## 3 Near-Infrared Silicon Absorption Physics
### Photoconductivity and Linear Absorption
#### 3.1.2 Surface-State Absorption (SSA)  
The spatial distributions and the energies of the electrons (and holes) near and on the clean surface of a chemically pure and physically perfect crystalline solid in a vacuum differ from those of bulk silicon due to the interruption of the periodic potential at the surface. Near and on the surface, some of the wave functions are not localized, while others are localized or bound with discrete energies. In contrast, wave functions in the bulk materials are all spread out over the entire crystal, and the electron energies represented by these wave functions will group into bands (allowed energy bands) separated by gaps (forbidden energy gaps). Surface electronic states are further modified by the presence of foreign atoms on the solid surface, as well as from contact with a gas, liquid or solid. The electronic states on a clean surface in a vacuum are known as surface states, while those on a surface in contact with another material are known as interface states. In addition, the electronic states may be intrinsic, owing to the displacement of the host atoms of the two materials, making the contact or forming the  
Figure 1: Absorption spectrum of deuteron-irradiated silicon. A: normal silicon; B and C: after successive deuteron irradiations [24]. Copyright 1959, American Institute of Physics. interface--or they may be extrinsic, due to the presence of foreign atoms or molecules. Finally, we note that--since the bulk and the surface of a crystal have distinct band structures, and the solid, considered as an isolated system, must have a constant Fermi level--there is an exchange of electrons between the surface and the bulk, which, in the case of a semiconductor, generates a space charge region close to the surface [25]. Among the oxide semiconductor systems, the SiO\({}_{2}\)-Si system is the most important one. There are four general types of trapped charges: fixed oxide charge, mobile oxide charge, oxide-trapped charge and interfacial-trapped charge [26]. They are described as follows:  
_Interface-trapped charge_**:** these are positive or negative charges due to structural defects, oxidation-induced defects, metal impurities or other defects caused by radiation or similar bond-breaking processes. The interface-trapped charge is located at the Si-SiO\({}_{2}\) interface and it is in electrical communication with the underlying silicon. _Fixed Oxide Charge_**:** This is a positive charge due to structural defects (ionized silicon) in the oxide layer less than 2 nm from the Si-SiO\({}_{2}\) interface [26]. The density of this charge, whose origin is related to the oxidation process, depends on the oxidation ambient and temperature and on the silicon substrate. This fixed oxide charge is not in electrical communication with the underlying silicon. _Oxide-Trapped Charge:_ This charge may be positive or negative due to holes or electrons trapped in the bulk of the oxide. Trapping may result from ionizing radiation, avalanche injection and other mechanisms. _Mobile Oxide Charge_**:** This is caused primarily by ionic impurities such as Na\({}^{+}\), Li\({}^{+}\), K\({}^{+}\) and possibly H\({}^{+}\). Negative ions and heavy metals may contribute to this charge. We note that surface states are known to be located within the first three or four atomic layers from the surface. It means that beyond 10 A from the surface, electron states are bulk states. When a monochromatic photon beam interacts with a solid, electronic transitions give an absorption coefficient which can be very low when the solid is transparent, but which cannot exceed \(10^{-6}\) cm\({}^{-1}\), whatever the wavelength. This means that in the case of strongly absorbed photons, the main part of the absorption process corresponds to transitions between bulk states since the depth of penetration of the photon is at least in the 100 A range. Therefore, one important difficulty in using optical methods to study surface states is to recognize where surface states are effectively involved in the experimental measurements.