“Physicists: people who believe what they read on the labels of chemical bottles. Chemists: people who believe what they read on the displays of analytical instruments.” – Bart Czirr, BYU Professor of Physics “Young people must be careful.” – Olexander Smakula, MIT, legendary crystal grower

Properties of Solids Measurement and Characterization Matt DeLong 18 March 2011

Lab Tasks Each pair of you will be given an unknown semiconductor Determine index of refraction Determine thickness of thin silicon film on sapphire and entire substrate Determine band gap of material Determine energies of free carrier absorption and phonon modes Determine lattice constant of material Identify material and doping level from resistivity

Measurement Techniques to Be Used Transmission/absorption with Cary 17DX UV/Visible/NIR spectrometer Transmission/absorption with Bruker IFS88 Fourier Transform InfraRed spectrometer (FTIR) Witech NSOM with micro-Raman attachment; Ar + laser excitation X-ray powder diffractometer

Optical Absorption Pankove chapter 3 Inter-band transitions leading to strong absorption Absorption coefficient (cm -1 ) GaAs 300 K Typically visible or near IR

Additional use of absorption measurements to investigate semiconducting solids Note units: absorption coefficient (cm -1 ) as a function of photon energy (eV)

Beer’s Law I (λ,t) = I 0 e -α(λ)t Light intensity reduction after transiting a piece of material whose thickness is t and whose absorption coefficient is α(λ). Absorbance ≡ log 10 (I 0 /I) = αtlog(e) = α’t Transmittance ≡ I/I 0 Percent transmission ≡ 100 x Transmittance Reflectance ≡ I R /I 0

Absorbance = Optical Density Transmittance (I / I 0 ) Percent transmittance (100 * I / I 0 )

Conservation of Energy Incident light is reflected, transmitted or absorbed by sample. Reflected light is responsible for baseline shift Baseline offset can be used to calculate index of refraction of material Pankove 4-26 In regions of minimal absorption 4-32

Baseline is about 0.3 away from absorption peaks =.5 = I T /I 0 T = 0.5 = R = 0.33 n = 3.7 c.f. n = 3.4 in Pankove table

Common Units Used in Spectroscopy (Have you ever noticed that the human brain likes to work in small, whole numbers?) E = hν = hc( ) hc = 1240 eV-nm = 1.24 eV-μm Energy is always measured in eV Wavelength is measured in nm or μm (or Å = m) In the IR energy is measured in “wavenumbers” 1 “wavenumber” = 1 cm -1. Obviously λ( ) = 1 10,000 μm x 1 cm -1 = 1 Product of wavelength (in microns) and wavenumber (in cm -1 ) is 10,000.

Transmission Windows

Grating spectrometer I 0 is detector output voltage when signal passes through reference. I is detector output voltage when signal passes through sample. Courtesy of Kathrine Skollingsberg

“Half-silvered mirror”: 50% of mirror surface is nominally 100% reflective Mirror rotates 50% of time beam is reflected, 50% of time is transmitted, so beam alternately follows two paths Courtesy of Kathrine Skollingsberg

Cary 17DX: Entire Unit

Reflectivity attachment

Cell Compartments

Operation of Dispersive Spectrometer Conceptually very simple. – Detector output is proportional to amount of light transmitted by sample. – Assumption: light not transmitted was absorbed or reflected Energy-independent loss of intensity is due to reflection “Baseline offset” can be used to calculate index of refraction Very important: Resolution depends on slit width – Resolution is inversely proportional to intensity of light transmitted/detected.

Technical Details 200 nm < λ < 2500 nm possible Deuterium lamp puts out greater intensity for 200 nm < λ < 500 nm Tungsten lamp is more intense for 500 nm < λ PMT has greater signal-to-noise for λ < 900 nm. PbS detector is superior for 900 nm < λ Cuvette and holder allow measuring transmission for liquids

The IR Beyond About 3 microns Sources are weak – Think of the black body emission curves! Detectors are less sensitive Transitions typically caused by – molecular vibrations – Rotations – Free carrier absorption FTIR to the rescue!

Onward Into the IR: the FTIR www3.wooster.edu A Michelson Interferometer

Crucial image correlating zero crossings of laser interferences and data sampling of signal at detector Source of Illumination here

Δx

Not Conceptually Simple! For the two beams headed toward the detector after having been transmitted and reflected by the beamsplitter after having first been reflected and transmitted by the beamsplitter, then (second) reflected by the moving and fixed mirrors, respectively. Now is that clear?

Intensity of Light Headed to Sample I(Δd) = B(k){1 + cos(k Δd)} I(Δd) is the intensity measured at the detector as a function of path difference between beams going to fixed or moving mirror B(k) is the “wavelength” dependence of the source emission as modified by all elements along the beam path. Obviously Since k and Δd are Fourier conjugates, the Fourier transform of I(Δd) gives I(k) = I(1/ λ)

FTIR Operating parameters

Interferogram Relative position coordinate of moving mirror

IR Spectrum: Fourier Transform of I(Δd)

Spectrum with Plastic Bag

Difference between absorption spectra of plastic bag and empty chamber

Operational Difference Between Spectrometers How to account for background effects? Cary does this by splitting beam between two paths which travel through identical media except one contains sample. – Data collected nearly simultaneously FTIR is sufficiently stable that background signal can be subtracted “long” after it has been taken.

Operational Difference Between Spectrometers Resolution – Grating Resolution increased by narrowing slits Narrowing slits decreases signal Decreasing signal decreases signal-to-noise – FTIR Resolution increased by increasing amplitude of moving mirror Increasing moving mirror path length increases scan time Increasing resolution does not affect signal-to-noise

Film Thickness Measurements Can be done with any spectrometer Film must be of uniform thickness Thick films require FTIR to be set for high resolution mλ = 2nt Normal incidence n = index of refraction t = film thickness m = index number

X-ray Diffractometry Bragg’s Law – mλ = 2d(h,k,l)sin(θ) – m = integer – λ = x-ray wavelength – d(h,k,l) = interplanar lattice spacing – θ = scattering angle

X-ray Diffractometry Technique uses monochromatic x-rays Powdered crystal used – X-ray beam intersects micro-crystals oriented in all directions – Micro-crystals are basically an “analog computer” that solves the Bragg Equation – Discrete values of d(h, k, l) lead to discrete values of θ[d(h,k,l)] – Discrete values of θ[d(h,k,l)] have cylindrical symmetry about beam axis – X-ray detector scans a diameter of hemisphere into which beam is scattered

Cullity Fig Debeye-Scherer powder diffraction patterns X-rays are spatially dispersed onto film. Diffractometer: identical except detector scans circumference as a function of time.

Diffractometer Spectrum (Random example from the web) home.ptad.pt Since λ is known, d(h,k,l) can be calculated for each line.

Resistivity Measurements Reference: Fourprobe_resistivity_AN2.pdf on course website ρ = bulk resistivity V = voltage measured between inner probe pins I = current applied between outer probe pins t = sample thickness k = correction factor, SEMI MF84-02

More on Resistivity 4-point probe works extremely well on silicon For III-V materials with reasonable conductivity, indium contacts may be applied with a dedicated soldering iron tip Indium melts at 156 C Indium may be diffused into the wafer at 200 C under a reducing atmosphere (hydrogen) Sophomore physics: