• “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 CharacterizationMatt 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 AbsorptionPankove 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) = I0e-α(λ)t

• Light intensity reduction after transiting a piece of material whose thickness is t and whose absorption coefficient is α(λ).

• Absorbance ≡ log10 (I0/I) = αtlog(e) = α’t

• Transmittance ≡ I/I0

• Percent transmission ≡ 100 x Transmittance• Reflectance ≡ IR/I0

Absorbance = Optical Density

Transmittance (I / I0)

Percent transmittance

(100 * I / I0)

0 1 1000.1 0.79 79

0.25 0.56 560.5 0.32 32

0.75 0.18 180.9 0.13 131 0.1 102 0.01 13 0.001 0.1

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 peaks100.3 = .5 = IT/I0

T = 0.5 =

R = 0.33

n = 3.7c.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 = 10-10 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 spectrometerI0 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

10551002.3

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. 3-12.Debeye-Scherer powder diffraction patternsX-rays are spatially dispersed onto film.Diffractometer: identical except detector scans circumference as afunction of time.

Diffractometer Spectrum(Random example from the web)

home.ptad.ptSince λ is known, d(h,k,l) can be calculated for each line.

Resistivity Measurements•Reference: www.keithley.com/data?asset=15222•Fourprobe_resistivity_AN2.pdf on course website

ρ = bulk resistivityV = voltage measured between inner probe pinsI = current applied between outer probe pinst = sample thicknessk = 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: