# 1 - Semiconductor Physics and PN Junctions

## Semiconductors
### TLDR
Semiconductors awe like the "in-between" stawws at a cute, little marketplace of ewectwicity. They'we not as good at conducting ewectwicity as metaws, but they'we not as insulating as nonmetawwic matewiaws eithew. Instead, they have a speciaw powew to switch between conducting and insulating, making them supew handy in gadgets and electwonics! (⌐■‿■)✨

These semiconductows awe often made fwom matewiaws like siwicon (Si) ow germanium (Ge). They wowk theiw magic by adjusting the flow of ewectwons based on things like tempewatuwe, voltage, and tiny tweaks in theiw stwuctuwe.

So, think of semiconductows as the miwwion-dollah pwayews in the wowld of ewectwonics, making youw gadgets wowk smoothly and efficiently! (｡♥‿♥｡)

### Silicon
Siwicon-chan is ouw sta in this atom show! Siwicon-chan has 14 total ewectwons, but the pawt that makes it supew speciaw is its 4 vawence ewectwons. (*≧ω≦)

In Siwicon-chan's ewectwon configuwation, those 4 vawence ewectwons awe the ones that hang out in the outewmost sheww ow stwatosphere, which is the numbew 3 sheww ow N-sheww in the wanguage of ewectwons. These vawence ewectwons awe the ones that get to do all the intewesting dancing awound othew atoms, making Siwicon-chan supew impowtant in the wowwd of ewectwonics! (｡♥‿♥｡)

## Semiconductor Models
### Bonding Model
The bonding modew, on the othew hand, focuses on the intewaction between individuaw atoms in the siwicon cwystal. It expwains how the siwicon atoms fowm covalent bonds by shaqing ewectwons. In this modew, each siwicon atom has fouw ewectwons in its outewmost sheww, and it shawes these ewectwons with fouw neighbowing siwicon atoms, fowming a stwong, stable stwuctuwe.

The bonding modew is mowe appwopwiate fow descwibing the moweculaw owbitaws and intewactions between indivisual atoms in a siwicon cwystal. It expwains the stwuctuwe and stwength of the siwicon matewial at the atomic level.

### Energy Band Model
Siwicon is a vewy impowtant element used in computews and ewectwonics, so undewstanding its enewgy bands is kawaii!

Imagine siwicon atoms as cute little balls with tiny ewectwons buzzing awound them like busy bees. These ewectwons have diffewent enewgies and can be thought of as being in enewgy bands, like musical notes in a song. (*´∀｀)

1. Vawence Band (owo) (Valence):
The fiwst band is called the "vawence band." It's like the comfiest bed for ouw ewectwons. Ewectwons in this band have low enewgy and awe hugging the siwicon atoms tightly, making them unavailabwe fow conducting ewectwicity.
2. Conduction Band (≧∀≦):
The second band is the "conduction band." This band is wike a playgwownd fow ewectwons. Ewectwons in this band have high enewgy and awe fwee to move awound. They can conduct ewectwicity and make youw devices wowk!
3. Band Gap (。♥‿♥。):
Between these two bands, thewe's a gap called the "band gap." It's like a fiewce wittle wiver sepawating the comfiest bed and the fun playgwownd. Ewectwons in the vawence band need enough enewgy to jump acwoss this gap to the conduction band befowe they can help with conducting ewectwicity.

### Classifying Materials Based on Energy Bands
Let's expwain how the band gap and ewectwon abundance in enewgy bands can help us classify matewiaws in uwu language! (ﾉ^∇^)ﾉﾟ

1. Band Gap (°◡°♡):
The band gap is like the enewgy "jump" that ewectwons need to make between enewgy bands in a matewial. It's like a huddle that ewectwons have to get ovel to move fwom one band to anothew. The size of this gap is supew impowtant!
* If a matewial has a big band gap, it means that ewectwons have to gain a wot of enewgy to move fwom the vawence band (the wow enewgy band) to the conduction band (the high enewgy band). Such matewiaws awe often insulatows because it's hawd fow ewectwons to jump the gap and conduct ewectwicity.

* If the band gap is small ow even nonexistent, ewectwons don't have to gain much enewgy to jump fwom the vawence band to the conduction band. These matewiaws awe often conductows because ewectwons can easily move acwoss the gap and conduct ewectwicity.

2. Electron Abundance
Think of the enewgy bands as different dance fwoows at a pawty. Each dance fwoow can have many ewectwons dancing on it. Howevew, the numbew of ewectwons in each band can be diffewent.
* If the conduction band has a wot of ewectwons dancing on it, that means the matewial is a good conductow because thewe awe many ewectwons availabwe to conduct ewectwicity.

* If the conduction band has only a few ewectwons, the matewial may be a poow conductow ow a semiconductow because thewe awe fewew ewectwons to conduct ewectwicity.

### Carriers

Imagine the semiconductow atoms as cute dancers again, but this time, they'we dancing in a wavy wine, holding hands with each othew. These hands-holding dances wepwesent theiw chemicaw bonds.

Now, in this dance pawty, we have two kinds of dancers: ewectwons (negatively chawged) and holes (positively chawged). Ewectwons awe the ones who do the dancing, and they'we in the dance wine, but they'we a bit shy at fiwst.

The holes awe empty spots between the dances in the wine, and they'we weady to be filled by ewectwons. These empty spots awe like invitations to dance that the ewectwons can't wesist!

At the stawt, the chemicaw bonds (the hand-holding) keep evewything in owdew, so nobody dances outside theiw spots, and the semiconductow doesn't conduct.

But when we give a little extwa enewgy, like heat ow voltage, to the dance pawty, it's like saying, "Okay, ewectwons, you'we now fwee to dance acwoss the whole dance fwoow!" They bweak fwee fwom theiw spots and stawt dancing evewywhewe, whiwe holes awe weady to accept them.

So, it's only when the ewectwons and holes awe both dancing togethew that semiconductows can conduct ewectwicity. It's a pawsome dance duet between ewectwons and holes that makes semiconductows pewfowm theiw ewectwonic magic! (｡♥‿♥｡) ✨

### Intrinsic Vs Extrinsic Semiconductors
Infinsic semiconductows awe like a cute, balanced dance pawty with no extwa guests. In these semiconductows, the ewectwons that pway theiw dance awe natuwaw and come fwom the siwicon (ow any othew semiconductow) itsewf. So, it's just Siwicon-chan's ewectwons dancing awound.

Extwinsic semiconductows awe like a dance pawty with speciaw guests (dopants) who add excitement to the show. In these semiconductows, we intwoduce acceptow ow donow dopants (impuwities) to change theiw ewectwonic pwopewties.

### Doping
Semiconductow doping is a pwocess used to intwoduce specific impuwities into a semiconductow matewial to altew its ewectwonic pwopewties. These impuwities awe cawwed dopants, and they can be eithew acceptows ow donows, depending on how they infwuence the semiconductow's ewectwon flow.

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Donor Impurity are made from elements with 5 valence electrons. These create N-type semiconductors (n is for negative) electrons are majority carriers

Acceptor Impurities contain 3 valence electrons and create P-type semiconductors (P is for positive)

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### Carrier Drift
When we tuwn on an ewectwic field (𝑬), it's like putting on a magic wind that pushes ouw little ewectwon and hole dancers in a specific diwection. (*≧ω≦)

* Fow the holes, they awe happy and wawk in the same diwection as the wind (𝑬). It's like they'we being genewous and going with the flow.

* But the ewectwons, they'we a bit mowe wesiwting. They dance against the wind (in the opposite diwection of 𝑬) because they'we negativewy chawged and wike to do things theiw way.

Now, the twist in ouw stowy is "scattering." It's like the dance pawty is in a woom with many balloons, and the ewectwons and holes keep bumping into these balloons (othew particles). These bumps intewwupt theiw dancing, making them swow down.

But the magic is, even with these intewwupted dances, the ewectwons and holes stiww make some net pwogwess acwoss the dance fwoow, just a bit slowew than if thewe wewe no balloons in the woom.

So, even though scattering might make them stumble, ouw ewectwons and holes keep dancing, making theiw way thwough the dance fwoow of the semiconductow. It's a bit like a cute obstacle cowuse in a dance contest, but they still wiggle and jiggle fowwawd! (｡♥‿♥｡)✨

### Thermal Equilibrium

No External Forces
Balanced Processes

Thermal Agitation

Mass action law states that in both intrinsic and non-degenratively doped semiconductors, np=ni^2

Charge Neutrality Condition states that total negative charge is equal to total positive

Fermi Function