In electronics and semiconductor physics, the law of mass action is a relation about the concentrations of free electrons and electron holes under thermal equilibrium. Lecture 3 electron and hole transport in semiconductors. The expression for thermal equilibrium majority carrier electron concentration in type semiconductor is, 1 here, is donor concentration, is acceptor concentration and is the intrinsic electron concentration. On the other hand, a free electron and a hole give rise to the generic term carriers. Where, n and p are the concentration of mobile electrons and holes respectively, e is absolute charge of each electron and hole and. What is the relation between current density and conductivity. Assuming the material is not degenerately doped, you can use the law of mass action, given by. Hence the electroncarrier concentration is equal to the holecarrier concentration.
Its basically the same as calculating the concentration of electrons, with a. A hole is essentially a way to conceptualize the interactions of the electrons within a nearly full valence band of a crystal lattice, which is missing a small fraction of its electrons. The electron motion, and the movement of holes in the opposite direction, constitute an electric current. Enee 3, spr 09 supplement ii examples on doping and fermi. At 300 k the generally accepted value for the intrinsic carrier concentration of silicon, n i, is 9. A semiconductor has equal electron and hole concentration of 6 10 8 m 3. Jan 26, 2019 where, n is the magnitude of free electron concentration, p is the magnitude of hole concentration and. When a ptype semiconductor is compensated, doped with both acceptors and donors n a n d n i and n d is nonzero, the equations may be simplified similarly to case 2 because we can still neglect n i in the equation for p o. A formula for the intrinsic carrier concentration in silicon as. The expression for thermal equilibrium minority carrier hole concentration in type semiconductor is. In this video i calculate the concentration of holes in a semiconductor. The expression for thermal equilibrium minority carrier hole concentration in type semiconductor is, 2. Intrinsic carrier concentration contains an insignificant concentration of impurity atoms under the equilibrium conditions, for every electron is created, a hole is created also n p ni as temperature is increased, the number of broken bonds carriers increases as the temperature is decreased, electrons do not receive enough.
Massachusetts institute of technology department of. Usually, the electron drift velocity in a material is directly proportional to the electric field, which means that the electron mobility is a constant independent of electric field. In physics, chemistry, and electronic engineering, an electron hole often simply called a hole is the lack of an electron at a position where one could exist in an atom or atomic lattice. Carrier concentrations southern methodist university. Derive the expression for carrier concentration of electron.
How to calculate the impurity carrier concentration in a host material by dft calculations. The electron and hole mobilities n and p, respectively each depend on the total dopant concentration. Fermi level in the middle of forbidden band indicates equal concentration of free electrons and holes. Equilibrium electron and hole concentration from doping mit. Calculate the electron and hole density in germanium, silicon and gallium arsenide if the fermi energy is 0.
Current density in metal and semiconductor electrical4u. Electrons in one atom one electron in an atom a hydrogenlike atom. Also, the hole mobility ptype is considerably less than the electron mobility ntype for a given concentration. Carrier concentration a intrinsic semiconductors pure singlecrystal material for an intrinsic semiconductor, the concentration of electrons in the conduction band is equal to the concentration of holes in the valence band. Where, n is the magnitude of free electron concentration, p is the magnitude of hole concentration and. Electron concentration nx hole concentration px electrical. Derive the expression for carrier concentration of. At thermal equilibrium, the creation of electronhole pairs is balanced by their recombination. The net increase in hole concentration per unit time, p p p p x x x x g r x.
Hole concentration px electrical resistivity sheet resistance fermi level ef x, electric field pn diode characteristics mos capacitor mos transistor carrier mobility. Pn diode characteristics mos capacitor mos transistor. Intrinsic semiconductor a silicon crystal is different from an insulator because at any temperature above absolute zero temperature, there is a finite probability that an electron in the lattice will be knocked loose from its position, leaving behind an electron deficiency called a hole. These equations are only valid when the semiconductor is in equilibrium and nondegenerate. As temperature increases, more number of electronshole pairs are generated. In intrinsic semiconductors, while calculating electron and. Total electron and hole concentrations may be functions of time andor position. Fdiff d limited by vibration of lattice atoms and ionized dopants.
Mar 15, 2020 where, n and p are the concentration of mobile electrons and holes respectively, e is absolute charge of each electron and hole and. Intrinsic carrier concentration physics and radioelectronics. Jul 07, 2015 even if the arsenic atom ionized twice, the second time will produce a electron hole pair like any silicon atom and reduce the hole concentration. Find the equilibrium electron concentration n 0, hole concentration p 0, and fermi level e f with respect to the intrinsic fermi level e i and conduction band edge e c.
Density ne is given by product of density states ne and a. In an intrinsic semiconductor, the number of electrons generated in the conduction band is equal to the number of holes generated in the valence band. When the electron concentration increases with x, the electrons diffuse toward the negative xdirection, resulting in the current flow toward the xdirection. Homework statement silicon is doped with an aluminum concentration of 2 x 1016 cm3 what are the free electron and hole concentrations at room temperature. Fermi level in intrinsic semiconductor physics and radio. Poor hole concentration and poor hole mobility affect algainp as well, yet, due to the smaller difference in electron and hole mobility, to a lesser degree than gan. E will be occupied by an ideal electron in thermal equilibrium. Electron and hole transport in semiconductors in this lecture you will learn. Calculate the electron and hole concentration unde. The humerothery electron concentration rule is the rule to link the family of a. Here, is donor concentration, is acceptor concentration and is the intrinsic electron concentration. At thermal equilibrium, the creation of electron hole pairs is balanced by their recombination. Determine the thermal equilibrium electron and hole concentrations for a given doping concentration. If the acceptor concentration is larger than the donor concentration, the hole.
Even after the field has passed its maximum value, the electronhole concentration continues to grow because the secondary carrier generation rate still remains above its average value. The calculated mobility values should have been rounded to three significant figures but we thought it would be interesting to leave them this way. If n is the concentration of conductionband electrons and p the concentration of valenceband holes, the electron hole recombination rate is proportional to the product np, according to the general law of mass action of chemical physics. When carriers are present there is a current flow, this only occurs if a bond is broken causing an electron to be in the conduction band andor a hole being created in the valence band of a band diagram. The difference in electron concentration between the two points n 1 and n 2. The net increase in hole concentration per unit time is the difference between the flux of holes entering and leaving the volume a. Both electron and hole mobilities are positive by definition. This explains why droop in algainpbased leds is only observed at very low temperatures shim et al. Enee 3, spr 09 supplement ii examples on doping and. Hence the free electron concentration n and hole concentration p increases by same amount.
May 06, 2015 electron concentration electrons per unit volume in conduction band is derived with the boltzmann approximation. If n is the concentration of conductionband electrons and p the concentration of valenceband holes, the electronhole recombination rate is proportional to the product np, according to the general law of mass action of chemical physics. If the semiconductor is ideally pure, then there would be the same number of free electrons and holes. Equilibrium electron and hole concentration from doping here is a list of new things we learned yesterday. Other articles where electronhole pair is discussed. How to find hole concentrations if the donor acceptor and. This is an ntype material, as it is doped with donor atoms. The holeconcentration in the valence band is given as the electronconcentration in the conduction band is. These levels may or may not be occupied by an electron. Finding the hole concentration in a semiconductor youtube. Doping donors and acceptors and charge neutrality 6. Finding the electron concentration in a semiconductor youtube. As temperature increases, more number of electrons hole pairs are generated. The calculation of the electron and hole density in a semiconductor is further illustrated by figure 2.
Chapter 11 density of states, fermi energy and energy bands. A formula for the intrinsic carrier concentration in silicon as a function of temperature is given by misiakos3. Effective mass in reality, an electron in a crystal. Massachusetts institute of technology department of electrical engineering and computer science.
What is the best electronhole concentration measurement method. Even after the field has passed its maximum value, the electron hole concentration continues to grow because the secondary carrier generation rate still remains above its average value. After much trial and tribulation, i am finally able to describe how we calculate the electron concentration of an intrinsic semiconductor under. Once we know how to determine the carrier distribution, we can find the carrier concentration by integrating over all energies. A semiconductor has equal electron and hole concentration. Derive the expression for carrier concentration of electron and holes it intrinsic and extrinsic semiconductor. E is the magnitude of the electric field applied to a material, v d is the magnitude of the electron drift velocity in other words, the electron drift speed caused by the electric field, and is the electron mobility.
The intrinsic concentration depends on temperature, due to thermal generation. The force that drives electrons and holes through a circuit is created by the junction of two dissimilar semiconducting materials, one of which has a tendency to give up electrons. The hole concentration in equilibrium is written as a function of the electron density by using the mass action law. Intrinsic semiconductor a silicon crystal is different from an insulator because at any temperature above absolute zero temperature, there is a finite probability that an electron in the lattice will be knocked loose from its position, leaving behind an electron deficiency called a hole if a voltage is applied, then both the electron and the hole can contribute to a small current flow. This equation can be used to calculate the exact position of the fermi energy.
Carrier concentration a intrinsic semiconductors inst. Problem 1 a piece of silicon is doped with na 2x10 cm and. Even if the arsenic atom ionized twice, the second time will produce a electronhole pair like any silicon atom and reduce the hole concentration. Electron concentration electrons per unit volume in conduction band is derived with the boltzmann approximation. Berkeley ee143 f2010 lectre 21 2 electron and hole concentrations for homogeneous semiconductor at thermal equilibrium n. How to calculate the impurity carrier concentration in a host. It states that, under thermal equilibrium, the product of the free electron concentration and the free hole concentration is equal to a constant square of intrinsic carrier concentration. Conductivity of intrinsic semiconductor your electrical home. These electrons and holes are responsible for conduction. The n o p o product relationship can then be used to solve for the electron concentration.
Total electron and hole concentrations may be functions of time and or position. In intrinsic semiconductor, when the valence electrons broke the covalent bond and jumps into the conduction band, two types of charge carriers gets generated. When an n type semiconductor is compensated, doped with both acceptors and donors n d n a n i and n a is nonzero, the equations may be simplified similarly to case 3 because we can still neglect n i in the equation for n o. According to equation 3 higher the carrier concentration n or p higher the mobility. This will determine the accumulated mobile electron density. The hole concentration in the valence band is given as the electron concentration in the conduction band is given as. Hence the electron carrier concentration is equal to the hole carrier concentration. Hole concentration an overview sciencedirect topics.
On doping with certain impurity, electron concentration. Excess electron and hole concentrations may be functions of time and or position. Hence, the electron concentration at this point will have a small value. Finding free electrons and hole concentration physics forums. The hole concentration in thermal equilibrium can be written as a function of the electron density by using the mass action law.
Calculate the electron and hole concentration under steadystate illumination in an ntype silicon with gl 1016 cm3 s1, nd1015 cm3, and tau n tau p10 mu s. The calculation of the electron and hole density in a semiconductor is further. The n o p o product relationship is one of the most useful equations because once you know one of. In intrinsic semiconductors, while calculating electron and hole concentration why always eefegkt and e. The calculation of the electron density starts by assuming that the semiconductor is neutral so that there is a zero charge density in the material. A semiconductor has equal electron and hole concentration of.
Since in a normal atom or crystal lattice the negative charge of the electrons is balanced by the positive charge of the atomic nuclei, the absence of an electron leaves a net positive charge at the holes. Electron concentration an overview sciencedirect topics. Another way to say a semiconductor is nondegenerate is that the fermi level, e f, is more than 3kt from any of the states for which we are counting electrons. Similarly, when the hole concentration increases with x, the holes diffuse toward the negative xdirection. How to calculate the impurity carrier concentration in a. Thermal electron and hole generation rates cm3s1 thermal equilibrium electron and hole recombination rates cm3s1 excess electron and hole generation rates cm3s1. They are free electrons and holes the number of electrons per unit volume in the conduction band or the number of holes per unit volume in the valence band is called intrinsic carrier concentration. It should be noted that the direction of current is opposite compared to electron.
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