Coherent phonon spectroscopy characterization of electronic bands at buried semiconductor heterointerfaces

Characterization of the electronic energy states at buried hetero-interfaces is one of the most pressing issues in device physics. Simple estimations based on the electron affinities of the two semiconductors¹ often fail due to the formation of new interfacial chemical bonds, extended defects, crystalline morphologies, and intermixing.^2–4 It is therefore crucial to determine the band alignment by measuring actual interfaces. Photoemission spectroscopy, which is the standard technique to directly evaluate the electronic states at surfaces and interfaces with thin overlayers,⁵ cannot be applied to deeply buried interfaces due to the limited probing depth (⁠$≲$5 nm). Capacitance-voltage measurements⁶ and internal photoemission spectroscopy⁷ can be applied to thicker overlayers, but they can be influenced by the carrier transport in the overlayers. Complementary all-optical techniques are desirable to evaluate the electronic states of deeply buried interfaces.

In polar semiconductors, the collective oscillations of charge carriers (plasmas) couple with the longitudinal optical (LO) phonons via the Coulomb interaction.⁸ The frequency of the resulting LO phonon-plasmon coupled (LOPC) mode depends crucially on carrier density and plasma damping rate. Raman observation of the LOPC mode has been employed extensively to determine the carrier distributions within polar semiconductors and at their interfaces.^9–11 The LOPC mode can also be excited as a coherent oscillation by femtosecond optical pulses.^12,13 Because coherent LOPC mode is generated predominantly by the instantaneous screening of the surface field by photoexcited electrons and holes,^14,15 the amplitude of the oscillation can be a quantitative measure for the pre-existing electric field and the resulting electronic band structure. Thus, coherent phonon spectroscopy is promising as an all-optical evaluation technique of the electronic states at buried interfaces including polar semiconductors.

The growth of group III-V semiconductors on Si is motivated by the potential for incorporating optoelectronic functions into Si based devices. GaP, an important material for light emitting diodes, photovoltaics, and photocatalysts, is particularly interesting because it has a good epitaxial relationship with the Si(001) surface.^16–19 In this letter, we report on the experimental characterization of the Fermi level at GaP/Si(001) interfaces by coherent phonon spectroscopy. The formation of a hetero-interface may affect the electronic structure of GaP significantly through, e.g., unintentional doping and differently charged pinning centers, even though the GaP films are not intentionally doped. We find that the Fermi level correlates with the density of antiphase domains (APDs) in GaP films and predicts the electronic band profiles by theoretical simulations.

The samples studied are nominally undoped GaP layers grown by metal organic vapour phase epitaxy on the n-type Si(001) substrates under three different conditions.²⁰ The GaP film samples I and II are grown at 675 and 450 °C on the Si(001) substrate with a very small miscut angle, whereas sample III is grown at 575 °C on a Si(001) substrate with a larger miscut angle. Whereas all the films are free from extended planar defects, the different growth conditions introduce different densities and shapes of APDs, in which the direction of the Ga–P bonds are reversed with respect to the main phase [Figs. 1(a) and 1(b)]. Sample I has self-annihilated (kinked) APDs with boundaries on the {112} and {110} planes [Fig. 1(c)], whereas sample II has APD boundaries vertically penetrating the film on the {110} planes [Fig. 1(d)]. Sample III, by contrast, has only a few small (<5 nm in height) APDs [Fig. 1(e)]. The film thicknesses for samples I, II, and III measured by x-ray diffraction are 57, 55, and 45 nm. We note that the unintentional doping levels of the GaP thin films cannot be determined directly, e.g., by Hall measurements, because they are grown on conductive substrates. Pump-probe reflectivity measurements are performed at room temperature in a near back-reflection configuration using optical pulses of ∼10 fs duration and 400-nm wavelength (3.1-eV photon energy).²⁰ The effective probing depth [(2α)⁻¹  = 58 nm for GaP with α as the absorption coefficient²¹] is comparable to the GaP layer thicknesses. The pump-induced change in the anisotropic reflectivity $ΔReo$ is measured as a function of time delay between the pump and probe pulses.

Figure 2 compares the oscillatory parts of $ΔReo/R$ and their Fourier-transformed (FT) spectra for the GaP/Si samples. The coherent responses of samples I and II roughly resemble those of the p-type GaP(001), which we studied previously¹³ and are also shown in Fig. 2. They are all dominated by a long-lived LO phonon at 12 THz, whose amplitude is nearly independent of pump density, and a faster-decaying LOPC mode with the amplitude growing with the pump density.²⁰ GaP/Si samples I and II also feature relatively weak oscillations at 11 and 15.6 THz, both of which are absent from the bulk GaP. The frequencies agree with those of the TO phonon of GaP and the optical phonon of Si, respectively. For sample III, by contrast, the LOPC and LO modes from the GaP overlayer have much smaller amplitudes than the optical phonon of the Si substrate, even though its thickness is comparable to the other samples.

The amplitudes, frequencies, and dephasing rates of the coherent phonon modes are obtained from fitting the time-domain data to damped harmonic functions.²⁰ The photocarrier density-dependent frequency and dephasing rate of the LOPC mode, shown in Fig. 3, confirm that this mode involves the photoexcited plasma. Static dielectric model²⁰ roughly reproduces the frequency and dephasing rate assuming heavy damping (⁠$γ=25−30$ THz) of the plasma. Based on the previous study,¹³ we attribute the LOPC mode to the mixed electron-hole plasma. Unlike when GaAs is photoexcited at 800 nm,²² the electrons photoexcited in GaP at 400 nm are scattered almost instantaneously into the X and L satellite valleys that have nearly as large effective masses and damping rates as the heavy holes. The mixed plasma consisting of electrons and holes therefore give rise to an effectively single-component, heavily-damped LOPC mode, like when GaAs is excited with 400 nm light.²³ 

The amplitude of the LOPC mode varies by almost an order of magnitude among the GaP/Si samples, as shown with broken lines in Fig. 4. The excitation of the coherent LOPC mode of GaP is dominated by the transient depletion field screening (TDFS) mechanism,¹³ in which the ultrafast drift of photoexcited electrons and holes, shown in insets of Fig. 4, suddenly screen the pre-existing surface electric field in the depletion region.^14,15 The variation in the LOPC amplitude among GaP/Si samples can therefore be a measure of the variation of the internal electric field within the GaP layers; large (small) LOPC amplitude implies steep (flat) band bending before photoexcitation.

To estimate the band bending quantitatively, we need to establish the relation between the LOPC amplitude and the electric field. This can be done by comparing the LOPC modes of differently doped bulk GaP crystals, which were measured under the same experimental conditions.¹³ The symbols in Fig. 4 plot the LOPC amplitudes of (001)-oriented GaP as a function of the Fermi level E_F. Because the bands bend up (down) toward the surface for the p-type (n-type) surface, as illustrated by insets in Fig. 4, we fit the amplitudes with a linear function $ΔRLOPC/R=C|EF−Epin|$ with C and E_pin as parameters.²⁰ We obtain the pinning energy at the GaP/air surface $Epin≃Evs+$ 1.8 eV, with $Evs$ being the valence band maximum at the surface. This value is close to that reported for the GaP(110)/vacuum surface, $Evs+$ 1.6 eV.²⁴ 

We now estimate the Fermi levels for the GaP/Si(001) samples assuming that they are pinned at the surface by the same electronic states as for the bulk GaP(001). This is a reasonable assumption because our GaP films have nearly atomically flat surfaces. From crossings between the amplitudes (broken lines in Fig. 4) and the linear fit (solid line), we obtain E_F within the films of 0.1, 0.6, and 1.7–1.9 eV above E_v for samples I, II, and III.

We consider two possible explanations for different interface Fermi levels of the differently grown GaP films. One is that the GaP films are unintentionally doped at different densities. The estimated E_F shows no correlation with the film growth temperature and thus excludes the possibility of doping via intermixing of Si atoms. However, we find a correlation between E_F and the APD density, which would suggest higher doping for higher APD density. Though the conventional atomic models of APD boundaries [Figs. 1(a) and 1(b)] are neutral with equal numbers of Ga-Ga and P-P bonds, the actual boundaries can deviate from the stoichiometric models at the atomic scale, as reported in a previous TEM study,²⁵ and thereby introduce charges localized at the APD boundaries throughout the GaP layer thickness. Another possible explanation is that the GaP films are nearly intrinsic but the interface Fermi level is determined by trapping centers at the GaP/Si interface, whose energy levels and charge states depend on the film growth conditions. It is plausible that both of the two scenarios contribute to determining the interface Fermi level.

Because the actual charge distributions within the GaP films and the energy levels of the interfacial pinning centers are unknown, we model the electronic energy bands by making several simplifying assumptions.²⁰ We solve the Poisson equation for electric potential assuming the charge neutrality between the GaP layer and the depletion region of n-type Si. We consider two limiting cases in the charge distribution; in one case, the electric charges distribute uniformly over the GaP film. This would model the GaP film unintentionally doped by the carrier trapping at the APD boundaries that extends over the whole thickness of the film. In another case, charges are mostly trapped at the interface and the surface. This would model the nearly intrinsic GaP film whose E_F is pinned by the trap centers at the interface and the surface. The actual situation probably lies between the two limiting cases. Figure 5 compares the energy bands calculated in these two limiting cases. The results are qualitatively similar, except that the bands are curved for uniform charge distribution and straight for the Fermi level pinning at the interface. In both cases, the band bending within the GaP film is accompanied by a bending of similar magnitude in the Si substrate. Though our model is very simple, our calculations give a qualitative picture of the band profiles within the GaP film without detailed knowledge of the charge distribution in the GaP films and the trap states at the interface.

The present method has an advantage that we can estimate the electronic band profiles also in non-polar Si. The band bending in Si cannot be obtained directly from the Si phonon amplitude, because the TDFS mechanism works only on the polar, infrared active phonon modes, which the Si phonon is not. Coherent Si phonons are generated solely via the impulsive stimulated Raman scattering mechanism through deformation potential interaction,^20,26 which is independent of the magnitude of the surface band bending.

In conclusion, the lattice-matched GaP/Si(001) interfaces give rise to the coherent LOPC mode, whose amplitude can be used as a measure for the internal electric fields within the GaP films. We find that higher density of APDs in the GaP film leads to larger electric field as probed by the amplitude of the coherent phonons. Our approach is also useful for heterostructures involving other polar semiconductors, such as GaAs and InN, whose coherent phonons can be excited via TDFS mechanism. We thus demonstrate the applicability of the coherent phonon spectroscopy to the nondestructive characterization of the electronic states at buried interfaces.

This work was partly supported by the Deutsche Forschungsgemeinschaft through SFB 1083 and HO2295/8, as well as by NSF Grant DMR-1311845 (Petek) and DMR-1311849 (Stanton). H.P. thanks support from the Alexander von Humboldt Foundation and the Chinese Academy of Sciences President's International Fellowship Initiative.