Question

Taking pure silicon (Si) as an example, explain what is meant by the terms electron-hole generation and recombination, how they affect the electrical conductivity, and define what is meant by the "intrinsic carrier density", n. [5 marks] Q3. a) b) With the aid of both lattice and energy band diagrams, explain how n-type doping of Si is achieved and state two types of suitable dopant atoms. [7 marks] c) An n-type region on a Si wafer has a donor concentration of 3.3 x 1022 per m³. A resistive track is formed in this region, which is 60 um wide and 750 um long. The doping can be assumed to be uniform to a depth of 0.89 µm. (i) Calculate the densities of the majority and minority carriers in the doped Si. [2 marks) (ii) Calculate the electrical conductivity of the doped Si, and the factor by which it has increased compared with pure (i.e. intrinsic) Si at room temperature. [4 marks] (iii) If a potential difference of 2 V is applied across the ends of the track, calculate the resulting drift current that flows. [3 marks]

Answer 1

a) An empty state in the valence band is referred to as hole. If the conduction band electron and the hole are created by the excitation of a valence band electron to the conduction band, they are called an electron-hole pair and the process is called electron-hole pair generation. Similarly, when an electron from the conduction band jumps back to the valence band and combine with a hole, the process is called electron-hole recombination. The equilibrium number of electron-hole pairs in pure Si at room temperature is about 10¹⁰ EHP/cm³, compared to the Si atom density of more than 10²² atoms/cm³. Thus the few electrons in the conduction band are free to move about via the many available empty states. This contributes to the increased conductivity. Intrinsic carrier density refers to the number of electrons (or holes) in the conduction (or valence) band in the case of zero doping.

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