In equilibrium the quasifermi levels are constant and have the same value for both electrons and holes e f,n e f,p 0 ev. Nov 27, 2007 i understand that for a semiconductor pn junction under zero voltage, the fermi level is constant throughout the junction because that is the condition for a system in thermodynamic equilibrium. The dopants are assumed to be shallow, so that the electron hole density in the ntype ptype region is approximately equal to the donor acceptor density. On the separation of quasifermi levels and the boundary. A quasi fermi level also called imref, which is fermi spelled backwards is a term used in quantum mechanics and especially in solid state physics for the fermi level chemical potential of electrons that describes the population of electrons separately in the conduction band and valence band, when their populations are displaced from. Apr 27, 2019 quasi fermi levels allow us to extend the idea of the fermi energy to nonequilibrium conditions when the original concept of a single fermi energy breaks down. A pn junction is a boundary or interface between two types of semiconductor materials, ptype and ntype, inside a single crystal of semiconductor. Low injection fermi level do not change in the depletion layer minority carrier densities p n n0 n d in nregion and similar in pregion 2. Department of eecs university of california, berkeley eecs 105 spring 2004, lecture 19 prof.
The fermi level actually the chemical potential is an equilibrium concept. This is a direct consequence of the fact that the concentration of minority carriers jumps by a large amount. In a strict sense of speaking, the fermi energy is not defined without equilibrium, but only after it has been restored. A quasi fermi level also called imref, which is fermi spelled backwards is a term used in quantum mechanics and especially in solid state physics for the fermi level chemical potential of electrons that describes the population of electrons separately in the conduction band and valence band, when their populations are displaced from equilibrium. Fermi level or fermi energy is a quantum phenomenon, which translates as the difference in energy state occupied by the lowest level close to the nucleus electrons to the highest level away from the nucleus electrons, it can also be measured a. The p positive side contains an excess of holes, while the n negative side contains an excess of electrons in the outer shells of the electrically neutral atoms there. Abrupt depletion layer approximation let apply bias and calculate current through the pn junction currents in pn junction from sze, 1981. Using the quasifermi level and the einstein relationship, the electron current entering the pregion becomes these relationships describe the behavior of the quasifermi level in the depletion region.
Quasifermi levels allow us to extend the idea of the fermi energy to nonequilibrium conditions when the original concept of a single fermi energy breaks down. The dopants are assumed to be shallow, so that the electron hole density in the n type p type region is. Definition of the quasi fermi energy if an equilibrium is disturbed, it takes a certain time before it is restored again. Hence, to find out what the voltage does under illumination, we need to have a look at how the photogeneration of electrons and holes acts on the quasi fermi energy. Naturally, the concept of quasi fermi imref levels qfls and their splitting was introduced, and it has now become a standard theoretical tool to describe finitebias nonequilibrium operations of semiconductor devices. The quasifermi level of the holes, however, is significantly away from the fermi level at equilibrium.
What happens when we join ptype and ntype semiconductors. On the separation of quasifermi levels and the boundary conditions for junction devices 1227 now e 1 and if nxp 340 lecture 24. The upward direction in the diagram represents increasing electron energy. Using the quasi fermi level and the einstein relationship, the electron current entering the pregion becomes these relationships describe the behavior of the quasi fermi level in the depletion region. If you have i can give you examples of quasifermi levels from that, but if not it would probably only confuse you at this stage. If we calculate carrier densities in nonequilibrium with the quasi fermi energies, we have to be careful to use the right quasi fermi energy in the fermidirac formula or in the boltzmann approximation after all, we now have two quasi fermi energies, one regulating the density of electrons in the conduction band, and the other one doing the. A quasi fermi level also called imref, which is fermi spelled backwards is a term used in quantum mechanics and especially in solid state physics for the fermi level chemical potential of electrons that describes the population of electrons separately in the conduction band and valence band, when their. Quantitative pn junction current but remember the fermi levels calculate the carrier concentrations minority carrier concentration usually varies the most and the majority carrier quasifermi level is close to the original fermi level.
For electrons, this guy 10 to the 14th is larger than the intrinsic carrier concentration. This allows electrical current to pass through the junction only in. If you have i can give you examples of quasi fermi levels from that, but if not it would probably only confuse you at this stage. Quasifermi levels and voc everything about solar energy. The carrier density and the electric field are used for determining the drift current and diffusion current of the pn diode. So your quasi fermi level for hole will be located in the upper half of the band gap. What happens to the fermi level after we apply a bias voltage. Electron energy band fermi level electrostatics of device.
Electrons and holes reach an equilibrium at the junction and form a depletion region. A pin junction is similar to a pn junction, but contains in addition an intrinsic or unintentionally doped region with thickness, d, between the ntype and ptype layer. Questions you should be able to answer by the end of todays lecture. The more quickly they recombine, the closer the two quasi fermi levels must be, other things equal. Diode characteristics dynamic resistance, transition time. Outside the space charge region the quasifermi levels vary linearly and. Fermi levels in pn junction under voltage physics forums.
Its a bit like water seeking the lowest level in a bowl. What is the physical significance of fermi level in diode. The region on the left is p type with an acceptor density na, while the region on the right is n type with a donor density nd. In semiconductor physics, a pn junction is formed, by shifting the p and n parts in a way that the quasifermi levels are on the same level and one can draw a straight line for the whole device from left to right, which means that an electron has the same potential energy throughout the entire device. A pn junction consists of two semiconductor regions with opposite doping type as shown in figure 4. Smith builtin field zin thermal equilibrium, the pn diode has.
In thermal equilibrium e f is constant and not a function of position. So, fermi level is not spatially constant throughout a biased pn junction. Now, if we were to define separate fermidirac distribution functions for electrons and holes, under this steadystate condition. Quasi fermi levels in semiconductor photovoltaic heterojunction. Such structure is typically used if one wants to increase the width of the depletion region, for instance to increase the optical absorption in the depletion region. The current is proportional to the mobility and the gradient of the quasifermi level e f. No generationrecombination in the depletion layer 6. Its a bit like water seeking the lowest level in a. Quasi fermi levels in reversebiased pn junction diode. Quasifermi level splitting in nanoscale junctions from ab. How is quasi fermi level related to voltage change in a diode. When thermionic emission is the limiting process, however, then the quasifermi level changes significantly across the depletion region.
At thermal equilibrium, that is, the steadystate condition at a given temperature without any external excitation, the individual electron and hole currents flowing across the junction are identically zero. I also understand that pn junction under applied voltage forward or reverse is not a system in thermal equilibrium because there is a nonzero total. Apr 29, 2019 the flow of current in the pn junction diode is determined by the charge carrier density, the electric field throughout the structure of pn junction diode and the quasi fermi level energies of the p type and n type. Fermi level of the side which has a relatively higher electric potential will have a relatively lower electron energy potential energy q electric potential.
As you probably know, you can use your knowledge of the location of the fermi level to find out the concentration of carriers. So if you express this number in terms of fermi level, that fermi level is going to be up above the intrinsic fermi level, just like in the ntype semiconductor. Then it is actually required for the conduction and valence band to have the approximately the same quasi fermi level. If pn is constant throughout the spacecharge region, then e fne fp must also remain constant.
A quasi fermi level is a term used in quantum mechanics and especially in solid state physics for the fermi level chemical potential of electron that defines the population of electrons separately in the conduction band and balance band, when. The value of the fermi level at absolute zero temperature. The fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied singleparticle states in a quantum system of noninteracting fermions at absolute zero temperature. The majority carrier quasi fermi levels are no longer flat in the bulk regions, the quasi fermi level splitting in the depletion region is less than qv a, the law of the junction must be generalized, and ambipolar transport coefficients must be used near the junction guckel et al. If you apply a potential across the junction, you impose an energy difference between the two sides thats the definition of a voltage or potential drop. That implies that you would have to supply energy to get an electron to go up on the diagram, and supply energy to get a hole to go down. Demo video on fermi level alignment at pn junction, which is a supplementary and helpful for the lecture of semiconductor engineering to be given by prof.
For a pn junction at equilibrium, the fermi levels match on the two sides of the junctions. Quasi fermi energies are extremely helpful for the common situation where we do have nonequilibrium, but only between the bands and that covers most of semiconductor devices under conditions of current flow due to an applied voltage or under illumination. You learned on the role of a pn junction page that the voltage difference between the two contacts is equal to the splitting of the quasi fermi energies. Demo video on fermi level alignment at pn junction youtube. Hence, to find out what the voltage does under illumination, we need to have a look at how the photogeneration of electrons and. We can then fill in the junction region of the band diagram as. Jul 10, 2016 fermi level or fermi energy is a quantum phenomenon, which translates as the difference in energy state occupied by the lowest level close to the nucleus electrons to the highest level away from the nucleus electrons, it can also be measured a. Quantitative pn junction current but remember the fermi levels we are out of equilibrium, so we need to use the quasi fermi levels to calculate the carrier concentrations minority carrier concentration usually varies the most and the majority carrier quasi fermi level is close to the original fermi level. The region on the left is ptype with an acceptor density n a, while the region on the right is ntype with a donor density n d. You learned on the role of a pn junction page that the voltage difference between the two contacts is equal to the splitting of the quasifermi energies. Only difference of the e s at both sides are important, not the absolute position. Socalled quasifermi levels which are different for electrons e f,n and holes e f,p are used to describe nonequilibrium carrier concentrations. The changes over in a pnjunction device from efn in the ntype to efp in the ptype part of the junction, while connecting horizontally to the corresponding minority quasifermi levels in the opposite part of the junction can be seen in fig.
Driftdiffusion current diffusion in quasineutral regions 4. Fermi energy and fermi level definition, applications, formula. Another example is in a material where electrons and holes combine extremely quickly, so the third bullet point is not true. Quasi fermi levels in semiconductor photovoltaic heterojunction b. Last time quasi fermi levels fermi distribution is only valid in equilibrium conditions. Space charge region an overview sciencedirect topics. Sep 24, 2018 demo video on fermi level alignment at pn junction, which is a supplementary and helpful for the lecture of semiconductor engineering to be given by prof.
In semiconductor physics, a pn junction is formed, by shifting the p and n parts in a way that the quasi fermi levels are on the same level and one can draw a straight line for the whole device from left to right, which means that an electron has the same potential energy throughout the entire device. In thermal equilibrium the probability of finding an energy level at e occupied is given by the fermi function, fe. Thus the quasi fermi level of the majority carrier is the same as the fermi level. By solving simulthus 41 shows that the pn product can exceed the taneously value n. A universal feature of semiconductor devices is that the functional channel region is driven out of equilibrium, or formally it cannot be characterized by one global fermi level.
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