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 (μ-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 μ-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 μ-PCD protocol in measuring the carrier lifetime in semiconductor materials and devices.
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–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 (μ-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: µ-PCD, time resolved photoluminescence (TR-PL), and time resolved free carrier absorption (TR-FCA)2,3,4,5,6,7. Among these techniques, µ-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, µ-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 μ-PCD1,20,21 is detailed here. In principle, it uses a reflected microwave as a probe. Here, the microwave reflectance of a sample R(σ) is equivalent to the ratio between the reflected microwave intensity P(σ) and the incident microwave intensity Pdi as expressed by Equation 1:
(1)
By irradiation of a pulse laser, the conductivity of a sample σ changes to σ + Δσ; likewise, R (σ) transforms to R(σ + Δσ). Thus, ΔR is given by Equation 2:
(2)
In a perturbation (small Δσ) approximation, R(σ + Δσ) is developed in Taylor series to yield
(3)
while Δσ becomes
, (4)
where q is the elementary charge, μp is the hole mobility, μn is the electron mobility, and Δp is the excess carrier concentration. From the preceding equations,ΔR and Δp are related by
. (5)
The dependence of microwave reflectance on excess carrier concentration allows μ-PCD to observe the time decay of excess carriers, which we can use to estimate the carrier lifetime of semiconductor materials.
In the μ-PCD protocol, step 4.7 is the most important point. The E–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 μ-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 , which is expressed by Equation 9:
(9)
where ω is the angular frequency of the microwave, and ε, ρ, and μ represent the sample’s dielectric constant, resistivity, and permeability, respectively. In the case of Si and SiC, approximate δ values for the 10 GHz microwave were 9 mm at 50 Ω∙cm, 2 mm at 10 Ω∙cm, 500 μm at 1 Ω∙cm, and 150 μm at 0.1 Ω∙cm. Therefore, measurements for samples with typical thicknesses (several hundred micron) at less than 0.1 Ω∙cm will lose δ 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−3. On the other hand, electron–hole scattering must be considered at excess carriers greater than 1016 cm−3, as discussed in ref. 13.
The μ-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 τ1/e would be overestimated. Figure 8 shows the μ-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, μ-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 μ-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, μ-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.
The authors have nothing to disclose.
This work was supported by the Nagoya Institute of Technology, Japan.
n-type 4H-SiC epilayer | Ascatron AB http://ascatron.com/ | Sample | |
266 nm pulsed laser | CryLaS GmbH http://www.crylas.de/ | FQSS 266-50 | Excitation light source |
Photodiode | THORLABS https://www.thorlabs.com/index.cfm | DET10A/M | Trigger signal detection |
Schottky barrier diode | ASI http://www.advancedsemiconductor.com/ | 1N23WE | Reflected microwave detection |
Gun diode | Microsemi https://www.microsemi.com/ | MO86751C | Microwave generation source |
E-H tuner | SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html | microwave component | |
Circulator | SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html | microwave component | |
Rectangular waveguide | SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html | microwave component | |
Double ridge waveguide | SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html | microwave component | |
Crystal mount | SPC ELECTRONICS CORPORATION http://www.spc.co.jp/index.html | microwave component | |
Acetone | KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/ | GE00001 | Sample cleaning |
Sulfuric acid | KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/ | GE00257 | Acidic aqueous solution |
Hydrochloric acid | KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/ | GE00238 | Acidic aqueous solution |
Hydrogen fluoride | KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/ | 18083-1B | Acidic aqueous solution |
Sodium hydroxide | KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/ | 37184-00 | Alkaline aqueous solution |
Sodium sulfate | KANTO CHEMICAL CO.,INC. https://www.kanto.co.jp/ | 37280-00 | Neutral aqueous solution |