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In order to change the electrical properties of a semiconductor, it is necessary to dope it. Impurities are added to the semiconductor so that the number of carriers in the semiconductor are increased.

A semiconductor may be doped p-type. When a group III impurity, such as Boron, is introduced into a group IV element such as Si, each boron atom has one less electron than the surrounding lattice. These type of dopants are called acceptors because they accept electrons. The accepted electron leaves in place a hole, and thus the semiconductor is called P type because holes carry positive charge.

Conversely, a semiconductor may be doped n-type. When a group V impurity, such as arsenic, is introduced into a group IV element such as Si, each arsenic atom has one more electron than the surrounding lattice. These type of dopants are called donors because they donate electrons. The donated electron means that there are many mobile electrons, and the semiconductor is called N type because electrons carry negative charge.

Donor states are typically just a little bit below the bottom of the conduction band edge, and acceptor states are a little bit above the top of the valence band edge.

Interfaces use analogous terms for states. At a semiconductor interface, there is an energy level referred to as the charge neutrality level. This energy level is generally at a different energy than the semiconductor Fermi level. If \phi_0 > E_f then, the surface is donor like and traps holes. These states are positively charged above the electron quasi-Fermi level (the state carries the charge of one hole when occupied) and neutral below. The band bend down near the surface and there is positive charge at the surface. If the substrate is p-type, then the band bending is more significant, but if it is n-type, the band bending is less.

If \phi_0 < E_f then, the surface is acceptor like and traps electrons. These states are negatively charged below the quasi-Fermi level (the state carries the charge of one electron) and neutral above. The band bend down up the surface and there is negative charge at the surface. If the substrate is n-type, then the band bending is more significant, but if it is p-type, the band bending is less.

Mnemonic: acceptor – negative below quasi-Fermi, neutral above; donor – positive above quasi-Fermi, neutral below

A solar cell consists of two parts

1. Light absorption.  Photons are absorbed and create electron hole pairs.

2. Charge separation and collection.  The electrons and holes are separated through some built in electric field and collected through contact metals.

Solar cells are quantified through quantum efficiency.

The separation and collection of mobile charges (part 2) is quantified through the internal quantum efficiency.   The internal quantum efficiency is the ratio of electron-hole pairs collected for each photon absorbed.

The external quantum efficiency quantifies both 1 and 2 above.  It is the ratio of electron-hole pairs collected for each photon shined on the solar cell.

The external quantum efficiency is thus always less than the internal quantum efficiency.

Materials are often classified into three distinct categories: insulators, semiconductors, and metals.

The three materials are distinguished from one another based on their band gap, or by their resistivities (conductivities).  Roughly speaking, metals are materials with bulk resistivity less than 10^{-3} \Omega \cdot cm.

Energy band theory can explain these differences in resistivity in terms of differences in band gap.  Every material has a band structure associated with it that results from electrons interacting with one another.  Those band that are filled are called valence bands, and those that are empty are referred to as conduction bands.  The difference between the bottom of the conduction band and the top of the valence band is called the band gap.

If the band gap is above 3 eV, then the material is generally considered an insulator.  If the material has a band gap of less than 3 eV, then it is generally a semiconductor.  Metals do not have a band gap, and instead have partially filled bands.

Semiconductors are materials that have band gap between that of insulators and that of conductors.

We can modify the electrical properties of semiconductors by doping the material.  For example, silicon has four valence electrons.  By doping silicon with boron (which has three electrons), we introduce holes into the valence band of silicon.  By doping silicon with phosphorus (which has five electrons), we introduce electrons in the conduction band of silicon.

Doping can be done with a variety of methods, such as ion implantation or gas phase doping.  Ion implantation is done by bombarding the material with high energy atoms.  The advantage of using ion implantation is that doping concentrations above that of the solid solubility limit can be achieved.  However, the use of ion implantation results in crystal damage, that must be fixed through an annealing step.  Ion implantation is modeled by monte carol methods.

Gas phase doping is performed by flowing the gas phase of the dopant atoms over the material.  Photoresist in photolithography or silicon oxide are often used to define the regions for doping.   This method of doping is limited by the solid solubility limit, and diffusion is used to drive the dopants into the material.

For III-V materials, such as InAs, the prospects of ion implantation do not look so favorable, as the crystal damage is more difficult to fix due to the stoichiometry of the lattice.  Researchers are currently doping these materials in-situ, by gas phase doping, or other exotic methods.

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