Terahertz emission from gradient InGaAs surfaces Terahertz emission from gradient InGaAs surfaces

We present an experimental study of the terahertz emission from In x Ga 1 − x As epitaxial layers that were grown varying the alloy fraction x . We observe a terahertz emission that is signiﬁcantly different depending on the var direction of the alloy fraction. We attribute the difference to the signiﬁcant change of the band bending induced growth direction and to the position-dependentvariation of the effective mass. The emission of terahertz electromagnetic transients from semiconductor surfaces after ultrafast photoexcitation is a topic that has attracted enormous attention over the last cou- ple of decades 1–6 . Not only because it provides a convenient and passive source of terahertz radiation 7,8 but also because it is a potential tool to understand the carrier dynamics of the semiconductor material in the picosecond timescale 9 .

The emission of terahertz electromagnetic transients from semiconductor surfaces after ultrafast photoexcitation is a topic that has attracted enormous attention over the last couple of decades [1][2][3][4][5][6] . Not only because it provides a convenient and passive source of terahertz radiation 7,8 but also because it is a potential tool to understand the carrier dynamics of the semiconductor material in the picosecond timescale 9 .
The generation of terahertz radiation at the surface of a semiconductor after photoexcitation has been attributed to two main effects. Firstly, the ballistic transport of electrons that acquire most of the kinetic energy resulting from the difference between the photon and the bangap 10 . Secondly the acceleration experienced by the electrons owing to the electric field caused by the band bending in the vicinity of the surface 11,12 . The relative wight of these two effects strongly depends on the wavelength of the laser pulse, the bandgap of the semiconductor and the effective mass of the carriers in the material 10 .
In this article we study the terahertz emission of gradient In x Ga 1−x As structures. In other words, samples in which the alloy fraction x was varied monotonically during the growth process. The resulting bandgap variation in the direction of growth brings an additional electric field in-built in the sample, which can point either towards the surface or towards the bulk. This modifies the carrier dynamics, and therefore the terahertz emission of the samples.
When excited by 800 nm pulses it is well known that the THz emission of GaAs is mostly due to the carrier acceleration caused by the band-bending near the surface which is schematically represented in Fig. 1a. On the other hand, for InAs, the main contribution comes from ballistic transport, owing to its very low carrier effective mass, and the rather large excess of energy of the photoexcited carriers associated to its narrow bandgap, also schematically represented in Fig. 1b 10 . In this article we propose two gradient In x Ga 1−x As structures in which the alloy fraction is continuously varied in the direction normal to the surface from 1 to 0 (Fig. 1c) and vice versa (Fig. 1d).
The following samples were grown by molecular beam epitaxy. The substrate temperature was set at 525 and 605•C for the growth of InAs and GaAs, respectively, and it was linearly changed between these values for the growth of the gradient structures. All samples were grown on SI-GaAs (100) sub- Each sample was cleaved into two pieces, one set wa served as-grown and the other set was annealed by ram the temperature slowly until reaching 250 • C where an A atmosphere was introduced, in order to avoid surface da the temperature was further increased until reaching 6 and maintained for 10 minutes 13 . All samples were studied by x-ray diffraction 14,15 .

GaAs and InAs samples show diffraction patterns typi
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0061918
Terahertz emission from gradient InGaAs surfaces the lattice constant of those two crystals and we will not discuss them here. The diffraction intensity for the gradient samples as a function of the angle is shown in Fig. 2a and b. What we observe is a strong peak at ∼33.03 • , which corresponds to the GaAs lattice. In addition, a less prominent, but still large peak is observed at ∼30.53 • , this corresponds to the 98% In lattice constant. However, these two peaks are continuously joined by a plateau of lower intensity, this demonstrates the presence of continuously varying lattice constant, consistent with the presence of a gradient. These features have been observed before in similar samples 14 . The gradient reported here is rather large, going from x∼0 to x∼1, therefore plastic relaxation of the film at certain thickness must have occurred, which lead to the low and continuous diffraction intensity plateau that corresponds to the graded film region. Additional subtle features can be seen in the curves of Fig. 2a and b; The small, but visible peak at around 32.6 • in Fig. 2b for the Ga>In sample corresponds to the diffraction of a 16% indium concentration alloy, which is consistent within our error to the composition of 12% at which the gradient started. Similarly, In>Ga sample started with an In concentration of 98% explaining the peak located at 30.74 • in Fig 2a. The slight differences with the nominal concentration for both of the gradients are related to strain. The annealing process seems to have two important effects on the samples. The plateau appears higher for both samples, which suggests an improvement of the crystallinity along both gradients, most likely owing to the removal of lattice defects. In addition, as seen in Fig. 2d, the plateau of Ga>In seems to be more constant, suggesting a "softening" of the lattice discontinuity in the vicinity of the pure GaAs substrate.
In order to characterize the samples, a terahertz timedomain spectroscopy setup was build based on a Ti:sapphire mode-locked laser that emits pulses of ∼33 fs duration centered at 800 nm at a repetition rate of 80 MHz. The pulses are split into two beams. The first one, with an average power of ∼50 mW is sent through a motorized delay line and then is used to excite the semiconductor sample at an incidence of 45 • . The THz radiation generated in the form of a s cycle electromagnetic transient, is collected at 45 • as s in Fig. 1e by using an off axis parabolic mirror. A s parabolic mirror focuses the THz radiation onto a 1 mm [110] ZnTe crystal. The second laser beam is also fo onto the ZnTe crystal and copropagates with the THz tion, subsequently an achromatic λ /4 waveplate, a Wol prism and a pair of balanced photodiodes are used to small changes in the relative intensity of the laser polari components, which is proportional to the instantaneous electric field. By changing the relative delay between the radiation and the second laser pulse it is possible to ma the time-dependent waveform of the THz electric field. ther details about electrooptic sampling of THz pulses c found in Valdmanis, Mourou, and Gabel 16 .
The time-domain signals for the four materials is sho Fig. 3a and b for the as-grown and annealed samples re tively. Among the as-grown samples, InAs has the stro emission, it is worth noticing that the as-grown InAs had excellent crystal quality according to in-situ high e electron diffraction except for the first ∼2 nm near the interface. The second strongest signal is the one produc the annealed In>Ga gradient sample. We calculated the grated power of the samples, which is shown in Fig. 3c. we can see that the emission of InAs is about 13 tim power emitted by as-grown GaAs, while the power em by annealed In>Ga is about 10 times that of as-grown G Among the interesting things to point out in this plot is th nificant reduction of the InAs power after annealing. It i remarkable that except for the two strongly emitting mat already mentioned, the rest all have relatively similar em powers. An exception is the annealed Ga>In sample, w shows the lowest emission of all. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0061918
Terahertz emission from gradient InGaAs surfaces The annealed In>Ga sample, is a very strong emitter, almost comparable to InAs. In order to explain this, we will refer to the schematics in Fig. 1a-d. The In>Ga sample is composed of GaAs on the surface, which has a relatively broadbandgap and, owing to the alloy-variation, the bandgap narrows down as we move into the bulk, this produces a strong acceleration of the electrons which adds to the acceleration caused by the surface field. In other words, the force experienced by an electron is mostly given by the difference of potential energy between the initial position, near the surface, and the final position, away from the surface. Thus, the large band bending of the gradient contributes with a significant acceleration. Furthermore, the force acting on the carrier is given by where p is the momentum, m * is the effective mass and a is the acceleration. Therefore, the acceleration will also have an additional term given by −v dm * /dt, in the case of the In>Ga, the derivative of the mass is negative, resulting in an additional positive term that contributes to the acceleration. In order to do an "order-of-magnitude" estimation of the terahertz emission caused by the acceleration experienced by the electrons in all four semiconductor samples (the contribution of the holes is neglected here), we assumed that the average electron was accelerated from 0 tov i = 2K/m, on average, over a period δt ∼100 fs which is about 2 to 3 times the duration of the laser pulse, where K is the kinetic energy, given by the difference between energy of the λ =800 nm photons and the bandgap energy at the surface K = hc/λ − E BG (0). In addition, if we make the right-hand-side part of Eq. 1 equal to −dU/dx the gradient of the potential, which we can approximate as a linear function that changes ∼ E BG (0)/2 about half the bandgap energy at the surface for all samples owing to surface pinning, plus the bandgap change owing to the alloy variation for the In>Ga and Ga>In samples. Therefore in total the acceleration experienced by the electrons will be approximately where δ x ∼ 1 µm is an estimation of the surface depletion, as well as the distance over which the alloy fraction is varied. In addition, ∆E BG and ∆m are the total change of the bandgap and the change of effective mass over the alloy-fraction layer. Using this simplistic approach and using the parameters show in Table I. Since the emission is proportional to the acceleration, in order to present the estimation, all the values obtained where normalized to that of GaAs, and are shown in Fig. 3c. The estimation shows qualitative resemblance, and predicts correctly the relative order of the strength of the materials, supporting the qualitative picture that we have presented. Of course, it is a rather approximate model that does not take into account many subtleties of the carrier dynamics, including the carrier screening of the fields, and the differences in absorption coefficient, among others. We attribute the enormous difference observed between the annealed and the as-grown sample to the defects in the lat- tice, which will contribute with both scattering center traps which will reduce the current transient responsib the emission. During the annealing process the lattice re and this reduces the number of defects, increasing the bility and reducing the number of traps, both in the bul those on the surface. This is consistent with the analy the X-ray diffraction presented earlier. In the case of t verted gradient, namely Ga>In, the situation is reverse band bending caused by the alloy-fraction variation pro an electric field that competes with the surface field, an points in the direction opposite to the ballistic motion of trons into the bulk, therefore reducing the emission. The applies to the −v dm * /dt term, which now points in the site direction since the effective mass increases. Finall want to point out that both InAs and Ga>In, which a samples that have Indium at the surface, experience a r tion of the emission with the annealing process. We b this is because these two samples became semi-metals to the surface during the baking process, which lead to I regation that we could observe by optical and atomic-f microscopy images of the annealed samples (not shown) resulted in a very high carrier density, and therefore high conductivity, which in turn reduces the terahertz emissio In summary, we have presented a terahertz emission of In x Ga 1−x As gradient samples. We observed that the sion strongly depends on the direction in which the alloy tion changes, producing strong emission when the band narrow in the bulk and larger at the surface and a weak sion in the opposite case. The strong terahertz emissi the first case is comparable to that of InAs. This is exp by the electric field imposed by the variation of the ban energy, which promotes acceleration of electrons towar bulk in the In>Ga sample, but inhibits the acceleration Ga>In case.

Growth direction
Bulk Surface

GaAs InAs
In>Ga Ga>In

(d) Ga>In annealed
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0061918