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Abstract
We study polarity reversal in terahertz pulses generated from p-doped Si(001) surfaces with different doping levels. The azimuthal dependence of both terahertz emission and second-harmonic generation caused by the bulk electric quadrupole and magnetic dipole process is measured to determine the contributions of optical rectification and the surface depletion field direction, respectively. By comparing the penetration depth of the excitation laser and the depletion field strength on Si surfaces, we show that competition between the photo-Dember effect and surface field accelerations causes the polarity reversal.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In electronics technology, silicon surfaces play essential roles in many semiconductor devices, including field-effect transistors (FETs), light-emitting diodes and solar cells. In addition to these well-known applications, recent years have seen silicon surfaces used in the gradual development of all-dielectric metasurfaces, which exhibit very low absorption losses and thus provide a way to overcome the intrinsic absorption losses of conventionally metallic metasurfaces [1,2]. In general, as-received native oxide layers or regrown native oxide layers are present on the silicon surfaces. To enhance the performances of both semiconductor devices and all-dielectric metasurfaces, the properties of ${\textrm {Si}}/{\textrm {SiO}}_2$ interfaces need to be characterized. Capacitance-voltage (C-V) measurements and X-ray photoelectron spectroscopy are the most commonly used methods for the analysis of material interface properties. However, the C-V method is incapable of providing localized evaluations and X-ray photoelectron spectroscopy requires bulky equipment and is a ‘destructive’ method. Therefore, optical probing methods, which are noninvasive and noncontact techniques, have been developed to study the properties of semiconductor surfaces and interfaces; these methods include second-harmonic generation (SHG) spectroscopy [3–9] and terahertz (THz) emission spectroscopy [10–17].
When femtosecond pulses interact with the ${\textrm {Si}}/{\textrm {SiO}}_2$ interface, SHG and THz emissions can be also detected. One important mechanism of THz emission is optical rectification, which is a second-order nonlinear process that is similar to the SHG process. In monocrystalline Si (mono-Si) with inversion symmetry, the second-order dipole response of the bulk material is zero. Therefore, second-order nonlinear optical processes around the surface and the electric quadrupole and magnetic dipole processes of the bulk would also arise [18]. While these mechanisms have been investigated using the SHG technique, there have been no previous studies of these mechanisms in mono-Si using THz emission spectroscopy. Another important mechanism of THz emission is that of transient currents. When a femtosecond laser irradiates the surface of a semiconductor, the electrons and holes (e-h pairs) that are generated via the absorption of photons are accelerated by either the surface depletion field or the Dember field. The sub-picosecond lifetimes of the induced e-h pairs are responsible for the transient currents that cause THz pulses to be radiated. Recently, several researchers have studied the properties of ${\textrm {Si}}/{\textrm {SiO}}_2$ interfaces via THz emission spectroscopy and have illustrated the advantages of this method [14–17]. The phase information of the interface is usually lost when only second-harmonic intensity measurements are performed using a photomultiplier tube [19–23]. However, coherent THz waves are emitted from the interface and can be measured using THz time-domain spectroscopy, which offers a complementary way to provide the phase and amplitude information simultaneously. The combination of these two techniques can provide more information about the interface properties and will be beneficial to the development of both semiconductor devices and all-dielectric metasurfaces.
In this work, THz emission has been detected from p-type Si(001) surfaces with resistivities of 1-5 $\Omega \cdot {\textrm {cm}}$ and 0.01-0.05 $\Omega \cdot {\textrm {cm}}$ at room temperature. By rotating each sample around the surface normal, the polarity flipping behavior of the THz emission from these two samples is confirmed and cannot be attributed to the optical rectification process. Under different excitation and emission polarizations, the azimuthal dependence of the THz emission is similar to that of SHG, indicating that the optical rectification is related to the bulk electric quadrupole and magnetic dipole process of Si(001). The surface depletion fields of the samples are determined using the azimuthal dependence of SHG. Following comparison of the penetration length of the pump beam and the Fermi level of the sample, we conclude that competition between the photo-Dember effect and the surface field accelerations is the key to the polarity flipping behavior of the THz emissions.
2. Experimental setup
In our experiments, the laser source is a Ti: sapphire oscillator (Mira 900, Coherent ) that generates $p$-polarized light pulses centered at 800 ${\textrm {nm}}$ with 150 ${\textrm {fs}}$ duration and a repetition rate of 76 ${\textrm {MHz}}$. As shown in Fig. 1(a), the laser pulses are split into an intense pump beam and a weak probe beam. Using a lens with a focal length of 15 cm, the pump beam excites the sample at an incident angle of $\theta =45^{\circ }$. The maximum intensity of pump laser is 1.5 ${\textrm {GW}}/{\textrm{cm}}^2$. The sample can be rotated around the surface normal. In Fig. 1(b), the azimuth $\phi$ is the angle between the plane of incidence and the $[100]$ direction of the Si(001) surface. In the reflected beam directions, THz emission and SHG from the sample surfaces are collected and detected, respectively, using different methods. The THz emissions are collected using two parabolic mirrors (diameter: 2 in. (1 in. = 2.54 cm); focal length: 3 in.) and are then focused on a ZnTe $(110)$ surface with thickness of 3 mm. By rotating the [001] direction of the ZnTe $(110)$ surface, we can detect either $s$- or $p$-polarized THz emissions [24]. The second harmonic passes through the hole of the first parabolic mirror and is detected using a photomultiplier tube (PMT) with a band-pass filter (@$400\pm 10nm$) and a polarizer. All measurements were performed in air at room temperature.
Fig. 1. (a) Optical diagram of the experimental setup. HR: high-resistance silicon; BPF: band pass filter (@400$\pm$10 $nm$); P: polarizer; PMT: photomultiplier tube; WP: Wollaston prism. (b) Sketch of a Si (001) sample. $\theta$ is the angle of incidence and $\phi$ is the azimuthal angle of the samples.
The parameters of the Si(100) wafers used in this study are given as follows: (1) wafer-A: p-type (boron), 1-5 $\Omega \cdot$cm, $1.14\times 10^{15} {\textrm {cm}}^{-3}$; (2) wafer-B: p-type (boron), 0.01-0.05 $\Omega \cdot$cm, $4.57\times 10^{18} {\textrm {cm}}^{-3}$. Both wafers were 500 $ {\mu} {\textrm{m}}$ thick. The carrier densities of wafer-A and wafer-B were measured using THz time-domain transmission spectroscopy and THz time-domain reflection spectroscopy [25], respectively. Both samples were exposed to ambient air for sufficient time to form a native oxide layer with a thickness of approximately 3 ${\textrm {nm}}$ that covered the entire sample surface [26]. Before the measurements, the sample surfaces were cleaned using successive sonication processes in acetone and deionized water. As stated by Park and his coworkers, no significant differences between the as-received native oxide interface and the regrown native oxide interface were observed in the time-dependent SHG measurements, indicating that the as-received native oxide interface and the regrown native oxide interface have similar interface properties [26].
3. Results and discussion
As shown in Fig. 2(a), $p$-polarized THz waves are generated from the wafers at azimuthal angles $\phi =0^\circ$ pumped by $p$-polarized laser with the intensity of 1.5 ${\textrm {GW}}/{\textrm{cm}}^2$. The inverse polarities of the THz waves from wafer-A and wafer-B may be caused by transient currents or optical rectification processes. The THz wave generated from a p-InAs surface under the same conditions are also shown in Fig. 2(a) (as the dashed green line). For convenience, the THz amplitude from p-InAs has been divided by a factor of 700 to enable direct comparison with the two wafer cases. The THz wave from p-InAs shows the same polarity and waveform as that from wafer-A, indicating that the radiation mechanism is related to transient currents [27]. Because Si has an indirect band-gap of 1.12 eV and direct band-gaps of more than 3 eV, optical pulses with energies of 1.55 eV can excite carriers by single-photon absorption via the indirect optical transition or by multi-photon absorption via the direct optical transition. Single-photon absorption requires electron-phonon coupling, which is not required for multi-photon absorption, and this leads to a lifetime of approximately 1 ${\mu} {\textrm {s}}$ for the electron-hole (e-h) pairs for single-photon absorption, in contrast to the sub-picosecond lifetimes for multi-photon absorption [28–30]. The sub-picosecond lifetimes of the induced e-h pairs are responsible for the transient currents that lead to radiation of THz waves [13]. Under the depletion fields of the wafers, the movement of the e-h pairs leads to transient currents called drift currents; under the Dember field, the different diffusion velocities of the electrons and holes (caused by the photo-Dember effect) result in transient currents called diffusion currents.
Fig. 2. (a) $p$-polarized THz waves generated from wafer-A, wafer-B and p-InAs with the pump intensity of 1.5 ${\textrm {GW}}/{\textrm{cm}}^2$. The THz amplitude from the p-InAs surface is divided by 700. (b) $p$-polarized THz amplitude peak from wafer-A as a function of the pump intensity.
In Fig. 2 (b), we show the measured THz amplitude peak from wafer-A as a function of pump intensity. THz radiation gradually becomes saturated with increasing pump intensity and the experimental data in Fig. 2 (b) are fitted using the saturation formula $E_\textrm {THz}\propto I/(I+I_\textrm {sat})$, where $I$ is the pump intensity and $I_\textrm {sat}\approx 0.79$ ${\textrm {GW}}/{\textrm {cm}}^2$ is the saturation intensity [31]. This saturation mainly results from the photoexcited carrier accumulation in the surface as pump fluence increases, which further leads to the electrostatic screening of photocarriers [31–36]. Therefore, the radiation intensity of transient currents is weakened and that of optical rectification may become dominant. In order to understand the physical mechanism behind the THz polarity reversal for heavely p-doped Silicon wafers pumped by p-polarized laser pulses, the contributions of the transient currents and the optical rectification processes to the THz emission must be identified.
Similar to the SHG process, the nonlinear processes on the Si surface can be described using the nonlinear polarization at the THz frequency $\Omega$ as [37]
where $\vec r$ is the radius vector of the nonlinear source location inside the semiconductor, $P^\textrm {BD} (\vec r,\Omega )$ is the bulk dipole (BD) polarization induced by the depletion field through the bulk third-order nonlinear susceptibility, and $P^\textrm {BQ} (\vec r,\Omega )$ is the bulk electric quadrupole and magnetic dipole (BQ) polarization. Here, the surface nonlinear polarization can be neglected because it occurs within a few atomic layers of the sample surfaces where the inversion symmetry is broken. For Si(001), $P^\textrm {BD} (\vec r,\Omega )$ is independent of the azimuthal angle [18]. Therefore, the azimuthal dependence of the SHG is related to the bulk electric quadrupole and magnetic dipole process alone. To distinguish the optical rectification components of the THz emission, we measured the azimuthal dependence of the peak-to-peak amplitude for $p$- and $s$-polarized THz waves pumped with $s$- and $p$-polarized laser pulses, respectively. Figure 3 shows the measured results for wafer-A with the pump intensity of 1.5 ${\textrm {GW}}/{\textrm {cm}}^{2}$. The azimuthal dependence of the THz emission ($\cos 4\phi$ for the $p$-polarized THz emission and $\sin 4\phi$ for the $s$-polarized THz emission) is consistent with the bulk electric quadrupole and magnetic dipole process in Si(100), which has been studied using the azimuthal dependence of SHG [18,38]. When compared with that of SHG, the azimuthal dependence of the THz emission provides a direct measurement method for this higher-order nonlinear process.Fig. 3. (a) The azimuthal dependence of peak-to-peak amplitude for $p$-polarized THz waves pumped by $p$- (PP) and $s$-polarized (SP) laser pulses. The red circles (PP) and blue squares (SP) are the experimental data. The red solid line and blue dashed line are fitting of Eqs. (2) and (3), respectively. (b) The azimuthal dependence of peak-to-peak amplitude for $s$-polarized THz waves pumped by $p$- (PS) and $s$-polarized (SS) laser pulses. The green circles (PS) and pink squares (SS) are the experimental data. The green solid line and pink dashed line are fitting results. The pumping intensity in (a) and (b) is 1.5 ${\textrm {GW}}/{\textrm {cm}}^2$.
When the studies of SHG from Si(001) [18,38] and the contributions from the diffusion current and the drift current [39] are considered, the THz emission under $p$- and $s$-polarized excitation can be expressed as
Figure 3(a) shows the azimuthal dependence of peak-to-peak amplitude for $p$-polarized THz waves pumped by $p$- (PP) and $s$-polarized (SP) laser pulses. The red circles (PP) and blue squares (SP) are the experimental data. The red solid line and blue dashed line are fitting of Eqs. (2) and (3), respectively. The azimuthally-dependent components of $E_\textrm {PP}$ and $E_\textrm {SP}$ are only related to the bulk electric quadrupole and magnetic dipole polarization, which are fitted in Eqs. (2) and (3) with $c_1$ and $c_2$ by 0.21 and -0.19, respectively. The opposite signs of $c_1$ and $c_2$ are consistent with the bulk electric quadrupole and magnetic dipole process of SHG in the surface of Si (001) [18]. The azimuthally-independent components of $E_\textrm {PP}$ and $E_\textrm {SP}$ originate from the diffusion current, the drift current and the bulk dipole polarization induced by the depletion field, which are fitted totally in Eqs. (2) and (3) by the offsets 2.3 and 2.5, respectively. The azimuthally dependent percentage of $E_\textrm {PP}$ and $E_\textrm {SP}$ are only $9.1\%$ and $7.5\%$. It’s obvious that the azimuthally-dependent contributions are too small to cause the flipping of the THz field polarity. Figure 3(b) shows the azimuthal dependence of peak-to-peak amplitude for $s$-polarized THz waves pumped by $p$- (PS) and $s$-polarized (SS) laser pulses. The green circles (PS) and pink squares (SS) are the experimental data. The azimuthally-dependent components of $E_\textrm {PS}$ and $E_\textrm {SS}$ are only related to the THz electric field from the bulk electric quadrupole and magnetic dipole polarization, which are fitted in Eqs. (4) and (5) with $c_3$ and $c_4$ by -0.11 and 0.08, respectively. Transient photocurrents and depletion-field-induced dipole polarization are along the surface normal of wafers and have no contributions to the $s$-polarized THz waves, which disagree with the azimuthally-independent offsets of $E_\textrm {PS}$ and $E_\textrm {SS}$ in Fig. 3(b). The noise in our system is approximately 0.1 and the offset of $E_\textrm {PS}$ may be caused by this noise. However, the offset of $E_\textrm {SS}$ is too large to be explained by the noise alone, and is possibly caused by other higher-order effects, such as the photon-drag effect [40].
To explain the polarity flipping of THz fields from wafer-A and wafer-B under $p$-polarized excitation and emission conditions, the direction of the surface depletion field in Eq. (2) must be determined. In the previous studies of SHG from Si(001), the azimuthal dependence was found due to the bulk electric quadrupole and magnetic dipole process, and SHG from Si(001) can thus be described using the equation below [28,41,42]
where $\chi ^{(3)}$ is the third-order electric susceptibility of Si(001) and $\chi ^{(2)}$ is the second-order electric susceptibility caused by the bulk electric quadrupole and magnetic dipole process. $I^{(2\omega )}$ and $I^{(\omega )}$ are the intensities of the second harmonic and fundamental light beams, respectively. When the direction of the depletion field is reversed, the azimuthal dependence of the SHG would then have a $45^{\circ }$ phase difference [26,42].The azimuthal dependences of the THz emission and the SHG shown in Fig. 4 were measured under $p$-polarized excitation and emission conditions. The azimuthal dependences of the SHG from wafer-A and wafer-B without the $45^{\circ }$ phase difference shown in Fig. 4(a) indicate that their surface depletion fields are in the same direction. Based on the azimuthal dependence of the SHG from Si(001) under applied gate voltages, the directions of the surface depletion fields are perpendicular to the surface in the inward direction [43]. As a result of the intrinsic defects on the ${\textrm {Si}}/{\textrm {SiO}}_2$ interfaces, the Fermi level of the interface lies close to the middle of the bandgap of the Si bulk [44]. For p-type Si, the Fermi level of the bulk moves closer to the valence band as the doping concentration increases. Because of the Fermi level difference between the interface and the Si bulk, the energy band around the surface bends downward and the depletion field is perpendicular to the surface in the inward direction , which agrees with the measured results for the azimuthal dependence of SHG.
Fig. 4. (a) The azimuthal dependence of $p$-polarized SHG intensity from wafer-A and wafer-B under $p$-polarized laser pumping. The red circles are experimental data and the red dashed line is fitting for wafer-A. The blue squares are experimental data and the blue solid line is fitting for wafer-B. (b) The azimuthal dependence of $p$-polarized peak-to-peak THz amplitude from wafer-A and wafer-B under $p$-polarized laser pumping. The red diamonds are experimental data and the red dashed line is fitting of Eq. (2) for wafer-A. The blue triangles are experimental data and the blue solid line is fitting of Eq. (2) for wafer-B. The pumping intensity in (a) and (b) is 1.5 ${\textrm {GW}}/{\textrm {cm}}^2$.
In Fig. 4(b), under $p$-polarized excitation and emission conditions, the azimuthal dependences of the THz emissions from wafer-A and wafer-B contain positive and negative offsets, indicating the reversal of the THz polarity without azimuthal dependence. Because the azimuthally-dependent term plays only a minor role and the surface depletion fields are in the same direction, the transient currents caused by the first term and the second term in Eq. (2) are the key elements required to explain the polarity reversal. Based on the directions of the depletion fields and the Dember field within the wafers, the drift currents and the diffusion currents would be perpendicular to the interface in the inward and outward directions, respectively . Because of the competition between the drift and diffusion currents, the direction of the total transient currents can be perpendicular to the interface in the outward or inward directions, which then determines the polarity of the THz emission.
When we consider the polarity of the THz emission shown in Fig. 1(a), the directions of the transient currents in wafer-A and wafer-B are the same as and opposite to that of the corresponding current in p-InAs, respectively. This carrier density dependence of the THz emission polarity, i.e., the directions of the transient currents, can be explained using the differences between the penetration depth of the excitation laser beam and the strength of the depletion field on the surfaces of wafer-A and wafer-B. The absorption coefficients of wafer-A and wafer-B at a wavelength of 800 nm are approximately 900 ${\textrm {cm}}^{-1}$ and 2800 ${\textrm {cm}}^{-1}$, so their penetration depths are approximately 10.5 ${\mu} {\textrm{m}}$ and 3.5 ${\mu} {\textrm {m}}$, respectively [45]. Because the penetration depth of wafer-B is three times shorter than that of wafer-A, the photo-Dember effect in wafer-B is weaker than that in wafer-A. On the other hand, the surface depletion field strength of highly-doped p-type Si (wafer-B) is stronger than that of weakly-doped p-type Si (wafer-A). The depletion layer thickness in a p-type semiconductor, $w$, is represented by the following equation [46]
where $\epsilon$ is the static dielectric constant, $\epsilon _0$ is the vacuum permittivity, $V$ is the surface barrier height, $q$ is the electron charge, and $N_\textrm {A}$ is the acceptor concentration. $\epsilon$ is equal to 11.7 for the wafers used here [47]. The $N_\textrm {A}$ values of wafer-A and wafer-B are approximately $1.14\times 10^{15} {\textrm {cm}}^{-3}$ and $4.57\times 10^{18} {\textrm {cm}}^{-3}$, respectively. $V$ is equal to $(E_\textrm {Fb}-E_\textrm {Fs})/ q$, where $E_\textrm {Fb}$ and $E_\textrm {Fs}$ are the Fermi levels of the bulk and the surface, respectively. $E_\textrm {Fb}$ can be calculated from the following formula [46]: where $n_\textrm {i}$ and $E_\textrm {i}$ are the intrinsic carrier concentration and the Fermi level of mono-Si, respectively, $k_0$ is the Boltzmann constant, and $T$ is the experimental temperature. At room temperature, $T=300$ K and $n_\textrm {i}=1.02\times 10^{10} {\textrm {cm}}^{-3}$. Because the Fermi level of the surface lies close to the center of the bandgap of the bulk, the values of the surface barrier height $V$ for wafer-A and wafer-B are equal to 0.30 V and 0.52 V, respectively. From Eq. (7), the thicknesses of the depletion layers are approximately 583 ${\textrm {nm}}$ and 12 ${\textrm {nm}}$ for wafer-A and wafer-B, respectively. Therefore, the surface depletion field strength of wafer-B is two orders of magnitude higher than that of wafer-A, which causes a larger drift current in wafer-B.As described above, because the photo-Dember effect is weaker and the drift currents are larger for wafer-B than for wafer-A, the dominant transient current mechanism for wafer-B is the drift current, while the dominant mechanism for wafer-A is the diffusion current. Additionally, screening of the photo-Dember field can become more significant as the doping concentration increases. Therefore, the polarity of the THz emission can be reversed for wafer-B with a high doping density.
4. Conclusions
We measured THz emission and SHG from Si(001) wafers excited using a 1.55 ${\textrm {eV}}$ pulsed laser and determined the azimuthal dependences of the THz emission and the SHG. The THz emission polarity from p-type Si with resistivity of 0.01-0.05 $\Omega \cdot {\textrm {cm}}$ is opposite to that of p-type Si with resistivity of 1-10 $\Omega \cdot {\textrm {cm}}$, and the azimuthal dependence of the THz emission from Si(001) shows a fourfold relationship. Comparison of the azimuthal dependence of the THz emission and SHG shows that the fourfold relationship can be attributed to the bulk electric quadrupole and magnetic dipole process of Si(001); additionally, the azimuthal dependence of the THz emission provides a method for direct measurement of the bulk electric quadrupole and magnetic dipole process without requiring coupling of the azimuthally-independent components. With the directions of the surface depletion fields having been identified, analysis of the penetration depth of the pump beam and the strength of the depletion field suggests that the polarity flipping of the THz emission can be explained by the weaker photo-Dember effect and the larger drift current that occur in Si with resistivity of 0.01-0.05 $\Omega \cdot {\textrm {cm}}$. Simultaneous measurement of the THz emission and the SHG has the potential to enable evaluation of more information from Si surfaces, and would be beneficial for advancements in the development of semiconductor devices and all-dielectric metasurfaces.
Funding
NSAF Joint Fund (U1830206); Major Research Plan (91850201); National Natural Science Foundation of China (NSFC) (11404400, 11474359, 11574396, 11604386, 11604387); Pre-Research Foundation of NUDT (ZK17-03-09).
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