Lecture 19 Optical Characterization 1

Lecture 19 Optical Characterization 1 1/60 Announcements Homework 5/6: Is online now. Due Wednesday May 30th at 10:00am. I will return it the following Wednesday (6 th June). Homework 6/6: Will be online on Wednesday 30 th June. Due Wednesday June 6th at 10:00am. I will return it at the final exam (14 th June). I will make the solutions available on June 6 th. 2/60 1

Lecture 19 Why Contactless? Time Resolved Microwave Conductivity. Parameter Extraction. Non-Idealities. 3/60 Why Contactless? 4/60 2

Contact-Based Measurements So far we have mainly focused on techniques to evaluate the electrical properties of a sample through electrical contact. 4 point-probe. Diode Measurements. E p-type n-type I V E F S S S Sample Anode Cathode + - 5/60 Contact-Based Measurements So far we have mainly focused on techniques to evaluate the electrical properties of a sample through electrical contact. Hall Measurements: B I V H 6/60 3

Contact-Based Measurements So far we have mainly focused on techniques to evaluate the electrical properties of a sample through electrical contact. Field-Effect Mobility: S E Dielectric Metal (Gate) D V D I D (A) 10-3 V = 100V D 10-4 10-5 10-6 10-7 10-8 10-9 V D = 10V V G 10-10 -20 0 20 40 60 80 V G (V) 7/60 Contacts But we have seen that contacts can have a big influence on electrical properties. E V = 0 E V > 0 E V 0 E F E F E F The ability of carriers to cross a metal-semiconductor interface depends on many factors. 8/60 4

Contact Resistance As a result, contact resistance is an important characteristic in electronic devices. Diodes: p-type n-type R o,p R p r d V d R n R o,n Field-effect transistors: V G V G G S R S R D 9/60 D Contactless Characterization There are some times when we wish to evaluate the electronic properties of a material without making contact. For example, testing a new semiconductor. We may want to know its properties as a material itself, rather than a device. How would we go about doing this? 10/60 5

Contactless Characterization We eluded to this in Lecture 9, when talking about photoconductance decay. light pulses rf or μwave pick-up We can create holes and electrons with light. Use a rf field as a pickup. 11/60 Contactless Characterization Today we are going to talk about a specific technique: Time Resolved Microwave Conductivity (TRMC). It allows us to measure the optically-induced conductivity (photoconductivity) without electrical contact. The operating principle is similar to (intentionally) putting metal into the microwave. https://www.youtube.com/watch?v=jwoxnpmw7dk 12/60 6

Time Resolved Microwave Conductivity 13/60 Operating Principles Oscillatory electrical signal is generated at microwave frequencies (8 9 GHz) Microwave Source and Detectors Microwaves 14/60 7

Operating Principles Electrical signal is fed into cavity and emits EM radiation at the same frequency from antenna. Microwave Source and Detectors Microwaves Cavity Antenna 15/60 Operating Principles Microwaves form standing wave inside of the cavity: Electric field strength E x, t = 2E 0 cos ωt sin kx Magnitude of E-field frequency time Reflected signal is detected and absorbance of microwaves in cavity is measured. wavenumber position Microwave Source and Detectors Microwaves Antenna EM Wave Cavity 16/60 8

Operating Principles Place sample at maxima of electric field: Electric field at maxima: Microwave Source and Detectors E t = 2E 0 cos ωt Microwaves Sample Antenna EM Wave Cavity 17/60 Operating Principles Any mobile charges will move under the influence of this field, with a velocity that depends on mobility: Microwave Source and Detectors v t = μe t = 2μE 0 cos ωt Microwaves Sample EM Wave Cavity Antenna 18/60 9

Operating Principles When free carriers are present, energy is absorbed in sample. Microwave Source and Detectors Reflected microwave intensity can be used to determine conductivity of sample. Sample Microwaves Antenna EM Wave Cavity 19/60 Operating Principles Laser used to create carriers in sample. Change in conductance used to determine figure of merit: φσμ Microwave Source and Detectors Microwaves Σμ = μ e + μ h Sample Optical Laser Antenna EM Wave Cavity 20/60 10

Operating Principles An intense, short (ns) pulse of optical photons is used to generate carriers in the semiconductor. ΔG t 21/60 Operating Principles After the pulse concludes, ΔG decays as function of time. Allows lifetime to be evaluated. ΔG t 22/60 11

TRMC Time Resolved Microwave Conductivity (TRMC) is very versatile in the form of sample it can study. Crystals. Thin-films. Powders. Pellets. Even fluids. 23/60 TRMC However there are a few requirements that must be met: Samples must be semiconducting. Must have a band gap accessible to optical radiation ( ~2.5 ev). Or can be sensitized. Must have reasonable free-carrier generation efficiency (φ). I.e. not φ=0. Mobility ~ 10-5 cm 2 /Vs. Pattanasattayavong et. al. JAP 112, (2012) 074507 24/60 12

Figure of Merit From the measured conductance (ΔG) we can evaluate what is called the TRMC figure of merit: φσμ. The sigma-mu component is the sum of electron and hole mobilities: Electron mobility Σμ = μ e + μ h Hole mobility The technique is unable (in its basic form) to separate the mobility of electrons and holes. When carried out in certain gases, the transport of one carrier type can be inhibited (e.g. via electron traps). This allows resolution of μ e and μ h. 25/60 Carrier-Generation Efficiency We do not get Σμ directly from TRMC measurements, instead we obtain the product of Σμ with φ: φσμ. φ is the charge-generation efficiency of the material. I.e. how many charge carriers are created for each absorbed photon. Recall (from Lecture 13) that sometimes we create bound excitons rather than free carriers. e - h + h + e - 26/60 13

Excitons (Lecture 13) The physical description is a follows: e - e - e - e - e - e - ee - - e - e - ee - - e - e - e - - e - - e e - - e e - - e e - - e - e - e - h + e - e - e - h + e - e - Light generates an electron and hole. e - They separate (conservation of momentum). e - e - e - e - e - e - e - e - e - e - e - e - e - ee - - e e - - Positively charged hole distorts electrons in lattice. This provides screening / repulsion to free electron. Equilibrium occurs with a binding energy (E B ). Thermal energy (k B T) required to collapse charges. 27/60 Carrier-Generation Efficiency The TRMC technique is not sensitive to excitons; it is sensitive to free-carriers only. E e - e - h + h + Hence if you generate excitons rather than free carriers the signal is reduced. For this reason we cannot separate φ from Σμ. (easily). 28/60 14

Figure of Merit However φσμ is a very good proxy for carrier mobility. For samples that do not show excitonic nature (e.g. silicon) φ 1, φσμ Σμ. For solar cell materials we want to maximize both φ and Σμ. We are prepared to give up a little knowledge and use φσμ to evaluate a material in the absence of contacts. 29/60 Direction of Mobility Note that the electric field component of the standing wave points in a particular direction. Sample Cavity EM Wave E This means that free carriers will move in this direction. Hence we are probing conductivity in this direction only. This allows us to probe anisotropy by rotating the sample in the cavity. 30/60 15

Real Systems In reality the system design is quite complex. This is the system we have at OSU: Supply Faraday Cage PC Controller Oscilloscope ND Filter Array ITO Window Isolator Detector Transfer Switch Fast Amplifier Slow Amplifier Transfer Switch Control Box Filter Box VCO Nd:YAG Laser ~5ns Laser Pulse Sample Cavity Circulator Attenuator Isolator Transfer Switch 31/60 OSU TRMC System TRMC systems cannot be purchased, so are all custom made. 32/60 16

Parameter Extraction 33/60 Evaluating Conductance We mentioned previously that any generated carriers in the sample will move under the influence of the electric field. We also talked about how these carriers result in an attenuation of reflected microwaves. In reality this is detected as a change in voltage. We employ microwave detectors that output a voltage proportional to microwave power. 34/60 17

Photoconductance The reflected microwaves under normal conditions (no illumination) are described to have a power P. The photo-induced change in microwave power is labeled ΔP. The photo-induced change in conductance (ΔG) is described to be proportional to the fractional change in reflected microwave power: ΔG t = 1 K ΔP t P K is the sensitivity factor of the cavity. 35/60 Photovoltage We choose detectors that output a voltage proportional to the intensity of the detected microwaves. This means that we can make the following statement: ΔP t P ΔV t = V Where V and ΔV t are the background voltage and photo-induced change in voltage, respectively. 36/60 18

Sensitivity Factor The sensitivity factor (K) is a property of the cavity. It encapsulates how sensitive the cavity is to changes in conductance. There are a few ways of evaluating K. One is to use a standard sample of known conductance (G). Measure the signal of the cavity empty (P). Measure the change in signal of the cavity with the sample present: (ΔP). ΔG = 1 ΔP K P 37/60 Sensitivity Factor This approach however is not ideal. It involves opening the cavity, inserting / removing the sample, and closing it again. There is no guarantee that there hasn t been a change in cavity sensitivity by doing this. Ideally we want to be able to evaluate the sensitivity factor of the cavity in situ. We can achieve this by carrying-out a frequency sweep of the cavity. 38/60 19

Cavity Sweep The cavity is designed to support standing waves only at particular frequencies. The cavity should exhibit a resonance at this frequency. For example, if the cavity is TE 102 mode it will support a standing wave of 1 full wavelength. You don t need to know what TE 102 means. 39/60 Cavity Sweep The frequency (f) and wavelength (λ) of EM radiation are related by: f = c Speed of light λ L = λ If our cavity is 33.3 mm long, and supports one full wavelength (TE 102 mode ), then it should have a resonance frequency of: f = 9 GHz 40/60 20

Cavity Sweep The reflectivity at resonance, and close to resonance, can be used to determine the sensitivity factor K. This is done by measuring the reflectivity of the cavity as a function of frequency R f. Some data from our system: 1.0 1.0 0.8 0.8 Reflectivity (a.u.) 0.6 0.4 0.2 Reflectivity (a.u.) 0.6 0.4 0.2 0.0 8.4 8.6 8.8 9.0 9.2 9.4 9.6 Frequency (GHz) Frequency (GHz) 0.0 8.98 9.00 9.02 9.04 9.06 9.08 41/60 Sensitivity Factor The sensitivity factor is given by the following: K = 2Q 1 + 1 R 0 πf 0 ε 0 ε r Lβ f 0 : Resonance frequency of the cavity. R 0 : Reflectivity of the cavity to microwaves at the resonance frequency f 0. ε 0 : Vacuum permittivity. ε r : Relative permittivity of the cavity medium (1 for air). 42/60 21

Sensitivity Factor The sensitivity factor is given by the following: L: Cavity length. K = β: Ratio of width (W) to depth (D) of cavity: 2Q 1 + 1 R 0 πf 0 ε 0 ε r Lβ D W β = W D L 43/60 Sensitivity Factor The sensitivity factor is given by the following: K = 2Q 1 + 1 R 0 πf 0 ε 0 ε r Lβ Q: Quality factor of the cavity. Q = f 0 ΔW ΔW: Full-width at half-maximum (FWHM) of resonance. 44/60 22

Cavity Sweep We can extract parameter from our frequency-sweep as follows: 1.0 Reflectivity (a.u.) 0.8 0.6 0.4 0.2 W 3.8 MHz f 0 9.0312 GHz 0.0 9.00 9.01 9.02 9.03 9.04 9.05 9.06 Frequency (GHz) R 0 0.03 45/60 Cavity Sweep Or a Lorentzian line shape can be fitted, and the parameters extracted from the fit. 1.0 0.8 Reflectivity (a.u.) 0.6 0.4 0.2 Experimental Fit 0.0 9.00 9.01 9.02 9.03 9.04 9.05 9.06 Frequency (GHz) 46/60 23

Sensitivity Factor For our cavity at OSU: L = 7.62 cm. W = 2.286 cm. D = 1.016 cm. β = 2.25. For the data I just showed: f 0 = 9.03 GHz. R 0 = 0.03. ΔW = 3.8 MHz. Q = 2376. 47/60 Conductance Once the sweep has been carried out and K been evaluated, we can carry out the measurement. By measuring the magnitude of the detected voltage as a function of time, we can establish a transient conductance plot. ΔG t = 1 K ΔP t P 48/60 24

Figure of Merit Conductance on its own is not that relevant as a parameter. It will depend on incident optical power density and sample dimensions. This is why the TRMC figure of merit (φσμ) is quoted: φσμ = ΔG max βei 0 F A ΔG max maximum photoconductance, ΔG, measured. e fundamental unit of charge. I 0 fluence (photons / unit area / pulse). 49/60 Figure of Merit F A is the fractional absorption of photons at the laser wavelength. This is just the fraction of photons [0,1], that are absorbed in the entire sample, at the laser wavelength. Can be measured via optical spectroscopy. φσμ = ΔG max βei 0 F A 50/60 25

Non-Idealities 51/60 Figure of Merit In reality the figure of merit is measured as a function of fluence (photon / unit area / pulse). Normally a fluence-dependence is observed, with a plateau at low fluences. 52/60 26

Figure of Merit To understand why this is the case, consider again how we evaluate ΔG max. We measure ΔG as a function of time, and take the peak value. This assumes that the measured peak is really representative of the maximum conductance of our sample. G max 53/60 Laser Pulse We briefly described how carriers are generated by the laser pulse. We have not yet considered the fact that the laser pulse duration is finite. Or that carriers will recombine during the pulse. ΔG ΔG t t 54/60 27

Laser power density Carrier density no recombination Carrier density with recombination 5/23/2018 Laser Pulse Normally a high power laser is employed (50mJ) energy per pulse. This normally means the pulse length is relatively long (~5ns). This is long enough for carriers to recombine if the power density is high enough. We will assume the optical power density can be described by a Gaussian distribution in time. Some lasers can have ~fs pulse widths 55/60 Laser Pulse It can be shown that for certain systems bimolecular and Auger recombination can lead to a reduction in carrier density vs what is expected. Fluence = 3 10 12 cm -2 Fluence = 1 10 15 cm -2 (a) (d) (b) (e) (c) (f) <10% of value without recombination 56/60 28

Laser Pulse This model can be used in reverse to evaluate recombination parameters from fluencedependent TRMC data. 57/60 Response Time It is also worth mentioning that since the cavity is at resonance, it will take a finite amount of time to ringdown, or respond to changes in conductance. The response time (τ RC ) of the cavity is described by: τ RC = Q πf 0 Q: Quality factor of the cavity. f 0 : Resonance frequency of the cavity. 58/60 29

Response Time For the our example data this comes out to be τ RC ~ 80ns. This is not a negligible amount of time. Reflectivity (a.u.) 1.0 0.8 0.6 0.4 0.2 Experimental Fit 0.0 9.00 9.01 9.02 9.03 9.04 9.05 9.06 Frequency (GHz) To reduce the response time you can either reduce the quality factor increase the resonance width. Or increase the frequency. This is the approach taken in terahertz time-domain spectroscopy (THz-TDS). This also requires faster (more expensive) lasers. 59/60 Next Time More optical characterization. emission PL Raman photoelectron spectroscopy incident refraction scattering hν absorption reflection optical microscopy ellipsometry reflection photoconductance spectroscopy transmission absorption IR spectroscopy 60/60 30