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>

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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. Principle and injection dependence.</a> Journal of Applied Physics. 84, 275-283 (1998).</li><li>Mae, S., Tawara, T., Tsuchida, H., Kato, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Microscopic+FCA+System+for+Depth-Resolved+Carrier+Lifetime+Measurement+in+SiC.">Microscopic FCA System for Depth-Resolved Carrier Lifetime Measurement in SiC.</a> Materials Science Forum. 924, 269-272 (2018).</li><li>Miyazawa, T., Ito, M., Tsuchida, H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Evaluation+of+long+carrier+lifetimes+in+thick+4H+silicon+carbide+epitaxial+layers.">Evaluation of long carrier lifetimes in thick 4H silicon carbide epitaxial layers.</a> Applied Physics Letters. 97, 202106 (2010).</li><li>Kimoto, T., Danno, K., 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=Lifetime-killing+defects+in+4H-SiC+epilayers+and+lifetime+control+by+low-energy+electron+irradiation.">Lifetime-killing defects in 4H-SiC epilayers and lifetime control by low-energy electron irradiation.</a> Physica Status Solidi B. 245, 1327 (2008).</li><li>&#352;&#269;ajev, P., Gudelis, V., Jara&#353;i&#363;nas, K., Klein, P. 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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><tbody><tr><td>n-type 4H-SiC epilayer</td><td>Ascatron AB http://ascatron.com/</td><td></td><td>Sample</td></tr><tr><td>266 nm pulsed laser</td><td>CryLaS GmbH http://www.crylas.de/</td><td>FQSS 266-50&amp;nbsp;</td><td>Excitation light source</td></tr><tr><td>Photodiode</td><td>THORLABS https://www.thorlabs.com/index.cfm</td><td>DET10A/M</td><td>Trigger signal detection</td></tr><tr><td>Schottky barrier diode</td><td>ASI http://www.advancedsemiconductor.com/</td><td>1N23WE</td><td>Reflected microwave detection</td></tr><tr><td>Gun diode&amp;nbsp;</td><td>Microsemi https://www.microsemi.com/</td><td>MO86751C</td><td>Microwave generation source</td></tr><tr><td>E-H tuner&amp;nbsp;</td><td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td><td></td><td>microwave component</td></tr><tr><td>Circulator</td><td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td><td></td><td>microwave component</td></tr><tr><td>Rectangular waveguide</td><td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td><td></td><td>microwave component</td></tr><tr><td>Double ridge waveguide</td><td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td><td></td><td>microwave component</td></tr><tr><td>Crystal mount</td><td>SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html</td><td></td><td>microwave component</td></tr><tr><td>Acetone</td><td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td><td>GE00001</td><td>Sample cleaning</td></tr><tr><td>Sulfuric acid</td><td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td><td>GE00257</td><td>Acidic aqueous solution</td></tr><tr><td>Hydrochloric acid</td><td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td><td>GE00238</td><td>Acidic aqueous solution</td></tr><tr><td>Hydrogen fluoride</td><td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td><td>18083-1B</td><td>Acidic aqueous solution</td></tr><tr><td>Sodium hydroxide</td><td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td><td>37184-00</td><td>Alkaline aqueous solution</td></tr><tr><td>Sodium sulfate</td><td>KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/</td><td>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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30.2K Views.  Nagoya Institute of Technology. Carrier levensduur is een belangrijke parameter voor halfgeleidergolf analyse en materialen. We hebben een gemeenschappelijke methode nodig voor aberratie van de levensduur van de drager. Hier introduceren we microgolf fotogeleiding verval zogenaamde micro-PCD.micro-PCD is vaak verouderd micro-PCD is vaak verouderd, omdat het lang gedrag en lange verstorende methode. Een ander voordeel van deze methode is ongevoeligheid die volgt aberratie van materialen van alle structuren. Het aanton...

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

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.

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

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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.

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Making Record-efficiency SnS Solar Cells by Thermal Evaporation and Atomic Layer Deposition

Tin sulfide (SnS) is a candidate absorber material for Earth-abundant, non-toxic solar cells. SnS offers easy phase control and rapid growth by congruent thermal evaporation, and it absorbs visible light strongly. However, for a long time the record power conversion efficiency of SnS solar cells remained below 2%. Recently we demonstrated new certified record efficiencies of 4.36% using SnS deposited by atomic layer deposition, and 3.88% using thermal evaporation. Here the fabrication procedure for these record solar cells is described, and the statistical distribution of the fabrication process is reported. The standard deviation of efficiency measured on a single substrate is typically over 0.5%. All steps including substrate selection and cleaning, Mo sputtering for the rear contact (cathode), SnS deposition, annealing, surface passivation, Zn(O,S) buffer layer selection and deposition, transparent conductor (anode) deposition, and metallization are described. On each substrate we fabricate 11 individual devices, each with active area 0.25 cm2. Further, a system for high throughput measurements of current-voltage curves under simulated solar light, and external quantum efficiency measurement with variable light bias is described. With this system we are able to measure full data sets on all 11 devices in an automated manner and in minimal time. These results illustrate the value of studying large sample sets, rather than focusing narrowly on the highest performing devices. Large data sets help us to distinguish and remedy individual loss mechanisms affecting our devices.

Tin sulfide (SnS) is a candidate material for Earth-abundant, non-toxic solar cells. Here, we demonstrate the fabrication procedure of the SnS solar cells employing atomic layer deposition, which yields 4.36% certified power conversion efficiency, and thermal evaporation which yields 3.88%.

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Light Enhanced Hydrofluoric Acid Passivation: A Sensitive Technique for Detecting Bulk Silicon Defects

A procedure to measure the bulk lifetime (&#62;100 &#181;sec) of silicon wafers by temporarily attaining a very high level of surface passivation when immersing the wafers in hydrofluoric acid (HF) is presented. By this procedure three critical steps are required to attain the bulk lifetime. Firstly, prior to immersing silicon wafers into HF, they are chemically cleaned and subsequently etched in 25% tetramethylammonium hydroxide. Secondly, the chemically treated wafers are then placed into a large plastic container filled with a mixture of HF and hydrochloric acid, and then centered over an inductive coil for photoconductance (PC) measurements. Thirdly, to inhibit surface recombination and measure the bulk lifetime, the wafers are illuminated at 0.2 suns for 1 min&#160;using a halogen lamp, the illumination is switched off, and a PC measurement is immediately taken. By this procedure, the characteristics of bulk silicon defects can be accurately determined. Furthermore, it is anticipated that a sensitive RT surface passivation technique will be imperative for examining bulk silicon defects when their concentration is low (&#60;1012 cm-3).

A RT liquid surface passivation technique to investigate the recombination activity of bulk silicon defects is described. For the technique to be successful, three critical steps are required: (i) chemical cleaning and etching of silicon, (ii) immersion of silicon in 15% hydrofluoric acid and (iii) illumination for 1 min.

A procedure to measure the bulk lifetime (&#62;100 &#181;sec) of silicon wafers by temporarily attaining a very high level of surface passivation when ...

Fabrication and Characterization of Superconducting Resonators

Superconducting microwave resonators are of interest for a wide range of applications, including for their use as microwave kinetic inductance detectors (MKIDs) for the detection of faint astrophysical signatures, as well as for quantum computing applications and materials characterization. In this paper, procedures are presented for the fabrication and characterization of thin-film superconducting microwave resonators. The fabrication methodology allows for the realization of superconducting transmission-line resonators with features on both sides of an atomically smooth single-crystal silicon dielectric. This work describes the procedure for the installation of resonator devices into a cryogenic microwave testbed and for cool-down below the superconducting transition temperature. The set-up of the cryogenic microwave testbed allows one to do careful measurements of the complex microwave transmission of these resonator devices, enabling the extraction of the properties of the superconducting lines and dielectric substrate (e.g., internal quality factors, loss and kinetic inductance fractions), which are important for device design and performance.

Superconducting microwave resonators are of interest for detection of light, quantum computing applications and materials characterization. This work presents a detailed procedure for fabrication and characterization of superconducting microwave resonator scattering parameters.

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Comprehensive Characterization of Extended Defects in Semiconductor Materials by a Scanning Electron Microscope

Extended defects such as dislocations and grain boundaries have a strong influence on the performance of microelectronic devices and on other applications of semiconductor materials. However, it is still under debate how the defect structure determines the band structure, and therefore, the recombination behavior of electron-hole pairs responsible for the optical and electrical properties of the extended defects. The present paper is a survey of procedures for the spatially resolved investigation of structural and of physical properties of extended defects in semiconductor materials with a scanning electron microscope (SEM). Representative examples are given for crystalline silicon. The luminescence behavior of extended defects can be investigated by cathodoluminescence (CL) measurements. They are particularly valuable because spectrally and spatially resolved information can be obtained simultaneously. For silicon, with an indirect electronic band structure, CL measurements should be carried out at low temperatures down to 5 K due to the low fraction of radiative recombination processes in comparison to non-radiative transitions at room temperature. For the study of the electrical properties of extended defects, the electron beam induced current (EBIC) technique can be applied. The EBIC image reflects the local distribution of defects due to the increased charge-carrier recombination in their vicinity. The procedure for EBIC investigations is described for measurements at room temperature and at low temperatures. Internal strain fields arising from extended defects can be determined quantitatively by cross-correlation electron backscatter diffraction (ccEBSD). This method is challenging because of the necessary preparation of the sample surface and because of the quality of the diffraction patterns which are recorded during the mapping of the sample. The spatial resolution of the three experimental techniques is compared.

The optical, electrical, and structural properties of dislocations and of grain boundaries in semiconductor materials can be determined by experiments performed in a scanning electron microscope. Electron microscopy has been used to investigate cathodoluminescence, electron beam induced current, and diffraction of backscattered electrons.

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Advanced Compositional Analysis of Nanoparticle-polymer Composites Using Direct Fluorescence Imaging

The fabrication of polymer-nanoparticle composites is extremely important in the development of many functional materials. Identifying the precise composition of these materials is essential, especially in the design of surface catalysts, where the surface concentration of the active component determines the activity of the material. Antimicrobial materials which utilize nanoparticles are a particular focus of this technology. Recently swell encapsulation has emerged as a technique for inserting antimicrobial nanoparticles into a host polymer matrix. Swell encapsulation provides the advantage of localizing the incorporation to the external surfaces of materials, which act as the active sites of these materials. However, quantification of this nanoparticle uptake is challenging. Previous studies explore the link between antimicrobial activity and surface concentration of the active component, but this is not directly visualized. Here we show a reliable method to monitor the incorporation of nanoparticles into a polymer host matrix via swell encapsulation. We show that the surface concentration of CdSe/ZnS nanoparticles can be accurately visualized through cross-sectional fluorescence imaging. Using this method, we can quantify the uptake of nanoparticles via swell encapsulation and measure the surface concentration of encapsulated particles, which is key in optimizing the activity of functional materials.

Here we present a reliable method to monitor the incorporation of nanoparticles into a polymer host matrix via swell encapsulation. We show that the surface concentration of cadmium selenide quantum dots can be accurately visualized through cross-sectional fluorescence imaging.

The fabrication of polymer-nanoparticle composites is extremely important in the development of many functional materials. Identifying the precise ...

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.

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Determination of the Excitation and Coupling Rates Between Light Emitters and Surface Plasmon Polaritons

We have developed a unique method to measure the excitation and coupling rates between the light emitters and surface plasmon polaritons (SPPs) arising from metallic periodic arrays without involving time-resolved techniques. We have formulated the rates by quantities that can be measured by simple optical measurements. The instrumentation based on angle- and polarization-resolved reflectivity and photoluminescence spectroscopy will be described in detail here. Our approach is intriguing due to its simplicity, which requires routine optics and several mechanical stages, and thus is highly affordable to most of the research laboratories.

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Luminescence Resonance Energy Transfer to Study Conformational Changes in Membrane Proteins Expressed in Mammalian Cells

Luminescence Resonance Energy Transfer, or LRET, is a powerful technique used to measure distances between two sites in proteins within the distance range of 10-100 &#197;. By measuring the distances under various ligated conditions, conformational changes of the protein can be easily assessed. With LRET, a lanthanide, most often chelated terbium, is used as the donor fluorophore, affording advantages such as a longer donor-only emission lifetime, the flexibility to use multiple acceptor fluorophores, and the opportunity to detect sensitized acceptor emission as an easy way to measure energy transfer without the risk of also detecting donor-only signal. Here, we describe a method to use LRET on membrane proteins expressed and assayed on the surface of intact mammalian cells. We introduce a protease cleavage site between the LRET fluorophore pair. After obtaining the original LRET signal, cleavage at that site removes the specific LRET signal from the protein of interest allowing us to quantitatively subtract the background signal that remains after cleavage. This method allows for more physiologically relevant measurements to be made without the need for purification of protein.

We describe here an improved Luminescence Resonance Energy Transfer (LRET) method where we introduce a protease cleavage site between the donor and acceptor fluorophore sites. This modification allows us to obtain specific LRET signals arising from membrane proteins of interest, allowing for the study of membrane proteins without protein purification.

Luminescence Resonance Energy Transfer, or LRET, is a powerful technique used to measure distances between two sites in proteins within the distance range ...

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