Relación entre turismo y parques temáticos

Diffusion of impurity atoms in silicon is a necessary step for the fabrication of semiconductor devices. Controlling of doping concentration, junction depth, uniformity, reproducibility and reducing the manufacturing costs are the main goals in this field. Rapid thermal processing is one method for diffusion which is widely being used for the fabrication of solar cells. In this chapter, firstly, general diffusion theories from Fick’s diffusion equation is described for the intrinsic and extrinsic case. Secondly, the method of spin-on dopants used in this work is introduced where dopant atoms are applied directly on the silicon surface. The diffusion of phosphorus and boron into silicon from spin-on dopants using rapid thermal processing is studied. Furthermore, the resulting diffusion samples were characterized by measuring sheet resistivity, and concentration profiles. Lastly, phosphorus as a emitter and boron as a back surface field are applied to produce RTP-solar cells and their parameters are analyzed.

7.1 Basic diffusion theory

7.1.1 Models of diffusion

Diffusion in a semiconductor can be visualized as atomic movement in the crystal lattice. There are two different atomic diffusion models, i. e., Interstitial diffusion models such as interstitial, interstitialcy, and crowdion mechanisms and substitutional diffusion models such as vacancy, exchange, and ring mechanisms. Figure 7.1 shows common atomic diffusion mechanisms for interstitial (a-c) and substitutional diffusion (d-f).

In the case of interstitial mechanism atoms migrate by jumping from their original site to a neighboring equivalent one (Figure 7.1 a). An atom smaller than the host atom often moves interstitially. If the interstitial atom displaces a lattice atom, which in turn becomes an new interstitial atom, the mechanism is called interstitialcy (or kick-out) mechanism (Figure 7.1 b). The crowdion mechanism (Figure 7.1 c) is related to interstitialcy mechanism, in which an interstitial atom located half-way between two lattice sites migrates into one of the lattice sites and displaces the lattice atom which becomes an interstitial atom at the half-way position. A vacancy mechanism (Figure 7.1 d) is a migration of a substitutional atom to the neighboring site of the vacancy. When two neighboring substitutional atoms exchange these substitutional site directly, this mechanism is called exchange mechanism (Figure 7.1 e). Substitutional atoms exchange indirect with a lattice atom. This occurs through a simultaneous jump of two or more atoms. This mechanism is called ring mechanism (Figure 7.1 f). For example, the diffusion of group III and V elements in silicon are generally considered to diffuse predominately substitutionally by vacancy and self-interstitials mechanism .

(a) (b)

(d) (e) (f)

(c)

Figure 7.1 Models of atomic diffusion mechanisms for a interstitial (a-c) and

substitutional (d-f): (a) interstitial mechanism (b) interstitialcy (or kick-out) mechanism (c) crowdion mechanism (d) vacancy mechanism (e) exchange mechanism (f) ring mechanism.

7.1.2 Diffusion equations

Diffusion is the movement of particles from high concentration to low concentration. The mathematical basis for the diffusion process was published by Fick [110]. He hypothesized that the rate of transfer of a diffusing particle through unit area is proportional to the magnitude of the gradient concentration to that area. In the x-direction this Fick’s law is given by

( )

x

t

x

C

D

J

∂

∂

−

=

,

where J is a diffusion flux and C is the concentration of particles, which is assumed to be a function of position x and time t only. D is the diffusion coefficient. The negative sign indicates the opposite direction of the flux compared to the concentration gradient.

In a steady state the concentration and the flux are related according to

( )

( )

x

t

x

J

t

t

x

C

∂

∂

−

=

∂

∂

,

,

the transport equation in one dimension. Combing the transport and diffusion equations, i. e., (2.3) or (2.4) and (7.2) yields

( )

( )

_,

,

x

t

x

C

D

t

t

x

C

∂

∂

−

=

∂

∂

7.1 Basic diffusion theory 109 The concentration from the solution of Eq. (7.3) should be considered for intrinsic diffusion and extrinsic diffusion, since the properties of the diffusion coefficient for the intrinsic and extrinsic cause are different. If the impurity concentration is lower than the intrinsic carrier concentration ni (T), the silicon is considered as intrinsic silicon and the diffusion is defined by Fick’s diffusion law with a constant diffusion coefficient. When the impurity concentration is higher than ni (T), the silicon is considered as extrinsic silicon and the diffusion coefficient is not constant. Therefore, in the following section properties of diffusion are described for intrinsic and extrinsic cases.

7.1.3 Intrinsic Diffusion

7.1.3.1 Diffusivities

In the intrinsic diffusion (n (T) < ni (T)) the diffusion process occurs due to the random movement of the impurity atoms and is a thermally activated process independent of the concentration. Therefore, the diffusion coefficients determine experimentally over a range of diffusion temperatures can often be expressed as











 −

=

kT

E

D

D

exp

where Do is the frequency factor (in unit of cm2/s) and Ea is the activation energy (in eV), T is temperature (in K), and k is the Boltzmann constant (in eV/K). Figure 7.2 (left) shows the diffusion coefficient of many impurities in silicon. As shown in Figure 7.2 (left) D is a straight line in an arrhenius-plot 1/T. Do is related to the atomic jumping frequency or the lattice vibration frequency (typically 1013 _{Hz) [62].}

The activation energy Ea depends on the energies of motion and the energies of formation of defect-impurity complexes. For example, the activation energy for substitutional impurities in silicon, which includes the group III and the group V element of the periodic table, is in the range of 3 to 4 eV, while the activation energy for self diffusion in silicon is approximately 5 eV. On the other hand, the activation energy for interstitial impurities, which consists of hydrogen, helium, and the alkali metals results in the range of 0.5 to 1.6 eV [111]. Therefore, substitutional diffusion has to be thermally activated by a larger energy than interstitial diffusion, since substitutional diffusion needs not only the jumping energy comparable to the one for interstitial diffusion, but also the energy which gives rise to the vacancies.

Often in solar cells fabrication diffusion of Al, P and B are used. The diffusion coefficient of Al in Si is 8×10-13 _cm2_{/s at 980 °C. P and B are reaching the same diffusion coefficient around} 1080 °C. Therefore, for the diffusion Al needs a low temperature, whereas P and B need a high temperature.

Figure 7.2 (left) diffusion coefficient (right) solubility in silicon [111].

Table 7.1 Properties of the intrinsic diffusion of boron and phosphorus [62].

Properties Boron Phosphorus

Dominating element for diffusion (

D

D

Do [cm2/s] 0.76 3.85

Ea [eV] 3.46 3.66

Table 7.1 shows the properties of the intrinsic diffusion coefficient of boron and phosphorus in terms of dominated diffusion element, a frequency factor Do and an activation energy Ea. The boron intrinsic diffusivity is dominated by the interaction of boron with an donor-type vacancy V+ ₍ +

B i

D_, ) and for phosphorus the intrinsic diffusivity is dominated by interaction of impurity atom with the neutral vacancy Vx ₍ x

P i

D_, ) [62].

7.1.3.2 Diffusion Profile