This article demonstrates a contactless, time-resolved, millimeter wave conductivity apparatus capable of measuring photoconductivity of a diverse range of materials. This cavity-less system determines the time-dependent magnitude of a sample’s charge carrier density-mobility product by monitoring the response of a continuous, millimeter-wave probe beam following excitation of the sample by an ultrafast laser pulse. The probe beam is tunable from 110 GHz to 170 GHz and the sample response data can be obtained over the sub-nanosecond to millisecond time interval. This system has been tested on silicon wafers, S-I GaAs, perovskite thin films, SiO2-Ge(nc), and CdSxSe1−x nanowire samples. We demonstrate a minimum detectable photoconductance change of ∼1 µS, an estimated time resolution for conductance decay of ∼100 ps, and a dynamic range greater than 57 dB. The calibration constant of the system, needed for quantitative calculation of photoconductivity from experimental data, has been determined using silicon wafers. This system has several advantages over currently used microwave and terahertz techniques, such as facile tunability of probe frequency and substantially wider time range for study of decay kinetics, while maintaining an open sample environment that enables characterization of a wide range of sample sizes under controlled environmental conditions.

Characterization of the dynamics and transport of photogenerated charge carriers is critically important to understanding fundamental physics in novel optoelectronic materials and to the development of devices based on these materials. Time-resolved photoconductivity techniques have gained popularity, as they provide direct measurement of the charge carrier density–mobility product without the often laborious process of depositing well-characterized electrical contacts.1–9 This sensitivity to carrier mobilities distinguishes photoconductivity measurements from time-resolved photoluminescence and transient absorption techniques that are only sensitive to population dynamics. We introduced here a time resolved millimeter wave conductivity (TR-mmWC) method as an alternative to well-established10,11 time resolved microwave conductivity (TRMC) and time resolved terahertz spectroscopy (TRTS) methods that have been applied to characterize time dependent photoconductivities of a wide variety of organic and inorganic materials for photocatalytic and photovoltaic applications. The TR-mmWC experiment, shown schematically in Fig. 1, is implemented with a frequency-tunable narrowband continuous wave (CW) 110–170 GHz probe beam in a single pass, free-space configuration.

FIG. 1.

Schematic of the TR-mmWC apparatus.

FIG. 1.

Schematic of the TR-mmWC apparatus.

Close modal

This technique is thus similar to TRMC, with two principal differences. First, TRMC measurements are typically carried out with probe beam propagation in waveguides,12,13 and the sample placed in a resonant cavity tuned to the probe frequency. The single pass configuration of TR-mmWC allows for much faster time response, decreasing the time resolution to an estimated 100 ps compared to the ∼10 ns time resolution of typical TRMC systems.22 This free space configuration also enables frequency dependent measurements that can be carried out without cavity retuning. Although sensitivity test data reported here were obtained at a single frequency (140 GHz), the system includes a source capable of tuning continuously from 110 to 170 GHz, which will allow studies of the photoconductive response as a function of frequency as well. TR-mmWC signals as a function of probe frequency for semi-insulating GaAs sample in reflection and transmission geometries are presented below to demonstrate the acquisition of frequency dependent data. The second principal difference between TRMC and TR-mmWC lies in the probe frequency regions. TRMC is typically carried out at discrete frequencies in the range of 9–38 GHz,14,15 while the current TR-mmWC system operates in a significantly higher frequency range that can easily be extended in the future by the use of frequency multipliers or dividers.

TRTS experiments are also performed in a free space configuration, but differ from TR-mmWC and TRMC in their use of broadband ultrafast probe pulses. Time dependence of the photoconductivity in TRTS experiments is measured by varying the time interval between the pump and probe pulses using a mechanical delay line, instead of digitizing the detector signal (as in TR-mmWC and TRMC). This results in improved time resolution but imposes constraints on the maximum delay achievable and the rate of data acquisition. The time resolution of the TR-mmWC system (∼100 ps as currently configured) is determined by the bandwidth of the detection electronics and the laser pulse width and is thus significantly longer than the pulse width (typically ∼100 fs) of the TRTS technique. The maximum delay time in TRTS experiments, however, is limited by the length of the mechanical delay line (1 m delay = 6.7 ns), while the delay time in TR-mmWC and TRMC is determined by the lower limit of the amplifier and detector bandwidths which are extendible to the >1 s. The rate of TRTS data acquisition is also limited because only one delay time is accessed at each laser shot, while the entire decay curve is collected for each laser shot in TRMC and TR-mmWC experiments.

The TR-mmWC system described in detail below is capable of digitizing a decay curve composed of one thousand points with sampling depth ∼50 ns (record length 1000 divided by 20 GSa/s) with about 81 averages obtained every second, while a TRTS system based on an amplified 1 kHz repetition rate Ti:Al2O3 laser system will require more than 1 s to capture a single decay curve. The broadband TRTS probe pulses span frequencies much wider than the tuning range of the TR-mmWC system, enabling frequency dependence of the photoconductivity to be extracted by taking the Fourier transform of the time profile of the probe pulse after transmission through the sample. However, TRTS data acquired with the relatively fast “1D” technique of capturing time dependent photoconductivity at the peak of the THz pulse, yield the average photoconductivity over a wide frequency range compared to the very narrowband (∼10 MHz) TR-mmWC probe pulse. For determination of the time dependence at a particular frequency in TRTS, the probe time profile must be obtained by electro-optic sampling using a gate pulse with a varying time delay. By contrast, the narrow band probe of the TR-mmWC system can easily be tuned through software control. The TR-mmWC experiment can thus be simply performed without use of any delay line.

TRTS is typically carried out over an effective frequency range of 0.2–10 THz.16–19 TRTS data overlapping the TR-mmWC probe frequency range (0.1–0.2 THz) have been published,20,21 but most published data extend only down to 0.2 THz since the probe pulse must be characterized over a wider time window to extract lower frequency data. The frequency range of the TR-mmWC (110-170 GHz) technique is situated between TRMC and TRTS, and TR-mmWC can thus contribute to the detailed exploration of the mechanisms underlying between carrier mobilities observed in TRTS and TRMC measurement regimes by providing additional information for theoretical modeling (e.g., Drude-Smith, etc.) of the frequency dependence of material conductivities. Fast TR-mmWC measurements with continuously tunable probes can complement TRMC and TRTS data14–19 and thus reveal the dependence of mobilities on grain sizes in polycrystalline materials over a wide frequency range.

Major attributes of TRMC, TR-mmWC, and TRTS methods are summarized below, in Table I.

TABLE I.

A summary of TRMC, TR-mmWC, and TRTS probing parameters.

TRMCTR-mmWC (this work)TRTS
Probe CW, narrowband CW, narrowband Pulsed, broadband 
Time-resolved measurements Entire time dependence per laser shot Entire time dependence per laser shot 1 delay time per laser shot 
Time resolution ∼10 ns (limited by resonant cavity)22  ∼100 ps (limited by bandwidth of detection electronics, can be extended to <10 ps) ∼200 fs (limited by laser pulse, THz probe widths)23  
Maximum probe delay accessible ∼s ∼ms (limited by data capacity can be extended to ≳1 s) ∼1 ns (limited by length of delay line) 
Typical frequency range 9–38 GHz12,14,15,24,25 110–340 GHz 0.2–5 THz (extended range down to 50 GHz, up to 40 THz possible)18,20,21,26–28 
Frequency dependent measurements Voltage/mechanical length tuning of oscillator, cavity Software controlled tuning of BWO source Fourier transform of time domain measurement of broadband pulse 
Experimental Configuration Resonant cavity Free space Free space 
Spatial resolution (far field, limited by wavelength) ∼cm ∼1–3 mm ∼0.1 mm 
Sensitivity High (SNR increased by cavity, rapid averaging) Medium (SNR increased by rapid averaging) Low 
Time required for single frequency decay curve collection Similar to TR-mmWC ∼0.012 s (1000 data points, 50 ns range, dependent on oscilloscope digitization + memory transfer time) ∼1 min (data points unknown, 250 ps range, dependent on lock-in signal stabilization, translation stage movement)29  
TRMCTR-mmWC (this work)TRTS
Probe CW, narrowband CW, narrowband Pulsed, broadband 
Time-resolved measurements Entire time dependence per laser shot Entire time dependence per laser shot 1 delay time per laser shot 
Time resolution ∼10 ns (limited by resonant cavity)22  ∼100 ps (limited by bandwidth of detection electronics, can be extended to <10 ps) ∼200 fs (limited by laser pulse, THz probe widths)23  
Maximum probe delay accessible ∼s ∼ms (limited by data capacity can be extended to ≳1 s) ∼1 ns (limited by length of delay line) 
Typical frequency range 9–38 GHz12,14,15,24,25 110–340 GHz 0.2–5 THz (extended range down to 50 GHz, up to 40 THz possible)18,20,21,26–28 
Frequency dependent measurements Voltage/mechanical length tuning of oscillator, cavity Software controlled tuning of BWO source Fourier transform of time domain measurement of broadband pulse 
Experimental Configuration Resonant cavity Free space Free space 
Spatial resolution (far field, limited by wavelength) ∼cm ∼1–3 mm ∼0.1 mm 
Sensitivity High (SNR increased by cavity, rapid averaging) Medium (SNR increased by rapid averaging) Low 
Time required for single frequency decay curve collection Similar to TR-mmWC ∼0.012 s (1000 data points, 50 ns range, dependent on oscilloscope digitization + memory transfer time) ∼1 min (data points unknown, 250 ps range, dependent on lock-in signal stabilization, translation stage movement)29  

This paper presents the TR-mmWC apparatus, and results of calibration experiments (connecting detector voltage response ratio to photoconductance) using c-Si wafers and an internal-field based model derived to relate the millimeter wave power response ratio with the pump-based charge carrier mobility product. This system yields useful data at relatively low laser fluence, i.e., a few μJ/cm2. We also discuss the sensitivity, time resolution, and dynamic range of the system as currently configured, and describe possible upgrades to improve system performance. Transmission and reflection signals for a semi insulating GaAs wafer are also shown for the BWO probe frequency range 110-160 GHz to demonstrate frequency tunability.

The TR-mmWC experiment is based on measurements of the differential transmission of a millimeter wave probe beam through the sample after excitation with an ultrafast laser pulse—the same principle that underlies both TRTS and TRMC. An internal field based model is derived to relate the mmw power response ratio with the pump (laser) based charge carrier-mobility product and connecting the same with the measured detector voltage response ratio through a system sensitivity factor (K) based on observations made using c-Si samples.

Let Es(σ) represent the field strength of the probe beam in the sample, which is a function of the bulk conductivity, σ. The time-average power (Pa) absorbed due to the photoconductivity can be expressed as an integral over the sample volume,

Pa(σ)=12Δσ|Es(σ)|2dV.
(1)

At the photon energies used for excitation here, the photo-induced charges are created within a narrow laser penetration depth, d, just inside the entrance face of the sample. For millimeter waves, the depth (d) of the active region (∼1 μm) is very small compared to the wavelength (∼2 mm), so the internal field can be treated as constant over this region. Hence,

Pa=12ΔσEs(σ)2V=12ΔσdEs(σ)2A.
(2)

Here A is the sample area and Δσ the average photoconductivity over the active volume. The power absorbed can be expressed in terms of the intensity of the radiation in the sample, IS,

Pa=Δσdnε0cISA=ΔGnε0cISA,  wheresamplephotoconductance,ΔG=Δσd.
(3)

Here n is the refractive index of silicon (n = 3.418) at 140 GHz, c is velocity of light, and ε0 is permittivity of free space. The additional absorption due to the photoconductivity will cause a change, ΔP, in the power transmitted through the sample. For simplicity, only samples with relatively low bulk conductivity are considered here, so the effect of changes in the internal probe field due to the photoconductivity can be neglected. In this case, the power change can be expressed solely in terms of the photoconductivity. If the product of bulk conductivity and fluence is large, corrections must be added,

ΔP=PA=Δσdnε0cISA.
(4)

If the intensity of the probe radiation incident on the sample is I0, it is a straightforward calculation to sum the effect of multiple reflections in the sample and obtain an expression for the intensity, IS, immediately within the entrance face, and for the net transmission, IT, through the sample. Treating the sample as a plane-parallel etalon of thickness, t, with bulk index, n, and bulk conductivity σ, we obtain

IS=SI0andIT=TI0,
(5a)

where

S=(1+2Reαtcos(δ)+Re2αt)(1R)12Reαtcos(δ)+R2e2αt
(5b)

and

T=(1R)2eαt12Reαtcos(δ)+R2e2αt.
(5c)

Here R=n1n+12, phase difference δ=2nk0t, wave no. k0=2πλ0, and α=σnε0c.

Substituting from Eq. (5a) into Eq. (4) we obtain

ΔP=PA=Δσdnε0cSI0A=Δσdnε0c(ST)(ITA)=Δσdnε0c(ST)PT,
(6)
ΔPPT=Δσdnε0c(ST)

where

ST=1+2Reαtcos(δ)+Re2αt(1R)eαt.
(7)

PT is the net power transmitted through the sample when there is no excitation. The photoconductivity, Δσ, can be expressed in terms of the charge carrier density, NC, as

Δσ=eNC(μe+μh)

assuming equal numbers of electrons and holes, NC = ne = nh. μe and μh are electron and hole mobilities, respectively. The maximum charge carrier density produced by a laser excitation with photon energy, hν, and laser fluence, F, can be calculated as

NCmax=Fhνd,
(8)

h being Planck’s constant and ν being the pump frequency. The maximum change in conductivity would be

Δσmax=e(μe+μh)hνdF.
(9)

Substituting Eq. (9) into Eq. (7), we obtain for the maximum response,

ΔPPTmax=e(μe+μh)hνncε0(ST)F=e(μe+μh)Z0hνn(ST)F.
(10)

If the fluence is low enough that the mobility can be treated as a constant, then each sample will respond to the applied excitation linearly. The slope, C, of the graph of response versus fluence is determined by the physical, optical, and electronic parameters of the sample,

ΔPPTmax=CFwithC=e(μe+μh)Z0hνn(ST).
(11)

At higher values of the fluence, decreasing mobility will produce a sublinear deviation.

A schematic diagram (not to scale) of the measurement system is shown below in Fig. 2 below. A detailed diagram of the TR-mmWC experimental layout is shown in Fig. 3.

FIG. 2.

Schematic of the measuring system (not to scale) using which we have estimated sensitivity at 140 GHz. ΔP(t) in Eq. (11) above is determined from ΔV(t) at the RF output of the ZBD (zero-bias diode) when the mm-wave probe is passing through the sample and the laser is switched on and PT is determined from the DC output of the ZBD; The 1 μm penetration depth for 532 nm laser is for c-Si samples only.

FIG. 2.

Schematic of the measuring system (not to scale) using which we have estimated sensitivity at 140 GHz. ΔP(t) in Eq. (11) above is determined from ΔV(t) at the RF output of the ZBD (zero-bias diode) when the mm-wave probe is passing through the sample and the laser is switched on and PT is determined from the DC output of the ZBD; The 1 μm penetration depth for 532 nm laser is for c-Si samples only.

Close modal
FIG. 3.

Detailed layout of the TR-mmWC system PSU: power supply unit, BWO/CIDO probe source: electrovacuum backward wave oscillator, or solid-state cavity-tuned IMPATT oscillator, DMM: digital multimeter, KGP: Kapton grid polarizer, ND: neutral density, ZBD: zero-bias diode. Note: For transmission, laser beam is swung at an angle 24.6° with respect to the sample surface which might lead to a total delay of only 30 ps.

FIG. 3.

Detailed layout of the TR-mmWC system PSU: power supply unit, BWO/CIDO probe source: electrovacuum backward wave oscillator, or solid-state cavity-tuned IMPATT oscillator, DMM: digital multimeter, KGP: Kapton grid polarizer, ND: neutral density, ZBD: zero-bias diode. Note: For transmission, laser beam is swung at an angle 24.6° with respect to the sample surface which might lead to a total delay of only 30 ps.

Close modal

Two probe beam sources are available for the system: a frequency tunable backwards wave oscillator (BWO, Elva-1 SGM-PLL-D-3) covering the 110 GHz–170 GHz range with maximum power emission of 80 mW at 150 GHz. The narrow linewidth (1 MHz) and high frequency accuracy (0.01%) of BWO enables frequency-dependent photoconductivity measurements. We also use a fixed frequency cavity-stabilized IMPATT (Impact Ionization Avalanche Transit Time) Diode Oscillator (Elva-1 CIDO-6) source emitting 10 mW at 140 GHz with high frequency and amplitude stability. The probe beam is coupled out of the oscillators using conical horn antennas with integrated teflon lenses and are further collimated with a TPX lens to minimize loss during propagation to the sample. The probe beam is then sent through a kapton grid polarizer (Millitech GFS-00-K20020R3) and directed to the sample by a 0.635 mm thick Mylar beam-splitter oriented 45° with reflection ∼3.2% at 150 GHz, which is used to reduce the beam power incident on the sample (<1 mW). The beam is focused onto the sample at normal incidence with a 5 cm focal length TPX lens, recollimated after the sample by a 2.5 cm focal length TPX lens, and then coupled into the detector with a conical horn antenna. Stand-off distance between the laser illuminated sample and detector30 has been optimized. Diffraction effects are pronounced with the millimeter wave probe, as optical element sizes approach the probe wavelength. We have carefully mapped the probe beam pattern and applied Gaussian beam analysis31 techniques to ascertain location of the beam splitter assembly on the emitter side and the sample holder on the collector portion.

The excitation laser pulse, which is generated by a 532 nm diode-pumped solid-state laser (Coherent Helios 532-1-50) is overlapped with the probe beam on the sample. The laser delivers pulse energy of 20 μJ at user controlled repitition rates up to 50 kHz. A small portion of the beam is picked off and directed to a fast photodiode detector (Newport 818-BB-45) to generate a trigger signal for data acquisition with minimum jitter. The same photodiode has been used to measure the 345 ps FWHM of the laser pulse. The laser beam is expanded to produce a spot area over 10 times larger than the probe beam area to increase uniformity of excitation by the Gaussian spatial profile pulse. Laser fluences are controlled through a combination of neutral density filters. The transmitted (or reflected) probe beam is detected by zero biased Schottky diodes30 (ZBDs, Virginia Diodes WR6.5ZBD-EXT) with specified responsivities >2000 V/W and noise equivalent powers of 2 pW/√Hz. Matched (50 Ω) bias-tees on the diodes (VSWR: 1.12 dB at 6 GHz with isolation of ∼40 dB for 10, 100, and 200 mA) serve to separate the large DC signal, V0, produced by the probe beam, from the much smaller transient component, ΔV(t), arising from the time dependent charge carriers generated by the excitation. The transient signal from the RF output of the signal ZBD is amplified by a wide bandwidth (3 kHz–10 GHz) amplifier (Miteq JSMF4-02K100-32-10P) with 30 dB gain and gain flatness of 1.5 dB and recorded by a 6 GHz input bandwidth, 20 GSa/s digital oscilloscope (Keysight Infiniium KT-DSO90604A). The oscilloscope digitizes with a depth of 8 bits, and can internally average up to 65 000 spectra to reduce noise and increase resolution up to 11 bits.

This apparatus can generate time-resolved transmission or reflection data as a function of frequency over the 110 GHz–170 GHz range. This range can be expanded to fill the gap between TRMC and TRTS measurements with the use of frequency multipliers since only a small fraction of the source output powers are required. Experiments in the reflection geometry can be useful for samples mounted on highly conductive substrates that are opaque to the millimeter wave probe or when only the near surface region of a sample is excited.

1. Sensitivity analysis and dynamic range

The system was initially tested on crystalline silicon wafers of known resistivity to determine the minimum detectable signal levels, the time resolution, and the calibration constant. Figure 4(a) shows a histogram of the baseline noise voltages collected when the laser pulse is blocked and the probe signal from the 140 GHz CW CIDO is passing through a p-type, (100) orientation silicon wafer. Figure 4(b) shows a typical signal decay trace from the same sample with the laser excitation on. This data was taken under normal operating conditions, averaging over 65 000 laser shots. Figure 4(c) shows a histogram of the peak voltages in this data set, from which the uncertainty in the peak voltage is estimated to be δ(ΔV) = 0.387 mV (FWHM), corresponding to a 3.3% error in the peak voltage. Calculation of the photoconductance from ΔV and estimation of the minimal detectable photoconductance will be treated in Sec. II C 2 below.

FIG. 4.

(a) Histogram of background noise when the excitation laser is blocked, (b) 4096 averaged typical detector voltage as function of delay for sample Si-4, (c) histogram of Si-4 peak voltage when the excitation laser is unblocked.

FIG. 4.

(a) Histogram of background noise when the excitation laser is blocked, (b) 4096 averaged typical detector voltage as function of delay for sample Si-4, (c) histogram of Si-4 peak voltage when the excitation laser is unblocked.

Close modal

For the study of carrier decay kinetics, the attainable time resolution is determined solely by the response time of the probe beam detection system. The 6 GHz bandwidth of the bias-tee limits the detector response time to approximately 60 ps, while the specified response times of the preamplifier and digitizer are 42.5 ps and 70 ps, respectively. In combination, these yield an estimated detection system response time of approximately 100 ps, which is substantially faster than that obtained with typical microwave-based system. This response time could potentially be reduced to approximately 1/3 of this value by use of electrical components with wider bandwidths that are now available.

The dynamic range being the ratio of the largest to smallest RF signal registered by the system for the instrument range of operation can be expressed as 20 log10(ΔVmax/ΔVmin). For the maximum response, we note the RF voltage acquired for Si-4 at full laser power (10.1 μJ/cm2) which is ∼1.2 V. Dividing this by the Low Noise Amplifier (LNA) gain (35.7) yields a 30.8 mV RF signal. The minimum discernible RF voltage recorded in our experiment for perovskite is 41 μV at laser fluence ∼40 nJ/cm2. The Dynamic Range (DR) so computed using ΔV voltage for high yielding silicon and low yielding perovskite is 57.51 dB, and DR for the TR-mmWC response ratio (ΔV/V0) for these 2 samples is 60.89 dB for the same high and low laser fluence levels.

2. Calibration factor

While relative measurements are often used to elucidate the effect of systematic changes in material processing or properties on charge carrier dynamics, we also determine approximate values for the calibration constant K needed to determine the photoconductivity from the experimentally measured peak change in detector voltage ratio, ΔV/V0, V0 being diode signal voltage (=Vdc) resulting from net power transmitted through sample when there is no laser excitation (PT). This apparatus-specific calibration constant relates the observed signal, ΔV/V0, to the actual power ratio, (ΔP/P0)max and accounts for variations in detector response, laser beam profile, and experimental alignment. It is defined in Eq. (12) below,

ΔVV0=KΔPP0max=KCF,
(12)

where K is the calibration constant, and P0 = PT [as in Eq. (7)].

The behavior of ΔV/V0 as a function of fluence as shown in Fig. 5 for a set of four Czochralski grown crystalline silicon samples with known resistivity in range 16.88–127.6 Ω-cm is studied. These silicon samples are labeled as Si-2, Si-4, Si-7, and Si-8, respectively. As expected, the response is linear for all samples at low fluence and becomes sub-linear at higher fluence. To obtain K, we consider Si-2, S-4, and Si-7 due to consistency in sample thickness. The entire curve for the TR-mmWC response with laser fluence (0 to maximum fluence, 10.1 μJ/cm2) for these samples are shown in Fig. 5(a). The linear region (fluence in range 0–0.5 µJ/cm2) for these 4 samples are shown in the inset [Fig. 5(b)]. For these data points, the value of the parameter C was computed from Eq. (11) using fluence-dependent carrier mobilities obtained from Klassens’ model32,33 after operating the PV Lighthouse (PVL) online calculator. For all samples combined, the resulting data for ΔV/V0 versus CF was fit to a linear function as shown in Fig. 6. From Eq. (12), the slope of this fit yields the value for K = 0.212 ± 0.01. The determination of absolute values of the photoconductance is limited by the uncertainty in K (∼4.7%). For measurement of relative values of photoconductance on a particular sample, the uncertainty arises almost entirely from the measurement of ΔV. During sensitivity analysis, this was estimated to be on the order of δ(ΔV) = 0.387 mV. From Eq. (12), using typical operating values, this corresponds to a minimal detectable change in the photoconductance of approximately 1 µS. The K estimation process used 1 N-type sample (Si-2) and 2 P type samples (Si-4, and 7). Since our K weighs on behavior of the TR-mmWC response ratio to the product of sample specific C and laser fluence F, we justify use of both N and P type for the linear fit from the point that both N type and P type mobilities are derived from the same PVL calculator after specifying the type of semiconductor; hence for a given charge carrier density while assuming 100% quantum efficiency, the answer specified for K from Fig. 6 is justified (Table II).

FIG. 5.

(a) Peak photoinduced probe beam absorption shown as a function of the entire laser fluence 0-10.1 μJ/cm2 for Si-2,4,7, and 8 [inset (b): only linear part shown for 0 to 0.5 μJ/cm2]. (Note: V0 = Vdc).

FIG. 5.

(a) Peak photoinduced probe beam absorption shown as a function of the entire laser fluence 0-10.1 μJ/cm2 for Si-2,4,7, and 8 [inset (b): only linear part shown for 0 to 0.5 μJ/cm2]. (Note: V0 = Vdc).

Close modal
FIG. 6.

Differential voltage response ratio (−ΔV/V0) as function of CF [Eq. (11)] for combined low resistivity sample (Si-2, Si-4, and Si-7) responses in the linear (low laser fluence) region. V0 = Vdc. Solid line: linear fit. This plot yields K = 0.212 ± 0.01.

FIG. 6.

Differential voltage response ratio (−ΔV/V0) as function of CF [Eq. (11)] for combined low resistivity sample (Si-2, Si-4, and Si-7) responses in the linear (low laser fluence) region. V0 = Vdc. Solid line: linear fit. This plot yields K = 0.212 ± 0.01.

Close modal
TABLE II.

A summary of resistivity and thickness for the silicon wafers tested.

SampleResistivity (Ω-cm)Thickness (μm)
Si-2 50.05, N-type (P) 525 
Si-4 16.88, P-type (B) 525 
Si-7 23.69, P-type (B) 500 
Si-8a 127.6, P-type (B) 725 
SampleResistivity (Ω-cm)Thickness (μm)
Si-2 50.05, N-type (P) 525 
Si-4 16.88, P-type (B) 525 
Si-7 23.69, P-type (B) 500 
Si-8a 127.6, P-type (B) 725 
a

Si-8 is not included for determination of sensitivity K due to fact it is very different from other samples.

3. Transmission and reflection response for GaAs

One sample of 600 μm, semi-insulating gallium arsenide (GaAs) of very high resistivity (107 Ω-cm) was used to perform transmission and reflection data acquisition using ZBDs 3-14 and 3-26, respectively. This sample yields about 50% transmission nominally at 150 GHz however, and as we sweep down further, the d.c. transmission coefficient (ratio of the d.c. voltage through sample to the d.c. response of probe beam through air) becomes maximum at around 130 GHz. This could be attributed to resonance in sample due to internal reflection. A very feeble sample surface reflected signal is observed at 133.65 GHz. This low value of Vdc (possibly due to destructive interference between front and back surface reflections) results in increase of the TR-mmWC response ratio (see Fig. 7). We observe a reversal of the surface reflected probe power between positive transient signifying more absorption into a negative transient (more reflection) at around 133.85 GHz and may be attributed to shift in refractive index due to photoexcitation. Figure 7 shows the spectrum of TR-mmWC response (ΔV/V0) as function of BWO frequency with an inset showing the d.c. coefficients with frequency.

FIG. 7.

Shows the TR-mmWC RF transmission and reflection response ratio (absolute values in logarithmic scale) for GaAs as function of BWO probe frequency. These responses are observed at maximum laser fluence (10.1 μJ/cm2) using 532 nm Helios laser with 1 KHz trigger; inset shows the d.c. transmission (- - -) and reflection coefficients (solid line) for the same frequency range computed by taking the ratio of through-sample (or reflected RF voltage) to no sample (or gold mirror reflected) voltages under dark condition (no laser) respectively.

FIG. 7.

Shows the TR-mmWC RF transmission and reflection response ratio (absolute values in logarithmic scale) for GaAs as function of BWO probe frequency. These responses are observed at maximum laser fluence (10.1 μJ/cm2) using 532 nm Helios laser with 1 KHz trigger; inset shows the d.c. transmission (- - -) and reflection coefficients (solid line) for the same frequency range computed by taking the ratio of through-sample (or reflected RF voltage) to no sample (or gold mirror reflected) voltages under dark condition (no laser) respectively.

Close modal

Figure 7 shows the typical TR-mmWC response ratio as a function of probe frequency which will enable us to benchmark frequency-dependent conductivity in GaAs (2 μs in reflection data and ∼100 ns using transmitted data) and compare with equivalent TRTS studies made earlier.23 Further evaluation of these GaAs derived RF and DC response data are underway in context of laser fluence-TR-mmWC response and application of the newly developed S/T model, effect of sample thickness, etc.

This article presents a newly developed apparatus for rapid characterization of time dependent photoconductivity in the frequency gap between microwave and terahertz methods. The system is capable of measuring frequency dependent photoconductivity in the 110 GHz–170 GHz range (D waveguide-band) over sub-nanosecond to millisecond time scales and is operated in a free space configuration that allows us control over the physical conditions during measurement and mapping of the spatial dependence of photoconductivity. The minimum detectable photoconductivity change has been determined to be ∼1 µS, and the time resolution for carrier decay processes is estimated to be ∼100 ps for the system as currently configured. The dynamic range of the system is inferred using the data for the highest and lowest laser fluence and almost for the entire probe frequency range. This is found to be 57.51 dB using silicon and perovskite sample data collected so far. The procedure for determination of the calibration constant (K = 0.212 ± 0.01) which can be used for calculation of photoconductances of sample responses measured in transmission mode is also reported here. Uncertainty in K mentioned here is only for the fit coefficient but experimental factors such as laser spot size, charge quantum efficiency, etc., could also be accounted to yield an overall figure. Currently, these results are being further refined and similar characterization will be extended to operation in the reflection mode. TR-mmWC is found to be more sensitive to lower laser fluences than TRTS and yields good quality datasets with laser fluences ∼40 nJ/cm2 to a few μJ/cm2; hence, this system is expected to yield charge dynamical datasets at nominal carrier densities.

Semi-insulating GaAs sample responses show a steady variation of full laser power TR-mmWC response in the transmission mode; however, in full laser power reflection mode, we note a large shift in the DC reflection coefficient from 0.78 at 110 GHz to 0.06 at 130 GHz based on a reference signal obtained using a gold mirror. The DC reflection coefficient starts building from 0.06 at 130 GHz to 0.76 at 150 GHz and 0.66 at 160 GHz. A strong peaking of the TR-mmWC reflection response ratio is observed at ∼130 GHz followed by a sharp fall off at the rate almost 3 × 10−4 (GHz). A systematic characterization of this reflection- and transmission-based conductance estimates can be obtained by varying the laser fluence (preferably in the low fluence regimes).

In future work, the TR-mmWC technique will be used to acquire data on the frequency dependence of the photoconductance over the available tuning range for materials of interest. Appropriate theories, (e.g., Drude-Smith, etc.) can then be utilized to model the frequency dependence of the photoconductivity and obtain insight into the processes by which the charge carriers decay. We will also explore reflection and transmission of millimeter waves (TE mode) for estimation of sample intrinsic resistivity such as those used by Golosovsky and Davidov34 and Ju et al.35 to enable the collection of data with high spatial resolution. Materials of interest at this time include perovskites, nanowires, gamma, and ion-beam irradiated silicon. Full automation of the data collection is in progress and will allow the study of multiple samples at high throughput with the goal of providing characterization services as unique materials become available.

The design and construction of this apparatus was supported by the University of North Carolina Research Opportunity Initiative (ROI) through the NC Carbon Materials Initiative and the Center for Hybrid Materials Enabled Electronics Technologies (CH-MEET). B.R. and M.H.W. were additionally funded by the NSF Center for Research Excellence in Science and Technology (CREST) program under Award No. HRD-1345219. M.H.W. was also partly funded through NSF Partnership for Research and Education in Materials (PREM) program under Award No. DMR-1523617. The authors like to thank Professor J. Huang of UNC, Chapel Hill, NC and Professor Franky So of NCSU for providing us the perovskite samples used to test system performance. This work was performed in part at the Duke University Shared Materials Instrumentation Facility (SMIF), a member of the North Carolina Research Triangle Nanotechnology Network (RTNN), which is supported by the National Science Foundation (Grant No. ECCS-1542015) as part of the National Nanotechnology Coordinated Infrastructure (NNCI).

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