240 CHAPTER 5. SEMICONDUCTOR JUNCTIONS
cannot be achieved by pure electric fields in homogeneous materials. These fields, which were
first described by Herbert Kroemer in 1957, are therefore referred to asquasi-electricfields.
In a given material, the total field acting on a hole or an electron is always the sum of the
applied field and the quasi field, or
Ee,tot = Eapp+Ee,quasi (5.6.22)
Eh,tot = Eapp+Eh,quasi (5.6.23)The applied field, which results from applying a voltage difference between the ends of the
material, will always be the same for both electrons and holes, but the quasi field could be
different for both. The band profiles in figure 5.13b and figure 5.13c can therefore be achieved
in a number of different ways. For example, the profile in figure 5.13b could be achieved in the
following two ways:
- An undoped (intrinsic) material with a graded composition and zero applied electric field
typically results in the profile in figure 5.13c. If an electric fieldEapp=−Ee,quasiis then
applied to this material, the resulting profile will be the one shown in figure 5.13b. - A uniformly dopedn-type material with a graded composition and zero applied electric
field will also result in the profile in figure 5.13b. In this case, the doping ensures that
the separation between the conduction band and the Fermi level remains approximately
constant. Notice that the resulting quasi-electric field in this structureactsonlyonminority
carriers.
Quasi-electric fields provide engineers with additional tools that can be exploited in device
design. They have proven to be very useful in decreasing transit times in devices that rely on
minority carrier transport. For example, in bipolar technology, a highly doped graded base layer
is often used to speed up the transport of minority carriers from the emitter to the collector. For
a base with uniform bandgap, minority carriers injected from the emitter must diffuse across
the base, a process that is generally slow. By using a highly doped graded base to generate a
quasi-electric field, such as was described in the second example above, minority carriers can be
swept across much more quickly, thus reducing the base transit time and improving the device
RF performance.
5.7 PROBLEMS ....................................
Temperature is 300 K unless stated otherwise.- Section 5.2
Problem 5.1A2μmthick× 10 μm Al interconnect is used in a semiconductor chip. If
the length of a particular interconnect is 1 cm, calculate the resistance of the line. Use
table 5.1 for the resistivity data.