From 59d9dd849351912951802d6f716a503e982b7e50 Mon Sep 17 00:00:00 2001 From: aj Date: Sat, 20 May 2023 01:33:56 +0100 Subject: [PATCH] initial commit --- AI/Literature.md | 6 + AI/Neural Networks/Properties+Capabilities.md | 53 +++++++++ CS/ABI.md | 35 ++++++ CS/Calling Conventions.md | 28 +++++ CS/Code Types.md | 41 +++++++ CS/Compilers.md | 30 +++++ CS/ISA.md | 106 ++++++++++++++++++ CS/Language Binding.md | 25 +++++ CS/Languages/Assembly.md | 11 ++ CS/Languages/C++.md | 19 ++++ CS/Languages/Python.md | 25 +++++ CS/Languages/Rust.md | 12 ++ CS/Languages/dotNet.md | 30 +++++ CS/Processors.md | 27 +++++ CS/Quantum.md | 1 + CS/Resources.md | 1 + Images/confinement-band-gaps.png | Bin 0 -> 91196 bytes Images/quantum-confinement.png | Bin 0 -> 39629 bytes Images/stack.png | Bin 0 -> 19123 bytes Images/tensor.png | Bin 0 -> 24332 bytes Images/x86registers.png | Bin 0 -> 24047 bytes Light.md | 10 ++ Maths/Vector Operators.md | 3 + Quantum/Confinement.md | 3 + Quantum/Orbitals.md | 26 +++++ Quantum/Schrödinger.md | 32 ++++++ Quantum/Standard Model.md | 23 ++++ Semiconductors/Doping.md | 21 ++++ Semiconductors/Equations.md | 30 +++++ Specific Energy.md | 5 + 30 files changed, 603 insertions(+) create mode 100644 AI/Literature.md create mode 100644 AI/Neural Networks/Properties+Capabilities.md create mode 100644 CS/ABI.md create mode 100644 CS/Calling Conventions.md create mode 100644 CS/Code Types.md create mode 100644 CS/Compilers.md create mode 100644 CS/ISA.md create mode 100644 CS/Language Binding.md create mode 100644 CS/Languages/Assembly.md create mode 100644 CS/Languages/C++.md create mode 100644 CS/Languages/Python.md create mode 100644 CS/Languages/Rust.md create mode 100644 CS/Languages/dotNet.md create mode 100644 CS/Processors.md create mode 100644 CS/Quantum.md create mode 100644 CS/Resources.md create mode 100644 Images/confinement-band-gaps.png create mode 100644 Images/quantum-confinement.png create mode 100644 Images/stack.png create mode 100644 Images/tensor.png create mode 100644 Images/x86registers.png create mode 100644 Light.md create mode 100644 Maths/Vector Operators.md create mode 100644 Quantum/Confinement.md create mode 100644 Quantum/Orbitals.md create mode 100644 Quantum/Schrödinger.md create mode 100644 Quantum/Standard Model.md create mode 100644 Semiconductors/Doping.md create mode 100644 Semiconductors/Equations.md create mode 100644 Specific Energy.md diff --git a/AI/Literature.md b/AI/Literature.md new file mode 100644 index 0000000..bf998f9 --- /dev/null +++ b/AI/Literature.md @@ -0,0 +1,6 @@ +[https://web.stanford.edu/~jurafsky/slp3/A.pdf](https://web.stanford.edu/~jurafsky/slp3/A.pdf) +[Towards Data Science: 3 Things You Need To Know Before You Train-Test Split](https://towardsdatascience.com/3-things-you-need-to-know-before-you-train-test-split-869dfabb7e50) +[https://machinelearningmastery.com/train-final-machine-learning-model/](https://machinelearningmastery.com/train-final-machine-learning-model/) +[https://medium.com/@canerkilinc/hands-on-tensorflow-2-0-multi-label-classifications-with-mlp-88fc97d6a7e6](https://medium.com/@canerkilinc/hands-on-tensorflow-2-0-multi-label-classifications-with-mlp-88fc97d6a7e6) +[https://stackoverflow.com/questions/61557536/how-tensorflow-keras-go-from-one-hot-encoded-outputs-to-class-predictions-for](https://stackoverflow.com/questions/61557536/how-tensorflow-keras-go-from-one-hot-encoded-outputs-to-class-predictions-for) +[https://stackoverflow.com/questions/35226198/is-this-one-hot-encoding-in-tensorflow-fast-or-flawed-for-any-reason/35227732#35227732](https://stackoverflow.com/questions/35226198/is-this-one-hot-encoding-in-tensorflow-fast-or-flawed-for-any-reason/35227732#35227732) diff --git a/AI/Neural Networks/Properties+Capabilities.md b/AI/Neural Networks/Properties+Capabilities.md new file mode 100644 index 0000000..57eac2d --- /dev/null +++ b/AI/Neural Networks/Properties+Capabilities.md @@ -0,0 +1,53 @@ +# Linearity +- Neurons can be linear or non-linear +- Network of non-linear neurons is non-linear +- Non-linearity is distributed +- Helpful if target signals are generated non-linearly + +# Input-Output Mapping +- Map input signal to desired response + - Supervised learning +- Similar to non-parametric statistical inference + - Non-parametric as in no prior assumptions + - No probabilistic model + +# Adaptivity +- Synaptic weights + - Can be easily retrained +- Can operate in non-stationary environments + - Can change weights in real-time + - In general, more adaptive = more robust + - Not always though + - Short time-constant system may be thrown by short-time spurious disturbances + - Stability-plasticity dilemma + +# Evidential Response +- Decisions are made with evidence not just declared + - Confidence value + +# Contextual Information +- Knowledge represented by structure and activation weight + - Any neuron can be affected by global activity +- Contextual information handled naturally + +# Fault Tolerance +- Hardware implementations +- Performance degrades gracefully with adverse conditions +- If some of it breaks, it won't cause the whole thing to break + - Like a real brain + +# VLSI Implementability +- Very large-scale integration + - Chips with millions of transistors (MOS) + - E.g. microprocessor, memory chips +- Massively parallel nature + - Well suited for VLSI + +# Uniformity in Analysis +- Are domain agnostic in application + - Analysis methods are the same + - Can share theories, learning algorithms + +# Neurobiological Analogy +- Design analogous to brain + - Already a demonstrable fault-tolerant, powerful, fast, parallel processor \ No newline at end of file diff --git a/CS/ABI.md b/CS/ABI.md new file mode 100644 index 0000000..4ca0cd9 --- /dev/null +++ b/CS/ABI.md @@ -0,0 +1,35 @@ +- How data structures & computational routines are accessed in machine code + - Machine code therefore hardware-dependent +- API defines this structure in source code +- Adherence usually responsibility of + - Compiler + - OS + - Library author + +# Components + +- Processor instruction set + - Register file structure + - Stack organisation + - Memory access types +- Size, layouts and alignments of basic data types +- ___Calling convention___ + - How function arguments are passed + - Stack or register + - Which registers for which function param + - Parameter order + - Return values retrieved +- How app makes sys calls to OS + - If ABI specifies direct sys calls over procedure calls to sys call stubs then sys call numbers +- Binary format of object files, program files + - For complete OS ABIs + +# Complete ABI +- Allows program from one OS to run on any other without change + - Provided all shared libraries and prerequisites etc + +# Embedded ABI +- File format, data types, register usage, stack frame organisation, function parameter passing conventions + - For embedded OS +- Compilers create object code compatible with code from other compilers + - Link libraries from different compilers \ No newline at end of file diff --git a/CS/Calling Conventions.md b/CS/Calling Conventions.md new file mode 100644 index 0000000..be3fd10 --- /dev/null +++ b/CS/Calling Conventions.md @@ -0,0 +1,28 @@ +- The order in which atomic (scalar) parameters, or individual parts of a complex parameter, are allocated +- How parameters are passed + - Pushed on the stack, placed in registers, or a mix of both +- Which registers the called function must preserve for the caller + - Also known as: callee-saved registers or non-volatile registers +- How the task of preparing the stack for, and restoring after, a function call is divided between the caller and the callee + +Subtle differences between compilers, can be difficult to interface codes from different compilers + +Calling conventions, type representations, and name mangling are all part of what is known as an [application binary interface](https://en.wikipedia.org/wiki/Application_binary_interface) ([[ABI]]) + +# cdecl +C declaration + +- Originally from Microsoft's C compiler + - Used by many C compilers for x86 +- Subroutine arguments passed on the stack +- Function arguments pushed right-to-left + - Last pushed first +- Caller cleans stack after function call returns + +# stdcall + +- Variation on Pascal calling convention +- Callee cleans stack +- Params pushed onto stack right-to-left + - Same as _cdecl_ +- Standard for Microsoft Win32 API \ No newline at end of file diff --git a/CS/Code Types.md b/CS/Code Types.md new file mode 100644 index 0000000..5c11609 --- /dev/null +++ b/CS/Code Types.md @@ -0,0 +1,41 @@ +## Machine Code +- Machine language instructions +- Directly control CPU +- Strictly numerical +- Lowest-level representation of a compiled or assembled program + - Lowest-level visible to programmer + - Internally microcode might used +- Hardware dependent +- Higher-level languages translated to machine code + - Compilers, assemblers and linkers + - Not for interpreted code + - Interpreter runs machine code +- Assembly is effectively human readable machine code + - Has mnemonics for opcodes etc + +## Microcode +- Layer between CPU hardware and instruction set architecture +- Normally written during design phase + - Deployed to ROM or PLA + - Programmable logic array +- Machine code often has some backward compatibility + - Microcode is circuit specific + +## Byte Code +Portable Code +- Efficient execution by interpreter +- Compact numeric codes, constants and references + - Encode compiler output following analysis and validation +- Can be further compiled + - JIT +- Typically passed to VM + - Java, Python + +## Object Code +- Product of compiler +- Sequence of statements + - Machine code + - Intermediate + - RTL +- Linked to form executable + - Object code portion of machine code not yet linked \ No newline at end of file diff --git a/CS/Compilers.md b/CS/Compilers.md new file mode 100644 index 0000000..60cccb4 --- /dev/null +++ b/CS/Compilers.md @@ -0,0 +1,30 @@ +## JIT +Just-in-Time +- Compilation during execution + - At run time +- Bytecode translation to machine code for execution +- Combination of AOT compilation and interpretation + - Speed of compiled code + - Flexibility of interpretation + - Overhead of an interpreter + - Overhead of compiling + - As well as interpreting +- Dynamic compilation +- Adaptive optimization + - Dynamic recompilation + - Microarchitecture-specific speedups + +## AOT +Ahead-of-Time +- Compile higher-level language or intermediate representation to machine code + - Runs natively +- Machine-optimized code + +## GCC +- Standard compiler for GNU projects and Linux +- Parse source code to produce abstract syntax tree + +## LLVM +- Compiler infrastructure +- Develop language front ends for ISAs +- Apple sponsored \ No newline at end of file diff --git a/CS/ISA.md b/CS/ISA.md new file mode 100644 index 0000000..ebda633 --- /dev/null +++ b/CS/ISA.md @@ -0,0 +1,106 @@ +Instruction Set Architecture + +___Not Microarchitecture___ +- Physical implementation of ISA + +- Abstract model of a computer +- CPU is an implementation +- Defines + - Data types + - Registers + - Hardware support for main memory + - Features + - Memory consistency + - Addressing modes + - Virtual memory +- Specifies behaviour of machine code + - Binary compatibility + - Allows many implementations + +# Complexity + +## Complex +- CISC + - Complex instruction set computer + +## Reduced +- RISC + - Reduced instruction set computer +- Simplifies processor + - Implementing only frequent instructions + - Less frequent as subroutines +- Typically requires less transistors than CISC + - Improves + - Cost + - Power consumption + - Heat dissipation + +## Very Long Instruction Word +VLIW + +## Long Instruction Word +LIW + +## Explicitly Parallel instruction Computing +EPIC + +# ARM +Acorn RISC Machine +Advanced RISC Machines + +- RISC architectures +- System-on-Chips, System-on-Modules + - SOC, SOM +- iPhones A Series +- 32-bit Profiles + - A + - Application + - Cortex-A + - R + - Real-time + - Cortex-R + - M + - Micro-controller + - Cortex-M + +# Instructions + +- Params + - Registers + - Functions + - Arithmetic + - Addressing + - Control + - Memory locations + - With offsets + - Addressing modes + - Interpret operands +- Types + - Data handling and memory + - Set register + - Copy data from memory to register or reverse + - Load and store operations + - Read and write from hardware + - Arithmetic and logic + - +, -, x, ÷ + - Bitwise + - Compare + - Floating point instructions + - Control flow + - Branch + - Another location in program to execute + - Conditionally branch + - Indirectly branch + - Branch with argument memory address + - Call + - Save the location to return to + - Coprocessor + - Load/store to and from coprocessor + - Perform coops + - Complex + - Multiple things at once + - Move multiple values between stack and memory + - Move large blocks of memory + - Complicated integer and floating point maths + - Square root, log, sin, cos + - ALU operations from memory not register \ No newline at end of file diff --git a/CS/Language Binding.md b/CS/Language Binding.md new file mode 100644 index 0000000..0d6421c --- /dev/null +++ b/CS/Language Binding.md @@ -0,0 +1,25 @@ +- Binding is an API that provides glue code + - Allows language to use a foreign library or OS + +## Runtime Environments + +### Object Models +- COM + - Component Object Model + - MS only cross-language model +- CLI + - .NET Common Language Infrastructure +- Freedesktop.org D-Bus + - Open cross-platform-language model + +### Virtual Machines +- CLR + - .NET Common Language Runtime +- Mono + - CLI languages + - Cross-platform +- Adobe Flash Player + - Tamarin +- JVM +- LLVM +- Silverlight \ No newline at end of file diff --git a/CS/Languages/Assembly.md b/CS/Languages/Assembly.md new file mode 100644 index 0000000..5a6019d --- /dev/null +++ b/CS/Languages/Assembly.md @@ -0,0 +1,11 @@ +[Uni of Virginia - x86 Assembly Guide](https://www.cs.virginia.edu/~evans/cs216/guides/x86.html) + +## x86 32-bit +![[x86registers.png]] + +## Stack +- push, pop, call, ret + +![[stack.png]] +- Growing upwards + diff --git a/CS/Languages/C++.md b/CS/Languages/C++.md new file mode 100644 index 0000000..259f97e --- /dev/null +++ b/CS/Languages/C++.md @@ -0,0 +1,19 @@ +## To Read +- [Iterators](https://en.cppreference.com/w/cpp/iterator) -> [spans](https://en.cppreference.com/w/cpp/container/span) -> [ranges](https://en.cppreference.com/w/cpp/ranges) +- [constexpr](https://en.cppreference.com/w/cpp/language/constexpr) + - Can be evaluated at compile-time instead of runtime + - Shift processing to compile-time, quicker at runtime + - Can be run at run-time + - Not the only way to be used in constant expressions + - `const` + - Can use with const + - `constexpr const int N = 5;` + - same as `constexpr int N = 5;` + - `constexpr` implies `const` + + +## Conan +cmake-conan +[https://github.com/conan-io/cmake-conan](https://github.com/conan-io/cmake-conan) + +[https://cliutils.gitlab.io/modern-cmake/](https://cliutils.gitlab.io/modern-cmake/) diff --git a/CS/Languages/Python.md b/CS/Languages/Python.md new file mode 100644 index 0000000..3933be9 --- /dev/null +++ b/CS/Languages/Python.md @@ -0,0 +1,25 @@ +pip freeze | %{$_.split('==')[0]} | %{pip install --upgrade $_} + +From <[https://www.activestate.com/resources/quick-reads/how-to-update-all-python-packages/](https://www.activestate.com/resources/quick-reads/how-to-update-all-python-packages/)> + +[poetry cheat sheet](https://gist.github.com/CarlosDomingues/b88df15749af23a463148bd2c2b9b3fb) + +## Twisted +Network engine + +numpy scipy jupyterlab matplotlib pandas scikit-learn + +## Nuitka +Compiler + +## Plotly +Publication-quality Graphs + +[NLTK](https://www.nltk.org) +NLP + +If you are not getting good results, you should first check that you are using the right classification algorithm (is your data well fit to be classified by a linear SVM?) and that you have enough training data. Practically, that means you might consider visualizing your dataset through PCA or t-SNE to see how "clustered" your classes are, and checking how your classification metrics evolve with the amount of data your classifier is given. + +If you then confirm that investing in tweaking your linear SVM is the right way to approach your problem, you can look at modifying the class weights. Note then that what you suggest as weights is probably the opposite of what you want to do: you are giving more weights to less frequent classes, marginalizing them further - said differently, you typically want to use weights that are inversely proportional to class frequencies. You can calculate these manually, or you can let sklearn do it automatically for you by specificing class_weight='balanced'. + +From <[https://stats.stackexchange.com/questions/254779/optimal-class-weight-for-svc](https://stats.stackexchange.com/questions/254779/optimal-class-weight-for-svc)> \ No newline at end of file diff --git a/CS/Languages/Rust.md b/CS/Languages/Rust.md new file mode 100644 index 0000000..03c371c --- /dev/null +++ b/CS/Languages/Rust.md @@ -0,0 +1,12 @@ +## Web + +#### Backend +- Actix-web + - Quick +- Rocket +[Benchmarks](https://github.com/programatik29/rust-web-benchmarks) + + +## Rayon +[https://crates.io/crates/rayon](https://crates.io/crates/rayon) +- Data parallelism \ No newline at end of file diff --git a/CS/Languages/dotNet.md b/CS/Languages/dotNet.md new file mode 100644 index 0000000..b1b8e96 --- /dev/null +++ b/CS/Languages/dotNet.md @@ -0,0 +1,30 @@ +# Common Language Infrastructure +## CLI +- Language-neutral platform + +# Common Language Runtime +## CLR +- Virtual Execution System + - VES + - Defined by CLI +- JIT managed code into machine instructions +- Execution engine + - VM +- Services + - Memory management + - Type safety + - Exception handling + - Garbage collection + - Security + - Thread management + +# Common Intermediate Language +## CIL +- Intermediate language for CLI +- Run by CLR +- Object-oriented, stack-based bytecode + +# Assemblies +- Compiled CLI code +- Portable executable (PE) + - DLL, EXE \ No newline at end of file diff --git a/CS/Processors.md b/CS/Processors.md new file mode 100644 index 0000000..6670a6a --- /dev/null +++ b/CS/Processors.md @@ -0,0 +1,27 @@ +## Execution Mode +Starts in Real Mode + +# Real Mode +- 16 bit +- 20 bit segmented memory + - Max 1 MB memory +- Direct access to peripherals +- No memory protection or multitasking +- BIOS computers start in this mode + +# Protected Mode +- 16 bit & 32 bit +- Max 16 MB of physical memory + - Max 1 GB virtual memory +- Privilege levels and protected memory + +# Long Mode +- 64 bit +- Largely an extension to 32 bit protected mode + +# System Management Mode +- 16 bit +- System-wide functions + - Power management + - System control hardware + - Proprietary OEM code \ No newline at end of file diff --git a/CS/Quantum.md b/CS/Quantum.md new file mode 100644 index 0000000..70d3580 --- /dev/null +++ b/CS/Quantum.md @@ -0,0 +1 @@ +[5 books](https://fivebooks.com/best-books/quantum-computing-chris-bernhardt/) \ No newline at end of file diff --git a/CS/Resources.md b/CS/Resources.md new file mode 100644 index 0000000..168060b --- /dev/null +++ b/CS/Resources.md @@ -0,0 +1 @@ +[Wigle - wifi enumerating](http://wigle.net) diff --git a/Images/confinement-band-gaps.png b/Images/confinement-band-gaps.png new file mode 100644 index 0000000000000000000000000000000000000000..a91188895d46f37d0298711e12fd1c08fdfa1729 GIT binary patch literal 91196 zcmYIv1CS`Ovi91xZQHhOowaS-wr$(qv$nlwZQFQzZ@u^blS*|@CexLfNv68L{t}@e 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The maximum KE of ejected electrons is independent of intensity, but dependent on frequency $n$ +2. There is a minimum frequency n0below which there is no emission +3. No time delay (less than 1 ns) before the onset of emission –but the rate of electrons depends on the intensity. \ No newline at end of file diff --git a/Maths/Vector Operators.md b/Maths/Vector Operators.md new file mode 100644 index 0000000..02d3fe9 --- /dev/null +++ b/Maths/Vector Operators.md @@ -0,0 +1,3 @@ +$$grad\equiv \nabla$$ +$$div\equiv \nabla \cdot$$ +$$curl\equiv \nabla \times$$ diff --git a/Quantum/Confinement.md b/Quantum/Confinement.md new file mode 100644 index 0000000..45af6d8 --- /dev/null +++ b/Quantum/Confinement.md @@ -0,0 +1,3 @@ +$$E_{ne}=\frac{\hbar^2}{2m_e^*} \frac{\pi^2}{L^2} n^2$$ +![[quantum-confinement.png]] +![[confinement-band-gaps.png]] \ No newline at end of file diff --git a/Quantum/Orbitals.md b/Quantum/Orbitals.md new file mode 100644 index 0000000..f3cb576 --- /dev/null +++ b/Quantum/Orbitals.md @@ -0,0 +1,26 @@ +$$\psi(r,\theta,\phi)=R(r)\cdot Y_{ml}(\theta, \phi)$$ +Wave functions are products of +Radial Function +- $R_{n,l}(r)$ +Spherical Harmonic +- $Y_{ml}(\theta, \phi)$ + +Absolute value of wave function squared gives probability density of finding electron inside differential volume $dV$ centred on $r, \theta, \phi$ + +$$|\psi(r,\theta,\phi)|^2$$ +# Quantum Numbers +$$n$$ +Principal quantum number +- 1, 2, 3... +- ***Electron shell***, electron energy and size of orbital +$$l$$ +Orbital Angualar Momentum Number +- $0-(n-1)$ +- ***Shape*** of the orbital + - 0 = s + - 1 = p + - 2 = d +$$m$$ +Z-component / Magentic of $l$ +- $-l$ to $+l$ +- ***Orientation*** of orbital \ No newline at end of file diff --git a/Quantum/Schrödinger.md b/Quantum/Schrödinger.md new file mode 100644 index 0000000..053345b --- /dev/null +++ b/Quantum/Schrödinger.md @@ -0,0 +1,32 @@ +$$-\frac{\hbar^2}{2m}\nabla^2\psi+V\psi=E\psi$$ +- Time Independent +- $\psi$ is the wave function + +Quantum counterpart of Newton's second law in classical mechanics + +$$F=ma$$ +[From](https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation) + +Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a [wave function](https://en.wikipedia.org/wiki/Wave_function), the quantum-mechanical characterization of an isolated physical system. + +[From](https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation) + +[Time–Independent Schrödinger Equation](https://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_4.pdf) +[RadialEquation.pdf](https://physics.weber.edu/schroeder/quantum/RadialEquation.pdf) + +## Hamiltonian +- Operator +- Total energy of a system + +- Kinetic + Potential energy + +$$\hat{H}=\hat{T}+\hat{V}$$ +- $\hat{V}$ + - Potential Energy +- $\hat{T}=\frac{\hat{p}\cdot\hat{p}}{2m}=-\frac{\hbar^2}{2m}\nabla^2$ + - Kinetic Energy +- $\hat{p}=-i\hbar\nabla$ + - Momentum operator + +## Wavefunction Normalisation +- Adds up to 1 under the curve \ No newline at end of file diff --git a/Quantum/Standard Model.md b/Quantum/Standard Model.md new file mode 100644 index 0000000..e7614d6 --- /dev/null +++ b/Quantum/Standard Model.md @@ -0,0 +1,23 @@ +- 4 fundamental forces + - Bosons +- Elementary particles + +- Fermions + - Spin 1/2 + - Fermi-Dirac statistics + - 3 generations of similar pairs + - Quarks + - Colour charge + - Strong interactions + - Leptons + - No colour + - Electroweak interactions + +- Bosons + - Scalar + - Spin 0 + - Higgs + - Gauge + - Spin 1 + - Force carriers + - y, W, Z, g \ No newline at end of file diff --git a/Semiconductors/Doping.md b/Semiconductors/Doping.md new file mode 100644 index 0000000..1934e8f --- /dev/null +++ b/Semiconductors/Doping.md @@ -0,0 +1,21 @@ +$$n=N_c\cdot e^{\frac{-(E_c-E_F)}{kT}}$$ +$$p=N_v\cdot e^{\frac{-(E_F-E_v)}{kT}}$$ +- $E_c$ is the position of the conduction band minimum +- $E_v$ is the position of the valence band maxmimum +- $k$ is Boltzmann's constant +- $N_x$ are the effective density of states + +$$np=n_i^2$$ +- $n_i$ = Intrinsic carrier concentration + +$$n_i=\sqrt{N_cN_v}e^{\frac{-E_g}{2kt}}$$ +- $E_g$ = Band Gap = $E_c-E_v$ + +## Substitutional Doping + +- Donated electrons are delocalised +- Ions are immobile + +$$N_c \equiv 2 \left[ \frac{2\pi m_nkT}{h^2}\right]^{3/2}$$ +$$N_v \equiv 2 \left[ \frac{2\pi m_pkT}{h^2}\right]^{3/2}$$ + diff --git a/Semiconductors/Equations.md b/Semiconductors/Equations.md new file mode 100644 index 0000000..b2fd25d --- /dev/null +++ b/Semiconductors/Equations.md @@ -0,0 +1,30 @@ +$$R=\frac{\rho L}{A}$$ +- $R$ = Resistance +- $\rho$ = Resistivity ($\Omega cm$) +- $L$ = Length +- $A$ = CS Area + +$$J=\sigma E$$ +- $J$ = Current Density +- $\sigma$ = Conductivity ($\frac{1}{\Omega cm}$) +- $E$ = Electric Field + +$$V_{bi} = \frac{kT}{q}ln(\frac{N_D N_A}{n_i^2})$$ +- $V_{bi}$ = Built-in Potential + +$$J=nev$$ +- $n$ = Charge Density +- $e$ = Charge +- $v$ = Drift Velocity + +$$v=\mu E$$ +- $v$ = Drift Velocity +- $\mu$ = Mobility +- $E$ = Electric Field + +$$\sigma = ne\mu$$ +$$\rho=\frac{1}{\sigma}$$ +$$\sigma=q(\mu_nn+\mu_pp)$$ +- $q$ = Electronic Charge +- $\mu$ = Carrier Mobility ($\frac{cm^2}{Vs}$) +$$1 eV = 1.602\times 10^{-19}J$$ \ No newline at end of file diff --git a/Specific Energy.md b/Specific Energy.md new file mode 100644 index 0000000..8a89712 --- /dev/null +++ b/Specific Energy.md @@ -0,0 +1,5 @@ +- Massic energy +- Gravimetric energy density +- Energy density + +- Can mean energy per unit volume \ No newline at end of file