This work was supported by the Nagoya Institute of Technology, Japan.

1. Preparation of the sample
<ol>
	<li>Prepare an n-type 4H-SiC epilayer (Table of Materials).</li>
	<li>Wash the sample with acetone and then with water, each for 5 min, using an</li>
	<li>ultrasonic washer.</li>
	<li>Use a nitrogen gun to remove moisture on the sample surface.</li>
</ol>
2. Preparation of aqueous solutions
<ol>
	<li>Prepare 1 M each of H2SO4, HCl, Na2SO4, NaOH, or HF at 1 wt% concentration. Select and prepare an aqueous solution to be measured.</li>
	<li>Prepare a quartz cell with 5 mm (length) x 20 mm (width) x 40 mm (height) dimensions and then pour the aqueous solution into it. Put the prepared sample into the cell and then immerse it into the aqueous solution. 
	NOTE: At least 4 mL of the aqueous solution in the quartz cell is required for the sample to be immersed entirely. When changing the solution, treat the sample with ultrasonic cleaning using acetone and pure water.</li>
</ol>
3. Preparation of the measuring equipment
<ol>
	<li>Turn on the power supply of the 266-nm pulsed laser to excite the light source. Afterwards, set the laser mode on standby.</li>
	<li>Connect the pulsed laser and an oscillator through a Bayonet Neill-Concelman (BNC) cable. Turn on the oscillator and input a 100 Hz pulse wave to the pulsed laser.</li>
	<li>Connect a photodiode for trigger acquisition through a trigger input channel of the oscilloscope with a BNC cable.</li>
	<li>Turn on the power supply of the photodiode.</li>
	<li>Irradiate the pulsed laser and place the aperture of the microwave waveguide on the optical path of the laser light at direction normal to the light. 
	CAUTION: In the latter process, the experimenter should wear safety eye glasses during laser irradiation.</li>
	<li>Install a half-mirror on the optical path of the pulsed laser, as shown in Figure 1, and reflect the pulsed laser to the photodiode.</li>
	<li>Turn on the oscilloscope and then set its trigger threshold to a voltage sufficient to signal from the photodiode. 
	NOTE: The threshold value may be set smaller than the peak of the trigger signal. When an unintentional reflected light enters the photodiode, the oscilloscope displays a frequency that differs greatly from the pulsed laser frequency. In this case, repeat step 3.6.</li>
	<li>Check the trigger frequency with an oscilloscope and tune the oscillator exactly.</li>
	<li>Put the laser mode on standby.</li>
	<li>Connect a Schottky barrier diode in a microwave waveguide for reflected microwave detection and a signal input channel of the oscilloscope, through a BNC cable.</li>
	<li>Apply a 9.5 V operating voltage to a Gunn diode.</li>
	<li>Place the quartz cell (step 2.2) on the stand in front of the aperture as close as possible. Fix with tape.</li>
</ol>
4. Measurement and saving data
<ol>
	<li>Turn on the laser light oscillation and irradiate the light to the sample.</li>
	<li>Place a half-waveplate (&#955;/2), a polarizer, and a power meter on the optical path (Figure 1).</li>
	<li>Irradiate the pulsed laser to the power meter, as shown in Figure 1. Check the excitation intensity of the laser.</li>
	<li>Adjust the &#955;/2 angle for control of the excitation intensity. 
	NOTE: &#955;/2 changes the polarization direction of the laser light, while the polarizer transmits only one light polarization direction, through which excitation intensity is controlled. Injected photon densities are set to 8 x 1013 cm&#8722;2 and for the 266-nm laser, the excitation carrier density in 4H-SiC is 4.5 x 1017 cm&#8722;3.</li>
	<li>Remove the power meter from the optical path.</li>
	<li>Adjust the time/div and V/div of the oscilloscope so that the peak signal is displayed on the oscilloscope.</li>
	<li>Adjust the amplitude and phase of the microwave through an E&#8211;H tuner. Check the oscilloscope and look for the E&#8211;H tuner where the peak signal is at maximum. Failed adjustment of the E-H tuner results in signal loss, as depicted in Figure 2. 
	NOTE: An amplifier is used to strengthen the decay signal in case of insufficiently large signal relative to background noise or when it is not observed even after adjusting the E&#8211;H tuner. The amplifier is placed between the Schottky barrier diode and the signal input channel of oscilloscope with a BNC cable, as illustrated in Figure 1.</li>
	<li>Repeat steps 4.6 and 4.7 to complete the tuning.</li>
	<li>Adjust the time/div of the oscilloscope and sketch a decay curve in the measurement area on the oscilloscope.</li>
	<li>Average the signal for an arbitrary number of times to improve the signal-to-noise ratio.</li>
	<li>Save the measurement data as an electronic file to a memory and then remove it from the oscilloscope.</li>
</ol>
5. Data processing
<ol>
	<li>Import the signal data to a personal computer.</li>
	<li>Plot decay curves obtained from the experiment as a function of time.</li>
	<li>Calculate the average value of background noise level, subtract it from the decay signal, and plot it as a function of time.</li>
	<li>Find the peak value of the decay signal obtained in step 5.3 and then divide the decay signal by the peak value.</li>
</ol>

<ol>
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B. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Carrier+lifetime+measurement+in+n&#8722;4H-SiC+epilayers.">Carrier lifetime measurement in n&#8722;4H-SiC epilayers.</a> Journal of Applied Physics. 103, 033702 (2008).</li><li>Linnros, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Carrier+lifetime+measurements+using+free+carrier+absorption+transients.+I.+Principle+and+injection+dependence.">Carrier lifetime measurements using free carrier absorption transients. I. 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R., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Effects+of+annealing+on+carrier+lifetime+in+4H-SiC.">Effects of annealing on carrier lifetime in 4H-SiC.</a> Journal of Applied Physics. 100, 113710 (2006).</li><li>Hayashi, T., Asano, K., Suda, J., Kimoto, T. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Temperature+and+injection+level+dependencies+and+impact+of+thermal+oxidation+on+carrier+lifetimes+in+p-type+and+n-type+4H-SiC+epilayers.">Temperature and injection level dependencies and impact of thermal oxidation on carrier lifetimes in p-type and n-type 4H-SiC epilayers.</a> Journal of Applied Physics. 109, 014505 (2011).</li><li>Okuda, T., Miyake, H., Kimoto, T., Suda, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Long+Photoconductivity+Decay+Characteristics+in+p-Type+4H-SiC+Bulk+Crystals.">Long Photoconductivity Decay Characteristics in p-Type 4H-SiC Bulk Crystals.</a> Japanese Journal of Applied Physics. 52, 010202 (2013).</li><li>Schofthaler, M., Brendel, R. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Sensitivity+and+transient+response+of+microwave+reflection+measurements.">Sensitivity and transient response of microwave reflection measurements.</a> Journal of Applied Physics. 77, 3162-3173 (1995).</li><li>Beck, G., Kunst, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Contactless+scanner+for+photoactive+materials+using+laser-induced+microwave+absorption.">Contactless scanner for photoactive materials using laser-induced microwave absorption.</a> Review of Scientific Instruments. 57, 197-201 (1986).</li><li>Kolen'ko, Y. 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The authors have nothing to disclose.

In the &#956;-PCD protocol, step 4.7 is the most important point. The E&#8211;H tuner was incorporated with a movable short circuit in the E and H planes, respectively. Thus, moving the short circuit of the E tuner or the H tuner changes the amplitude and phase of the reflected microwave and maximizes the signal amplitude. Tuning has a large influence on the waveform of the decay curve and must be performed strictly. In case of a weak signal strength where tuning might be difficult, a few tens of tuning averages may be used. For failed tuning, the &#956;-PCD decay curves are not observable; only the noise signal of an oscilloscope is observed. Figure 2 shows the oscilloscope waveform in such a case.
It is easy to measure highly resistive samples as there is no lower conductivity limit. When the sample resistivity is low or when the sample is thick, the skin effect of the microwave is not negligible. The distance until the electric field intensity of the microwave becomes 1/e times is referred to as skin depth <img alt="Equation 11" src="/files/ftp_upload/59007/59007eq11.jpg" />, which is expressed by Equation 9:
<img alt="Equation 12" src="/files/ftp_upload/59007/59007eq12.jpg" />&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; (9)
where &#969; is the angular frequency of the microwave, and &#949;, &#961;, and &#956; represent the sample&#8217;s dielectric constant, resistivity, and permeability, respectively. In the case of Si and SiC, approximate &#948; values for the 10 GHz microwave were 9 mm at 50 &#937;&#8729;cm, 2 mm at 10 &#937;&#8729;cm, 500 &#956;m at 1 &#937;&#8729;cm, and 150 &#956;m at 0.1 &#937;&#8729;cm. Therefore, measurements for samples with typical thicknesses (several hundred micron) at less than 0.1 &#937;&#8729;cm will lose &#948; accuracy. On the other hand, the microwave and optical radiation are incident from the opposite of the wafer in this protocol. A negligible skin effect indicates better microwave and optical radiation from the same side.
Lower limits depend on the resistivity and thickness of the sample resulting from its interaction with the microwave. For highly resistive samples, the typical lower limits of the excess carriers are on the order of 1012 cm&#8722;3. On the other hand, electron&#8211;hole scattering must be considered at excess carriers greater than 1016 cm&#8722;3, as discussed in ref. 13.
The &#956;-PCD decay curves became gentle at high excitation density due to unproportionality of the microwave reflectivity to the excess carrier concentration such that Equation (3) would lose its validity13,25,26 and &#964;1/e would be overestimated. Figure 8 shows the &#956;-PCD decay curve of a chemical mechanical polishing surface treatment n-type 4H-SiC with excitation on the Si-face by 266 nm under high excitation intensity.
Moreover, time resolution depends on the performance of the measurement apparatus such as an excitation source, an oscilloscope, and an amplifier. For example, in this study, the apparatus consisted of a pulsed laser with pulse width of 1 ns as the excitation source and an oscilloscope having a frequency band of 500 MHz. Consequently, the minimum measurable lifetime was estimated at 2 ns.
As mentioned earlier, &#956;-PCD is very useful for characterization of semiconductors such as Si. Nevertheless, its application can be extended to other materials, for instance, in photoactive materials including TiO227,28,29,30.
Furthermore, aside from the &#956;-PCD, TR-PL2 and TR-FCA introduced at the earlier sections are the other two carrier lifetime measurement techniques. TR-PL observes the time change of photoluminescence caused by carrier recombination while TR-FCA observes the time change of probe light absorption4. Specifically, free carrier absorption occurs when light with energy smaller than the band gap is irradiated during carrier excitation3. Nevertheless, compared to these two, &#956;-PCD directly observes electrical conductivity by microwave and has a high surface roughness and signal sensitivity, making it the more ideal method for carrier lifetime measurement for semiconductor device applications.

Excess carriers in semiconductors are optically excited by the injection of photons with energy larger than the gap between the conduction and valence bands. Excited excess carriers, then, disappear by an electron&#8211;hole recombination within a time constant known as the carrier lifetime, which greatly affects the performance of semiconductor devices during operation. As one of the important parameters for semiconductor devices and materials, the carrier lifetime is very sensitive to the presence of defects in these materials, and further requires a convenient method of evaluation. J. Warman and M. Kunst developed a transient technique they named the time resolved microwave conductivity (TRMC), which involves microwave absorption to follow charge carrier dynamics in semiconductors1. Other researchers proposed the transient photo conductivity (TPC), otherwise known as the microwave photoconductivity decay (&#956;-PCD), which is the commonly adopted material qualification technique in semiconductor industries due to its noncontact and nondestructive measurements of the carrier lifetime. In particular, for silicon carbide (SiC), three major techniques are applicable: &#181;-PCD, time resolved photoluminescence (TR-PL), and time resolved free carrier absorption (TR-FCA)2,3,4,5,6,7. Among these techniques, &#181;-PCD is the most widely employed because compared to the other two as it exhibits surface roughness insensitivity (i.e., measurable for any given various surface roughness8,9,10) and high signal sensitivity for excited carriers (i.e., using an optimum microwave component). In general, &#181;-PCD has been preferred for carrier lifetime measurement in SiC and other semiconductor materials2,5,6,11,12,13,14,15,16,17,18,19.
The measurement protocol and principle of &#956;-PCD1,20,21 is detailed here. In principle, it uses a reflected microwave as a probe. Here, the microwave reflectance of a sample R(&#963;) is equivalent to the ratio between the reflected microwave intensity P(&#963;) and the incident microwave intensity Pin as expressed by Equation 1:
<img alt="Equation 1" src="/files/ftp_upload/59007/59007eq1.jpg" /> (1)
By irradiation of a pulse laser, the conductivity of a sample &#963; changes to &#963; + &#916;&#963;; likewise, R (&#963;) transforms to R(&#963; + &#916;&#963;). Thus, &#916;R is given by Equation 2:
<img alt="Equation 2" src="/files/ftp_upload/59007/59007eq2.jpg" /> (2)
In a perturbation (small &#916;&#963;) approximation, R(&#963; + &#916;&#963;) is developed in Taylor series to yield
<img alt="Equation 3" src="/files/ftp_upload/59007/59007eq3.jpg" /> (3)
while &#916;&#963; becomes
<img alt="Equation 4" src="/files/ftp_upload/59007/59007eq4.jpg" />, (4)
where q is the elementary charge, &#956;p is the hole mobility, &#956;n is the electron mobility, and &#916;p is the excess carrier concentration. From the preceding equations,<img alt="Equation 5" src="/files/ftp_upload/59007/59007eq5.jpg" />&#916;R and &#916;p are related by
<img alt="Equation 6" src="/files/ftp_upload/59007/59007eq6.jpg" />. (5)
The dependence of microwave reflectance on excess carrier concentration allows &#956;-PCD to observe the time decay of excess carriers, which we can use to estimate the carrier lifetime of semiconductor materials.

<table border="0" cellpadding="0" cellspacing="0" style="width:1061px;" width="1061">
	<tbody>
		<tr height="20">
			<td height="20" style="height:20px;width:171px;">n-type 4H-SiC epilayer</td>
			<td style="width:533px;">Ascatron AB http://ascatron.com/</td>
			<td style="width:108px;"></td>
			<td style="width:249px;">Sample</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">266 nm pulsed laser</td>
			<td>CryLaS GmbH http://www.crylas.de/</td>
			<td style="width:108px;">FQSS 266-50&#160;</td>
			<td>Excitation light source</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:171px;">Photodiode</td>
			<td>THORLABS https://www.thorlabs.com/index.cfm</td>
			<td style="width:108px;">DET10A/M</td>
			<td>Trigger signal detection</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">Schottky barrier diode</td>
			<td style="width:533px;">ASI http://www.advancedsemiconductor.com/</td>
			<td style="width:108px;">1N23WE</td>
			<td>Reflected microwave detection</td>
		</tr>
		<tr height="20">
			<td height="20" style="height:20px;width:171px;">Gun diode&#160;</td>
			<td style="width:533px;">Microsemi https://www.microsemi.com/</td>
			<td style="width:108px;">MO86751C</td>
			<td>Microwave generation source</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">E-H tuner&#160;</td>
			<td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td>
			<td></td>
			<td>microwave component</td>
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			<td height="21" style="height:21px;">Circulator</td>
			<td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td>
			<td></td>
			<td>microwave component</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">Rectangular waveguide</td>
			<td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td>
			<td></td>
			<td>microwave component</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;">Double ridge waveguide</td>
			<td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td>
			<td></td>
			<td>microwave component</td>
		</tr>
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			<td height="21" style="height:21px;width:171px;">Crystal mount</td>
			<td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td>
			<td style="width:108px;"></td>
			<td>microwave component</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:171px;">Acetone</td>
			<td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td>
			<td style="width:108px;">GE00001</td>
			<td>Sample cleaning</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:171px;">Sulfuric acid</td>
			<td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td>
			<td style="width:108px;">GE00257</td>
			<td>Acidic aqueous solution</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:171px;">Hydrochloric acid</td>
			<td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td>
			<td style="width:108px;">GE00238</td>
			<td>Acidic aqueous solution</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:171px;">Hydrogen fluoride</td>
			<td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td>
			<td style="width:108px;">18083-1B</td>
			<td>Acidic aqueous solution</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:171px;">Sodium hydroxide</td>
			<td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td>
			<td style="width:108px;">37184-00</td>
			<td>Alkaline aqueous solution</td>
		</tr>
		<tr height="21">
			<td height="21" style="height:21px;width:171px;">Sodium sulfate</td>
			<td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td>
			<td style="width:108px;">37280-00</td>
			<td>Neutral aqueous solution</td>
		</tr>
	</tbody>
</table>

carrier lifetime measurements in semiconductors through the microwave photoconductivity decay method

This work presents a protocol employing the microwave photoconductivity decay (&#956;-PCD) for measurement of the carrier lifetime in semiconductor materials, especially SiC. In principle, excess carriers in the semiconductor generated via excitation recombine with time and, subsequently, return to the equilibrium state. The time constant of this recombination is known as the carrier lifetime, an important parameter in semiconductor materials and devices that requires a noncontact and nondestructive measurement ideally achieved by the &#956;-PCD. During irradiation of a sample, a part of the microwave is reflected by the semiconductor sample. Microwave reflectance depends on the sample conductivity, which is attributed to the carriers. Therefore, the time decay of excess carriers can be observed through detection of the reflected microwave intensity, whose decay curve can be analyzed for estimation of the carrier lifetime. Results confirm the suitability of the &#956;-PCD protocol in measuring the carrier lifetime in semiconductor materials and devices.

Figure 1 shows a schematic diagram of the &#956;-PCD apparatus consisting of a 10 GHz microwave frequency, X waveguide band, and a rectangular waveguide. The microwave was focused by the double ridge waveguide and irradiated on the sample. The Gunn diode output power was 50 mW and the phase noise was nearly -80 dBc/Hz.
Figure 3 shows the &#956;-PCD decay curve of a 100-&#956;m-thick n-type 4H-SiC sample excited on the Si-face by 266 nm in the air; &#956;-PCD signal (V) scaled logarithmically was the dependent variable and time (&#956;s) was the independent variable. The signal voltage peak was approximately 0.046 V prior to amplification. Moreover, the observed voltage of the direct current (DC) component of the reflected microwave obtained from the oscilloscope DC mode was of the order of several volts. As recombination of excess carriers progressed with time, the sample&#8217;s conductivity and microwave reflectance decreased.
Figure 4 shows the normalized &#956;-PCD decay curve of Figure 3. Normalization enables comparison of the time constants with different peak intensities. Typically, carrier lifetime estimation based on the decay curve is carried out with the 1/e lifetime &#964;1/e parameter, indicating that time expended to obtain signal intensity decreases from the peak to 1/e (~0.368). Note that &#181;-PCD decay was not a single exponential and &#964;1/e was influenced by both bulk and surface recombination. However, comparing the time constant of samples having different thickness or surface condition necessitated a reference parameter. Usage of &#964;1/e was convenient given the good signal-to-noise ratio at the initial part of the decay curve and the simplicity of the data analysis. To characterize the &#181;-PCD signal, half-time lives, I40/Imax, and kD constant also adopted such parameters22,23,24. In fact, &#964;1/e was adopted in the SEMI standard: SEMI MF 15358 as the standard for carrier lifetime measurement of Si. For the decay curve in Figure 4, &#964;1/e was approximately 0.34 &#956;s.
In Figure 5, the quartz cell, containing the aqueous solution and with the sample on its wall, was placed on the stand in front of the aperture11. Each intensity of the irradiated microwave and the reflected microwave from the sample, as well as the &#956;-PCD signal-to-noise ratio, were dependent on the distance between the sample and the aperture, which, ideally, should be as close as possible. In the actual measurement, the distance obtained was as close as possible; measurement using the quartz cell yielded a distance of 0.5 mm, which was of the same as the thickness of the quartz cell glass.
Figure 6 shows &#956;-PCD decay curves of the n-type 4H-SiC in the air and in aqueous solutions. An excitation light of 266 nm was irradiated to the Si-face of the 4H-SiC. Aqueous solutions used had concentrations, as mentioned previously, as follows: 1 M each of H2SO4, HCl, Na2SO4, or NaOH, or 1 wt% of HF. The time constant of the decay curves was longer with the sample immersed into the acidic aqueous solutions (i.e., H2SO4, HCl, or HF), implying that acidic solutions passivated surface states on the Si-face and reduced surface recombination of the excess carriers.
Figure 7 shows the pH dependence of &#964;1/e of the n-type 4H-SiC sample excited on the Si-face at 266 nm of light. The pH was calculated from the molar concentrations of H2SO4, HCl, and NaOH. This figure indicated the carrier lifetime dependence on pH aqueous solutions; therefore, lower pH would have more effects on the carrier lifetime.
Surface recombination velocity S was calculated to reproduce the &#964;1/e used for the samples. The decay model of excess carriers has been reported in refs. 2 and 3. To obtain the excess carrier concentration Dn(x, t), the following continuity equation was solved. Here, Dn(x, t) was defined as a function of time t and depth x in a semiconductor layer; thus,
<img alt="Equation 7" src="/files/ftp_upload/59007/59007eq7.jpg" />, &#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; (6)
where &#964;B is bulk lifetime due to the Shockley&#8211;Read&#8211;Hall (SRH) recombination, Da is the ambipolar diffusion coefficient, B is the radiation recombination coefficient, and C is the Auger recombination coefficient.
At the excited and other surfaces, boundary conditions were given by Equation 7:
<img alt="Equation 8" src="/files/ftp_upload/59007/59007eq8.jpg" />and <img alt="Equation 9" src="/files/ftp_upload/59007/59007eq9.jpg" />&#160; &#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; (7)
where S0 and SW denote the surface recombination velocity of the excited and other surfaces, respectively, and W is the layer thickness.
Moreover, the initial excess carrier concentration profile using light pulse illumination could be expressed using Equation 8:&#160;
<img alt="Equation 10" src="/files/ftp_upload/59007/59007eq10.jpg" />&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160;&#160; (8)
where g0 is carrier concentration at x = 0 and a is the absorption coefficient.
Solving Equation 6 by employing the boundary conditions of Equation 7 and the initial condition of Equation 8 provided the excess carrier decay curves. In the process, S was estimated by comparing the &#964;1/e obtained from the experiments and from the calculated decay curves. Least squares fitting minimized errors between the experimental &#964;1/e in the all conditions and the calculated &#964;1/e with parameters S0, Sw, and &#964;B.
As depicted in Equation 6 carrier recombination is the summation of various decay components, namely, surface, SRH, radiative, and Auger recombinations, the last two having remarkable high carrier density. On the other hand, SRH recombination depends on point defects and dislocations in the bulk of the semiconductor material that form energy levels in the semiconductor band gap. The energy levels act as stepping stones for carrier transition between the valence and conduction bands.
&#956;-PCD also shows nonlinearity at a high injection condition, and overestimates carrier lifetime13,25,26. Figure 8 shows the measured &#956;-PCD under a high excitation condition. Note that the decay curve for an injected photon density of 1015 cm&#8722;2 became more gradual compared to that for photon density of 1014 cm&#8722;2, owing to microwave nonlinearity. Furthermore, the measurement examples shown in Figure 3, Figure 4, and Figure 6 were obtained for an injected photon density of 8 x 1013 cm&#8722;2 resulting in negligible microwave nonlinearity, and Auger and radiative recombinations but dominant SRH and surface recombinations.
Figure 6 can be taken to exemplify decay curve calculations for the n-type 4H-SiC Si-face excited by 266 nm light, by referring to the dashed lines, where &#964;B = 3 &#956;s and S for the Si-face SSi = 200 cm/s or 700 cm/s. For both SSi settings, the experimental decay curve measured in neutral pH (air, 1 M Na2SO4) and in the acidic condition (1 M H2SO4), respectively, were well reproduced, which meant that SSi for the n-type 4H-SiC signi&#64257;cantly reduced from 700 cm/s to 200 cm/s in acidic aqueous solutions as hydrogen passivated the surface states on the Si-face.
<img alt="Figure 1" class="xfigimg" src="/files/ftp_upload/59007/59007fig1.jpg" /> 
Figure 1: Schematic diagram of the &#956;-PCD device. A part of the laser light is reflected by the half-reflection mirror. The reflected laser is detected by the photodiode, and a signal coming from the photodiode is used as a trigger for the oscilloscope. A microwave is generated from the Gunn diode in the direction bent by the circulator; then, a microwave goes through the aperture and irradiates the sample. The reflected microwave from the sample comes back to the aperture and into the circulator, where it is detected by the Schottky barrier diode. Finally, the signal coming from the Schottky barrier diode is observed by the oscilloscope. <a href="https://www.jove.com/files/ftp_upload/59007/59007fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 2" class="xfigimg" src="/files/ftp_upload/59007/59007fig2.jpg" /> 
Figure 2: The &#956;-PCD signal for a failed tuning of E-H tuner. No measurable peak is observed for a failed tuning. <a href="https://www.jove.com/files/ftp_upload/59007/59007fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 3" class="xfigimg" src="/files/ftp_upload/59007/59007fig3.jpg" /> 
Figure 3: The &#956;-PCD decay curve for the n-type 4H-SiC sample with excitation on the Si-face by 266 nm in air. The pulsed laser is irradiated at time = 0 s at which the signal intensity is at maximum. This figure has been modified from Ichikawa et al.11 with permissions. <a href="https://www.jove.com/files/ftp_upload/59007/59007fig3large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 4" class="xfigimg" src="/files/ftp_upload/59007/59007fig4.jpg" /> 
Figure 4: Normalized &#956;-PCD decay curve for the n-type 4H-SiC sample with excitation on the Si-face by 266 nm in air. The maximum value of the decay curve in Figure 2 is normalized to unity. The value of the dashed line is 1/e, and &#964;1/e is approximately 0.34 &#956;s as depicted. This figure has been modified from Ichikawa et al.11 with permissions. <a href="https://www.jove.com/files/ftp_upload/59007/59007fig4large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 5" class="xfigimg" src="/files/ftp_upload/59007/59007fig5.jpg" /> 
Figure 5: Image of &#956;-PCD measurement in an aqueous solution in a quartz cell. The quartz cell is placed on the stand in front of the aperture to allow &#956;-PCD decay curve measurement in an aqueous solution. The cell dimension is 5 mm x 20 mm x 40 mm (length x width x height). <a href="https://www.jove.com/files/ftp_upload/59007/59007fig5large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 6" class="xfigimg" src="/files/ftp_upload/59007/59007fig6.jpg" /> 
Figure 6: Normalized and calculated &#956;-PCD decay curves for the n-type 4H-SiC sample with excitation on the Si-face by 266 nm, in air and aqueous solutions. Solid lines represent the &#956;-PCD experimental result curves for the aqueous solutions of H2O, H2SO4, HCL, Na2SO4, NaOH, or HF. The dashed lines are calculated curves with the bulk carrier lifetime in the epilayers, &#964;B = 3 &#956;s, and the surface recombination velocity for the Si-face, SSi = 200 cm/s or 700 cm/s. This figure has been modified from Ichikawa et al.11 with permissions. <a href="https://www.jove.com/files/ftp_upload/59007/59007fig6large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 7" class="xfigimg" src="/files/ftp_upload/59007/59007fig7.jpg" /> 
Figure 7: The pH dependence of &#964;1/e for the n-type 4H-SiC sample with excitation on the Si-face by 266 nm. Carrier lifetime increases as the pH of the aqueous solution decreases. This result indicates that lower pH will have more effects on the carrier lifetime. This figure has been modified from Ichikawa et al.11 with permissions. <a href="https://www.jove.com/files/ftp_upload/59007/59007fig7large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
<img alt="Figure 8" class="xfigimg" src="/files/ftp_upload/59007/59007fig8.jpg" /> 
Figure 8: The &#956;-PCD decay curve of n-type 4H-SiC with excitation of injected photon density of 1014 or 1015 cm&#8722;2 on the Si-face by 266 nm. Measurement with high excitation at photon density of 1015 cm&#8722;2 makes a more gradual decay curve than that with lower photon density due to nonlinearity of microwave reflectivity. <a href="https://www.jove.com/files/ftp_upload/59007/59007fig8large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

Watch this Scientific Journal Video about Carrier Lifetime Measurements in Semiconductors through the Microwave Photoconductivity Decay Method at JoVE.com

Carrier Lifetime Measurements in Semiconductors through the Microwave Photoconductivity Decay Method

As one of the important physical parameters in semiconductors, carrier lifetime is measured herein via a protocol employing the microwave photoconductivity decay method.

This work presents a protocol employing the microwave photoconductivity decay (&#956;-PCD) for measurement of the carrier lifetime in semiconductor ...

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29.7K Views.  Nagoya Institute of Technology. As one of the important physical parameters in semiconductors, carrier lifetime is measured herein via a protocol employing the microwave photoconductivity decay method.

Video: Carrier Lifetime Measurements in Semiconductors through the Microwave Photoconductivity Decay Method

Microwave Photonics Systems Based on Whispering-gallery-mode Resonators

Microwave photonics systems rely fundamentally on the interaction between microwave and optical signals. These systems are extremely promising for various areas of technology and applied science, such as aerospace and communication engineering, sensing, metrology, nonlinear photonics, and quantum optics. In this article, we present the principal techniques used in our lab to build microwave photonics systems based on ultra-high Q whispering gallery mode resonators. First detailed in this article is the protocol for resonator polishing, which is based on a grind-and-polish technique close to the ones used to polish optical components such as lenses or telescope mirrors. Then, a white light interferometric profilometer measures surface roughness, which is a key parameter to characterize the quality of the polishing. In order to launch light in the resonator, a tapered silica fiber with diameter in the micrometer range is used. To reach such small diameters, we adopt the "flame-brushing" technique, using simultaneously computer-controlled motors to pull the fiber apart, and a blowtorch to heat the fiber area to be tapered. The resonator and the tapered fiber are later approached to one another to visualize the resonance signal of the whispering gallery modes using a wavelength-scanning laser. By increasing the optical power in the resonator, nonlinear phenomena are triggered until the formation of a Kerr optical frequency comb is observed with a spectrum made of equidistant spectral lines. These Kerr comb spectra have exceptional characteristics that are suitable for several applications in science and technology. We consider the application related to ultra-stable microwave frequency synthesis and demonstrate the generation of a Kerr comb with GHz intermodal frequency.

The customized techniques developed in our lab to build microwave photonics systems based on ultra-high Q whispering gallery mode resonators are presented. The protocols to obtain and characterize these resonators are detailed, and an explanation of some of their applications in microwave photonics is given.

Microwave photonics systems rely fundamentally on the interaction between microwave and optical signals. These systems are extremely promising for various ...

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

The application of femtosecond four-wave mixing to the study of fundamental properties of diluted magnetic semiconductors ((s,p)-d hybridization, spin-flip scattering) is described, using experiments on GaMnAs as a prototype III-Mn-V system.&#160; Spectrally-resolved and time-resolved experimental configurations are described, including the use of zero-background autocorrelation techniques for pulse optimization.&#160; The etching process used to prepare GaMnAs samples for four-wave mixing experiments is also highlighted.&#160; The high temporal resolution of this technique, afforded by the use of short (20 fsec) optical pulses, permits the rapid spin-flip scattering process in this system to be studied directly in the time domain, providing new insight into the strong exchange coupling responsible for carrier-mediated ferromagnetism.&#160; We also show that spectral resolution of the four-wave mixing signal allows one to extract clear signatures of (s,p)-d hybridization in this system, unlike linear spectroscopy techniques.&#160;&#160; This increased sensitivity is due to the nonlinearity of the technique, which suppresses defect-related contributions to the optical response. This method may be used to measure the time scale for coherence decay (tied to the fastest scattering processes) in a wide variety of semiconductor systems of interest for next generation electronics and optoelectronics.

The technique of femtosecond four-wave mixing is described, including spectrally-resolved and time-resolved configurations. We illustrate the utility of this technique for the investigation of crucial physical properties in the III-V diluted magnetic semiconductors, afforded by its nonlinearity and high temporal resolution.

The application of femtosecond four-wave mixing to the study of fundamental properties of diluted magnetic semiconductors ((s,p)-d hybridization, ...

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Recently, disordered photonic materials have been suggested as an alternative to periodic crystals for the formation of a complete photonic bandgap (PBG). In this article we will describe the methods for constructing and characterizing macroscopic disordered photonic structures using microwaves. The microwave regime offers the most convenient experimental sample size to build and test PBG media. Easily manipulated dielectric lattice components extend flexibility in building various 2D structures on top of pre-printed plastic templates. Once built, the structures could be quickly modified with point and line defects to make freeform waveguides and filters. Testing is done using a widely available Vector Network Analyzer and pairs of microwave horn antennas. Due to the scale invariance property of electromagnetic fields, the results we obtained in the microwave region can be directly applied to infrared and optical regions. Our approach is simple but delivers exciting new insight into the nature of light and disordered matter interaction.

Our representative results include the first experimental demonstration of the existence of a complete and isotropic PBG in a two-dimensional (2D) hyperuniform disordered dielectric structure. Additionally we demonstrate experimentally the ability of this novel photonic structure to guide electromagnetic waves (EM) through freeform waveguides of arbitrary shape.

Disordered structures offer new mechanisms for forming photonic bandgaps and unprecedented freedom in functional-defect designs. To circumvent the computational challenges of disordered systems, we construct modular macroscopic samples of the new class of PBG materials and use microwaves to characterize their scale-invariant photonic properties, in an easy and inexpensive manner.

Recently, disordered photonic materials have been suggested as an alternative to periodic crystals for the formation of a complete photonic bandgap (PBG). ...

Ambient Method for the Production of an Ionically Gated Carbon Nanotube Common Cathode in Tandem Organic Solar Cells

A method of fabricating organic photovoltaic (OPV) tandems that requires no vacuum processing is presented. These devices are comprised of two solution-processed polymeric cells connected in parallel by a transparent carbon nanotubes (CNT) interlayer. This structure includes improvements in fabrication techniques for tandem OPV devices. First the need for ambient-processed cathodes is considered. The CNT anode in the tandem device is tuned via ionic gating to become a common cathode. Ionic gating employs electric double layer charging to lower the work function of the CNT electrode. Secondly, the difficulty of sequentially stacking tandem layers by solution-processing is addressed. The devices are fabricated via solution and dry-lamination in ambient conditions with parallel processing steps. The method of fabricating the individual polymeric cells, the steps needed to laminate them together with a common CNT cathode, and then provide some representative results are described. These results demonstrate ionic gating of the CNT electrode to create a common cathode and addition of current and efficiency as a result of the lamination procedure.

A method of fabricating, in ambient conditions, organic photovoltaic tandem devices in a parallel configuration is presented. These devices feature an air-processed, semi-transparent, carbon nanotube common cathode.

A method of fabricating organic photovoltaic (OPV) tandems that requires no vacuum processing is presented. These devices are comprised of two ...

Selective Area Modification of Silicon Surface Wettability by Pulsed UV Laser Irradiation in Liquid Environment

The wettability of silicon (Si) is one of the important parameters in the technology of surface functionalization of this material and fabrication of biosensing devices. We report on a protocol of using KrF and ArF lasers irradiating Si (001) samples immersed in a liquid environment with low number of pulses and operating at moderately low pulse fluences to induce Si wettability modification. Wafers immersed for up to 4 hr in a 0.01% H2O2/H2O solution did not show measurable change in their initial contact angle (CA) ~75&#176;. However, the 500-pulse KrF and ArF lasers irradiation of such wafers in a microchamber filled with 0.01% H2O2/H2O solution at 250 and 65 mJ/cm2, respectively, has decreased the CA to near 15&#176;, indicating the formation of a superhydrophilic surface. The formation of OH-terminated Si (001), with no measurable change of the wafer&#8217;s surface morphology, has been confirmed by X-ray photoelectron spectroscopy and atomic force microscopy measurements. The selective area irradiated samples were then immersed in a biotin-conjugated fluorescein-stained nanospheres solution for 2 hr, resulting in a successful immobilization of the nanospheres in the non-irradiated area. This illustrates the potential of&#160;the method for selective area biofunctionalization and fabrication of advanced Si-based biosensing architectures. We also describe a similar protocol of irradiation of wafers immersed in methanol (CH3OH) using ArF laser operating at pulse fluence of 65 mJ/cm2 and in situ formation of a strongly hydrophobic surface of Si (001) with the CA of 103&#176;. The XPS results indicate ArF laser induced formation of Si&#8211;(OCH3)x compounds responsible for the observed hydrophobicity. However, no such compounds were found by XPS on the Si surface irradiated by KrF laser in methanol, demonstrating the inability of the KrF laser to photodissociate methanol and create -OCH3 radicals.

We report on a process of in situ alteration of HF treated Si (001) surface into a hydrophilic or hydrophobic state by irradiating samples in microfluidic chambers filled with&#160;H2O2/H2O solution (0.01%-0.5%) or methanol solutions using pulsed UV laser of a relative low pulse fluence.

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Speciation and Bioavailability Measurements of Environmental Plutonium Using Diffusion in Thin Films

The biological uptake of plutonium (Pu) in aquatic ecosystems is of particular concern since it is an alpha-particle emitter with long half-life which can potentially contribute to the exposure of biota and humans. The diffusive gradients in thin films technique is introduced here for in-situ measurements of Pu bioavailability and speciation. A diffusion cell constructed for laboratory experiments with Pu and the newly developed protocol make it possible to simulate the environmental behavior of Pu in model solutions of various chemical compositions. Adjustment of the oxidation states to Pu(IV) and Pu(V) described in this protocol is essential in order to investigate the complex redox chemistry of plutonium in the environment. The calibration of this technique and the results obtained in the laboratory experiments enable to develop a specific DGT device for in-situ Pu measurements in freshwaters. Accelerator-based mass-spectrometry measurements of Pu accumulated by DGTs in a karst spring allowed determining the bioavailability of Pu in a mineral freshwater environment. Application of this protocol for Pu measurements using DGT devices has a large potential to improve our understanding of the speciation and the biological transfer of Pu in aquatic ecosystems.

The technique of diffusive gradients in thin films (DGT) is proposed for speciation studies of plutonium. This protocol describes diffusion experiments probing the behavior of Pu(IV) and Pu(V) in presence of organic matter. DGTs deployed in a karstic spring allow assessment of the bioavailability of Pu.

The biological uptake of plutonium (Pu) in aquatic ecosystems is of particular concern since it is an alpha-particle emitter with long half-life which can ...

Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis

Nuclear reaction analysis (NRA) via the resonant 1H(15N,&#945;&#947;)12C reaction is a highly effective method of depth profiling that quantitatively and non-destructively reveals the hydrogen density distribution at surfaces, at interfaces, and in the volume of solid materials with high depth resolution. The technique applies a 15N ion beam of 6.385 MeV provided by an electrostatic accelerator and specifically detects the 1H isotope in depths up to about 2 &#956;m from the target surface. Surface H coverages are measured with a sensitivity in the order of ~1013 cm-2 (~1% of a typical atomic monolayer density) and H volume concentrations with a detection limit of ~1018 cm-3 (~100 at. ppm). The near-surface depth resolution is 2-5 nm for surface-normal 15N ion incidence onto the target and can be enhanced to values below 1 nm for very flat targets by adopting a surface-grazing incidence geometry. The method is versatile and readily applied to any high vacuum compatible homogeneous material with a smooth surface (no pores). Electrically conductive targets usually tolerate the ion beam irradiation with negligible degradation. Hydrogen quantitation and correct depth analysis require knowledge of the elementary composition (besides hydrogen) and mass density of the target material. Especially in combination with ultra-high vacuum methods for in-situ target preparation and characterization, 1H(15N,&#945;&#947;)12C NRA is ideally suited for hydrogen analysis at atomically controlled surfaces and nanostructured interfaces. We exemplarily demonstrate here the application of 15N NRA at the MALT Tandem accelerator facility of the University of Tokyo to (1) quantitatively measure the surface coverage and the bulk concentration of hydrogen in the near-surface region of a H2 exposed Pd(110) single crystal, and (2) to determine the depth location and layer density of hydrogen near the interfaces of thin SiO2 films on Si(100).

We illustrate the application of 1H(15N,&#945;&#947;)12C resonant nuclear reaction analysis (NRA) to quantitatively evaluate the density of hydrogen atoms on the surface, in the volume, and at an interfacial layer of solid materials. The near-surface hydrogen depth profiling of a Pd(110) single crystal and of SiO2/Si(100) stacks is described.

Nuclear reaction analysis (NRA) via the resonant 1H(15N,&#945;&#947;)12C reaction is a highly effective method of depth profiling that quantitatively and ...

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a new and inexpensive procedure to force mode locking in a pre-adjusted nonlinear polarization rotation fiber laser. This procedure is based on the detection of a sudden change in the output polarization state when mode locking occurs. This change is used to command the alignment of the intra-cavity polarization controller in order to find mode-locking conditions. More specifically, the value of the first Stokes parameter varies when the angle of the polarization controller is swept and, moreover, it undergoes an abrupt variation when the laser enters the mode-locked state. Monitoring this abrupt variation provides a practical easy-to-detect signal that can be used to command the alignment of the polarization controller and drive the laser towards mode locking. This monitoring is achieved by feeding a small portion of the signal to a polarization analyzer measuring the first Stokes parameter. A sudden change in the read out of this parameter from the analyzer will occur when the laser enters the mode-locked state. At this moment, the required angle of the polarization controller is kept fixed. The alignment is completed. This procedure provides an alternate way to existing automating procedures that use equipment such as an optical spectrum analyzer, an RF spectrum analyzer, a photodiode connected to an electronic pulse-counter or a nonlinear detecting scheme based on two-photon absorption or second harmonic generation. It is suitable for lasers mode locked by nonlinear polarization rotation. It is relatively easy to implement, it requires inexpensive means, especially at a wavelength of 1550 nm, and it lowers the production and operation costs incurred in comparison to the above-mentioned techniques.

A protocol to detect and automate mode locking in a pre-adjusted nonlinear polarization rotation fiber laser is presented. The detection of a sudden change in the output polarization state when mode locking occurs is used to command the alignment of an intra-cavity polarization controller in order to find mode-locking conditions.

When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a ...

Recombination Dynamics in Thin-film Photovoltaic Materials via Time-resolved Microwave Conductivity

A method for investigating recombination dynamics of photo-induced charge carriers in thin film semiconductors, specifically in photovoltaic materials such as organo-lead halide perovskites is presented. The perovskite film thickness and absorption coefficient are initially characterized by profilometry and UV-VIS absorption spectroscopy. Calibration of both laser power and cavity sensitivity is described in detail. A protocol for performing Flash-photolysis Time Resolved Microwave Conductivity (TRMC) experiments, a non-contact method of determining the conductivity of a material, is presented. A process for identifying the real and imaginary components of the complex conductivity by performing TRMC as a function of microwave frequency is given. Charge carrier dynamics are determined under different excitation regimes (including both power and wavelength). Techniques for distinguishing between direct and trap-mediated decay processes are presented and discussed. Results are modelled and interpreted with reference to a general kinetic model of photoinduced charge carriers in a semiconductor. The techniques described are applicable to a wide range of optoelectronic materials, including organic and inorganic photovoltaic materials, nanoparticles, and conducting/semiconducting thin films.

A Time Resolved Microwave Conductivity technique for investigating direct and trap-mediated recombination dynamics and determining carrier mobilities of thin film semiconductors is presented here.

A method for investigating recombination dynamics of photo-induced charge carriers in thin film semiconductors, specifically in photovoltaic materials ...