Fundamentals of Carrier Transport, Second Edition
Including many homework exercises and a variety of worked examples, this book is an accessible introduction to the behavior of charged carriers in semiconductors and semiconductor devices.
TABLE OF CONTENTS Fundamentals of Carrier Transport, Second Edition
2.10: Carrier-Carrier Scattering
2.10 Carrier-Carrier Scattering
When the carrier density is high, collisions between carriers are an important scattering mechanism. Two types of processes must be distinguished a binary process in which one carrier collides with another and a collective process in which a carrier interacts with the plasma comprised by the carriers.
2.10.1 Binary carrier-carrier scattering
For the binary process, which is depicted in Fig. 2.17, momentum and energy conservation dictate that
| (2.99a) |  |
Fig. 2.17: Binary collision between a carrier with momentum p and one with momentum p 2.
and
| (2.99b) |  |
where p and p ? are the momentum of the carrier before and after the collision, and p 2 and 
refer to the carrier it collides with. Although the total momentum and energy of the carrier ensemble cannot change by carrier-carrier scattering, the distribution of momenta can be affected. By altering the distribution, carrier-carrier scattering affects the average relaxation times and, therefore, the value of observables such as the average carrier velocity and energy.
To write the collision term for carrier-carrier scattering, we define a pair transition rate, S (p, p 2; p ?, ) which is the probability per unit time that carrier at p and p 2 collide and scatter to p ? and . When viewed in the center-of-mass reference frame, the binary carrier-carrier collision looks just like an ionized impurity scattering event. By analogy with eq. (2.36a) for ionized impurity scattering, we write the pair...
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