Semiconductor & Computer Engineering
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Where <math>m_{n,p}</math> is the mass of an electron or a hole. | Where <math>m_{n,p}</math> is the mass of an electron or a hole. | ||
| − | The problem is that electrons do not just drift through, they also collide very frequently. Let <math>\tau_c</math> represent the average time interval between collisions, then the average net velocity, or the '''drift velocity''', in the direction of the electric field will depend on the mean time the carrier travels. | + | The problem is that electrons do not just drift through, they also collide very frequently. Let <math>\tau_c</math> represent the [[mean free time|average time interval between collisions]], then the average net velocity, or the '''drift velocity''', in the direction of the electric field will depend on the mean time the carrier travels. |
:<math>v_d = \pm \frac{q E}{2 m_{n,p}} \tau_c = \pm \frac{q \tau_c}{2 m_{n,p}} E</math> | :<math>v_d = \pm \frac{q E}{2 m_{n,p}} \tau_c = \pm \frac{q \tau_c}{2 m_{n,p}} E</math> | ||
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* <math>\mu_{n,p}</math> is the [[carrier mobility]] [cm<sup>2</sup>/Vs] | * <math>\mu_{n,p}</math> is the [[carrier mobility]] [cm<sup>2</sup>/Vs] | ||
* <math>E</math> is the magnitude of the [[electric field]] being applied to a material. | * <math>E</math> is the magnitude of the [[electric field]] being applied to a material. | ||
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| + | Therefore the drift velocity for electrons is: | ||
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| + | :<math>v_{\text{dn}} = - \mu_n E</math> | ||
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| + | and for holes: | ||
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| + | :<math>v_{\text{dp}} = \mu_p E</math> | ||
Latest revision as of 13:05, 23 November 2017
Drift velocity () is the average net velocity of a charge carrier in the direction of the electric field. Drift velocity is expressed in cm/s.
Overview[edit]
Without an electric field being applied, electrons in a material move about randomly due to the thermal velocity of the material. Despite moving at very high velocities, with lots of random collisions, the mean free path ends up being roughly zero. That is, the electrons do not go anywhere. When an electric field is applied across the material, there is a new net force on the carriers.
In between collisions, the carriers accelerate in the direction of the electrostatic field. We can use the equation for the velocity at constant acceleration to model this.
Where the acceleration , from Newton's second law of motion is:
- , therefore
Therefore we can say that the velocity of the carriers are:
Where is the mass of an electron or a hole.
The problem is that electrons do not just drift through, they also collide very frequently. Let represent the average time interval between collisions, then the average net velocity, or the drift velocity, in the direction of the electric field will depend on the mean time the carrier travels.
Where
is the carrier mobility.
Note that the equation can be expressed in the form of Ohm's law.
Where,
- is the drift velocity [cm/s]
- is the carrier mobility [cm2/Vs]
- is the magnitude of the electric field being applied to a material.
Therefore the drift velocity for electrons is:
and for holes: