EEE 3394 Electronic Materials Chris Ferekides Fall 2014 Week 6

Electrical Conductivity

Charges “under the influence” Everyone must know what happens to a charge in the presence of an electric field   E

Charges “under the influence” Everyone must know what happens to a charge in the presence of a magnetic field   B

Right vs. Left-Handed Oriented x y z System … and the Cross Product

Example with p-type semiconductor; i.e. holes are the majority charge carriers;  apply voltage in x direction i.e. current Ix.  apply a B-field in the z-direction.  Total Force on the charge carriers due to E and B fields is  The y-component of the force is  As the holes flow in the x-direction they experience a force in the y-direction due to the B- field.  Holes will accumulate in the -y end of the bar setting up an electric field, i.e. a voltage V AB in the y direction.  The net force in the y-direction becomes zero when the two components of the force i.e. due to the electric and due to the magnetic field are equal. The Hall Effect

 The “setting up” of the E-field in the y-direction is known as the Hall Effect.  The voltage V AB is known as the Hall Voltage.  This experiment is used to measure the mobility of the charge carriers as explained below: The Hall Effect

Note: the current and magnetic fields are known quantities since they are externally applied; the hall voltage can be measured.  The resistivity ρ of the sample can also be calculated by measuring the resistance R of the bar. The Hall Effect

A B V AB >0 >0 V AB >0 <0

Chapter 3 Wave-particle Duality … ?? Particle – electron has wave-like properties & … wave – light has particle-like properties. First let’s look at a wave …

Waves What are some wave characteristics (behavior) ? … interference

Waves What are some wave characteristics (behavior) ? … diffraction g/

Waves What are some wave characteristics (behavior) ? … diffraction

Photoelectric Effect Light frees electrons which can be collected at the anode by applying a voltage – or reach there if they have enough KE Increasing the light intensity leads to higher current V O – is the “stopping voltage”, i.e. the voltage required to “stop” electrons with enough KE from reaching the anode Therefore V O is proportional to the max KE energy of the emitted electrons A V + CATHODE ANODE Light - Evacuated quartz tube I V I Saturation I 2 I 1 ­V 0 0 Electrons

Photoelectric Effect When the voltage is negative, i.e. acts against the electrons, the electrons must do work against the potential equal to eV O which is equal to the max KE at the cathode If the light frequency (wavelength) is the same, V O remains the same regardless of the light intensity … Therefore, the light intensity is independent of the electron energy A V + CATHODE ANODE Light - Evacuated quartz tube I V I Saturation I 2 I 1 ­V 0 0 Electrons

Photoelectric Effect If the light frequency is varied then the stopping potential changes Therefore the frequency of the light is proportional to the energy of the emitted electrons Let’s look at the relationship between the electron KE and the light frequency: the KE decreases with the frequency … The behavior is similar for several metals … BUT the slope is the same A V + CATHODE ANODE Light - Evacuated quartz tube I Electrons V 0 ­V 03 ­V 02   >     I   <       ­V 01

Photoelectric Effect Below a certain frequency NO electrons are emitted – i.e. the KE of the electrons is zero! The Photoelectric Effect results tell us that: – The number of electrons is proportional to the light intensity but independent of the light frequency – The energy of the electrons is proportional to the frequency of the light but the frequency does not affect the total number of electrons emitted A V + CATHODE ANODE Light - Evacuated quartz tube I Electrons

Photoelectric Effect CONCLUSION: – light has particle like behavior! As the “intensity” of the light increases, more light “particles” are striking the metal target, therefore more electrons being emitted. As the frequency increases the energy of each particle increases Light Particle: PHOTON! A V + CATHODE ANODE Light - Evacuated quartz tube I Electrons

Example – (a) Green Light with wavelength 522 nm is the longest wavelength that can cause electron photoemission from a sodium surface – What is the work function of sodium? A V + CATHODE ANODE Light - Evacuated quartz tube I Electrons

Example – (b) If UV light of 250 nm is used what will be the KE of the photo-emitted electrons? A V + CATHODE ANODE Light - Evacuated quartz tube I Electrons

Example – (b) If the intensity of the 250 nm UV is 20 mW/cm 2 and all electrons are collected using a positive bias on the anode what will be the current density? A V + CATHODE ANODE Light - Evacuated quartz tube I Electrons

Compton Scattering What happens when an x-ray “strikes” an electron ? The scattered x-ray has a different frequency … and the electron “moves” … The electron’s KE is related to the characteristics of the incoming and scattered x-rays Since the electron also gains momentum … due to the principle of conservation of momentum … then the photon (x-ray) also has momentum

Therefore light … exhibits particle-like behavior …comes in “packets” … quanta … is quantized … photons! … energy of a photon … has momentum

Electrons

Example 2000 Kg car running at 70 mph (~30m/s). What is the wavelength ! Wavelength = 1.1 x m

Electrons Behave Like Waves

Electrons can behave like waves … a behavior that can be described by … Schrodinger’s Equation! Schrodinger’s time independent equation; V is only a function of space! … (otherwise we would be in trouble!) Its solution results in information on the probability of finding an electron “somewhere” and on its energy “characteristics”

Properties of Ψ From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005) Fig 3.14

Infinite Potential Well We will solve Schrodinger’s time independent equation; We will confine an electron in a specified location … How? To complete the solution we need to apply BC’s! 0a x V(x) 0  V = 0 Electron V =  V = 

Infinite Potential Well THEREFORE the Energy of the Electron can only have “quantized” values corresponding to n=1,2,3,4…. Eigen-energies!

Infinite Potential Well

Infinite Potential Well … bottom line

Heisenberg’s Uncertainty Principle We cannot exactly and simultaneously know the position and momentum of a particle along a certain coordinate … … mathematically Essentially what the above means is that due to the wave nature of quantum mechanics we cannot simultaneously know exactly the position and momentum of a particle … this is a theoretical limitation … i.e. the quantum nature of the universe limits us to only knowing the product of position and momentum within ħ

Electron confined in a well size of 0.1nm. Calculate the ground energy. Calculate the energy required to move it to the 3 rd level. How can this energy be provided? Ground level, E 1 = 6.025x J or 37.6 eV 3 rd level, E 3 = E 1 n 2 = (37.6 eV)(3) 2 = eV Energy required = eV This exact amount of energy can come from a photon with wavelength, λ = hc/E = 4.12nm “Electron” in an isolated Atom …