Factors Affecting Terahertz Emission from InGaN Quantum Wells under Ultrafast Excitation

InGaN quantum wells (QWs) grown on c-plane sapphire substrate experience strain due to the lattice mismatch. The strain generates a strong piezoelectric field in QWs that contributes to THz emission under ultrafast excitation. Physical parameters such as QW width, period number, and Indium concentration can affect the strength of the piezoelectric field and result in THz emission. Experimental parameters such as pump fluence, laser energy, excitation power, pump polarization angle, and incident angle can be tuned to further optimize the THz emission. This review summarizes the effects of physical and experimental parameters of THz emission on InGaN QWs. Comparison and relationship between photoluminescence properties and THz emission in QWs are given, which further explains the origin of THz emission in InGaN QWs.


Introduction
With the advent of THz radiation-based spectroscopic techniques, efcient THz generation has become an urgent need [1][2][3][4].Te THz spectroscopy has applications in environmental monitoring [5], imaging [6], biomedical diagnosis [7], material characterization [8], food inspection [9], medicine inspection [10], communication technologies [11], detection of explosives [12,13], etc. Te THz generation has been observed upon ultrafast excitation of semiconductors, alloys, gas plasmas, and some material combinations including LiNbO 3 [14], ZnTe [15][16][17], GaAs [18], InAs [2,19], W/Co 40 Fe 40 B 20 /Pt [20][21][22][23], InGaN [24], and quantum wells (QWs) [25][26][27][28][29][30][31][32][33], to name a few.Te THz pulse generation is accomplished using various methods including photocurrent transients in gas plasmas, photocurrent surge from electro-optic materials [34][35][36][37][38], Cerenkov radiation in ferroelectric materials, diference frequency generation in nonlinear materials, spintronic emission from magnetic metal multilayers [23], and dynamic screening of electrostatic feld in QWs [25,27,29,30,32,33,[39][40][41].Due to the extensive research on QWs for their importance in lighting applications, the growth technologies of QWs are mature and the rich underlying physics of QWs have been widely explored over the last few decades.One of the unique characteristics of InGaN/ GaN QWs is the built-in electric feld (of the order of MV/ cm) originating from spontaneous and piezoelectric polarization in QWs grown along the [0001] crystal orientation of (c-plane) sapphire [42,43].Te lattice mismatch between the QW and barrier materials results in a strain that causes piezoelectric polarization in QWs [44,45].Te strong built-in piezoelectric felds result in a quantum confned stark efect (QCSE) [46,47].QCSE is the band-structure tilt in QWs due to the strong built-in piezoelectric feld [48][49][50][51].It leads to low optical transition energy and poor recombination efciency in QW-LEDs as the wave function overlap decreases under the infuence of this feld [25,[52][53][54][55][56][57].Tis built-in feld however plays a central role in terahertz generation upon ultrafast excitation of InGaN/ GaN QWs [33].Te frst photon from an ultrafast laser source increases the overlap of the electron-hole wave function and absorption coefcient for the subsequent photon [58].Te instantaneous absorption of the photon results in the spatial separation of wave functions and the creation of polarized electron-hole pairs in a time interval much shorter than the typical recombination time [31].Te electric feld of such a dipole has a polarity opposite to the built-in piezoelectric feld.Due to the opposite polarity of these dipoles, the partial screening of the built-in feld occurs, which leads to a local microscopic modifcation of both the optical and electronic properties of the system.Te sufcient density of these dipoles excited by the ultrafast laser can cause complete screening of the built-in feld.Tis process is known as "dynamical screening" in QWs.Te screening efect induced by the carriers excited in the spatially separated states modifes the band structure, absorption coefcient, and electron-hole wave function within the duration of pulse excitation.Te screening of the piezoelectric feld results in THz emission.Te efect was explained by considering a nanoscale capacitor that releases the stored electrostatic energy.Te energy stored in QWs is released via THz emission under the infuence of ultrafast excitation.Tese nonlinear efects can be observed since the time scale is much shorter than the typical recombination time of the carriers [58].
THz emission in QWs depends on many factors such as piezoelectric feld strength, QW width, period, band gaps of QWs and barriers, efective masses of electrons and holes, and band ofsets.Te most important parameter is the piezoelectric feld strength which defnes the optical and electronic properties of the QWs [25].Here, we present a review of the most important factors that afect the THz emission from QWs under ultrafast excitation.

THz Emission Mechanism in InGaN QWs
Te band tilt in QWs due to a strong piezoelectric efect is an obvious phenomenon in the absence of a restoring force.Te band shape can be restored by strong excitation, which is known as screening [27,39].Te screening efect is responsible for the THz emission in QWs under ultrafast excitation.Figure 1(a) depicts the band tilt and screening efects.Te shorter time scale of the ultrafast excitation does not allow the excitons to recombine for photoluminescence (PL) emission.It rather leaves the system in a perturbed state for the subsequent photon.Te absorption of the subsequent photon results in THz emission.No THz emission is observed when the sample is excited at normal incidence [33].Excitation at θ in � 45 °and −45 °angles of incidence results in THz emission of the opposite polarities indicating its strong dependence on the piezoelectric feld.Figure 1(b) is a schematic representation of the phenomenon.At this particular angle, the nonzero projection P x of the transient dipole vector can be obtained in the direction orthogonal to the propagation direction of the THz pulse [58].Tis observation is clear evidence of THz emission dependence on the built-in piezoelectric feld that is directed perpendicular to the sample surface.Sun et al. attained the highest THz power at an angle of incidence of 72 ° [59].Tey suggest that the angular distribution of THz radiation is consistent with the concept of THz generation in QWs as a "radiation of dipoles." Turchinovich et al. performed calculations that allow the derivation of polarization density P t (t) on a given instant of time in QWs under coherent photon fux ϕ(t) as follows [25]: where P o is the initial polarization, eL z is the 2D array of elementary dipoles, and α is the absorption coefcient.α(t) can be derived from the following equation: 2 International Journal of Optics where M(t) � ψ e (t)|ψ h (t) is the time-varying overlap integral of the empty wave function of conduction and valence band states and α max is the absorption coefcient of unbiased QW.Te efective feld F(t) can be derived as a function of time by using the following equation:

Factors that Affect the THz Emission from InGaN QWs under Ultrafast Excitation
Te THz emission in InGaN QWs is mainly governed by the strong built-in piezoelectric feld under ultrafast excitation.QW width, period number, and Indium concentration are the main physical parameters that can infuence the strength of the piezoelectric feld and the resulting THz emission.Te THz emission can be further tuned by changing experimental parameters such as laser energy, pump fuence, and excitation power.Here, we will discuss the most important parameters that have been reported to infuence the THz emission in QWs.

QW Period Number. Te THz emission from InGaN
QWs is strongly infuenced by the number of QWs.Te THz emission has been studied for QW samples with up to 16 QW period numbers [31].It is observed that the increased period number results in an increased piezoelectric feld due to strain accumulation in the respective QWs, leading to higher THz emission.Prudaev et al. compared THz emission spectra obtained by ultrafast excitation of samples with diferent QW period numbers [26].Figures 2(a)-2(c) show the structures of the samples studied.Figure 2(d) shows the emission spectra under excitation power densities that provided maximal energy for THz signals from each sample structure.With a further increase in the power densities, the THz signal was reduced.Tey found that an increased period number required increased excitation power densities to achieve the same maximal amplitudes of the THz pulse.Te spectral maximum was found to shift to higher frequencies for samples with higher QW period numbers.THz absorption was also observed to increase with the increase in QW period number.
Sun et al. observed a continuous increase in THz output power with the increase in the QW period number [31].Tey used a maximum of 16 periods.PL-saturated for period numbers above 4. Te phenomenon was explained in terms of the increased piezoelectric feld with the increase in QW period number due to the accumulated strain.An increased piezoelectric feld reduces the wave function overlap.Terefore, the carrier recombination efciency decreases, resulting in poor PL emission efciencies in QWs.

Indium Content. Guan Sun et al. suggested that an
increase Indium content should result in higher THz emission due to increased electron-hole separation leading to higher dipole strength [31].Norkus et al., on the other hand, found that an increase Indium content can result in the screening of built-in felds due to the high density of electron gas in QWs [41].Tey explained that the ultrafast excitation of such a structure can result in the formation of a higher number of dipoles of polarity opposite to the piezoelectric feld.Tis may suppress the piezoelectric feld under increased excitation energies.It results in the saturation of THz emission efciency for increased photon energies as shown in Figure 3(a).Te screening and saturation may occur at relatively low excitation energies for such structures, limiting the extent of the THz emission.

Power Density and Pump
Fluence.Excitation power densities strongly afect the THz emission in QWs.Higher emissions are observed up to certain power densities, above which the THz emission can either be reduced or saturated.Te saturation is generally explained in terms of complete screening of the piezoelectric feld by sufciently high power densities.In their pioneering work, Turchinovich et al. reported THz emission from InGaN/GaN multiple QWs [58].Tey found that the built-in piezoelectric feld can be completely screened by the carriers excited in spatially separated states when the excitation is strong enough.Prudaev et al. observed an increase in THz signal amplitude with an increase in power densities to a certain level [26].For sufciently high power densities, the THz signal amplitude was found to decrease.Te increased free-carrier concentration, the increased THz absorption within the material, or the optical damage under high excitation power densities were attributed to this behavior.In previous works, saturation was observed instead [27,30,31,59].Compared with previous works, the excitation was performed at an 800 nm wavelength, when the photon energy is not enough for interband transitions to occur.Te In content was also comparatively lower compared with previous works, which leads to a lower piezoelectric feld.
Sun et al. observed that the increased pump fuence lead to a quadratic increase in the THz output power up to the pump fuencies of 40 μJ/cm 2 [31].Further increases in pump fuencies resulted in a slight deviation from a quadratic ft due to the screening efect.
Te polarization dynamics in QWs for a weak and an extremely strong excitation have been studied by Turchinovich et al. [25,58].Tey calculated the excitation kinetics in a QW for variable excitation pulse fuencies, QW widths, and piezoelectric feld strengths [25].Tey also calculated the time evolution of the absorption coefcient for diferent pump fuences as shown in Figure 3(b).Tey found that the optical absorption coefcient is strongly afected by the excitation pulse fuence.Trough calculations, they predicted the spectral broadening and shift of the THz spectra with increased excitation fuence.Te lowest bandwidth limit they calculated was equal to the excitation pulse bandwidth.Tey suggested that such a broadening could not be detected with the conventional TDS approach, since it uses laser pulses of the same duration for both temporal shape generation and sampling.It needs to be further verifed by a temporally stretched excitation and a short detection pulse.
In their experimental work, Turchinovich et al. reported the THz pulses generated in a sample with 10 identical QWs of 2.7 nm widths each [58].Te excitation fuences ranged from 0.02 to 1.3 mJ/cm 2 .Te shapes of the THz pulses were identical.Tey suggested that the limited bandwidth of their setup resulted in identical pulse shapes as shown in Figure 4(a).Van Capel et al. had similar observations of the THz pulse shapes as shown in Figure 4(b) [30].For confrmation, Guan Sun et al. measured the THz spectra under diferent pump fuences by using a homemade submillimeter difraction grating system [31].Te system could detect the spectral bandwidths beyond the laser spectra.Tey did not observe the broadening and frequency shift of the THz spectra since the screening efect was negligible in their pump fuence range.Higher fuences may allow the observation of such behavior.4 International Journal of Optics Above a certain pump fuence value, a saturation of THz output was observed in some works [27,30,31,59].Te phenomenon is explained in terms of the depletion of the electrostatic energy in QWs by the excitation of a substantial density of polarized electron-hole pairs.Te total internal refection on the material surface and increased absorption within the material are also reported to contribute to the saturation behavior [31].Turchinovich et al. reported the dependency of peak-peak amplitudes on the excitation fuence for two samples of 10 QWs each [58].Te QW widths were 2.7 and 3.6 nm.Te pulse amplitudes increased rapidly and saturated for fuences higher than 0.5 mJ/cm 2 , as shown in Figure 5(a).Te saturation was explained by the example of a capacitor.If we consider the QW structure as a nanoscale capacitor, the maximum THz pulse energy stored in the capacitor is limited by the partial or complete discharge of the electrostatic energy stored in the nanocapacitor.
Van Capel et al. observed a monotonous increase in THz output with an increase in pump fuence and saturation above a certain fuence value, as shown in Figure 5(b) [30].At this fuence value, complete screening of the QWs occurs, and all the energy stored in the QWs is released.For relatively lower fuence values, the screening in QWs is a negligible phenomenon [31].[30,58].Van Capel et al. observed a 13% increase in the THz output power by increasing the QW width from 1.8 to 3.6 nm [30].However, screening is also a dominant phenomenon in thicker QWs.Turchinovich et al., calculated the excitation kinetics in a QW for variable excitation pulse fuencies, QW widths, and piezoelectric feld strengths [25].Teir calculations suggest that the thicker QWs can provide a higher number of e-h pairs with higher spatial separations, leading to higher screening in thicker QWs.
Turchinovich and Van Capel et al. found that regardless of the thickness of the QWs, saturation occurred for the same fuence value as shown in Figures 5(a) and 5(b) [30,58].It was explained in terms of the complete screening of the piezoelectric feld that results in the release of electrostatic energy in QWs.Te symmetry in QWs is restored at this moment.

Incident Angle. Guan Sun et al. measured the THz
output power propagating in the transmission direction for various pump beam angles (the angle of the surface normal being formed with the pump beam).Tey used a p-polarized pump beam for this measurement [59].Te output power was zero when the pump beam angle approached zero, whereas the THz output power maximum for an incident beam angle of 72 °.Te data was well-ftted by the equation P THz ≈ f(θ) sin 2 (θ), where P THz is the THz output power, f(θ) is the contribution from the Fresnel refection of the pump beam, and sin 2 (θ) represents a typical angular distribution of the dipole radiation.Trough this work, they proved that the angular distribution of the THz radiation is consistent with the concept of THz generation in InGaN QWs as the "radiation of dipoles" generated in the spatially separated electron and holes under the infuence of a strong built-in piezoelectric feld.

Pump Polarization Angle. Guan Sun et al. measured the dependences of the THz output power and polarization
(angle between the THz polarization and the incident plane) on the polarization angle of the pump beam (angle between the pump polarization and the incident plane) and azimuth angle [59].Te incident angle was set to be around 72 °to collect the maximum THz output power.Te THz output power oscillated with the pump polarization angle.Te data were well-ftted by their theoretical curve when considering the Fresnel refection.Tis is primarily because of the dependence of the Fresnel refection on the polarization angle of the pump beam.It further confrmed the concept of "radiation of dipoles" in QWs discussed above.

Correlation between THz Emission, PL, and Piezoelectric Field
Te PL emission usually increases with a certain number of QWs in QW-LEDs.Further increase in period number results in saturation.Guan Sun et al. proposed that such behavior is due to the increased nonradiative structural defects with the increase in QW period number [31].Tey found that THz emission is not reduced by defects because THz emission occurs as a result of absorption.On the other hand, PL emission is a radiative recombination process that is strongly afected by structural defects.It is also afected by the absorption process.Te piezoelectric feld also increases in QWs with the increase in period number.PL emission is strongly infuenced by the piezoelectric feld due to the QCSE.Te QCSE is caused by band structure tilt due to the higher piezoelectric feld that reduces wave function overlap.It decreases the recombination efciencies of excitons in QWs, leading to poor PL emission efciencies.THz emission, on the other hand, benefts from the increased piezoelectric feld and lower wave function overlap.Te dipoles Sun et observed that the THz output power quadratically increases with the pump fuencies up to 40 μJ/cm 2 [31].A slight deviation from quadratic ft was observed for further increase in fuencies up to 85 µJ/cm 2 .Tis deviation is because of the screening efect supported by the blue shift of PL observed in such experiments.However, since theoretical observations predict an increase in the absorption coefcient, a more than linear increase in PL intensity should be observed with pump fuencies (the absorption coefcient is proportional to the ratio of integrated PL intensity with the pump fuence).But the PL intensities scaled up less than linearly with the pump fuencies indicating a reduction in absorption coefcients, which is not consistent with the screening efect.Tey concluded that the saturation behavior was because of the lower absorption coefcient at high excitation fuencies.
Ilya Prudaev et al. indicated that the local inhomogeneities in In concentration could result in an additional PL peak [26].Tis additional peak, caused by asymmetric broadening and spectral shift at high excitation intensities, is attributed to the low In regions in QWs as shown in Figure 6(a).Tey suggested that the emission data for quantifcation of the piezoelectric feld could thus give erroneous results.Tey proposed that the screening efect could not be completely understood by monitoring the PL.Te localized states play an important role in the emission process that induces a band-flling efect.Te band-flling efect can result in a blue shift at higher pump powers.Te combination of screening and band-tail flling efects can be responsible for the observed blue shift.
Turchinovich et al. observed a broad PL peak at lower excitation fuences [58].An additional PL peak was observed at high excitation fuences in their time-integrated PL measurements, as shown in Figure 6(b).Te intensity of the additional peak increased with excitation fuences.Te peak moved to 435 nm at low excitations and remained there for further increase in excitation fuences.Tey explained that the QW was completely biased by the built-in electric feld at low excitation fuences.At high excitation intensities, the PL spectrum showed a superposition of screened (zero built-in electric felds) and biased (when all the carriers have recombined) states.
Mu et al. reported the formation of InGaN quantum dots within the InGaN QW layers [29].Tey observed that the regions of high THz emission gave poor PL emissions attributed to lower densities of QDs at those locations as shown in Figure 7(a).Te QDs provide photogenerated carriers localized inside them.Te internal polarization feld in QDs is expected to be lower compared with that in QWs.Te screening of the polarization feld must be higher in the areas of high QD densities, supporting the higher THz output powers.Similarly, Guan Sun et al. compared the THz and PL emissions in staggered and conventional QWs [60].THz emission in staggered QWs was lower while the PL was higher as shown in Figures 7(b) and 7(c).Staggered QWs are designed to reduce the charge separation in QWs and increase the recombination efciencies [61].THz emission is obviously lower in such structures due to the lower built-in piezoelectric felds.

Conclusions and Outlook
Te efects of certain physical and experimental parameters on THz emission in QWs have been reviewed and sumin this work.In conclusion, an increased period number of QWs results in increased strain accumulation in the respective layers, a high piezoelectric feld, increased THz emission, and increased THz absorption.Due to increased THz absorption in QW samples, emission loss within the sample may also increase.Te THz frequency also shifts to higher frequencies for samples with increased QW period numbers.Increased Indium content can result in a higher number of dipoles of polarity opposite to that of the piezoelectric feld under ultrafast excitation.Te saturation of THz emission is an obvious phenomenon at sufciently high excitation energies due to the complete screening of the piezoelectric feld.Te increased number of dipoles of opposite polarity can suppress the piezoelectric feld, resulting in screening and saturation for even relatively lower excitation energies.Te total internal refection on the material surface and increased absorption within the material may also contribute to saturation.On the other hand, THz emission may also quench (instead of reaching saturation) due to the increased THz absorption within the material, optical damage under high excitation power densities, or increased free carrier concentration.Higher THz emissions can be obtained by growing thicker QWs.Although thicker QWs result in higher THz emission, saturation occurs for almost the same fuence values regardless of the thickness.Te THz signal can be further optimized by calibrating the angle of incidence and pump polarization.
Mostly, the QW samples that give poor PL emission efciencies ofer higher THz emissions due to QCSE.Compared with PL, THz emission is not afected by structural defects.It may allow the use of low-quality samples and relatively less sophisticated growth techniques for low-cost THz generation from QWs. Te luminescence behavior in QWs can thus predict the expected THz emission properties of QWs.Furthermore, the studies of temperature and pressure dependence on THz emission may further elaborate the emission process.Te study of dipoles and magnetic moments of dipoles should lead us to an even better understanding of the phenomenon.A bigger challenge in this feld may be the use of the piezoelectric feld component in the growth direction to get higher TH emissions.THz emission and piezoelectric feld enhancement using novel QW structures may open more opportunities in this feld.

Figure 1 :
Figure 1: (a) Principle of the optically induced screening of a QW.(b) Excitation geometry for the successful THz emission from QWs.

Figure 2 :
Figure 2: (a) Experimental samples with (a) one, (b) fve, and (c) ten InGaN/GaN quantum wells.(d) Terahertz emission spectra generated in samples A, B, and C under the excitation power densities which provide maximal energy of the THz signal.Reprinted with permission from [26].Reproduced with permission from Wiley materials.Copyright Wiley materials.

Figure 3 :
Figure 3: (a) THz feld amplitude as a function of excitation energy in In X Ga 1-X N layers with x � 0.68 (blue) and 0.8 (green) where x represents the doping concentration.Copyright nature portfolio (b) Temporal evolution of absorption coefcient.Te dashed line represents the normalized temporal shape of the photon fux in the excitation pulse.Reproduced with permission from AIP Publishing.Copyright AIP Publishing.

3. 4 .
QW Width.Van Capel and Turchinovich et al. found that the wider QWs produced stronger pulses, as shown in Figures 5(a) and 5(b)

Figure 4 :
Figure 4: (a) THz pulses detected from samples with 2.7 nm and (b) 3.6 nm QW widths for varying pump fuences.Reproduced with permission from the American Physical Society.Copyright American Physical Society.

Figure 5 :
Figure 5: (a) Peak-peak feld strengths of THz pulses for varying excitation fuences.(b) THz peak-peak amplitudes versus fuence for various QW thicknesses.Reproduced with permission from the American Physical Society.Copyright American Physical Society.

Figure 7 :
Figure 7: (a) Integrated PL intensity and average THz output powers.0 and 8 in the horizontal axis represent the center and edge of the multiple QWs, respectively.(b) Comparison of PL and (c) THz spectra of staggered and conventional InGaN QWs.Copyright Optica publishing group.