Session 5 Carrier Transport

5.1 Overview of Carrier Transport

Electronic devices rely on transport of electrons（holes）in materials. This transport occurs either under the influence of an electric field or carrier concentration gradients. The charges in a solid can be loosely classified as fixed and mobile. 1. The charges in a solid can be loosely classified as fixed and mobile. 提示：loosely有“松散的，宽松的”之意，在这里可以翻译为“粗略的，大致的”。 When an external perturbation is applied（e. g.，an electric field）the mobile charges can move from one point in space to another. In particular they can move from one contact on a device to another. The fixed charge，however，can only be disturbed slightly from its equilibrium position，but cannot move over the length of a device. 2. The fixed charge，however，can only be disturbed slightly from its equilibrium position，but cannot move over the length of a device. 提示：over the length of a device可翻译为“相当器件尺寸这一距离的”。注意本句英语是被动语态，翻译时采用主动方式，效果更好。 As shown in Fig.5.1 both fixed charges and mobile charges play an important role in the physics of semiconductors. Essentially all electronic devices such as field effect transistors，bipolar transistors，diodes，as well as optoelectronic devices，such as lasers and detectors depend upon free or mobile charges. 3. Essentially all electronic devices such as field effect transistors，bipolar transistors，diodes，as well as optoelectronic devices，such as lasers and detectors depend upon free or mobile charges. 提示：句中出现两个such as，看似多余，实际上它们分别补充说明electronic devices和optoelectronic devices。 Mobile charges are the electrons in the conduction band and holes in the valence band for semiconductors and insulators. As we have discussed in the previous chapter，in metals the mobile charges are the electrons in the conduction band.

Before discussing issues in free carrier（or mobile carrier）transport we remind the reader of the nature of electronic states in solids in Fig.5.2. In the case of the perfect crystal we see that in the conduction and valence bands the electronic states are “free”. There are no allowed energy levels in the bandgap（density of states is zero in the bandgap，as shown）. In the case of a crystal with defects we still have the free states in the conduction and the valence bands，but we also have defect-related allowed states in the bandgap region，as shown in Fig.5.2（b）. In these states（trap states）electrons are not free to move.

Fig.5.1 An overview of fixed and mobile charges in solids and their impact on physical phenomena. Semiconductor devices are dependent upon mobile electrons and holes.

Fig.5.2 A schematic of the nature of electronic states in solids：（a）for a perfect crystal，（b）for a crystal with defects.

We will first provide a simple overview of how electrons respond to applied electric fields. In Fig.5.3 we show a schematic of how electrons（holes）move through a sample when an electric field is applied.

In Fig.5.3（a）we show the situation in a good-quality crystalline material. The electron moves under the electric field force，but suffers a number of scattering processes. The scattering occurs due to various imperfections，such as defects and vibrations of atoms（due to thermal energy）. The relation between the electron velocity or distance traveled and applied field is complex. However at low fields the relation can be described by a simple relation. If we examine the distance versus time trajectory of a typical electron we observe that the electron shows a path as shown in Fig.5.3（b）. On average the electron trajectory is described by

d＝vt，v＝μE （5.1）

Fig.5.3 A typical electron trajectory in a sample（a）and the distance versus time profile（b）.

where d is the distance traveled in time t. The velocity v is proportional to the electric field applied through μ，the mobility . When the electric field is large the relationship between velocity and applied field is not so simple and will be discussed later.