Influence of doping level on Brillouin oscillations in GaAs
Adam Dodson, Andrey Baydin, Hongrui Wu, Halina Krzyzanowska, Norman Tolk
aa r X i v : . [ c ond - m a t . m t r l - s c i ] O c t Influence of doping level on Brillouin oscillations in GaAs
Adam Dodson † , Andrey Baydin † , ∗ and Hongrui Wu Department of Physics and Astronomy,Vanderbilt University, Nashville, TN 37235, USA
Halina Krzyzanowska
Department of Physics and Astronomy,Vanderbilt University, Nashville, TN 37235, USA andInstitute of Physics, Maria Curie-Sklodowska University,Pl. M. Cuire-Sklodowskiej 1, 20-031 Lublin, Poland
Norman Tolk
Department of Physics and Astronomy,Vanderbilt University, Nashville, TN 37235, USA bstract Time-domain Brillouin scattering has proved to be a unique tool for determining depth dependentmaterial properties. Here, we show the influence of doping level in GaAs on Brillouin oscillations.Measurements were performed on intrinsic, n-type and p-type GaAs samples. The results show highsensitivity of the amplitude of Brillouin oscillations to the doping concentration. The theoreticalcalculations are in a good agreement with the experimental data. This work provides an insightinto the specific dopant profiling as a function of depth.
I. INTRODUCTION
Time-domain Brillouin scattering (TDBS) is an ultrafast pump-probe experimental tech-nique based on generation and detection of coherent acoustic phonons (CAPs). The inho-mogeous absorption of a pump pulse ( < µ m textures in materialscompressed at megabar pressures [8, 9], doping profiles [10], depth-dependent stress [11],imaging of grain microstructure [12, 13], and determination of laser-induced temperaturegradients in liquids [14]. It has been shown that TDBS is sensitive to ion implantationinduced damage in gallium arsenide [15–17], diamond [18] and silicon carbide [19] at lowfluences.In this paper, we report on the influence of doping level in GaAs on Brillouin oscillations. ∗ [email protected]; current address: Department of Electrical and Computer Engineering,Rice University, Houston, Texas 77005, USA II. RESULTS AND DISCUSSION
The molecular beam epitaxy grown samples of GaAs (100) used in the experiment werepurchased from the Institute of Electronic Materials Technology, Warsaw, Poland. Total ofthree samples were studied: intrinsic, n-type, and p-type. The doping densities for n-type(Te) and p-type (Zn) were 1 . − . × cm − and 2 . × cm − , respectively. ATi layer (19 nm) was deposited onto all samples using an e-beam evaporator for efficientgeneration of CAPs. Ti was chosen due to its acoustic impedance that matches one of GaAswith less than 10% mismatch and, therefore, acoustic reflections are suppressed at Ti andGaAs interface.TDBS experiments were performed in a standard time-resolved pump-probe setup in areflection geometry. A Coherent Mira 900 with 150-fs pulses at 76 MHz was used as a lasersource. Wavelength of the laser was varied between 825 nm and 900 nm. Both beams werefocused onto the specimen with spot diameters of 100 µ m and 80 µ m for pump and probe,respectively. The pump beam was chopped using a Thorlabs optical chopper operating at 3kHz.Figure 1 shows representative Brillouin oscillations measured for intrinsic, n-type Te-doped (1 . − . × cm − ), and p-type Zn-doped (2 . × cm − ) GaAs at severalprobe wavelengths. The thermal background due to excited carriers in the Ti layer was sub-tracted out. The differences in experimental spectra for three samples are clearly seen in the3
50 100 150 Δ R / R intrinsic n-doped p-doped FIG. 1. Brillouin oscillations for intrinsic, n-type Te-doped (1 . − . × cm − ), and p-typeZn-doped (2 . × cm − ) GaAs at different probe wavelengths. amplitude of Brillouin oscillations. The amplitude changes as a function of probe wavelengthfor intrinsic and n-type GaAs, while it is constant for p-type GaAs in the probed wavelengthrange. The frequency of Brillouin oscillations for the studied samples is shown in Figure 2.The frequency dependence is well described by the equation f = 2 √ n − sin θvE probe , where θ is an angle of incidence of the probe beam (30 ◦ ), v is the longitudinal speed of sound, n is the index of refraction of GaAs, and E probe is the probe energy. The index of refractionwas measured by ellipsometry for all samples. The changes in the frequency with respect todoping concentration are negligible and will not be discussed further in this paper.The amplitude of Brillouin oscillations as a function of probe wavelength for differentdoping levels is plotted in Figure 3. As it has been shown before [22], the amplitude ofBrillouin oscillations changes drastically near the band edge and is maximized at the bandgap (Γ point). Such dependence can be explained by the sharpness of the band edge. It hasbeen shown in case of GaP that the energy dependence of the amplitude of the Brillouinoscillations, A osc , agrees well with the derivative of the dielectric function [20]. A osc ∝ (cid:12)(cid:12)(cid:12)(cid:12) ∂ǫ∂E (cid:12)(cid:12)(cid:12)(cid:12) = s(cid:18) ∂ǫ r ∂E (cid:19) + (cid:18) ∂ǫ i ∂E (cid:19) , (1)where ǫ is the dielectric function and ǫ r and ǫ i are the real and imaginary parts of thedielectric function, respectively. E is the probe energy. Therefore, as it can be seen in4 .37 1.40 1.43 1.46 1.49 1.52Energy (eV)36373839404142 F r e q u e n c y ( G H z ) intrinsicn-typep-type FIG. 2. Frequency of Brillouin oscillations as a function of probe wavelength for intrinsic, n-typeTe-doped (1 . − . × cm − ), and p-type Zn-doped (2 . × cm − ) GaAs. The dashedlines represent theoretical calculations. The error bars are of the order of the marker size. Figure 4 showing the dielectric function of GaAs, when one takes the derivative of thedielectric function, it is maximized near the band gap energy as the slope in this region issteep. To match the scale of the experimental data, all theoretical curves (the derivatives)are multiplied by the same factor which includes the photoinduced strain magnitude andother experimental parameters which are, to a good degree of approximation, constant withrespect to the probe energy.For n-type GaAs sample, the peak in the amplitude of Brillouin oscillations shifts tohigher energies (shorter wavelengths) and broadens. While, for p-type GaAs sample, nodependence of the amplitude of Brillouin oscillations on probe energy is observed in theprobe energy region. Note, that in our case, p-type sample has higher concentration ofcarriers than the n-type sample. The response of the n-type and p-type samples also agreeswell with predicted energy dependence based on the derivative of the dielectric function. Asdopants are added to the GaAs lattice, donor or acceptor states depending on the type ofdoping form near the conduction or valence bands, respectively. This formation of dopantstates results in the changes in the dielectric function such as smearing of the band edge forthe imaginary part of the dielectric function (see Figure 4b) and shifting and broadening ofthe peak associated with the band gap for the real part of the dielectric function (see Figure4a). Our results demonstrate that TDBS can be used to distinguish between different5 A m p li t u d e o f B r ill o u i o s c ill a t i o s , − -type840 855 870 885 900Wavelength ( m)36912 p-t(pe1.48 1.45 1.43 1.4 1.38E erg( (eV) 145494134145494134 ) ∂ ε / ∂ E ) FIG. 3. Amplitude of Brillouin oscillations as a function of probe wavelength for intrinsic, n-type Te-doped (1 . − . × cm − ), and p-type Zn-doped (2 . × cm − ) GaAs. Theexperimental data (dots) is compared to the theoretical model (lines). The error bars are of theorder of the marker size. dopant concentrations. While, there are other techniques to measure doping levels, TDSBcan uniquely provide depth resolution simultaneously with doping concentration.As mentioned earlier, our n-type and p-type samples have different doping concentrations.In order to get some insight how the type of the doping would affect the TBDS response, wetook the dielectric functions for several doping concentrations from previous studies [23, 24].Figure 5 shows the derivative of the dielectric functions for n- and p-type GaAs at differentdoping concentrations. According to these theoretical estimations, the peaks for the p-typeare higher and narrower than those for the n-type GaAs. This indicates that TDBS can besensitive both to the doping concentration and the type of doping.6 .2 1.4 1.6 1.8Energy (eV)12131415 R e [ ε ] (a)n-typep-typeIntrinsic 1.2 1.4 1.6 1.8Energy (eV)0.00.51.01.52.0 I m [ ε ] (b)n-typep-typeIntrinsic FIG. 4. Real (a) and imaginary (b) parts of the dielectric function for intrinsic , n-type Te-doped(1 . − . × cm − ), and p-type Zn-doped (2 . × cm − ) GaAs obtained using ellipsometry.
840 860 880Wavelength (nm)020406080100120140160 | ∂ ε / ∂ E | (p) cm −3 (p) cm −3 (n) cm −3 (n) cm −3 FIG. 5. Derivative of the dielectric function for different doping types and concentrations. Thedielectric function was taken from Casey et. al. [23, 24].
III. CONCLUSION
We have investigated the influence of type and level of doping in GaAs on Brillouinoscillations using TDBS. The experiments were carried out for intrinsic, n-type and p-type7aAs samples. The amplitude of Brillouin oscillations changes with respect to dopant levelwhile the change in their frequency is negligible. The energy dependence of the amplitudeof Brillouin oscillations is well explained by the theoretical model based on the derivativeof the dielectric function. Our results show that TDBS can be used to measure dopantconcentrations. This new report on the energy dependence of Brillouin oscillations addsanother approach in an application of TBDS for nanoscale imaging. Particularly, we envisionthat TDBS spectra taken for a range of probe energies near direct optical transitions couldbe used to measure specific dopant concentrations as a function of depth. For example,applications can include monitoring wafer doping homogeneity with respect to depth, ordetermining the position and interface between different doping levels and types. As varioustypes of defects and impurities have different effects on the dielectric function, it shouldbe possible to distinguish them and monitor their depth distribution. This is especiallyrelevant for understanding the degradation of devices operating in harsh environments thatare subject to radiation damage as well as for defect inspection in semiconductor wafermetrology.
ACKNOWLEDGMENTS
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