Surface mapping of carrier density in a GaN wafer using a frequency-agile THz source

We developed a method for mapping the carrier density on a semiconductor substrate surface based on terahertz (THz)-reflective measurement. Reflectivity in the THz-frequency region away from the optical phonon frequency is sensitive to the carrier density in semiconductors. However, reflectivity in the optical phonon frequency regions is around 1.0, independent of the carrier density. We developed a THz-reflective spectral imaging system using a frequency-agile, ultra-widely tunable THz source (1–40 THz). Different reflective images were obtained from GaN samples of carrier density 2.5 × 1016 cm-3, 1.0 × 1018 cm-3 and 1.5 × 1018 cm-3 using 22.7 and 26.5 THz. The image contrast reflected the GaN crystals’ carrier density. [DOI: 10.2971/jeos.2009.09012]


INTRODUCTION
Monitoring the carrier density in semiconductors is a practical way of analyzing physical phenomena in these materials.Hall measurements using a four-terminal method are traditionally applied to obtain information on carrier density, mobility, and conductivity in semiconductors.However, measuring the density distribution in a surface of samples is difficult because electrical contact is required.In addition, the destructive nature of this method makes it unsuitable for industrial semiconductor manufacturing.Some studies have applied a nondestructive optical method to measure the surface carrier distribution [1]- [3].Electromagnetic waves of terahertz (THz)band frequencies are well known to be sensitive to carrier density and optical phonon properties in semiconductors.Huber et al. recently reported extremely high sensitivity and spatial resolution for carriers in a semiconductor using a THz-wave and atomic-force microscopic technique [4].The sensitivity of THz-waves to carriers enables the near-field nanoscopy using THz-waves to achieve extremely high sensitivity for carriers in a single nanodevice.
Our research group has developed monochromatic ultrawidely tunable THz-wave sources (1-40 THz) [5].The purpose of the presenting work is to devise a nondestructive measurement method for carrier density in semiconductors using a THz-wave source.GaN is one of the most remarkable semiconductors, as it has a wide bandgap, large heat capacity, and high breakdown voltage [6].Here, we use our new measurement system to analyze a GaN substrate.

THEORY
To study the response of semiconductors to THz-waves, one may consider the dielectric function and contribution of optical phonons in the media applying the Drude model.The dielectric function ε(ω) for THz-wave ω in semiconductors can be modeled as where ω L and ω T are the optical phonon frequencies of the longitudinal mode and transverse modes, respectively.The quantity, ω P = Ne 2 /ε 0 m * is a plasma frequency that is a function of carrier density N in the medium, and Γ and γ are damping parameters for the optical phonons and carriers, respectively [7].The relationship between reflectivity and dielectric function is where ε and ε" represent the real and imaginary part of the dielectric function, respectively.Using ( 1) and ( 2), the reflectivity R in semiconductors can be obtained.
When the THz-wave frequency is in the range from ω T to ω L , the reflectivity R ω∼ω T is not dependent on the carrier density N because the second term on the right side in (1), which does not include N, is dominant.
This highly reflective band is well known as the reststrahlen band of ionic crystals.We used THz-waves in this region as an intensity reference for the measurement of reflectivity.Furthermore, our results showed that the reflectivity R ω =ω T , which is out of the high reflective region, is useful for sensing the carrier density N. Frequency agility and wide tunability are required for a source that compares the THz-wave reflectivity between ω ∼ ω T and ω = ω T .The frequencies ω T and ω L in wurtzite GaN crystal were reported as 16.8 THz and 22.3 THz , respectively [8].

EXPERIMENTAL SETUP
The monochromatic ultra-widely tunable THz-wave source developed by our research group was used to measure the reflective spectra in GaN wafers.Figure 1 shows the experimental setup.A frequency-agile dual wavelength (λ 1 and λ 2 ) source of around 1.3 µm from KTP-OPO was used for collinear THz-difference frequency generation (DFG), satisfying the phase-matching condition in the DAST crystal [5].This OPO consisted of two KTP crystals and two mirrors, which were pumped by the second harmonic of a Q-switched Nd:YAG laser (532 nm, 8 ns, and 100 Hz).Here, M1 was coated for high reflectivity of the signal waves and high transmittance of 532 nm and idler waves (around 1.3 µm); M2 was a broadband silver mirror.In addition, M3 was coated for the high reflection of idler waves and high transmittance at 532 nm.Each KTP crystal was mounted on a galvano scanner, and the angle was controlled independently.The KTP-OPO was tunable within 1250 to 1700 nm, enabling phasematched THz-wave generation over a wide range.The idler waves from the KTP-OPO were focused onto a polished DAST crystal (Furukawa Co., Ltd.), and the THz wave was generated from the DAST crystal.The THz-wave frequency could change from pulse to pulse using synchronized control of the galvano scanner angle, with a pump-laser repetition frequency of 100 Hz.A low-pass filter was placed in the wave path to block the λ 1 and λ 2 outputs.The THz wave, which was collimated using an off-axis parabolic mirror, was fed into a reflective imaging system.To make the reflective signal, an off-axis parabolic mirror and sample positions were controlled as shown in Figure 1.The movable distances of the sample stage and off-axis parabolic mirror were 85 mm in the x and y directions, respectively.The reflected THz wave was detected using a pyrodetector, which was operated at room temperature.The total THz range of 3 to 32 THz of this reflective spectrometer is reduced by the tuning range of the KTP-OPO and the sensitive range of a pyrodetector.In this experiment, the spatial resolution was estimated to be higher than 2 mm, based on measurements of a line and space in a reflective image from a resolution target (Edmund Optics Inc., USAF Resolution Target 2" SQ Positive).The spatial resolution depends on the spot size of pump beams in a DAST crystal, and the focusing lengths of a pair of off-axis parabolic mirrors for the collimation and focusing of the THz-wave onto a sample.We could achieve a maximum resolution of 0.5 mm changing these factors relative to the THz-wave power and depth of field (DOF) of the reflective image.

RESULTS AND DISCUSSION
We prepared three samples of n-type GaN substrates with different carrier densities.These n-type GaN samples were made by doping silicon.The carrier density of silicon is changed by varying the volume of SiH 2 Cl 2 (dichlorosilane).This dichlorosilane flows when the GaN wafer is grown on a sapphire substrate via hydride vapor phase epitaxy (HVPE).The carrier density of the GaN substrates, which were measured by secondary ion-microprobe mass spectrometer (SIMS), were 1) 2.5 × 10 16 cm −3 , 2) 1.0 × 10 18 cm −3 , and 3) 1.5 × 10 18 cm −3 .
The reflective spectra shown in Figure 2 were measured at the center of the GaN substrates.In the frequency region above 10 THz , they were in agreement with (2) for each carrier density, with values of Γ = 17 cm −1 , γ = 12 cm −1 , ω L = 744 cm −1 , ω T = 560 cm −1 , m * = 0.2 m, and ε inf = 5.35 used [6,9].γ was obtained from the typical value of the mobility µ = 150 cm/Vs from the literature.Note that the larger γ (> 100 cm −1 ) was necessary for agreement in a wider frequency region.We mapped THz-reflective intensities for all samples aligned in the region of 18 mm × 40 mm with frequencies switched to 19.2, 22.7, and 26.5 THz with averaging in each set of 160 pulses.These values were selected because of their good signal-to-noise ratios within the reference and sensing regions.We used the 19.2-THz map as a reference for reflective intensity because the carrier density had no effect on the reflectivity at this frequency, as shown in Figure 2.  for a sample of N= 1 × 10 18 cm −3 was estimated to be approximately 0.2 using (2) and the fluctuation of measured reflectivity ∆R < 5% at 22.7 THz and averaging the number 1000 pulses per pixel in the current system.

FIG. 2
FIG.2THz reflective spectrum in GaN substrates with carrier density of 1) 2.5 × 10 16 cm −3 , 2) 1.0 × 10 18 cm −3 , and 3) 1.5 × 10 18 cm −3 .The normalized reflective images at 22.7 and 26.5 THz for each sample are shown in Figure3.The reflective intensities at 22.7 or 26.5 THz differed among the samples, and the reflectivity depended on the carrier density.Figure4shows the relationships between carrier density and relative reflectivity averaged over all pixels for samples at 22.7 and 26.5 THz .The rel-