Chapter 5
Spin Diffusion in Silicon

”I keep six honest serving men, They taught me all I knew: Their names are What and Why and When and How and Where and Who.”
Rudyard Kipling

In order to design and fabricate high-performance silicon-based spintronic devices, a comprehensive understanding of the spin transport properties of a semiconducting channel (~ μm) is needed. In this chapter, the spin injection in silicon from a ferromagnetic semiconductor (FMS) by electrical means is investigated, when spin is injected from a charge neutral source. Even though a sufficient analysis of the spin transport under charge neutrality is available in literature [173174175], the attention there has been on the magnetoresistance. Thus, it becomes mandatory to also investigate the spin signal when the charge neutrality condition is violated. In such a case, one has to solve the spin drift-diffusion equations coupled with the Poisson equation. This is done because from the Poisson equation one can derive the electric potential (and hence the electric field) in the conducting channel, which prominently influences the spin diffusion [173]. In fact, experiments have shown that electric fields can severely affect spin diffusion in semiconductors [176177].

At first the fundamental charge transport equations [178] will be discussed. Afterwards it will be shown how to extend those equations for spin transport.

 5.1 Semi-Classical Model of Charge Transport
  5.1.1 Poisson’s Equation
  5.1.2 Continuity Equations
  5.1.3 Drift-Diffusion Equations
  5.1.4 Quasi-Fermi Levels
 5.2 Spin Transport Equations
  5.2.1 Spin Continuity Equation
  5.2.2 Spin Drift-Diffusion
  5.2.3 Discretized Form
  5.2.4 Transport Channel
 5.3 Solution
  5.3.1 Solution with Charge Neutrality Constraint
  5.3.2 Solutions without Charge Neutrality Constraint
 5.4 Spin Diffusion from a Space-Charge Layer
  5.4.1 Solution with Charge Neutrality Constraint
  5.4.2 Solution without Charge Neutrality Constraint