Method and apparatus for performing heterodyne lock-in imaging and quantitative non-contact measurements of electrical properties

• US 9,131,170 B2
• Filed: 03/14/2013
• Issued: 09/08/2015
• Est. Priority Date: 04/13/2012
• Status: Active Grant

• Current Assignee: Alexander Melnikov, Mandelis, Andreas
• Original Assignee: Alexander Melnikov, Mandelis, Andreas
• Inventors: Mandelis, Andreas, Melnikov, Alexander
• Primary Examiner(s): Kelley, Christopher S
• Assistant Examiner(s): Zhou, Zhihan
• Application Number:
  US13/827,110
• Publication Number:
  US 20130278749A1
• Time in Patent Office: 908 Days
• Field of Search: 348/86, 348/87, 250/338.1, 250/341.1, 250/341.4, 250/341.5, 250/341.7, 250/341.8
• US Class Current: 1/1
• CPC Class Codes: G01N 21/6489 Photoluminescence of semiconductors
• CPC Class Codes: G01N 21/9501 Semiconductor wafers manufacturing processes per se of semiconductor devices implementing a measuring step H01L22/10
• CPC Class Codes: H04N 5/33 Transforming infrared radiation cameras or camera modules for generating image signals from infrared radiation H04N23/20; circuitry of SSIS for transforming infrared radiation into image signals H04N25/20

Abstract

Methods are provided for producing optical carrierographic images of a semiconductor sample. Focused and spatially overlapped optical beams excite carriers across within the semiconductor sample, where the optical beams are modulated such that a beat frequency is substantially less than either modulation frequency. An infrared detector detects infrared radiation emitted from the semiconductor sample in response to absorption of the optical beams, thereby obtaining a plurality of carrierographic signals at different points in time during at least one beat period, which are processed with a lock-in amplifier, with a reference signal at the beat frequency, to obtain an amplitude signal and a phase signal. Carrierographic lock-in images of the sample are obtained in a scanning configuration, or in an imaging format using an imaging detector. The images carry quantitative information about recombination lifetimes in substrate Si wafers and electrical parameters in solar cells, namely photogeneration current density, diode saturation current density, ideality factor, and maximum power photovoltage.

Claims

1. A method of producing an optical carrierographic image of a semiconductor sample, the method comprising:

a) generating a first modulation signal having a first modulation frequency and a second modulation signal having a second modulation frequency, wherein a beat frequency between the first modulation frequency and the second modulation frequency is substantially less than both the first modulation frequency and the second modulation frequency;

b) generating a reference signal having a reference frequency equal to the beat frequency;

c) providing a first optical beam and a second optical beam, the first optical beam and the second optical beam having wavelengths selected for excitation of carriers within the semiconductor sample;

d) focusing and spatially overlapping the first optical beam and the second optical beam onto a location of the semiconductor sample;

e) modulating the first optical beam according to the first modulation signal and modulating the second optical beam according to the second modulation signal;

f) detecting, with an infrared detector, infrared radiation emitted from the semiconductor sample in response to absorption of the first optical beam and the second optical beam, and obtaining a plurality of carrierographic signals at different points in time during at least one beat period; and

g) providing the reference signal to a lock-in amplifier and processing the carrierographic signals with the lock-in amplifier to obtain an amplitude signal and a phase signal.

2. The method according to claim 1 further comprising the step of synchronizing the first modulation signal, the second modulation signal, and the reference signal prior to the step of obtaining the carrierographic signals.

3. The method according to claim 1 wherein the first optical beam and the second optical beam are focused onto the semiconductor sample.

4. The method according to claim 3 further comprising the step of repeating steps d) to g) for one or more additional locations of the semiconductor sample.

5. The method according to claim 4 wherein the first optical beam and the second optical beam are scanned over an area of the semiconductor sample, the method further comprising the step of forming an amplitude image and a phase image of the area based on the amplitude signals and the phase signals obtained while scanning the first optical beam and the second optical beam.

6. The method according to claim 1 wherein the infrared detector is an infrared camera, and wherein steps f) and g) include:

detecting, with the infrared camera, infrared radiation emitted from the semiconductor sample in response to absorption of the first optical beam and the second optical beam, and obtaining a plurality of carrierographic signal frames at different points in time during at least one beat period, wherein an exposure time of the infrared camera exceeds the inverse of the first modulation frequency and the inverse of the second modulation frequency, and wherein a frame rate of the infrared camera exceeds the beat frequency;

providing the reference signal to a lock-in amplifier and processing the carrierographic signal frames with the lock-in amplifier to obtain carrierographic images including an amplitude image and a phase image.

7. The method according to claim 6 wherein said lock-in amplifier is configured for parallel lock-in detection over all camera pixels using in-phase and quadrature operations.

8. The method according to claim 6 wherein a maximal value of the exposure time of the infrared camera is selected.

9. The method according to claim 6 wherein an optical power of the first optical beam and an optical power of the second optical beam are sufficiently low to avoid substantial optical flooding of the semiconductor sample.

10. The method according to claim 6 wherein the infrared camera is an InGaAs camera.

11. The method according to claim 6 further comprising the step processing one or both of the amplitude image and the phase image to determine one or more properties of the semiconductor sample.

12. The method according to claim 11 wherein the one or more properties are obtained by comparing one or both of the amplitude image and the phase image, or comparing a measure based one or both of the amplitude image and phase image, with previously measured calibration data.

13. The method according to claim 11 wherein the step of processing one or both of the amplitude image and the phase image includes obtaining one or more statistical measures of the semiconductor sample based on a statistical analysis of image pixel values.

14. The method according to claim 11 wherein the step of processing one or both of the amplitude image and the phase image includes inferring a spatially dependent carrier lifetime from one or both of the amplitude image and the phase image.

15. The method according to claim 11 wherein the step of processing one or both of the amplitude image and the phase image includes determining diffusion coefficient, surface recombination velocity, defects, series resistance, shunt resistance, quality of p-n junction, photoluminescence nonlinearity.

16. The method according to claim 11 wherein the semiconductor sample is a solar cell, and wherein the step of processing one or both of the amplitude image and the phase image includes calculating a surface averaged amplitude from the amplitude image and determining a solar cell efficiency based on calibration data relating the solar cell efficiency to the surface averaged amplitude.

17. The method according to claim 11 wherein the semiconductor sample is a solar cell, and wherein the step of processing one or both of the amplitude image and the phase image includes calculating a maximum phase from the phase image and determining a solar cell efficiency based on calibration data relating the solar cell efficiency to the maximum phase.

18. The method according to claim 1 wherein the first modulation frequency and the second modulation frequency exceed approximately 10 kHz.

19. The method according to claim 1 wherein the first modulation frequency and the second modulation frequency lie between approximately 10 kHz and 50 kHz.

20. The method according to claim 1 wherein the first modulation frequency and the second modulation frequency exceed approximately 50 kHz.

21. The method according to claim 1 wherein the beat frequency is less than 1 kHz.

22. The method according to claim 1 wherein the first optical beam and the second optical beam are provided by super bandgap lasers.

23. The method according to claim 1 wherein the first modulation frequency and the second modulation frequency are selected such the carrierographic images are sensitive to a recombination lifetime limiting one or more of defect-state densities and trap-state densities.

24. The method according to claim 1 wherein the first optical beam and the second optical beam have approximately equal average wavelengths.

25. The method according to claim 1 further comprising the step of filtering radiation incident on the infrared detector to avoid the detection of scattered light from one or more of the first optical beam and the second optical beam.

26. The method according to claim 1 wherein the first optical beam and the second optical beam are configured generate nonlinear carrierographic images.

27. The method according to claim 1 wherein the first optical beam and the second optical beam absorbed without acting as external local oscillator.

28. The method according to claim 1 wherein the semiconductor sample is a semiconductor substrate.

29. The method according to claim 1 wherein the semiconductor sample comprises silicon.

30. The method according to claim 1 wherein the semiconductor sample is a semiconductor device.

31. The method according to claim 30 wherein the semiconductor device is a solar cell.

32. A method of measuring the effective lifetime of carriers in a semiconductor substrate using lock-in-carrierography, the method comprising:

measuring lock-in-carrierography images of the semiconductor substrate at a plurality of modulation frequencies, each lock-in-carrierography image comprising a plurality of lock-in-carrierography signals corresponding to different locations of the substrate, where the lock-in-carrierography images are measured according to the method of claim 1;

fitting a frequency dependence of the lock-in-carrierography signals from the lock-in-carrierography images to a rate equation model having the effective lifetime as a parameter; and

calculating the effective lifetime at a plurality of locations of the semiconductor substrate.

33. The method according to claim 32 further comprising generating a lifetime map of the substrate based on the calculated effective lifetimes.

34. The method according to claim 32 wherein rate equation model is of the form:

S(omega)=tau_—

e*K/(1+i*omega*tau_—

e)

where S(omega) is the lock-in-carrierography signal, tau is the effective lifetime, omega is the modulation frequency, and K is a constant.

35. The method according to claim 32 wherein the fitting of the lock-in-carrierography image to the rate equation model is performed based on the phase of the lock-in-carrierography image.

36. The method according to claim 32 wherein the fitting of the lock-in-carrierography image to the rate equation model is performed based on the amplitude of the lock-in-carrierography image.

37. A method of optically measuring one or more electrical parameters of a solar cell using lock-in-carrierography, the method comprising:

determining a mathematical relationship between a lock-in-carrierographic signal and one or more electrical properties of the solar cell, the mathematical relationship involving a calibration factor relating the lock-in-carrierographic signal to an electrical model of the solar cell;

measuring a plurality of lock-in-carrierography images of the solar cell, where the lock-in-carrierography images are measured according to the method of claim 1;

calculating average signals from the lock-in-carrierography images; and

determining the one or more electrical parameters by fitting the mathematical relationship to the average signals.

38. The method according to claim 37 wherein the plurality of lock-in-carrierography images are measured at different load resistances.

39. The method according to claim 37 wherein the plurality of lock-in-carrierography images are measured for different optical intensities in a non-contacting configuration.

40. The method according to claim 37 wherein the one or more electrical parameters are selected from the group consisting of J_g, J₀, the ideality factor n, shunt resistance, P_max voltage, open-circuit voltage, fill factor, and solar conversion efficiency η

_e.