22 Diffusion

Dr. Ayushi Paliwal and Dr. Monika Tomar

Introduction

Diffusion is a simplified process in which dopants or impurities are introduced in the semiconductors in order to enhance their electrical conductivity. Both single and multiple diffusion steps can be used for this purpose. The laws governing the diffusion of impurities were established many years before the development of semiconductors. It is only since reasonably defect-free materials of high purity have become available, however, that the method has become generally accepted for semiconductor device fabrication. At the present time, diffusion is a basic process step in the fabrication of both discrete devices and microcircuits.

In silicon technology, diffusion allows the formation of (a) sources and drains for metal-oxide-semiconductor (MOS) devices and (b) the active regions of bipolar transistors. This method has certain advantages like no crystal damage; thus high-quality junctions, with a minimum leakage current as compared to other techniques such as ion implantation. Diffusions are most extensively used for silicon as compared to GaAs because many advanced GaAs structures use juxtaposed layers of different materials, such as AlGaAs, and require epitaxial processes. Another reason is that the behavior of diffusion in GaAs is more complex, and less well understood than in silicon. As a result, diffusion can only be controlled precisely in special situations and hence a flexible process which it is with silicon technology.

A number of simplifying assumptions can be made in the development of diffusion theory as it applies to semiconductor device fabrication. Thus the single-crystal nature of the solid in which diffusion takes place often allows the effects of grain boundaries to be ignored. Moreover, since

• a very small number of impurities are involved, dimensional changes during the diffusion process are not cons Finally, the almost exclusive use of parallel-plane device and circuit structures has allowed the initial development of this tool, and our understanding of the basic physics of diffusion, by relatively simple mathematical methods. More recently, computer-aided methods have extended the application of these physical principles to situations where two-dimensional (and sometimes three-dimensional) effects are important.

6. Nature of Diffusion

Diffusion describes the process by which atoms move in a crystal lattice. Although this includes self-diffusion phenomena, our goal is to study the diffusion of impurity atoms that are introduced into the lattice for the purpose of altering its electronic properties. In addition to concentration gradient and temperature, crystal structure and defect concentration play an important part in this process.

The wandering of an impurity in a lattice takes place in a series of random jumps. These jumps occur in all three dimensions, and a flux of diffusing species results if there is a concentration gradient. The mechanisms by which jumps can take place are now outlined.

Interstitial Diffusion. This is illustrated in Figure 1, where an impurity atom moves through the crystal lattice by jumping from one interstitial site to the next. Interstitial diffusion requires that jump motion occur from one interstitial site to another adjacent interstitial site. This process is relatively fast, because of the large number of vacant sites of this type in a semiconductor. Impurities such as sodium and lithium move in silicon by this mechanism.

Substitutional Diffusion: Here (see Figure 2) an impurity atom wanders through the crystal by jumping from one lattice site to the next, thus substituting for the original host atom. However, it is necessary that this adjacent site be vacant; that is, vacancies must be present to allow substitutional diffusion to occur.

Since the equilibrium concentration of vacancies is quite low, it is reasonable to expect substitutional diffusion to occur at a much slower rate than interstitial diffusion. Many dopants used in silicon microcircuit fabrication are substitutional diffusers.

Divacancies are also present in the semiconductor, so that diffusion can be accomplished by movement into these sites and their energy of formation is somewhat lower than that for isolated vacancies. The diffusion of n-type impurities in GaAs has been ascribed to this type of movement.

Figure 2: Diffusion by the substitutional mechanism.

Interstitial-Substitutional Diffusion: In this case, impurity atoms occupy substitutional   as well as interstitial sites.  However,  they  only move at a significant  rate  when  in interstitial sites (by interstitial diffusion).  The dissociative mechanism, by which a substitutional impurity atom can become an interstitial, leaving behind a vacancy, can be the controlling factor for this process. As a result, the effective diffusivity is a function of the dissociation rate, and depends on both impurity concentration and crystal quality. Figure 3 illustrates this mechanism in schematic form. Copper and nickel move in silicon by this mechanism, as do zinc, cadmium, and copper in GaAs.

An alternative pathway for interstitial diffusion is the kick-out mechanism illustrated in Figure 4. Here, a rapidly moving interstitial diffuser can move into a substitutional site by displacing an atom which is already in place, resulting in the formation of a self-interstitial. The behavior of both gold and platinum in silicon has been described by this process.

Interstitialcy Diffusion: This is a modified version of substitutional diffusion. Here, as shown in  Fig.5,  interstitial   host atoms (self-interstitials) can be   annihilated by pushing substitutionally located impurity atoms into interstitial sites. These impurities can now diffuse to adjacent substitutional sites and create new self-interstitials. Thus, the interstitial position of the diffusing impurity atom is purely a transition state, in moving from one substitutional site to another. This increases the concentration of vacant substitutional sites over its equilibrium value, so that interstitialcy diffusion is somewhat faster than substitutional  diffusion. All substitutional diffusers move, in part, by this mechanism. The diffusion of boron and phosphorus in silicon is  dominated by this process.

Interchange Diffusion: This occurs when two or more atoms diffuse by an interchange process. Such a process is known as a direct interchange process when it involves an impurity and host atom, and as a cooperative interchange when a larger number of host atoms is involved. The probability of occurrence of interchange diffusion effects is extremely low.

Grain Boundary Diffusion: Diffusion also occurs by movement along dislocations and grain boundaries. This process is anisotropic, being much faster in directions parallel to the dislocation core or to the grain boundary edge than at right angles to it. Furthermore, atom movement is two or more orders of magnitude faster than that obtained by the lattice diffusion processes outlined above. Enhanced diffusion along dislocations often leads to emitter-collector shorts in bipolar devices, by the formation of “diffusion pipes”.

Combination Effects: Combination of these mechanism may occur within a crystal. For example, a certain fraction of impurity atoms may diffuse substitutionally and the rest interstitially, resulting in a two-stream process. With many substitutional diffusers, it is necessary to assume that diffusion proceeds in part by a substitutional mechanism, and partly by an interstitialcy mechanism.

Finally, it should be emphasized that diffusion describes the movement of impurities, and not their ultimate destination. Thus, it is possible that some of the diffusing species may end in substitutional sites, with others in interstitial sites.

7. Diffusion in a concentration gradient

The jumping of impurities in a semiconductor is thermally activated, and random in character. However, directed motion occurs, by diffusion, in the presence of a concentration gradient. The net flux of diffusing species is now determined for this situation, for impurities which diffuse substitutionally in the zincblende lattice. However, the arguments have broad general application to all types of diffusion mechanisms.

Consider a crystal of cross section A, divided up by a series of parallel planes at right angles to the [100] axis. Let the spacing between planes be d/√3 where d is the distance between tetrahedral sites. Figure 6 depicts the arrangement with crystal divided into layers 1, 2 and so on of the same width. Thus, each layer contains atoms (impurity and host) whose tetrahedral neighbor are in adjacent layers on either side; substitutional diffusion takes place by jump motion between tetrahedral sites. A single jump has projections of length d/√3 along the [100] direction.

For diffusion in this lattice, atoms in any one layer must jump into neighboring layers. Each atom has four such neighbors, two in the layer to the left and two in the layer to the right. Let n be the jump frequency for these atoms. Then, in time 1/n, half of the moving atoms jump right while the other half jump left, on the average.

The net fl ow of at om s across t he pl ane P i n a di rect i on x i s gi ven b y

Writing t he fl ux densi t y j as t he t i m e rat e of change of t he number of i m purities per unit are a, Eq . (4) reduces to

diffusivity with doping concentration that has been experimentally observed for substitutional diffusers. Here interaction with charged defects can play a dominant role.

7.2 Interstitial Diffusion

Interstitial diffusion involves impurity jumps via interstitial voids. These voids are arranged tetrahedrally in the zincblende lattice. Although some are occupied by point defects, their equilibrium concentration is low, even at normal diffusion temperatures (700-l100°C). Consequently, nearly all interstitial sites are available for receiving impurity atoms as they wander through the lattice. Calculation of the diffusivity under these conditions is a relatively straightforward process.

Each tetrahedral void can readily accommodate an interstitial atom. However, there is an energy barrier which must be surmounted in order for interstitially located impurity atoms to jump from one void to the next. This barrier for interstitial diffusers is periodic in nature, as shown in Fig. 7.

The jump frequency, v , is the frequency with which thermal energy fluctuations occur with sufficiently large magnitude to overcome this potential barrier. Let:

Em= activation energy of impurity migration, in eV

T = temperature of the lattice, in K

v0 = frequency of lattice vibrations, about 1013-1014/s at typical diffusion temperatures. This is the frequency with which atoms strike the poten• tial barrier depicted in Fig. 7.

Assuming a Boltzmann energy distribution, the probability that an atom has an energy in excess of Em is given by e-EmtkT_ Atoms in the zincblende lattice can jump from one interstitial site to the next in four different ways. If these jumps are uncorrelated, and all sites are vacant, the frequency of jumping is given by

This expression is in a more convenient form than Eq . (7) since it involves only measurable quantities such as volume concentration, diffusion depth, and diffusion time . It can be used to obtain the impurity distribution for a variety of diffusion conditions .

9. Summary 

• The nature of diffusion
• Diffusion in a concentration gradient discussed in detail.