Showing papers by "Boris I Shklovskii published in 1984"

Electronic properties of doped semiconductors

Abstract: First-generation semiconductors could not be properly termed "doped- they were simply very impure. Uncontrolled impurities hindered the discovery of physical laws, baffling researchers and evoking pessimism and derision in advocates of the burgeoning "pure" physical disciplines. The eventual banish ment of the "dirt" heralded a new era in semiconductor physics, an era that had "purity" as its motto. It was this era that yielded the successes of the 1950s and brought about a new technology of "semiconductor electronics." Experiments with pure crystals provided a powerful stimulus to the develop ment of semiconductor theory. New methods and theories were developed and tested: the effective-mass method for complex bands, the theory of impurity states, and the theory of kinetic phenomena. These developments constitute what is now known as semiconductor phys ics. In the last fifteen years, however, there has been a noticeable shift towards impure semiconductors - a shift which came about because it is precisely the impurities that are essential to a number of major semiconductor devices. Technology needs impure semiconductors, which unlike the first-generation items, are termed "doped" rather than "impure" to indicate that the impurity levels can now be controlled to a certain extent."

Variable-Range Hopping Conduction

Abstract: This chapter deals with hopping conduction at temperatures which are so low that typical resistances between neighboring impurities become larger than those connecting some remote impurities whose energy levels happen to be very close to the Fermi level In this case the characteristic hopping length increases with lowering temperature (hence the name variable-range hopping, or VRH), and for a constant density of states one obtains the celebrated Mott’s law Derivation of this law is given in Sect 91 In that section it is also discussed how Mott’s law should be modified in the presence of a Coulomb gap Section 92 studies the effect of a magnetic field on hopping conduction in the VRH regime Section 93 describes a peculiar size effect which occurs in thin films of amorphous semiconductors with VRH conduction, and arises due to the finite volume accessible to current Finally, in Sect 94 we discuss theory of the pre-exponential factor in hopping conductivity, and compare results of different authors and their approaches to this problem

A General Description of Hopping Conduction in Lightly Doped Semiconductors

Abstract: This chapter is concerned with the basic experimental facts related to hopping conduction, and the simplest models used in their interpretation. Section 4.1 describes the range of temperatures and degrees of compensation for which electrical conduction in semiconductors occurs by the hopping mechanism. It also shows the typical dependences of hopping conductivity on the temperature and impurity concentration. Section 4.2 shows how, following Miller and Abrahams, one can reduce the problem of calculating the hopping conductivity to that of calculating the conductivity of a random network of resistors connecting donor pairs. Naive approaches to that problem based on averaging either resistances or conductances are critically considered.

The Structure of the Impurity Band for Lightly Doped Semiconductors

Abstract: The problem of calculating the impurity-band structure (i.e., finding the Fermi level, the density of states, and so on) cannot be solved analytically in general. A detailed investigation of the impurity band has been carried out recently by computer (Chap. 14). In the present chapter we formulate the problem (Sect. 3.4), and discuss its solutions in the limiting cases of low compensation (Sects. 3.2 and 3.3) and high compensation (Sect. 3.4).

Electronic States in Heavily Doped Semiconductors

Abstract: In this chapter we use the quasiclassical method to study electronic states in a heavily doped semiconductor The advantage of this method lies in its simplicity and physical transparency With its help we can obtain a description of the density of states “tails” in the forbidden gap

Correlation Effects on the Density of States and Hopping Conduction

Abstract: In this chapter it is shown that the density of states has two humps in its dependence on energy. Because of Coulombic correlations, the density of states vanishes at the Fermi level. This has an important effect on the temperature dependence of hopping conduction, especially in the variablerange hopping region. The existence of correlation implies that the random resistor network model, which underlies the theory of hopping conduction desribed in the preceding chapters, becomes strictly speaking inadequate. The model remains useful for physical problems, but its use requires special justification.

Hopping Conduction in a Magnetic Field

Abstract: Measurement of magnetoresistance is a common tool in semiconductor physics. When the conduction is due to band carriers, the resistivity has a power-law dependence on the magnetic field. The theory of this phenomenon is well developed. The effect of the magnetic field is taken into account with the help of a kinetic equation or an equation for the density matrix.

Localization of Electronic States

Abstract: In the preceding chapter we considered the structure of electron states in the vicinity of a single impurity center. We now proceed to the most fundamental questions in the theory of doped semiconductors: how do impurity states belonging to different centers influence one another, and what is the resultant energy spectrum for a crystal containing a finite concentration of impurities?

The Structure of Isolated Impurity States

Abstract: This chapter is a brief introduction to the theory of impurity centers in semiconductors. The reader interested in more detail is recommended a review by Kohn [1.1], the more recent one by Bassani et al. [1.2], and the book by Bir and Pikus [1.3].

Activation Energy for Hopping Conduction

Abstract: In this chapter we shall be using the percolation method to calculate the activation energy є 3 for hopping conduction. The simplest and most accurate solution for this problem is available in the case of low compensation (Sect. 8.1). For this case we shall give a detailed comparison of the theory with experimental data. Behavior of the activation energies є 1 and є 3 in the limit of K → 1 is discussed in Sect. 8.2. As K → 1, both energies increase because of the lowering of the Fermi level into the forbidden gap (cf. Sect. 3.4). Section 8.3 develops a perturbation method for percolation theory and proves that in a lightly doped semiconductor the activation energy є 3 is independent of the temperature at any degree of compensation. The perturbation theory recipe is then used to calculate the activation energy for an isoelectronic solid solution of different semiconductors — when the main contribution to the impurity level scatter results not from the Coulomb interaction but from fluctuations in the composition of the solution within the volume of an impurity state.

The Density-of-States Tail and Interband Light Absorption

Abstract: In this chapter we describe the “optimal fluctuation” method, which permits one to calculate the density-of-states exponent in the forbidden gap, where the density of states is very low. We also discuss a simple modification of this method which allows to estimate the exponent using only the Poisson distribution and elementary quantum mechanics. A classification is proposed for the types of density of states which occur in doped semiconductors. The same method is then used to describe the interband light absorption.

The Theory of Heavily Doped and Highly Compensated Semiconductors (HDCS)

Abstract: At sufficiently high degrees of compensation all heavily doped semiconductors undergo a transition from metallic to activated conduction. The purpose of this chapter is to calculate critical values of the compensation at which this transition occurs, as well as the activation energy є 1 in the nonmetallic phase. The results strongly depend on whether the impurity distribution in the semiconductor is correlated or it is of a purely Poisson form.

Modelling the Impurity Band of a Lightly Doped Semiconductor and Calculating the Electrical Conductivity

Abstract: In Chap. 3 we discussed the analytic methods of describing the impurity band of a lightly doped semiconductor. Unfortunately, these methods hold only in the limiting cases of high and low compensations, where the small parameters of the problem are the quantities (1 − K) and K. In the case of intermediate compensation such methods fail, and in order to describe the density of states over the whole energy interval one has to use computer simulations. Our group at the A. F. Ioffe Physical-Technical Institute in Leningrad began such studies in 1977.

Dependence of Hopping Conduction on the Impurity Concentration and Strain in the Crystal

Abstract: The percolation method described in Sect. 5.6 is employed in this chapter to calculate the exponential factor for hopping resistivity ρ 3. The case of isotropic impurity-state wave functions is considered in Sect. 6.1. The obtained theoretical dependence of ρ 3 on the impurity concentration is compared with a large number of experimental data for different semiconductors. On the whole, a good agreement is found. In Sect. 6.2 the theory is applied to semiconductors with anisotropic impurity wave functions, of which a typical example is n-Ge. The effect of strain on hopping conduction is analyzed. The anisotropy of hopping conductivity is calculated for the case of large strain in n-and p-Ge, where the wave functions of impurities are associated with a single ellipsoid in the electron spectrum.