Equilibrium carrier concentrations lesson equilibrium. Carrier diffusion diffusion particle movement flux in response to concentration gradient elements of diffusion. Quasineutrality if the dopant concentration profile varies gradually with position, then the majority carrier concentration distribution does not differ much from the dopant concentration distribution. Hence, electron current density can be written in term of quasi fermi level as followed. In this specific quasi equilibrium state this constant will be larger than ni 2, the pnproduct in thermal equilibrium. 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.
Calculating an equilibrium concentration chemistry libretexts. Equilibrium carrier concentration formulas for n and. Moreover, in the quasineutral approximation 5, 17 the charge carrier concentration at each point of the sample is equal to the concentration value that in an uniform semiconductor kept at the. Calculate the electron concentration in silicon at t 300k.
The thermalequilibrium electron concentration in cb. Sum minority carrier electron and hole diffusion currents at scr edge. We could summarize the effects in a table like the one below in which. Equilibrium carrier concentration is the number of carriers in the conduction and valence band with no externally applied bias. In this chapter, we have first described the equilibrium properties of charge carriers in a semiconductor. Carrier concentration in thz qcls is a critical component to control during growth. Lecture 5 equilibrium carrier concentration youtube. If the number of minority carriers is increased above that at equilibrium by some transient external excitation such as incident sun, the excess minority carriers will decay back to that equilibrium carrier concentration due through the process of recombination. Lecture 4 carrier generation and recombination february 12, 2007 contents. When a crystal is doped such that the equilibrium carrier concentrations n. The product of minority and majority charge carriers.
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. Dynamic and static equilibrium describe how equilibrium behaves. Below is given a simple model based on nearestneighbor pair interaction, which is essentially equivalent to the wellknown regular solution model. In thermal equilibrium, there are fundamental relationships between.
We introduced the concepts of effective density of states, mass action law, and intrinsic and extrinsic semiconductor. Quasineutrality if the dopant concentration profile varies gradually with position, then the majoritycarrier concentration distribution does not differ much from the dopant concentration distribution. The equilibrium shift ratio for the total activity at a high aerosol concentration was 1. In thermal equilibrium, there is a fundamental relationship between the. Carrier concentrations southern methodist university. So if n d is the donor concentration, for an ntype material at equilibrium. Le chateliers principle is not the same as dynamic equilibrium. Lecture 9 equilibrium carrier concentration youtube. The intrinsic carrier concentration of silicon sample at 3000 k is 1. Carrier concentration a intrinsic semiconductors inst. 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. As we approach the junction, carrier concentrations change and we get a combination of drift and diffusion.
The minority carrier hole concentration is p 0 n i 2 n 0 2. Chen electrophysics, nctu 2 equilibrium thermal equilibrium no external forces such as voltages, electric fields, magnetic fields, or temperature gradients are acting on the semiconductor all properties of the semiconductor will be independent of time at equilibrium. Calculate minority carrier diffusion current at scr edge. The fermi level is not constant through the structure. When hydrogen and iodine react they form hydrogen iodide, so the concentration of hydrogen iodide will be higher than it was in the original equilibrium conditions. The thermalequilibrium majority and minority carrier concentrations can differ by many orders of magnitude. Dec 29, 2008 lecture series on solid state devices by dr. An ntype silicon sample contains a donor concentration of nd 1016 cm3. In a slowly varying doping profile, majority carrier concentration tracks well the doping concentration. Semiconductor electrostatics in thermal equilibrium.
Equilibrium and concentration answer key vocabulary. What is the concentration of each species in the flask when equilibrium has been established. What is the lifetime of the majority carrier electrons. The expression for thermal equilibrium minority carrier hole concentration in type semiconductor is, 2. If we add the intrinsic carrier concentration to the number of free carriers we obtain by doping the semiconductor, we have the equilibrium carrier concentration of the majority carrier in the material. The number of carriers in the conduction and valence band with no externally applied bias is called the equilibrium carrier concentration. After a lot of words and math we derive simple equations we can understand and use. The equilibrium concentration of vacancies in a concentrated binary alloy, which was briefly discussed in section 6. K is the equilibrium constant or vaporliquid equilibrium ratio.
For practical doping levels at room temperature, a valid approximation is that. The ability to change the carrier concentration from its. The equilibrium carrier concentration for majority carriers is equal to the intrinsic carrier concentration plus the free carriers number added by doping the semiconductor. Dec 29, 2008 lecture 4 equilibrium carrier concentration nptelhrd. When a semiconductor is not doped, n a 0 and n d 0, the semiconductor is intrinsic and n o p o n i. Transport of nonequilibrium carriers in bipolar semiconductors.
Integrating minority carrier concentration with boundary condition and the minority electron current using diffusion length. Equilibrium carrier concentration engineering libretexts. Equilibrium shifts towards one side or the other depending on concentration, temperature, pressure, and volume. Equilibrium carrier concentration sinovoltaics zero.
Semiconductor in equilibrium tu delft opencourseware. At thermal equilibrium, the creation of electronhole pairs is balanced by their recombination. The product of minority and majority charge carriers is a constant. Lecture 8 equilibrium carrier concentration duration. Calculation of carriers concentration in a semiconductor. Gilbert ece 340 lecture 9 091712 intrinsic carrier concentrations we recall that by using the density of states and the fermi function for electrons. The concentration of minority carriers in an extrinsic semiconductor under equilibrium is a directly proportional to the doping concentration.
Developing the mathematical model for electrons and holes. It electrical characteristics such as concentration of charge carriers, depend only on pure crystal. The minority carrier concentration at the scr is an exponential function of applied bias. Electron and hole concentrations for homogeneous semiconductor at thermal equilibrium n. At the conclusion of these notes, you should be able to calculate any carrier concentration in equilibrium in a semiconductor material majority, minority, doping, fixed charge, etc. Le chateliers principle describes how equilibrium can change. Carriers concentration in intrinsic semiconductor at equilibrium. Lecture 6 equilibrium carrier concentration duration. To derive carrier concentration in thermal equilibrium condition that is in a steady state condition at a given temperature. Currents in pn junction from sze, 1981 n n p p p d n n x n w 0 2 2 w w v a v t a i p p n e n n x 2 p n n a t v x x d n p x n p n p e e 1 w 0 0 p n a t v x x l n n p n n e e.
Semiconductor in equilibrium density of states function, ge fermidirac distribution function, fe distribution function and fermi energy equilibrium distribution of electrons and holes n 0 and p 0 equation intrinsic carrier concentration fermi level for intrinsic semiconductor. Carrier concentration an overview sciencedirect topics. Calculate the concentration of minority carriers at edges of scr. This also occurs when n a and n d are approximately equal, or n i n d n a the equations for the carrier concentrations for a ptype semiconductor, n a n i and n d 0, can be simplified. View test prep calculation of carriers concentration in a semiconductor at equilibirum from electrical eee 531 at arizona state university. Thermalequilibrium concentration of electron and holes.
The minority carrier hole concentration is p 0 n i 2 n 0 1. Microwave diodes, quantumeffect, and hotelectron devices. The excess carrier will decay over time and the decay rate depends on the concentration of excess carrier. Energy bands and carrier concentration in thermal equilibrium. Lecture 5 carrier concentrations in equilibrium reading. The henrys law constant h and m have units of pressuremolar concentration and pressuremole fraction, respectively. Determine the thermal equilibrium generation rate for electrons and holes in this material. 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. The minority carrier hole lifetime is found to be p0 20 s. Find the spatial distribution of the minority carrier concentrations in each qnr. Equilibrium carrier concentrations once we know how to determine the carrier distribution, we can find the carrier concentration by integrating over all energies. To derive carrier concentration in thermal equilibrium condition that is in a steady state.
Excess carrier concentrations minority carrier lifetime reading. The concentration of each species is raised to the power of that species coefficient in the balanced chemical equation. Ravindran, carriers concentration in semiconductors iv uio. For an ntype semiconductor, the majority carrier concentration is. Equilibrium carrier concentrations equilibrium electron concentration is given by.
Equilibrium carrier concentration with impurities now lets consider the case with impurities. In the bulk most of the current is drift as there are no gradients in the concentrations. Lecture 4 equilibrium carrier concentration youtube. Karmalkar, department of electrical engineering, iit madras. Because the activation energy is low, at room temperature almost all of the donor atoms included in the crystal will give an electron to the conduction band. There will instead be separate quasifermi levels for electrons and holes, respectively. The purpose of these questions is to activate prior knowledge and get students thinking. The total number of carriers in the conduction and valence band is called the equilibrium carrier concentration. In analogy to thermal equilibrium, this quasi equilibrium state is expressed in terms of a quasifermi level, which is the quantity used in place of e f that gives the carrier concentration under non equilibrium. These equations can be simplified under a number of situations. Furthermore, we will find it useful to relate the these concentrations to the average energy fermi energy in the material. Equilibrium charge carrier statistics in semiconductors. At equilibrium, the product of the majority and minority carrier concentration is a constant, and this is mathematically expressed by the law of mass action. Equilibrium minority carrier concentration overwhelmed but.
Equilibrium carrier concentration formulas for n and p. Calculation of carriers concentration in a semiconductor at. Therefore, the new equilibrium concentration of iodine will be lower than it was in the original equilibrium. The creation of excess electrons and holes means that the semiconductor is no longer in thermal equilibrium. Since current electron and hole flow is dependent on the concentration of electrons and holes in the material, we need to develop equations that describe these. Students are not expected to know the answers to the prior knowledge.
Law of the junction is valid if minority carrier concentration is less than equilibrium majority concentration. Equilibrium concentration an overview sciencedirect topics. Equilibrium electron and hole concentration from doping mit. The approximate values of the concentrations in these three ranges are written here. Equilibrium electron and hole concentration from doping here is a list of new things we learned yesterday. Doping donors and acceptors and charge neutrality 6. Since current electron and hole flow is dependent on the concentration of electrons and holes in the material, we need to develop equations that describe these concentrations. For practical doping levels at room temperature, a valid approximation is that the number of free majority carriers is equal to the. Under thermal equilibrium conditions, the pn product remains constant, or p 0n 0n i 2, where the subscript indicates equilibrium and n i is still the intrinsic carrier concentration. Carrier statistics tells us that the electron concentration then. An equilibrium constant, k c, is the ratio of the concentrations of the products to the concentrations of the reactants at equilibrium. Not like fermi level at equilibrium, the non equilibrium quasi fermi level is affected by non equilibrium carrier concentration within the material.
971 1404 1379 1026 720 1437 1211 1398 1417 1212 577 1374 179 411 1503 894 1077 217 915 747 1122 247 31 1468 223 1128 1137 798 119 217 1249 722 1301 111 931 971 460 947 680 1499 1462 536 45 1096