In this chapter, we first discuss the results of optical properties of InN:Mg samples measured by the electric-optical THz-TDS system. Afterward we discuss the a-plane experimental results. In this work, we can obtain all the transmittance of terahertz spectrum information.
5.1 - THz-TDS Measurement of c-plane InN and InN:Mg films Undoped InN film
By using the THz-TDS system, the calculated of complex conductivity ( ) and refractive index ( ) can be studied from 0.3 to 2.1 THz. The details of sample description can be found in . For the parameter extraction, the temporal profiles of terahertz signal are recorded twice, the first time without the sample (only substrate), and the second time with the sample. The substrate of InN film is 370-m-thick silicon(111).
Figure 5-1(a) shows THz time domain waveforms with and without (in the free space) the silicon substrate. The amplitude and phase spectrums of air and silicon substrate are shown in Fig. 5-1 (b). The frequency dependent transmittance obtained via Fast Fourier Transform (FFT) is approximately 60% to 70% as shown in Fig. 5-1 (c). The extracted frequency-dependent refractive index and extinction coefficient (n and k value) are shown in Fig. 5-2 (a) and Fig. 5-2 (b), respectively. The frequency-dependent refractive index value of silicon is 3.4 which is the same as our previous result. Because the extinction coefficient (k value) is less than 0.05, it could be ignored for later calculation. After analysis of silicon substrate, we measured the terahertz time-domain spectrums of InN and InN:Mg samples. In the Fig 5-3 (a), the transmittance of InN film is about 20%.
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Fig. 5-1 (a) The terahertz time-domain signal transmitted through air and silicon
Fig. 5-1 (b) The corresponding amplitude and phase spectrums of air and silicon
0.0 0.5 1.0 1.5 2.0 2.5 3.0
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0.3 0.6 0.9 1.2 1.5 1.8 2.1
0.0 0.2 0.4 0.6 0.8 1.0
Transmittance
Frequency (THz)
Fig. 5-1 (c) The amplitude transmittance of silicon substrate
0.3 0.6 0.9 1.2 1.5 1.8 2.1
2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
Refractive Index n
Frequency (THz)
Fig. 5-2 (a) Frequency dependent refractive index of silicon
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0.3 0.6 0.9 1.2 1.5 1.8 2.1
0.00 0.05 0.10 0.15 0.20
Extinction coefficient k
Frequency (THz)
Fig. 5-2 (b) Frequency dependent extinction coefficient of silicon
0.3 0.6 0.9 1.2 1.5 1.8 2.1
0.0 0.2 0.4 0.6 0.8 1.0
Transmittance
Frequency (THz)
091110
Fig. 5-3 (a) The amplitude transmittance of InN film
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The complex refractive index and conductivity of the InN film were calculated by using the methods at section 2.4 and are shown in Fig. 5-3 (b) and Fig. 5-3 (c), respectively. The frequency dependent conductivity results can be fitted theoretically by using the simple Drude model. The complex optical conductivity is defined by
The fit parameters, is the plasma frequency and is the carrier scattering time or called carrier damping rate. The fitting curves agree with the experimental data and two fitting parameters
40 THz and 49 fs were obtained. The real conductivity of undoped indium nitride (091110 InN) decreases as the frequency increases, imaginary conductivity slowly increases. The best fitting curves for the real part and imaginary part of refractive index and conductivity are shown in Fig. 5-3 (c). Assuming an electron effective mass [34] for the undoped InN film, these fit parameters correspond to the carrier concentration about 1.5x1018 cm-3 and the carrier mobility 1155 cm2/V-s, in reasonable agreement with room-temperature electrical Hall effect measurement result of 2x1018 cm-3 and 1120.0 cm2/V-s.
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Fig. 5-3 (b) Experimental data of refractive index and extinction coefficient of InN film
Fig. 5-3 (c) Experimental data (open symbols) and fitting data complex conductivity (solid line) of InN film
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Mg-doped InN film
Fig. 5-4 (a) shows the terahertz time-domain waveform of silicon substrate and the c-InN:Mg film. The amplitude and phase spectrums of silicon substrate and InN:Mg film are shown in Fig 5-4 (b). The transmittance of undoped InN film is less than 20%, whereas that of doping magnesium acceptors into InN films enhances the transmittance of terahertz around three times (>60%). Fig. 5-5 (c), (d), (e), and (f) are show the transmittance of each sample with different carrier concentration N from 4.3x1017 to 2.1x1018 cm-3. Interestingly, we found the terahertz transmittance does not have particular dependence on carrier concentration. After doping magnesium acceptors, acceptors and carries are to combine in the semiconductor. Thus all the transmittance of InN doping magnesium films are increase that indicates the conductivity were decrease. First, it is seen InN:Mg film with Hall measurement of carrier concentration (N=2.1x1018 cm-3) has similar to that of undoped InN film, but the transmittance is three times higher than that of undoped InN film. It is clearly indicating doping the magnesium acceptors affect the material property of InN semiconductor.
Fig 5-5 to 5-8 show the complex refractive index ( ) and optical conductivity ( ) of four selected c-InN:Mg films with different carrier concentrations. The calculated results shows the conductivity of imaginary part is almost zero for the c-InN:Mg films. The carrier concentration of each sample measured by Hall measurement is 2.1x1018, 1.6x1018, 9.9x1017, and 4.3x1017 cm-3, respectively. Despite of different carrier concentration, all the four samples of c-InN:Mg have a nearly frequency-independent conductivity of ~50cm-1Ω-1. This result can be fitted theoretically by using the simple Drude model. With the assumption of me=0.075m0, the whole best fitting parameters and
are given in
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Fig. 5-4 (a) The terahertz time-domain signal transmitted through silicon and InN:Mg
Fig. 5-4 (b) The corresponding amplitude and phase spectrums of silicon and InN:Mg
0.0 0.5 1.0 1.5 2.0 2.5 3.0
-40000
0.0 0.5 1.0 Frequeancy (THz) 1.5 2.0 2.5 3.0
P h a s e
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0.3 0.6 0.9 1.2 1.5 1.8 2.1
0.0 0.2 0.4 0.6 0.8 1.0
Transmittance
Frequency (THz)
080611
Fig. 5-4 (c) The amplitude transmittance of InN:Mg film (N=2.1x1018 cm-3)
0.3 0.6 0.9 1.2 1.5 1.8 2.1
0.0 0.2 0.4 0.6 0.8 1.0
Transmittance
Frequency (THz)
080525
Fig. 5-4 (d) The amplitude transmittance of InN:Mg film (N=1.6x1018 cm-3)
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0.3 0.6 0.9 1.2 1.5 1.8 2.1
0.0 0.2 0.4 0.6 0.8 1.0
Transmittance
Frequency (THz)
090317
Fig. 5-4 (e) The amplitude transmittance of InN:Mg film (N=9.9x1017 cm-3)
0.3 0.6 0.9 1.2 1.5 1.8 2.1
0.0 0.2 0.4 0.6 0.8 1.0
Transmittance
Frequency (THz)
080624
Fig. 5-4 (f) The amplitude transmittance of InN:Mg film (N=4.3x1017 cm-3)
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Fig. 5-5 (a) Experimental data (open symbols) and fitting data complex conductivity (solid line) of InN:Mg film (080611 | N=2.1x1018 cm-3)
Fig. 5-5 (b) Experimental data of refractive index and extinction coefficient of InN film (080611 | N=2.1x1018 cm-3)
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Fig. 5-6 (a) Experimental data (open symbols) and fitting data complex conductivity (solid line) of InN film (080525 | N=1.6x1018 cm-3)
Fig. 5-6 (b) Experimental data of refractive index and extinction coefficient of InN film (080525 | N=1.6x1018 cm-3)
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Fig. 5-7 (a) Experimental data (open symbols) and fitting data complex conductivity (solid line) of InN:Mg film (090317 | N=9.9x1017 cm-3)
Fig. 5-7 (b) Experimental data of refractive index and extinction coefficient of InN film (090317 | N=9.9x1017 cm-3)
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Fig. 5-8 (a) Experimental data (open symbols) and fitting data complex conductivity (solid line) of InN:Mg film (080624 | N=4.3x1017 cm-3)
Fig. 5-8 (b) Experimental data of refractive index and extinction coefficient of InN film (080624 | N=4.3x1017 cm-3)
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(c-plane InN and InN:Mg)
Parameters comparison of Hall effect measurement and TDS fitting by Drude model
Table 5-1 Parameters comparison of Hall effect measurement and TDS fitting by Drude model
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5.2 - Discussion of c-InN:Mg results
Our calculated carrier concentrations of all the InN:Mg films in Table 5-1 that agree well with those obtained by Hall measurement. The consistency of the results between Hall effect measurement and THz-TDS has an important implication that are n-type conductivity of InN:Mg films measured by Hall effect measurement may represent the electrical property of the whole film. In contrast, if we change to the hole effective mass ( ) to calculate the conductivity that is assumed the p-type conductivity of InN:Mg.[35][36] Thus the corresponding carrier concentration of each InN:Mg film can be much higher than the electron concentration and mobility lower than carrier mobility measured by Hall effect measurement. Despite the THz-TDS method cannot clearly make sure the type of semiconductor. Nontheless, we use electron effective mass to calculate the carrier concentration and carrier mobility are similar Hall effect measurement that may indicate our result is n-type semiconductor.
In Table 5-1, we found that the fitting of carrier scattering times of the InN:Mg films in our results are significantly reduced compared to undoped to that of undoped InN film. This result shows that magnesium doping induces the reduction of the conductivity and refractive index reduction. For semiconductor, the major contribution to the scattering time includes below：[37]
phonons：both acoustic and optical
ionized impurities
neutral defects
other carriers (e. g. scattering between electrons and holes)
The photoluminescence (PL) intensity of the InN:Mg films is typically much weaker than that of undoped InN, implying the inferior crystalline quality of InN:Mg films
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combined with impurities, defects, and dopants during the film growth.[38] A first-principles study also shows that dopants like magnesium in InN create the deep formation energy and magnesium acceptors substituted on In or N sites lead to the reduction in local symmetry associated with the relative positions of magnesium dopant and provide the scattering centers.[39] In addition, doped semiconductors, which are typically ionized, are charged and higher ionized impurity scattering slao occurs for highly doped semiconductor. Therefore, it clearly that impurity or defect scattering introduced by magnesium doping shortens the scattering time in the InN:Mg film and consequently leads to the terahertz transparency accompanied by low conductivity.
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5.3 - THz-TDS Measurement of a-plane InN film
In this section, we will discuss the a-plane InN film experimental data. The substrate of a-plane InN film is grown on r-plane { } sapphire and the thickness is approximately 430-um-thick. Fig. 5-9 (a) and Fig. 5-9 (b) show the crystal structure of sapphire. We know sapphire is an anisotropic material, rhombohedral crystal structure. If the wave incidence to an anisotropic material that brings the birefringence.
Because the anisotropic medium supports two modes with distinctly different phase velocities, therefore we can obtain different refractive index.
Fig. 5-9 (a) The crystal structure of sapphire
(http://www.namiki.net/product/jewel/sapphire/index.html)
Fig. 5-9 (b) The sapphire crystal orientation[40]
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Fig. 5-10 (a) shows the terahertz time-domain waveforms of sapphire substrate with different polarization field which are c-axis perpendicular and parallel terahertz wave, respectively. The time-domain terahertz signals of ordinary and extraordinary rays have different time delay. The amplitude and phase spectrums of air and sapphire substrate are shown in Fig. 5-10 (b). The transmittance of sapphire substrate obtained via Fast Fourier Transform (FFT) is approximately 70% as shown in Fig. 5-10 (c).
The extracted frequency-dependent refractive index and extinction coefficient (n and k value) are shown in Fig. 5-10 (d) and Fig. 5-2 (e), respectively. The frequency-dependent refractive index value of sapphire is approximate 3.32 and 3.10 as terahertz field is parallel and perpendicular to c-axis, respectively and the extinction coefficient (k value) both orientations are approximately 0 (<0.02).
0 2 4 6 8 10 12 14 16
Fig. 5-10 (a) The terahertz time-domain signal transmitted through air and sapphire with electric field perpendicular and parallel c-axis
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Fig. 5-10 (b) The corresponding amplitude and phase spectrums of air and sapphire substrate with electric field perpendicular and parallel c-axis
0.3 0.6 0.9 1.2 1.5 1.8 2.1
Fig. 5-10 (c) The amplitude transmittance of sapphire substrate with electric field perpendicular and parallel c-axis
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Fig. 5-10 (d) Frequency dependent refractive index of sapphire with electric field perpendicular and parallel c-axis
Fig. 5-10 (e) Frequency dependent extinction coefficient of sapphire with electric field perpendicular and parallel c-axis
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Fig. 5-11 (a) and Fig. 5-11 (b) show the terahertz time-domain waveform of sapphire substrate and the a-InN film whose electric field is perpendicular and parallel to in-plane c-axis, respectively. The amplitude and phase spectrums of sapphire substrate and a-InN film for different polarization are shown in Fig. 5-11 (c) and Fig.
5-11 (d), respectively. The transmittance of a-InN film in Fig. 5-11 (e) is less than 20% when the terahertz polarization is perpendicular to the c-axis. After we change the THz polarization, the transmittance of InN film is increased by 10%. Fig. 5-12 (a) to Fig. 5-12 (d) shows the complex conductivity and refractive index of a-plane measured at the orientation perpendicular to c-axis. Both results were then theoretically fit using the simple Drude model. The best complex conductivity fitting curves are shown in Fig. 5-12 (a) and Fig. 5-13 (c), respectively and the best fit values of and
are presented in Table 5-2. We assuming the electron effective mass [18] for InN film, these fitting parameters correspond to carrier concentration 0.8x1019 cm3 whatever the electric field perpendicular or parallel to the c-axis. These values are similar to room-temperature Hall effect measurement results of 1.1x1019 cm3. The carrier mobility have difference value when the terahertz polarization perpendicular or parallel the c-axis, respectively.
The experimental results measured for the electric field perpendicular to the c-axis have higher mobility than those measured for the electric field parallel to c-axis. We compared these results with those measured by room-temperature Hall effect measurement and got the excellent agreement. The fitting parameters corresponding to carrier mobility are 333 ( c-axis) and 148 ( c-axis) cm2/Vs, respectively which are similar to room-temperature Hall effect measurement results as shown in Table 5-2.
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Fig. 5-11 (a) The terahertz time-domain signal transmitted through sapphire and InN film ( c-axis)
Fig. 5-11 (b) The terahertz time-domain signal transmitted through sapphire and InN film ( c-axis)
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Fig. 5-11 (c) The corresponding amplitude and phase spectrums of sapphire substrate and InN film with electric field parallel to c-axis ( c-axis)
Fig. 5-11 (d) The corresponding amplitude and phase spectrums of sapphire substrate and InN film with electric field perpendicular to c-axis ( c-axis)
-400000.0 0.5 1.0
Frequency (THz)
1.5 2.0 2.5 3.0Phase
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0.3 0.6 0.9 1.2 1.5 1.8 2.1
0.0 0.2 0.4 0.6 0.8
1.0 E c-axis
E c-axis
Transmittance
Frequency (THz)
Fig. 5-11 (e) The amplitude transmittance of a-plan InN film with electric field perpendicular and parallel c-axis
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Fig. 5-12 (a) Experimental data (open symbols) and fitting data complex conductivity (solid line) of InN ( c-axis)
Fig. 5-12 (b) Experimental data of refractive index and extinction coefficient of InN film ( c-axis)
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Fig. 5-12 (c) Experimental data (open symbols) and fitting data complex conductivity (solid line) of InN ( c-axis)
Fig. 5-12 (d) Experimental data of refractive index and extinction coefficient of InN film ( c-axis)
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(a-plane InN film)
Parameters comparison of Hall effect measurement and TDS fitting by Drude model
Sample p / 2 (THz)
0
(fs)
N (TDS) (x1018 cm-3)
N (Hall) (x1018 cm-3)
(TDS) (cm-2 /V-s)
(Hall) (cm-2 /V-s) InN
(061229) ( c-axis)
83 18 0.8 1.1 333 359
InN (061229) ( c-axis)
83 8 0.8 1.1 148 184
Table 5-2 Parameters comparison of Hall effect measurement and TDS fitting by Drude model (a-plane InN film)
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5.4 - Discussion of a-InN results
The THz-TDS experimental results show the anisotropy of refractive index and electrical conductivity which depend on the in-plane c-axis orientation. Fig. 5-12 (a) and (c) clearly show two difference complex conductivity, but the carrier concentration 0.8x1019 cm3 calculated from the conductivity is independent on the orientation of electric field. In the Table 5-2, we found that the carrier scattering time which determines the carrier mobility is largely different for two orthogonal field orientations. And the calculated carrier mobility are
333 ( c-axis) and 148 ( c-axis) cm2/Vs, respectively. For comparison,
electrical properties were measured by Hall effect measurement. For Hall measurement, the a-InN sample was cut into narrow slabs with two different orientation of m-axis and c-axis direction. The Hall measurements were done by Hall bar configuration with a magnet field of 0.5 T and the current of 10 mA. The results are showen in Table 5-2, and are consistent with the THz-TDS results. While the carrier concentration of two crystal orientation is nearly similar, the electric mobilities are quite different. Usually, the carrier mobility is higher in better crystalline quality.
It suggests that the nonpolar InN crystalline qualities are different in c-axis and m-axis orientation. X-ray diffraction (XRD) experiment was also done to obtain the InN film crystalline quality. We measured x-ray diffraction rocking curve (XRC) of InN(11-20) Bragg refraction in c-axis and m-axis orientation. The full width at half maximum (FWHM) of InN ( ) Bragg refraction in c-axis and m-axis orientation are 1.0 and 6.1 degree, respectively. This result is also seen in other groups.[41-43]
Usually, the smaller XRC FWHM corresponding to better crystalline quality. It is suggested that the crystalline quality in c-axis is better than in m-axis, which results in the higher carrier mobility in c-axis than in m-axis. But in our THz-TDS and Hall
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effect measurement experimental results, we got opposite results. That means the carrier in m-axis has higher mobility, but the crystal crystalline quality is not better than c-axis. We come up with two reasons in this experimental results：
Crystalline structure anisotropy
Electronic structure anisotropy
We eliminate the first reason, because the carrier mobility is not dependence on crystal crystalline quality. Thus, we try to use the second reason to explain our results.
It’s indicate that the InN structure induce the internal electrical field affect the carrier mobility. We find that other groups has a similar results, but it’s not in the same experiment.[44] Thus, we want doing another different experiment and got more information that help us to find correct answer.
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