of x-ray radiography the THz radiation does not penetrate macroscopic conductive materials. As a result, a lone metallic object can be fairly easily identified, but multiple overlapping conductive objects become indistinct. This can be partially resolved by using multiple detectors to measure reflected, scattered, and transmitted radiation from the subject. Additionally, while the images are clear, the system’s resolution is fundamentally limited to the THz wavelength. Finally, the system shown here utilizes only one detector with point scanning, systems utilizing a matrix or linear array of detectors would be more suitable for real-time imaging applications.

This article will discuss in detail the free-space pulsed terahertz radiation generated by the motion of photo-excited electrons and holes that are accelerated by the built-in surface field in semiconductor microstructures. The amplitudes (intensities) of the THz radiation are measured for series of GaAs and InAlAs surface intrinsic-n⁺ (SIN⁺) structures with various built-in surface fields. It is found that as the surface field in the intrinsic layer is lower than the so-called “critical electric field, E_c” of the semiconductor, the amplitude of the THz radiation depends not only on the strength of the surface field but also the number of photo-excited carriers. At the high field limit, on the other hand, at which the surface field exceeds the critical electric field, the THz amplitude is independent of the surface field but proportional to the number of photo-excited carriers. The critical electric field is closed related with the L valley offset (intervalley threshold, intervalley splitting) in the semiconductors. Both the critical electric field and L valley offset are estimated from THz radiation in this study.

Fig.5. PR spectra from all the as-grown samples

GaAs and In_0.52Al_0.48As SIN⁺ structures grown by conventional molecular beam epitaxy (MBE) are used as the THz emitters in this study. A built-in static electric field exists across the intrinsic layer similar to a parallel-plate capacitor with electrons accumulated at the surface and ionized positive donors behind the interface. The schematic diagram of the SIN⁺ structure, location of the charged carriers and field distribution in the SIN⁺ structures are shown as Fig. 4(a). Figure 4(b) shows the direction of the electric field, normal to the surface, pointing from the buffer layer to the surface as well as the directions of the motion and acceleration of the electrons induced by the electric field. Various intrinsic layer (undoped layer) thicknesses are also obtained from as-grown samples by subsequent etches. Figure 5 displays the PR spectra from all the as-grown samples. Features near 1.3-1.4 eV originate from the GaAs substrate, while features from 1.5-1.8 eV are the Franz-Keldysh oscillations, (FKO, labeled 1-9 in Fig. 1) originating from the built-in electric field in the intrinsic layer. The photon energy E_n of the n_th extremum of the FKO plotted as a function of F_n, defined by [3π(n+1/2)/2]^2/3, yields a straight line. From the slope of this straight line, the built-in electric field and energy gap E_g of the sample can be deduced. The energy gap obtained is 1.42 eV for all GaAs samples and is independent of the intrinsic layer thickness d. Figure 6 displays the built-in electric fields of all the GaAs samples as a function of d. Data obtained from samples successively etched from as-grown samples with undoped layer of 800 nm, are shown in solid squares. The built-in electric fields from samples in which the intrinsic layer is completely etched away or all the way through to the buffer layer are also included in Fig. 6. The negative values of d represent the thickness of the buffer layer that is etched away and the measured electric field locates in the charge depletion layer of the buffer. The surface fields in these samples measured by modulation spectroscopy of photoreflectance (PR) ranges from 14 to 297 kV/cm, a rang which brackets the critical electric field.

A standard experiment setup using a free-space co-propagating electro-optic sampling system is employed (Fig. 7). THz radiation is detected in reflection geometry. A mode-locked Ti-Sapphire laser operated at 82 MHz is used to generate 80 fs pulses with a central wavelength of around 790 nm. The incident angle of the pump laser on the sample is 45^o from normal. The pump beam is uniformly focused on the emitter surface in s-polarization and maintained at 200 mW over an area with radius of 500 μm. Since the pump beam intensity is low (around 0.3μJ/cm²) and the emitter possesses inversion symmetry, there is little contribution from nonlinear process. Figure 8 depicts the amplitude of the THz radiation from the GaAs SIN⁺ structure as a function of the thickness of the intrinsic layer. The inset displays several time domain THz spectra of samples with different intrinsic layer thicknesses.

Fig.6. Built-in electric fields of all the samples as a function of intrinsic layer thickness d

The amplitude of THz radiation is proportional to volume integral of the time derivative of the transient current density J(x,t), which equals en_ph(x,t)μE_loc, where n_ph(x,t) is the density of photo-excited carriers, e is the electron charge, μ is the electron mobility and E_loc is the local electric field. Here we have neglected the contribution from diffusion of electrons due to KBT << eE/α in our case. By neglecting the change of electric field due to the photo-generated carrier screening effect and the change of electron of mobility related to the relaxation of hot electron energy which is in a time scale much larger than the excitation of photo-carriers, we obtain

(1)
where n_ph is the total number of photo-excited carriers in the depletion and surface-intrinsic layers per excitation pulse

(2)

Fig.7. Standard THz experiment setup using a free-space co-propagating electro-optic sampling system

with R the reflectivity of the emitter, α the absorption coefficient ( 1.40x10⁴ cm^-1 for GaAs); η the quantum efficiency,

the photon energy of the pump beam, 、

is the repetition rate of the pump beam, 、

the angle that the intrinsic layer optical path makes with the surface normal (x-direction), d the thickness of the intrinsic layer in the SIN⁺ structure used as an emitter, and s the width of the charge depletion layer defined by

, where

is the dielectric constant of the semiconductor, N is the doping concentration, and

is the potential barrier height across the interface or the charge depletion layer on the surface. In the experiment reported herein, I_o is maintained at 200 mW over an area with radius of 500 μm. The number of photo-excited free carriers, nph, estimated by Eq. (2), and the product, nphEloc, are plotted in open circle and solid squares, respectively, as a function of the thickness of the intrinsic layer, in Fig. 9. Figures 6 and 9, however, reveal that the variations of the amplitude of the THz radiation and the product, n_phE_loc, are not consistently related to each other when the thickness of the intrinsic layer is less than 200 nm or the built-in electric fields in the emitters is larger than 40 kV/cm. Leitenstorfer et al. found that, below the so-called critical electric field, the maximum drift velocity of free charged carriers in a semiconductor is proportional to the electric field in the semiconductor. However, as the field rises above the critical electric field, Ec, the maximum drift velocity declines slightly as the field increases. The maximum drift velocity of the free charged carriers peaks at the critical electric field, which depends on the energy difference between the Γ to L valley (intervalley threshold, L valley offset) in the semiconductor. Leitenstorfer et al. also found that the critical electric field in GaAs is 40 kV/cm corresponding to an intervalley threshold of 330 meV. Figure 6 indicates that while the intrinsic layer thickness is less than 200 nm, the electric field of GaAs is larger than the critical field thus the drift velocity is approximately constant. The amplitude of THz radiation, above the so-called critical electric field, is not proportional to nphEloc but proportional to n_phE_c. We can define an effective electric field, E_eff, which equals to the critical field, E_c as the Eloc is larger than the critical field, and equals to E_loc as the Eloc is smaller than the critical field. Figure 10(a) plots n_phE_eff as a function of the intrinsic layer thickness d. For comparison, the amplitude of the THz is also plotted as a function of d in Fig. 10(a). The dependence of THz and n_phE_eff on the thickness of the intrinsic layer are almost identical to each other implying that there is a critical electric field, E_c, in the semiconductor such that E_THz is dependent on E_loc when E_loc is smaller than E_c and is independent of Eloc when Eloc exceeds Ec. Figure 10(b) depicts the amplitude of the THz radiation and the number of photo-excited free charged carriers estimated by Eq. (2), as a function of the thickness of the intrinsic layer the number. Both the amplitude of the THz radiation and the number of carriers depend identically on the thickness of the intrinsic layer indicating that the amplitude of the THz radiation is proportional to the number of photo-excited carriers, as indicated by Eq. (2). The critical electric field in In0.52Al0.48As is approximately 47 kV/cm corresponding to a 430 meV L valley offset. The surface built-in electric fields in all InAlAs samples exceed the critical electric field, thus the amplitude of THz radiation is independent of the built-in field.

In conclusion, THz radiation from GaAs and InAlAs SIN⁺ structures with various surface fields as the bias is studied. The amplitude of the THz radiation peaks at the critical field which depends on the energy difference between the Γ to L valley of the semiconductor. As the field is lower than the critical field, the amplitude is proportional to the product of the surface field and the number of photo-excited carriers. In the high field limit where the surface field exceeds the critical field, the amplitude is independent of the surface field but proportional to the product of the critical field and the number of the photo-excited carriers. In addition, both L valley offset can be estimated from THz radiation.

Fig.8. Amplitude of the THz radiation from the GaAs SIN⁺ structures with various intrinsic layer thickness. The inset displays several time domain THz spectra of samples with different intrinsic layer thicknesses.

Fig.9. Amplitude of the THz radiation and the product, n_phE_loc, plotted in solid squares and open circles, respectively, as a function of the thickness of the intrinsic layer.

Fig.10. Product of carrier number and effective electric field, n_phE_eff, carrier number, and the amplitude of the THz as functions of the intrinsic layer thickness d.