In this video, we will introduce pn junction. So, pn junction is an intimate contact between an n-type semiconductor and the p-type semiconductor. What do we mean by intimate contact? Intimate contact is an interface between two materials that allows free exchange of carriers. In other words, electrons and holes can freely move across the boundary. So, if we have an intimate contact between n-type semiconductor and p-type semiconductor, we call that a pn junction. The naming convention is that the n-type material is called the cathode, emitter of electrons, and the p-type material is called the anode, collector of electrons, and the four bias is defined when the p-type material is at a higher voltage than the n-type material. So, as shown here in this figure, if you apply a positive voltage on the p-type and the negative voltage on the n-type, this we call a forward bias, or we use a positive sign for the applied voltage. In the opposite case, it will be a reversed bias. So, let's consider a simple thought experiment that would help us understand the pn junction. So, we look at the formation of a pn junction in stages. So, before forming pn junction, you can consider an n-type material and the p-type material separately. These are the isolated n-type material and an isolated p-type material. In an n-type material, your Fermi level is in the upper half of the band gap closer to the conduction band, and in the p-type material, your Fermi level is in the bottom half of the band gap closer to the valence band. Once you form a contact, immediately after forming the contact, then electrons and holes had no time to adjust. So, the energy band diagram and the carrier concentration will remain the same as the isolated n-type material and isolated p-type material shown here. However, now the contact allows free exchange of carriers. So, the electrons on the n-type side will find a region where there is a very low electron concentration which is a p-type region. So, electrons will diffuse from n-type to p-type region. Holes will do the same, holes will diffuse from p-type to n-type region. Now, as they diffuse, these electrons will leave on isolated ionized donor behind the donors where they originally come from. Holes on the p-type side, as they diffuse into n-type, they will leave ionized acceptors behind, the acceptors where they originally come from. So, as the diffusion precede, there is a charge building up on the n-type side due to the ionized donor which is a positive charge. Also, there is a charge building up on the p-type side due to ionized acceptors which has a negative charge. So, there is a electric field building up due to these charge, positive charge on the n-type side and negative charge on the p-type side. The electric field will build up in the direction pointing from n to p. The direction of the electric field is in such a way that it would oppose diffusion. So, it wants to hold the electrons back and it wants to hold the holes back to the p-type. When the tendency of diffusion due to driven by the carrier concentration difference between the p and n side, and the electric field building up which opposes the tendency of diffusion, when those two balance each other out, then you have an equilibrium pn junction. Now, at equilibrium, the Fermi level is constant throughout the system. This is a very general result that arise from the statistical physics, and it is true for a variety of devices, not only pn junction and any other devices that we will discuss in later in this course. When the device reaches equilibrium, then the Fermi level is constant throughout the system. Now, another important consideration is that if you are very far away from the junction, now we're assuming a semi infinite n-type region and p-type region. So, if you are infinitely far away from the junction, then in that region, you would naturally assume that the electrons there, carriers there will not be impacted by the presence of junction because it's so far away. Therefore, they would retain all the properties of the isolated n-type material before forming junction. Same thing for the p-type side. Far away from the junction, the material properties on the p-type side would remain the same as the isolated p-type material. With these two assumptions, we can define the energy barrier that is caused by band bending, and why do you have an energy barrier that causes band bending? Because of the electric field. When you have an electric field, then that means that there is a potential difference, and the electric potential energy difference is depicted in the energy band diagram as a band bending. So, as shown in the previous slide, Fermi level at equilibrium pn junction, Fermi level is constant, and your conduction band and the valence band bends, and this band bending represents the energy difference between the p-type side and n-type side, and that energy difference is equal to the potential energy difference, electric potential energy difference due to the building up of the electric field across the junction. That potential difference is characterized by this quantity called the built-in potential, and we're going to call it Phi sub i, and that energy is equal to the difference in Fermi level before forming junction. So, that is, if you look at the the energy band diagram before forming junction, the n-type Fermi level was here, and the p-type Fermi level was down here. When you form a contact as shown here, then the diffusion takes place and eventually the pn junction will reach equilibrium, and when in equilibrium, this Fermi level down here should line up with the Fermi level of the n-type material up here. In order to do that, you have to bend the conduction and valence band, and what is the magnitude of the banding? That should be equal to the initial difference, energy difference between these two Fermi levels. So, use the definition of the potential introduced earlier, which is the E_F minus E_i divided by q. For the n-type side, the potential of the n-type side is given by the carrier concentration and the majority carrier concentration n, which is equal to the doping density in that case. Likewise, the p-type side potential is given by the doping density on the p-type side. The difference between these two potential, n-type and p-type side far away from the junction, should give you the potential difference between a cross junction. So, that's the the built-in potential, and it is given by this equation right here. This is a very useful information and you would find it very handy. Now, we introduce a very important approximation called the depletion approximation. The depletion approximation says that the junction, pn junction can be divided into two regions. One is depletion region, and depletion region builds up near the junction and inside the depletion region, there are no mobile carriers. No electrons, no holes. Just ionized donors and ionized acceptors and that's it. That's the depletion region. Now, outside the depletion region, we have a quasi-neutral region or just neutral region. In this quasi-neutral region, the carrier concentration equals the doping density, doping concentration, just like the isolated n-type and isolated p-type material. We further assume that there is an abrupt boundary between these two regions, depletion region and quasi neutral region, there is an abrupt transition. In reality, you would imagine that there was a gradual transition from depletion region to the neutral region, which we will discuss later. But, the theories, the approximation, the approximation is that there is an abrupt boundary between depletion region and quasi-neutral region that allows our mathematical analysis very simple. So, here we introduce a step junction using the depletion approximation. Step junction is a junction where there is an abrupt boundary between p-type region and the n-type region. So, n-type and p-type have a well-defined flat boundary. So, the doping profile is a step function, and therefore it's called a step junction. Now, in the depletion approximation within the depletion region here from X sub n to negative X sub p, there are no carriers. So, carrier concentration is zero. Outside your carrier concentration, majority carrier concentration on the inside is equal to the doping density, and the minority carrier concentration here is equal to the doping density on the p-side. So, if you express this in terms of the charge density, then outside the depletion region in the quasi-neutral region that is, then you're neutral. So, the electron concentration exactly matches the donor density. So, net charge is zero. Same thing in the p-type region that charge is zero. Inside the depletion region because there are no carriers, you have a net positive charge due to ionized donors on the n-type side. Net negative charge due to ionized acceptors on the p-type side. So, this is the charge density profile as you can see, and you can use this charge density profile plug it into the Poisson's equation, and you can calculate the potential and also the electric field.