Microwave photoconductance spectrometer and methods of using the same

1. A steady-state microwave conductivity method comprising:

modulating a light beam to form a modulated light having a modulation frequency ω 1 ;

producing a microwave waveform;

exposing a sample to the modulated light and a first portion of the microwave waveform to produce an amplitude modulated waveform;

mixing, in a four-port waveguide structure, a second portion of the microwave waveform and the amplitude modulated waveform to produce a first signal and a second signal; and

creating a frequency-filtered amplified difference signal based on ω 1 , wherein:

the four-port waveguide structure produces the first signal resulting from constructive interference of the amplitude modulated waveform with the second portion of microwave waveform,

the four-port waveguide structure produces the second signal resulting from destructive interference of the amplitude modulated waveform with the second portion of microwave waveform,

the frequency-filtered amplified difference signal is calculated from at least one of subtracting the first signal from the second signal or measuring a difference signal resulting from the destructive interference, and

the frequency-filtered amplified difference signal represents a photoconductivity parameter of the sample.

2. The steady-state microwave conductivity method of claim 1 , further comprising producing the light beam using a light source comprising at least one of a xenon arc lamp, a supercontinuum laser, or a light emitting diode.

3. The steady-state microwave conductivity method of claim 2 , further comprising:

filtering the light beam produced by the light source to create a filtered light, wherein:

the light beam produced by the light source has a first bandwidth, and

the filtered light has a second bandwidth that is narrower than the first bandwidth.

4. The steady-state microwave conductivity method of claim 3 , further comprising chopping the filtered light to create the modulated light.

5. The steady-state microwave conductivity method of claim 1 , wherein the exposing comprises placing the sample in a microwave resonator.

6. The steady-state microwave conductivity method of claim 1 , wherein the exposing comprises:

impinging the microwave waveform onto the sample using a first antenna; and

receiving the amplitude modulated waveform using a second antenna, wherein:

the first antenna may be the same as the second antenna or the first antenna may be an antenna distinct from the first antenna.

7. The steady-state microwave conductivity method of claim 6 , wherein the impinging the microwave waveform onto the sample is performed with the sample positioned on a metal electrode surface.

8. The steady-state microwave conductivity method of claim 1 , further comprising:

splitting the modulated light into a first portion and a second portion;

directing the first portion to a reference photodiode; and

directing the second portion to the sample, wherein:

the first portion is between 5% and 15% of the modulated light, and

the reference photodiode produces a frequency reference signal proportional to ω 1 .

9. The steady-state microwave conductivity method of claim 1 , further comprising:

splitting the microwave waveform into the first portion of the microwave waveform and the second portion of the microwave waveform;

directing the first portion of the microwave waveform through a first isolator to the sample; and

directing the second portion of the microwave waveform through a second isolator to the four-port waveguide structure.

10. The steady-state microwave conductivity method of claim 9 , further comprising, after producing the microwave waveform:

receiving the first portion of the microwave waveform at a first port of a circulator, wherein the circulator redirects the first portion of microwave waveform through a second port of the circulator to the sample resulting in the amplitude modulated waveform, and

redirecting the reflected amplitude modulated waveform through a third port of the circulator.

11. The steady-state microwave conductivity method of claim 10 , further comprising, after producing the microwave waveform and before the circulator, rotating a polarization axis of the first portion of the microwave waveform by 90 degrees.

12. The steady-state microwave conductivity method of claim 9 , further comprising, after producing the microwave waveform and before the four-port waveguide structure, passing the second portion of the microwave through a variable phase-shifter configured to shift the second portion between zero degrees and 180 degrees.

13. The steady-state microwave conductivity method of claim 1 , further comprising:

producing the microwave waveform using a microwave source; and

modulating the microwave waveform at the microwave source to a separate frequency ω 2 , wherein the photoconductivity parameter is determined by at least one of the difference of ω 1 and ω 2 or the sum of ω 1 and ω 2 .

14. The steady-state microwave conductivity method of claim 1 , further comprising calculating the photoconductivity parameter as a photoconductance ΔG.

15. The steady-state microwave conductivity method of claim 14 , wherein the calculating comprises:

Δ

⁢

⁢

G

=

-

1

K

⁢

Δ

⁢

⁢

P

P

,

where K is a sensitivity factor of a microwave resonator or an antenna,

ΔP is a first microwave power reflected from at least one of the sample, the microwave resonator, or the antenna, and

P is a second microwave power reflected from at least one of the sample, the microwave resonator, or the antenna.

16. The steady-state microwave conductivity method of claim 14 , wherein the calculating comprises plotting ΔG versus a wavelength of the modulated light.

17. The steady-state microwave conductivity method of claim 1 , wherein the microwave waveform has a frequency between about 1 GHz and about 100 GHz.

18. The steady-state microwave conductivity method of claim 1 , wherein the microwave waveform has a frequency between about 8.2 GHz and about 12.4 GHz.

19. The steady-state microwave conductivity method of claim 1 , further comprising, prior to the exposing and the mixing, splitting the microwave wave form into the first portion and the second portion, wherein after the splitting, neither the first portion or the second portion are amplified prior to the exposing and mixing.

20. The steady-state microwave conductivity method of claim 1 , wherein the sample comprises a thin film comprising at least one of a perovskite, an OPV, a CIGS, or CdTe.

21. The steady-state microwave conductivity method of claim 1 , wherein the four-port waveguide structure is a magic tee.