Direct comparison of time-resolved terahertz spectroscopy and Hall Van der Pauw methods for measurement of carrier conductivity and mobility in bulk semiconductors
Brian G. Alberding, W. Robert Thurber, and Edwin J. Heilweil
Brian G. Alberding, W. Robert Thurber, and Edwin J. Heilweil, "Direct comparison of time-resolved terahertz spectroscopy and Hall Van der Pauw methods for measurement of carrier conductivity and mobility in bulk semiconductors," J. Opt. Soc. Am. B 34, 1392-1406 (2017)
Charge carrier conductivity and mobility for various semiconductor wafers and crystals were measured by ultrafast above bandgap, optically excited time-resolved terahertz spectroscopy (TRTS) and Hall Van der Pauw contact methods to directly compare these approaches and validate the use of the non-contact optical approach for future materials and in situ device analyses. Undoped and doped silicon (Si) wafers with resistances varying over 6 orders of magnitude were selected as model systems because contact Hall measurements are reliably made on this material. Conductivity and mobility obtained at room temperature by terahertz transmission and TRTS methods yield the sum of electron and hole mobility which agree very well with either directly measured or literature values for corresponding atomic and photodoping densities. Careful evaluation of the optically generated TRTS frequency-dependent conductivity also shows it is dominated by induced free carrier absorption rather than small probe pulse phase shifts, which is commonly ascribed to changes in the complex conductivity from sample morphology and evaluation of carrier mobility by applying Drude scattering models. Thus, in this work, the real-valued, frequency-averaged conductivity was used to extract sample mobility without application of models. Examinations of germanium (Ge), gallium arsenide (GaAs), gallium phosphide (GaP), and zinc telluride (ZnTe) samples were also made to demonstrate the general applicability of the TRTS method, even for materials that do not reliably make good contacts (e.g., GaAs, GaP, ZnTe). For these cases, values for the sum of the electron and hole mobility also compare very favorably to measured or available published data.
Jonas D. Buron, David M. A. Mackenzie, Dirch. H. Petersen, Amaia Pesquera, Alba Centeno, Peter Bøggild, Amaia Zurutuza, and Peter U. Jepsen Opt. Express 23(24) 30721-30729 (2015)
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Un, undoped; , -type; , -type; (P), phosphorous; (B), boron; (Sb), antimony.
DSP and SSP stand for double-side and single-side polish, respectively.
Estimated thickness and resistivity quoted by the commercial provider.
Table 2.
Summary of THz-TDS and Van der Pauw Hall Measurements of Conductivity for the Variously Doped Silicon Samples
Average and standard deviation of multiple micrometer measurements.
Given by commercial provider.
Value at lowest measured frequency as an approximation to the DC limit.
Frequency-averaged conductivity between 0.4 THz to 2.0 THz.
Accurate to uncertainty ( analysis).
Table 3.
Summary of TRTS Data for Silicon Samples at Various Excitation Wavelengths and Excitation Fluences
The absorbed density is the fraction of photons absorbed from the incident fluence, where the absorbance is given by , and is the reflectivity at the pump wavelength. For 400 nm excitation, , and for 800 nm excitation, , as determined from the Fresnel equation for silicon.
The carrier density is given by the absorbed density divided by the penetration depth. For 400 nm, the penetration depth is and for 800 nm the penetration depth is .
Table 4.
TRTS Results for Each Silicon Wafer Averaged over Multiple Excitation Fluences Compared to Hall Van der Pauw Measurements on the Same Samples and Comparable Literature Values
TRTS results averaged over multiple excitation fluences ranging over order of magnitude.
Change in carrier density generated by photoexcitation for both electrons and holes (given by pump fluence and penetration depth).
Carrier densities equal to the sum of the intrinsic carriers (determined by Hall measurements) and those generated by photoexcitation were considered to determine the appropriate literature value for comparison.
See Refs. [37–40].
Table 5.
Summary of Results for Conductivity Measurements of Non-Photoexcited Semiconductors
Average value measured using multiple micrometers.
Provided by commercial provider.
Accurate to uncertainty ( uncertainty analysis).
Published reference value for pure or lightly doped samples [40].
Table 6.
TRTS Data for Various Semiconductor Samples at the Indicated Excitation Wavelengths and Excitation Fluences
The absorbed density is the fraction of photons absorbed from the incident fluence, where the absorbance is given by , and is the reflectivity at the pump wavelength. Values for reflectivity at the excitation wavelength are given for each semiconductor in Table 7.
The carrier density is given by the absorbed density divided by the penetration depth. The details used to calculate this are given in Table 7.
Table 7.
Tabulated Parameters Needed to Determine Carrier Density from Photoexcitation in TRTS Experiments
For ZnTe see [41]. For the other samples see [21].
Percent reflectivity at the visible excitation wavelength was determined for each sample using the Fresnel equation. See [21].
Table 8.
TRTS Results for Each Semiconductor Sample Averaged over Multiple Excitation Fluences Compared to Hall Van der Pauw Measurements and Literature Values
Literature values given for room temperature measurement at a carrier density equivalent to from TRTS. Literature data obtained for Si [39], GaAs [42–44], Ge [44–46], GaP [44,47]. For ZnTe literature data is limited [48] and could not be found for the TRTS experimental carrier density.
This experiment was performed at a single excitation power.
Tables (8)
Table 1.
Summary of Bulk Semiconductors Studied and Their Characteristics as Received from Commercial Sources [32]
Un, undoped; , -type; , -type; (P), phosphorous; (B), boron; (Sb), antimony.
DSP and SSP stand for double-side and single-side polish, respectively.
Estimated thickness and resistivity quoted by the commercial provider.
Table 2.
Summary of THz-TDS and Van der Pauw Hall Measurements of Conductivity for the Variously Doped Silicon Samples
Average and standard deviation of multiple micrometer measurements.
Given by commercial provider.
Value at lowest measured frequency as an approximation to the DC limit.
Frequency-averaged conductivity between 0.4 THz to 2.0 THz.
Accurate to uncertainty ( analysis).
Table 3.
Summary of TRTS Data for Silicon Samples at Various Excitation Wavelengths and Excitation Fluences
The absorbed density is the fraction of photons absorbed from the incident fluence, where the absorbance is given by , and is the reflectivity at the pump wavelength. For 400 nm excitation, , and for 800 nm excitation, , as determined from the Fresnel equation for silicon.
The carrier density is given by the absorbed density divided by the penetration depth. For 400 nm, the penetration depth is and for 800 nm the penetration depth is .
Table 4.
TRTS Results for Each Silicon Wafer Averaged over Multiple Excitation Fluences Compared to Hall Van der Pauw Measurements on the Same Samples and Comparable Literature Values
TRTS results averaged over multiple excitation fluences ranging over order of magnitude.
Change in carrier density generated by photoexcitation for both electrons and holes (given by pump fluence and penetration depth).
Carrier densities equal to the sum of the intrinsic carriers (determined by Hall measurements) and those generated by photoexcitation were considered to determine the appropriate literature value for comparison.
See Refs. [37–40].
Table 5.
Summary of Results for Conductivity Measurements of Non-Photoexcited Semiconductors
Average value measured using multiple micrometers.
Provided by commercial provider.
Accurate to uncertainty ( uncertainty analysis).
Published reference value for pure or lightly doped samples [40].
Table 6.
TRTS Data for Various Semiconductor Samples at the Indicated Excitation Wavelengths and Excitation Fluences
The absorbed density is the fraction of photons absorbed from the incident fluence, where the absorbance is given by , and is the reflectivity at the pump wavelength. Values for reflectivity at the excitation wavelength are given for each semiconductor in Table 7.
The carrier density is given by the absorbed density divided by the penetration depth. The details used to calculate this are given in Table 7.
Table 7.
Tabulated Parameters Needed to Determine Carrier Density from Photoexcitation in TRTS Experiments
For ZnTe see [41]. For the other samples see [21].
Percent reflectivity at the visible excitation wavelength was determined for each sample using the Fresnel equation. See [21].
Table 8.
TRTS Results for Each Semiconductor Sample Averaged over Multiple Excitation Fluences Compared to Hall Van der Pauw Measurements and Literature Values
Literature values given for room temperature measurement at a carrier density equivalent to from TRTS. Literature data obtained for Si [39], GaAs [42–44], Ge [44–46], GaP [44,47]. For ZnTe literature data is limited [48] and could not be found for the TRTS experimental carrier density.
This experiment was performed at a single excitation power.