Section A5: Current Flow in Semiconductors


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1 Section A5: Current Flow in Semiconductors Conductive behaviors in materials, defined by the parameter conductivity, are a primary factor in the development of electronic and optoelectronic devices. Electrical conductivity (denoted by the symbol σ and expressed in units of (Ωcm) 1 ) is purely a material property that describes how easily the material allows charges to move or through it, equivalently, how easily electric current can flow. Alternatively, we can talk about the resistivity (ρ) of a material, where ρ=1/σ and has units of Ωcm. Since conductive behavior is intimately tied to charge movement, it makes sense that we should take into consideration all free charges in the medium. In the modified version of Figure 3.1, we saw that electrons may break the covalent bonds that bind them to a parent atom and move throughout the material. When each electron leaves its position in the valence band, a hole is created which can be considered as a unit of positive charge (not negative is positive, right?). Looking at it from a slightly different view, and using the band edges defined in Figure 3.3, we can look at the development of charge movement (current flow) as follows: For a pure (intrinsic) semiconductor at T=0 o K, all electrons are associated with their covalent bonds. The conduction band (above energy ) is empty of electrons, while the valence band (below energy ) is full. NOTE: is the forbidden gap and is the difference between and. For a pure (intrinsic) semiconductor at T>0 o K, some electrons gain enough energy to break their bonds and jump the forbidden gap (only one shown). The conduction band now contains free electrons, while the valence band now has free holes.
2  + With a potential applied as shown, electrons in the conduction band move to the right. s in the valence band also move to the right, but move by filling a hole. This process is equivalent to holes moving to the left. NOTE: An intrinsic semiconductor is shown; i.e., the number of holes in the valence band is equal to the number of electrons in the conduction band.  + The same process applies to an ntype semiconductor; only now electrons are the majority carrier (i.e., there are more free electrons in the conduction band than holes in the valence band).  + Likewise for a ptype semiconductor; only now holes are the majority carrier (i.e., there are more holes in the valence band than electrons in the conduction band).
3  + Regardless of the semiconductor type, electron flow hole flow Conventional direction for positive current with the potential applied as shown, the net effect is as indicated in the figure. Note that both electrons and holes contribute to the total current flow. Although they are moving in opposite directions, they are of opposite charge two negatives is a positive! Remember that, at any temperature above absolute zero, a certain number of electrons gain enough energy to break their covalent bonds and become free to move in the conduction band (leaving holes free to move in the valence band). This is not a static process and there is a continuous exchange of energy between these electrons and the lattice in the form of elastic and inelastic collisions. Without an externally applied potential, the result is electron motion that is totally random, yielding a zero net movement and therefore a zero net current. Now notice that carrier movement in the above figures is due to an applied potential (and the resulting electric field), and that the charge of the carrier determines the direction of movement. This illustrates the first of two ways by which current can flow through a material and is called drift. Drift current occurs with the application of an electric field to the medium. The electric field causes a net, or directed, movement of carriers in the medium. The drift velocity of the carriers in the medium is a direct function of the electric field strength and the carrier mobility (µ n for electrons and µ p for holes), as illustrated in Equation 3.17 of your text. The drift velocity is ultimately limited by the saturation velocity in the material of interest. So how do we get current out of all this mess? We ve got moving charges, we ve got mobilities, we ve got an electric field due to an applied potential, and somehow we ve got to put it all together to get something we can use! Believe it or not, if we take the number of charges, the elemental charge and the mobility of the carrier type, we can get the current density (J) which is current per unit area and by multiplying by area we can get the total current (I). Yeah, right well, let s see how this goes
4 Starting with Equation 3.24 (with slightly modified notation from your text to be consistent with our discussions): J = q( pµ p + nµ n ) E (Equation 3.24: modified) where: J is the current density (in A/m 2 =C/m 2 s=v/ωm 2 ) q is the elemental charge ( 1.602x1019 C) n is the number of free electrons in the medium p is the number of free holes in the medium µ n is the mobility of electrons in the medium (in m 2 /Vs) µ p is the mobility of holes in the medium (in m 2 /Vs) E is the electric field strength (in V/m) Keep in mind that, although electrons and holes have opposite charge they are also moving in opposite directions. This allows us to add the contribution of each carrier type to the total current density. Using the relationship for conductivity (σ=nqµ) where N is the number of free carriers and µ is the mobility of the carrier type, we can rewrite Equation 3.24 in the form of Equation 3.21 by defining a composite conductivity term (σ = σ p + σ n ) which, believe it or not, is a form of our old friend Ohm s law: J = ( σ + σ ) E = σe p n (Equation 3.21: modified) Let s look at the units of what we ve got, 1 V V A σe in units of = = 2 2 Ωm m Ωm m Hmm.. looks like we just have to multiply by the area that the charges are moving through to get the total drift current! Another way of getting this result is illustrated by your author in Equation All he s done to Equation 3.21 here is multiply by area (to get an expression in I instead of J) and multiply and divide by L. This allows the use ρ L L R = = of the expression for resistance, A σa, along with the units of electric V I = field, to be substituted and manipulated to come up with Ohm s Law: R.
5 Pretty cool, huh? However you prefer to look at it If you ve got an applied potential, you ve got an electric field. If you ve got free charges in your medium, you ve got directed carrier movement. If you ve got directed carrier flow, you ve got net (nonzero) current flow that has possible contributions from both carrier types. At typical doping levels and normal operating conditions, it is usually valid to make the simplification: o In an ntype material, electrons are the majority carriers and the current contribution of holes is generally considered negligible (n N D, p 0). o In a ptype material, holes are the majority carriers and the current contribution of electrons is generally considered negligible (p N A, n 0). Well, that s drift for you. The second contribution to current is known as diffusion. Unlike drift, diffusion has nothing to do with the charge of the carrier and arises whenever there is a nonuniform concentration, or concentration gradient, of charges in a medium. Using the classic example, if you would spray perfume in the corner of a room, the smell (Can you tell I m not a perfume fan?) diffuses throughout the available space until it is equally spread out. This is exactly what happens when a charge concentration gradient exists they want to move, or spread out, until an equilibrium concentration is achieved. Since we ve been talking about intrinsic materials and either uniformly doped n or ptype extrinsic materials, this is a nice segue into what happens when we put these two types of extrinsic materials together.
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