Band Lineup Theories and the Determination of Band Offsets from Electrical Measurements

Semiconductor heterojunctions have been used in the last decades to build devices with enhanced electrical or optoelectrical properties compared to those of equivalent homojunction devices. Examples of heterojunction devices are encountered in laser applications using band gap engineering possibilities in crystalline III-V compounds, and in bipolar transistors in crystalline silicon based electronics. More recently, heterojunctions formed between hydrogenated amorphous silicon (a-Si:H) and crystalline silicon (c-Si) were introduced for the fabrication of silicon solar cells. The main advantage of heterojunctions over homojunctions is due to the band offsets that can provide selective barriers for one type of carriers. The determination of band offsets and band lineup at the interface is thus of crucial importance. A lot of theoretical work has been devoted to this issue. In parallel, various characterization techniques have been developed to provide experimental insight into band offsets. In this chapter the principal models for band lineup at interfaces are recalled, with particular emphasis on Anderson’s electron affinity rule and Tersoff’s branch-point energy alignment theory. The application to the a-Si:H/c-Si system is discussed. Then, the principal electrical characterization tools based on capacitance and admittance measurements are presented. After a general overview of the widely used capacitance versus bias voltage technique (so-called C-V or 1/C

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method), the main potential problems and sources of uncertainty when applying this technique to the a-Si:H/c-Si system are addressed. Some features specific to the a-Si:H/c-Si interface are identified and illustrated using both numerical simulations and experimental data. These features are related to the amorphous nature of a-Si:H, e.g. the high density of band gap states, and to the existence of a strong inversion regime at the c-Si surface that can lead to two dimensional electron or hole gases. A simple technique based on the measurement of the planar conductance of a-Si:H/c-Si structures is presented. The determination of band offsets from such measurements and related modelling on both (p) a-Si:H / (n) c-Si and (n) a-Si:H / (p) c-Si structures is discussed. For interfaces used in high efficiency solar cells the band offsets are found to be 0.15 eV for the conduction band and 0.40 eV for the valence band.