00:33 Understanding recombination is crucial for device performance 03:31 Non-equilibrium conditions drive recombination and resistance 06:41 Excess carrier generation and recombination 09:37 Shining light on a semiconductor generates carriers 12:53 The total rate of particle flow within a volume is given by the difference between the current flowing in and the current flowing out. 16:12 The total rate of particle flow is determined by the difference between flow out and flow in, as well as generation and recombination rates. 20:16 There are two situations that can be approximated: when the length of the semiconductor is much larger than the diffusion length and when it is much shorter. 23:17 Diffusion length in semiconductors can significantly affect the decay behavior of excess carrier concentration. 25:55 Excess carriers in diode decay exponentially, and assumptions made in solving the continuity equation. 28:19 Continuity equation is a vital starting point in semiconductor devices 30:47 Move to p-n junction Crafted by Merlin AI.
The continuity equation for conductors in simple DC circuits is seldom found and derived in textbooks though derivations in case of semiconductors are found in several textbooks. The charge density and current density functions are related by the continuity equation (see Electricity and Magnetism by Edson Ruther Peck, McGraw Hill, 1953) which maybe derived by applying the principle of conservation of charge. Since most textbooks on circuit theory do not discuss this important aspect of the conduction process in the dc steady state in particular, I have discussed this in textbook 4 (see last frame of video 1 to be discussed below). In its most general form the equation of continuity is ∂J_x/∂x + ∂J_y/∂y + ∂J_z/∂z + ∂ρ/∂t = 0. (Eq. 1) where J is the current density and ρ is the charge density, as derived from the conservation of electric charge law. The current density J in an isotropic medium is given by the relation J = σE (Eq. 2) where E is the electric field intensity and where σ is the conductivity of the medium. [Note: The expression J = σE denotes the macroscopic view of conduction and originates from the microscopic view of motion of charges in a conductor subject to an electric field E which produces a drift velocity v given by μE, where μ is the mobility of charge in the material.] It is also written from Eq. 1 as ∂J_x/∂x + ∂J_y/∂y + ∂J_z/∂z = 0. (Eq. 3) when there is no excess charge in the conductor or that there is no unpaired charge density (lattice ion and conduction electron). In the absence of emf in a region in the circuit (say, away from the source or battery and within a small section of the conductor or a resistor), the total electric field E, may be expressed in terms of a scalar potential function U; E_x = - ∂U/∂x E_y = - ∂U/∂y, and E_z = - ∂U/∂z (Eq. 4) Eqs. (2), (3) and (4) characterize the current flow within a region of a homogeneous, linear, isotropic conductor where there is no emf. If a dc circuit of a battery and a wire is laid in a straight line along the x-axis then evidently, the presence of surface charges will guarantee that the total field E will be a constant E_x along the axis in the region. Therefore, the solution of Eq. (3) gives J_x = a constant, so using Eq. 2, we get J_x = σE_x = I/A (Eq. 5) where σ is the conductivity of the wire, I is the current in the circuit and A the cross-sectional area of the wire. Eq. 5 is the equation of continuity applicable to the steady-state in a simple DC circuit. Electrostatics and circuits belong to one science not two and it is instructive to understand Current, the conduction process and Voltage at the fundamental level as in the following two videos: i. ruclips.net/video/TTtt28b1dYo/видео.html and ii. ruclips.net/video/8BQM_xw2Rfo/видео.html The last frame References in video #1 lists textbook 4 in which a supplementary article “Charge Densities and Continuity and Prop of em signals in wires.pdf” in the pdf files folder in the CD discusses these topics in more detail with several diagrams using a unified approach and includes a description of the application of the general continuity equation in special situations like conductors in isolation and in semiconductors.
00:33 Understanding recombination is crucial for device performance
03:31 Non-equilibrium conditions drive recombination and resistance
06:41 Excess carrier generation and recombination
09:37 Shining light on a semiconductor generates carriers
12:53 The total rate of particle flow within a volume is given by the difference between the current flowing in and the current flowing out.
16:12 The total rate of particle flow is determined by the difference between flow out and flow in, as well as generation and recombination rates.
20:16 There are two situations that can be approximated: when the length of the semiconductor is much larger than the diffusion length and when it is much shorter.
23:17 Diffusion length in semiconductors can significantly affect the decay behavior of excess carrier concentration.
25:55 Excess carriers in diode decay exponentially, and assumptions made in solving the continuity equation.
28:19 Continuity equation is a vital starting point in semiconductor devices
30:47 Move to p-n junction
Crafted by Merlin AI.
The continuity equation for conductors in simple DC circuits is seldom found and derived in textbooks though derivations in case of semiconductors are found in several textbooks.
The charge density and current density functions are related by the continuity equation (see Electricity and Magnetism by Edson Ruther Peck, McGraw Hill, 1953) which maybe derived by applying the principle of conservation of charge. Since most textbooks on circuit theory do not discuss this important aspect of the conduction process in the dc steady state in particular, I have discussed this in textbook 4 (see last frame of video 1 to be discussed below).
In its most general form the equation of continuity is
∂J_x/∂x + ∂J_y/∂y + ∂J_z/∂z + ∂ρ/∂t = 0. (Eq. 1) where J is the current density and ρ is the charge density, as derived from the conservation of electric charge law.
The current density J in an isotropic medium is given by the relation J = σE (Eq. 2)
where E is the electric field intensity and
where σ is the conductivity of the medium.
[Note: The expression J = σE denotes the macroscopic view of conduction and originates from the microscopic view of motion of charges in a conductor subject to an electric field E which produces a drift velocity v given by μE, where μ is the mobility of charge in the material.] It is also written from Eq. 1 as
∂J_x/∂x + ∂J_y/∂y + ∂J_z/∂z = 0. (Eq. 3)
when there is no excess charge in the conductor or that there is no unpaired charge density (lattice ion and conduction electron).
In the absence of emf in a region in the circuit (say, away from the source or battery and within a small section of the conductor or a resistor), the total electric field E, may be expressed in terms of a scalar potential function U;
E_x = - ∂U/∂x E_y = - ∂U/∂y, and
E_z = - ∂U/∂z (Eq. 4)
Eqs. (2), (3) and (4) characterize the current flow within a region of a homogeneous, linear, isotropic conductor where there is no emf.
If a dc circuit of a battery and a wire is laid in a straight line along the x-axis then evidently, the presence of surface charges will guarantee that the total field E will be a constant E_x along the axis in the region. Therefore, the solution of Eq. (3) gives J_x = a constant, so using Eq. 2, we get J_x = σE_x = I/A (Eq. 5) where σ is the conductivity of the wire, I is the current in the circuit and A the cross-sectional area of the wire.
Eq. 5 is the equation of continuity applicable to the steady-state in a simple DC circuit.
Electrostatics and circuits belong to one science not two and it is instructive to understand Current, the conduction process and Voltage at the fundamental level as in the following two videos:
i. ruclips.net/video/TTtt28b1dYo/видео.html and
ii. ruclips.net/video/8BQM_xw2Rfo/видео.html
The last frame References in video #1 lists textbook 4 in which a supplementary article “Charge Densities and Continuity and Prop of em signals in wires.pdf” in the pdf files folder in the CD discusses these topics in more detail with several diagrams using a unified approach and includes a description of the application of the general continuity equation in special situations like conductors in isolation and in semiconductors.
Sir, its really classy session, great explanations and way of teaching. Your voice so good.
Awesome
Thank you very much sir
Summary 11:12 ,27:59
Dear Professor, Which book did you refer for the derivation of Recombination rate?
Thanks
Neaman is good
Semiconductor physics and devices by Donald A. Neamen (3rd edition 197 page no. ) 🙂
19:09
20:50
23:28
Can i prepare from this for gate
tell me also bro whether this will be good for GATE??
@@animeshgautam6197 for a good concept
@@chiracutzasap3467 can I fully trust this lecture series for my upcoming gate exam (excluding practice part because I can do practice by my own)
@@animeshgautam6197 did it work bro???
Complete