Battery History

The following are notes on battery history

• History of Batteries
• 2000 years ago Baghdad battery
• created in Mesopotamia 
• Jar of ceramics created with a speculated structure of copper with walls of iron
• if filled with unknown composition of electrolytes meets the requirements for a battery
• Maybe used to plate gold onto silver?
• 200 Years Ago Animal Electricity
• Galvani while doing a dissection a steel scalpel touched a brass hook that was holding a frog leg in place
• Battery composition
• Steel scalpel has iron 
• brass hook has copper
• preservatives acted as electrolytes
• First Battery
• Voltaic Pile 
• set of individual galvanic cells placed in series
• copper and zinc stacked together with electrolytes sandwiching the two metals
• History of electrochemical energy storage
• Galvani
• Volta - Voltaic Pile 
• Daniell - Zn/Cu Cell
• Faraday - Basic Principles of electrochemistry
• Grove - H2/02 cell
• Plante - Lead Acid Cell
• Leclanche - Zn Carbon dry cell
• Edison Zn/Ni and Fe/Ni cells
• Modern Batteries
• modern development started around half a century ago
• Solid Electrolytes
• 1966 Yao and Kummer Beta Alumina Solid Electrolyte: Fast Na Ion Conductor
• birthed solid state ionics
• Rubidium silver iodide
• Internal Phenomena
• Whittingham steele insertion reaction electrodes
• created Le/TiS2 cells
• Sony commercialized the first Lithium ion batteries

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Battery Applications and Parameters

The following are notes on Batteries for their common applications and parameters

• Battery Applications
• Portable Applications
• Portable electronics, laptops, iphones, toys, medical devices
• battery used to start engine in cars is the largest market
• lead acid and lithium ion
• High energy batteries, highest energy for given size
• Stationary Applications
• Pairing with with intermittent sources of electricity
• high energy is less important
• Common Forms Factors of Batteries
• Button Cells in Watches
• Cylinder Cells
• Lithium Ion
• Prismatic Cells
• Sizes of Batteries
• 4.5-volt (3R12) battery 
• D Cell
• C cell
• AA cell
• AAA cell
• AAAA cell
• A23 battery
• 9-volt PP3 
• button cells
• Types of Batteries
• Chargeable or non-chargeable
• Battery Chemistry
• Alkaline 
• Lead acid 
• NiCd nickel cadmium
• NiMH nickel metal hydride
• Lithium ion
• Important Parameters of Batteries
• Energy (Watt Hour)
• Energy Density - Energy Per Unit Volume
• Specific Energy - Energy Per unit Weight
• Characterize the total amount of energy it carries, lifetime of battery once you charge it up, distance of electric car
• Power (Watt)
• How fast you can take the energy out of a battery
• Power Density Power per unit volume
• Example more important for Laptop, fitting into size constraint for a high usage device
• Specific Power Power per unit weight
• Car, heaviness of battery impacts performance
• Life
• Cycle Life, times we can charge and discharge a battery with its capacity still above 80% of the original
• Calendar Life Time a battery can last if left on shelf
• Electrical car ensure it can last for about 10 years?
• Safety
• Battery intrinsically is in unstable state
• Temperature Performance
• Cost
• Currently its difficult to justify batteries for cars and grid use

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Electrical Engineering ToC

Table of Contents

1. Batteries
1. Battery Applications and Parameters
2. Battery History
2. Digital Design
1. Finfet

Physics - Classical Theory of Conduction

The following is a brief overview of the classical theory of conduction.

Fluid Analogy
First I would like to invoke the fluid analogy to electricity. Basically there are many similarities between different phenomena for fluid mechanics and electronics. The reason why we have this analogy is simply that most people are used to dealing with fluids, especially those of us with access to plumbing and running water. However, most of us don't even think about electricity, we just put a plug in an outlet and stuff works.

Now how does a battery work? Its no mystery though Bill O'Reilly might disagree. We can see on a battery's label a + and a - sign. We can think of this as a lake at the top of a mountain and a lake on the bottom of the mountain. They have different potential energy due to gravity. When we plug in a battery its like digging a trench to connect the two lakes and putting a water mill in between it to drive our machine.

Relation to Conduction
We can then relate two other phenomena. Current in a wire is very similar to trying to get water to move through a pipe. The smaller our pipe, the less current can get through, which is similar to a wire with high resistivity. In electronics we can think of a wire as a lattice of of atoms. Our electrical current is then though of as electrons traveling through this lattice. An electrical field caused by our difference in potential drives electrons through this lattice but the lattice is stationary and stops/causes ricochets when an electron hits it. We can describe this with the following two equations:

I =ΔQ/Δt = neAv_d and
λ = <v> τ =1/n_aπr² as

Where for the first equation I is the current described by n the number of electrons, with charge e, passing through an area A with electron drift velocity v_d. The second equation gives us λ is the mean free path, or the average distance a particle travels before a collision with <v> the average velocity multiplied against τ the average time between collisions. Through this we can figure out resistivity and conductivity and can derive Ohm's law. 

V = IR

Defects

This is a great approximation but there are significant errors when scaled to different temperatures and other quantum effects.

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Physics - Quantum Tunneling

The following is a brief overview of Quantum tunneling.

What is it?
Quantum Tunneling is the effect where a particle tunnels through a barrier it could not penetrate in classical physics.

Why does it happen?
Quantum physics tells us that matter exhibits both particle and wave-like behavior. Therefore if we apply this idea to an electron going up against an potential barrier, we can relate its behavior similarly to a more well known event, light traveling through a material such as glass. In this case, the brightness of the light passing through the surface is reduced and some is reflected back away from the observer behind the glass. With our electron, some of its probability function travels through the potential well, and some of it reflected, depending on the width of the energy barrier, which we can relate the opacity of an object.

Brief Overview of Formulation
The time independent Schrodinger equation is as follows

(-ħ²/2m)(d²Ψ(x)/dx²) + U(x)Ψ(x) = EΨ(x)

The full derivation will be done elsewhere but we can use these to get the solutions for traveling waves, which represents the probability function of a particle in motion. This represents our electron moving. Using the WKB approximation and a few other mathematical tricks such as series expansion, we arrive at the following equation for T the transmission coefficient or percentage chance at quantum tunneling.

The important part of this equations are, x1 and x2 which are the classical turning points for the energy barrier. We can therefore see that this equation depends primarily on two characteristics, the difference in energy between the particle/wave represented as E. V(x) which is the potential of the energy barrier given x, and the width of the barrier x where a higher energy difference results in a lower transmission coefficient, and a greater "width" again results in a lower transmission coefficient.

Relation to Electrical Engineering

This is a material science concept and when used in reference to tunneling in electrical components, we don't have to go into the full Feynman path integral method to just get an idea of how it works. We can get a good idea of the effects with the explanation above. Tunneling occurs with barriers the size of around 1-3 nanometers which will be extremely significant when dealing with finfets which promise to move the total size of the transistor to around the 10 nm range. Efforts must be made to maintain detection of the on and off state due to thermal noise and summation of inductance effects of nearby inductance effects. This means design rules must be made with greater spacing margins than might be otherwise done for normal mosfet design. 

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Electrical Engineering - Finfet

The following will be notes taken on the subject of FinFets

• Summary
• Classical Mosfet
• Transistor that operates by using an Electrical field to invert the channel allowing conduction from source to drain

• The Classical Mosfet Dimensions
• Include length the short distance in this picture, Width is the longer dimension
• Functionality
• Length reduction results in loss of control over the channel
• performance reduction

• Finfet
• Goal
• solve performance reduction caused by smaller sizes 
• Wrap the gate electrode around the channel

• Thin fin of sillicon acts as the channel and it is encased by the gate electrode
• Silicon fin surrounded by extension implant and poly oxide
• Premise
• di-electric and metal gate allows for a stronger e-field to be formed as it increases the dimensions of the gate effective using the height/thickness of the fin as the channel length allowing for a decrease in overall size when compared to a typical Mosfet

• Source and Drain can be wrapped in silicon germanium or silicon carbon stressors just like classical transistors
• Shown below is a representation of a finfet design used for production

• The gate electrode is uniform for ease of construction

• Clarification of terminology
• After seeing the design used for production, we can see that it is nearly identical to the construction of the tri-gate

• The only difference is that a tri-gate includes multiple sources and drains whereas the finfet description shows only a single source and drain but the process of construction seems identical, and terminology could be used interchangeably assuming you're fine with annoying Intel
• The original papers indicate that the original process of the finfet did not wrap around on top of the fin, lowering the overall z or height of the overall transistor but this is too complicated of a process for mass production so the standard finfet is equivalent to the tri-gate which does wrap around 

• Benefits
• Maintain performance which includes
• Conductivity when turned on
• Insulation when turned off
• Finfet in relation to a standard mosfet reduces electron tunneling effect when insulation is small
• Main issues are - weaker dielectric, small size
• Finfet significantly increases volume of dielectric reducing leakage currents
• increase switching speed
• due to lower size due to gate capacitance being smaller
• note - non-issue in modern constructions, interface delay between metals is more significant as we get to smaller scale
• Lower's Voltage requirements
• increases lifetime/efficiency of product per charge
• Company Promises
• estimation, 2-5% higher price in exchange for 37% speed increase and 90% reduction in leakage current

• Complications
•  Adds complexity to construction process
• possible reduction in yield
• can increase price significantly above 2-5% estimate for the company overall
• Depending on process
• high k-dielectrics are more expensive, but already required as transistor size decreases
• Increased modeling difficulty
• geomotries now are first order effects
• random fluctuations in manufacturing can now cause deviations in result
• impacts possible econcomic forecasts for the division
• Verification
• requires new software to ensure design rules for fin to fin spacing is followed

• History
• construction process has roots in 1990s

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Flip Flops and Memory

Flip/Flops

This is a simple flip/flop which acts as a latch. It operates through the use of feedback. Basically there are 4 scenarios. If you don't have a signal through either set or reset then whatever state the flip flop was in, it will stay in. If you input something into the reset but not the set the not Q will change. You can envision this as just a separate signal though through only the bottom wire. If you input into set but not reset, then the Q output will change, or the proper signal setting your "memory" bit to one. Which is why it can be called set. Then the Final is if you input a signal through both set and reset which clears all information, putting both states to 0.

S R Q Q̅

0 0 No change

0 1 0 1

1 0 1 0

1 1 0 0

This flip/flop is equivalent to one bit of memory as it is capable of holding a state.

Binary, 2's complement, Hexadecimal-

So since we are capable of storing a bit of memory, we can string them together to form larger sections of memory. We often refer to bytes of memory, which is 8 bits, which represents 256 different states.

2⁷ 2⁶ 2⁵ 2⁴ 2³ 2² 2¹ 2⁰
0 1 0 0 1 1 0 1 would then = 77

You can then partition the byte into two halves and write the number in hexadecimal 

the high is
0 1 0 0 = 4
the low is
1 1 0 1 = d

Hexadecimal goes as 0 1 2 3 4 5 6 7 8 9 A B C D E F

2's complement is a way of making the operations of addition multiplication and subtraction identical. If we had these 8 bits be positive only we would count through 256 possible numbers from 0-255. Using two's complement we go from 0 -> 127 and then go back down from -128 to -1.

Boolean Operations

Boolean operations are used to develop logical circuits. This will be a brief overview of these functions. We will establish a truth table, where 1 represents an on signal, 0 represents an off signal. Q is just the result of applying our function using the Boolean operation specified

Q = A.B

AND Gate
The AND gate is an important function, we can think of this as multiplication as if we multiple the two signal together here we arrive at the following truth table for an AND gate.

A B Q

0 0 0

0 1 0

1 0 0

1 1 1

Q = Q̅ = A.B

Function NAND
This is the NAND gate or the not AND gate. This simply reverses all the outputs of our AND gate.

A B Q

0 0 1

0 1 1

1 0 1

0 0 0

Q = A + B

Function OR
The OR gate is similar to addition. However, its a version of addition that does not know how to carry over, as we can see by the last part of the truth table, but otherwise functions similarly.

A B Q

0 0 0

0 1 1

1 0 1

1 1 1

Q = Q̅ = A + B

Function NOR

Again like the NAND gate, the NOR gate simply reverses the signal of the OR gate.

A B Q

0 0 1

0 1 0

1 0 0

1 1 0

Electronics - Fluid Analogy Resistance

A good way to visualize electricity is to relate it to the movement of fluids. They have a lot of similarities as we will discuss below.

Resistance

ΔV = -IR

This is simply stating that the change in voltage is the current multiplied by the resistance. The way we can think about this is that the voltage loss is due to the current passing through a volume more difficulty, otherwise known as resistance. We can show the resistance with the equation

R=ρl/a

Where rho is the resistivity due to impediments in the material, multiplied against the length, divided by the area.

Pressure

ΔP = IR

This is the change in pressure due to an increase in resistance. We can visualize this increase in pressure by thinking about water flow through a pipe. Let us think about a large pipe transitioning to a smaller one. The change in pressure from the area before the small pipe to after the small pipe can be approximated by thinking about the smaller pipe as a resistive element, similar to resistance in a current. However instead of impediments as a function of the material, it is just the smaller size of the pipe. Therefore the resistance in this case would be proportional to (1/A) where A is the area of the smaller pipe.

Computer Science - BOINC

BOINC is an open-source software that can be used in a volunteer fashion and for grid computing. It can be found at http://boinc.berkeley.edu/. The idea is to use the processing power of computers in idle time. The easiest use is as a donation service of extra computational power to already ongoing research projects. An example is the computation of a 3-D model of the SDSS or sloan digital sky survey. This project can be found here http://milkyway.cs.rpi.edu/milkyway/. It can also be used in a private sense in order to set up a grid supercomputer at a university by linking together the campus computers. The same system can be set up for company long term grid computing, with the application running in the background without need for screensaver graphics.

BOINC works by getting a set of tasks from a project's scheduling server. The computer then downloads executables and input files from the project's data server. The pc then runs the computations and uploads the output files back to the data server. Later the pc will report on completed tasks and receive new tasks indefinitely.

Electrical Engineering-Intro to Digital

What are the basic goals for Digital systems? One of the key properties of digital systems is its data storage accuracy and resistance to corruption. A basic example where we can apply this idea is the storage of information in Magnetic tapes. So if we assume some magnetic reader/writer using some inductance principle to store information on some tape, we can see that there must be some noise by necessity due to random thermal effects in the data. Thus we have some signal to noise ratio.

In an analog sense, if we want to get a better S/N ratio, we would make the magnetic tape wider. We can take

W = Β x W₀

With our increase in width, we can increase our Signal in analog by

S = Β x S₀

However our noise will increase by a factor of

N = Β^1/2 x N₀

S/N = Β^1/2

so if we want a S/N of 10³, we would need a Β of 10⁶ over some initial length.

In a digital sense, since we are storing information in on and off bits of information, our signal increases as

S = 2 ^Β

However our Noise will remain as 1 due to the inaccuracy of the least bit.

N = 1

S/N = 2 ^Β / 1

so here we only need a Β = 10, which is a huge decrease in the width necessary for the same increase in accuracy.

Electrical Engineering-Intro to Analog

The following is a review of some electrostatics necessary for understanding analog electronics.

Force exerted on a point charge moving in a B and E field, magnetic and electric field.

F = q(E + v x B)

Electric field generated by a point charge.

E = (1 / 4 π ε ₀ ) Q / r 2

Change in electric potential associated with charge and capacitance.

Δ V = ∫ E . dl = k Q / r = Q / C

Work done by an electric field.

Work = ∫ q E . dl = q Δ V

Power done by an electric field

Power = d Work / dt = dq Δ V / dt

Power = I Δ V

Power = I² R = V² / R (in situations where ohm's law applies)

Ohm's Law

V = I R (ohm's law)

Properties of one electron

e = 1.6 x 10 ^-19 Coulomb

1eV = 1.6 x 10 ^-19 Joule

= 11,600 ^o K

Properties of Temperature

1/40 eV ≈ 300 ^o K = 4140 Yocto-Joules

13.8 Yocto-Joule = 1^o K

Constants

ε₀ = 8.85 x 10 ^-12 Coulomb / Volt m = 8.85 pF / m

k = 1 / 4 π ε₀ = 9 x 10 ^-9 Volt m / Coulomb

μ0  = 4 π x 10 ⁷ T m / A

c = 0.3 x 10 ⁹  m / s

When E is energy in electron volts

Ε = h fλ = 1240 nm (Ε / 1eV) ^-1 

f = .24 x 10 ¹⁵  (Ε / 1eV)

Masses

m_e = .511 MeV / c²

m_p = .938 MeV / c²

N_a = 6.02 x 10²³