Electron concentration is the number of electrons per unit volume in the conduction band of the material. Ravindran, carriers concentration in semiconductors ii. Chapter 1 electrons and holes in semiconductors nanopdf. These materials are grouped into several classes of similar behavior, the classification being based on the position in the periodic table of the elements. Electron and hole concentrations for homogeneous semiconductor at thermal equilibrium n. The concentration of electrons holes is the intrinsic concentration, ni. This electron further enters the conduction band and takes part in the conduction of current. Derive the expression for carrier concentration of electron and holes it intrinsic and extrinsic semiconductor. Jan 03, 2016 this video describes how charge carriers move in both intrinsic and extrinsic semiconductors. Knowing electron and hole densities and mobilities, one can calculate the electrical resistance of semiconductors.
Derive the expression for carrier concentration of. In an intrinsic semiconductor, the electrons generated in the conduction band is equal to the number of holes in the valence band. For example, group v elements such as as shown in fig. Therefore the electron concentration n is equal to the hole concentration p in an intrinsic semiconductor. Semiconductor doping is often proposed as an effective route to improving the solar energy conversion efficiency by engineering the band gap. Well this doesnt hold true for extrinsic semiconductors. Equilibrium electron and hole concentration from doping mit. Total electron and hole concentrations may be functions of time and or position.
Dopant concentration 1cm3 mobility cm 2 vs mobility vs doping. After increasing t by 60c, n remains the same at 1015 cm3 while p increases by about a factor of 2300 because. Doping donors and acceptors and charge neutrality 6. In solidstate physics, an electron hole usually referred to simply as a hole is the absence of an electron from a full valence band.
Example 3 determine the thermal equilibrium electron and hole concentrations in a compensated ntype semiconductor. Ravindran, carriers concentration in semiconductors iv. So if n a is the acceptor concentration, for a ptype material at. Derive the expression for carrier concentration of electron. In a semiconductor heterojunction or quantum well the electron and hole concentrations are largely determined by the conduction and valence band offsets. Phosphorous p donates an extra ethat can freely travel around. The band offsets have, historically, been difficult to.
Nc is the effective density of states in conduction band. This chapter covers the fundamentals of conduction in semiconductors. What is the hole concentration in an ntype semiconductor with 1015 cm3 of donors. The electron concentration in the conduction band is given as. Excess electron and hole concentrations may be functions of time and or position. Thermal electron and hole generation rates cm3s1 thermal equilibrium electron and hole recombination rates cm3s1 excess electron and hole generation rates cm3s1. 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 hole left behind by that electron does, and is counted in the hole concentration p. Intrinsic semiconductor and extrinsic semiconductor energy. Electron concentration nx hole concentration px electrical. Intrinsic carrier concentration physics and radioelectronics. The fermi level, ef, is related to the density of electrons and holes in the. Since there are many extra electrons in ntype material due. Intrinsic semiconductor and extrinsic semiconductor. Because the activation energy is low, at room temperature almost all of the acceptor atoms included in the crystal will accept an electron from the valence band. In intrinsic semiconductor, when the valence electrons broke the covalent bond and jumps into the conduction band, two types of charge carriers gets generated. N d where n o is the free electron concentration in the ntype material and n d is the donor concentration number of added impurity atomscm3. Ravindran, phy02e semiconductor physics, 17 january 2014.
Density of electron energy states bond easily filled leaving mobile hole. Electron concentration electrons per unit volume in conduction band is derived with the boltzmann approximation. These electrons and holes are responsible for conduction. In order to understand the operation of these devices, the basic mechanism of how currents. Estimate the electrical conductivity of intrinsic silicon at 300 k, given that the electron and hole mobilities are m vs and m vs. The n o p o product relationship can then be used to solve for the electron concentration. Consider a silicon semiconductor at t 300k in which n d 1016 cm3 and n a 3 x 1015 cm3. There will instead be separate quasifermi levels for electrons and.
Based on the photomultiplication measurements on pin and nip diodes, the temperature dependence of the electron and hole ionisation coefficient from 20 300 k in in 0. The fermi level is not constant through the structure. Electron and hole transport in semiconductors in this lecture you will learn. Charge carriers electrons and holes in semiconductors.
Extrinsic semiconductors this classi cation is related to the purity of the semiconductors. Mar 16, 2019 this electron further enters the conduction band and takes part in the conduction of current. May 18, 2020 the probabilities for electron occupation and hole occupation are represented by equations one and two respectively. There are two di erent types of extrinsic semiconductors. Equilibrium electron and hole concentration from doping here is a list of new things we learned yesterday. Lecture 3 electron and hole transport in semiconductors.
The ability to controllably change the doping in different regions of a. In this problem the hole concentration is given and intrinsic carrier. Extrinsic material this is a type of impure semiconductor that has been doped in order to enhance its conductivity. 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. The hole concentration in the valence band is given as. Electronhole condensation in semiconductors science. Liquid metallic drops 1 to 300 m in size are formed, with lifetimes ranging from 0. The total electronhole concentration per unit volume is found by integrating the corresponding function over the entire conductionvalence band energy. At thermal equilibrium, the creation of electron hole pairs is balanced by their recombination. T is the absolute temperature of intrinsic semiconductor. Semiconductors crystal structure and bonding semiconductors include a large number of substances of widely different chemical and physical properties. Intrinsic or pure semiconductors are those that are ideal, with no defects, and. 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.
The electron and hole concentrations are closely linked to the fermi level. Semiconductors are materials which have a conductivity between conductors generally metals and nonconductors or insulators such as most ceramics. The materials introduced in this chapter will be used repeatedly as each new device. The hole concentration in equilibrium is written as a function of the electron density by using the mass action law. 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. What is the carrier concentration in undoped semiconductor.
A semiconductor that has a hole concentration that is greater than the electron concentration is known being ptype. Hole concentration an overview sciencedirect topics. A unique property of diamond that differs from other conventional semiconductors is the appearance of ptype surface conductivity with a sheet hole concentration of 10 cm. The statistics has sofar only considered semiconductors in thermal equilibrium.408 173 168 115 615 846 467 1444 745 830 235 375 1324 1627 1664 1053 13 187 1571 885 1444 815 1501 1488 976 541 1289 512 658 952 94 426 1253 198 801 1151 596