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CARRIER TRANSPORT - Coggle Diagram

- - - - Obeys Fick's Law
        
        q= electric charge,D = Diffusion constant, dn/dx =change in carriers with distance.
        
        Diffusion constant measures how well the carriers move as a result of density gradient
      - Total Current
    - - The charge carriers will move from high density region to low density region of carriers.This movement of carriers is called the diffusion current
    - - The relation between mobility and diffusion constant through the thermal voltage Vt
  - - - The mobility of a carrier is defined as the ratio of carrier's speed and the applied E-field strength, which is proportional to the relaxation time and inversely proportional to the effective mass of the carrier
    - - The moving charge carrier will produce a net current in the material. The current density depends on the charge density and the velocity.
    - - For low E-field the v-E relation is linear, however for high E-field the speed will reach the saturation velocity.
  - - - The net charge carrier density remains constant at equilibrium
      - Electron - holes pair are created
        
        Photon Absorbtion
        
        Carriers can be generated by illuminating semiconductor with light
        
        The electron-hole generation rates:
        
        Occurs when the phonon energy is large enough to raise an electron from the valence band into an empty conduction band state. Thus, the electron-hole pair are generated.
        
        Impact Ionization
        
        A process in a material by which one energetic charge carrier can lose energy by the creation of other charge carrier.
        
        Occurs when electric field in a semiconductor material increase above a certain value
        
        Carrier gain enough energy so that they can excite electron-hole pair by the impact of ionization.
        
        Impact ionization rate :
        
        G in doped material = G in intrinsic material
      - Electron moves from valence band to conduction band by gaining energy from heat or radiation
    - - A conduction band loses ebergy and re-occupies the energy state of an electron hole in a valence band
      - A process where a mobile charge carrier are eliminated
      - Recombination process
        
        Radiative recombination
        
        energy is emitted in the form of photon
        
        Non- radiative recombination
        
        No photon emitted
        
        It is passed on to one or more phonons and in the case of Auger recombination it is given off in the form of kinetic energy to another electron.
      - Type of recombination
        
        Band to band
        
        occurs when an electron moves from its conduction band state into the empty valence band state associated with the hole.
        
        Trap- assisted
        
        occurs when an electron falls into a "trap", an energy level within the band gap caused by the presence of a foreign atom or a structural defect
        
        Auger recombination
        
        a process in which an electron and a hole recombine in a band-to-band transition, but now the resulting energy is given off to another electron or hole.
- - - - Carrier Excitation
  - - - Thermal Velocity
        
        In the absence of an electric field, electrons in a semiconductor move randomly because of thermal motion.
        
        The thermal velocity is the average speed at which electrons (or holes) move between two successive collisions.
        
        Thermal velocity of electron and hole in semiconductors is constant.
      - Mean Free Path
        
        The term "mean free path" refers to the average distance travelled between collisions.
      - The carrier moves randomly in the absence of an applied electric field, moves quickly through the semiconductor, and frequently changes directions as a result of scattering.
      - The net current in any direction is zero without applied E-field.
    - - Mobility
        
        When the particle is acceralated and has reach constant average velocity
        
        Velocity is proportional to the applied electric field
      - Average Carrier Velocity
        
        By combining Newton's law and scattering force, we get:
      - :smiley: When an electric field is applied, the random motion still occurs and it has average net motion along the direction of the field.
      - :smiley: Charge carrier do not follow straight lines instead they bounce and change direction and v.
  - - - Carrier Recombination.There are three type of recombination - Band to Band - Trap-assisted - Auger recombination
        
        Band to Band: emitted photon has an energy similar to the band gap and only weakly absorbed
        Trap-assisted: electron is likely to be re-emitted to the conduction band edge
        Auger recombination : energy is given to a third carrier, an electron in the conduction band