Energy Bands

[Sunil]

Hi....We did energy bands in class a few weeks ago...i should say that
i am clueless to a certain extent....

I have no idea about what effective mass is...can someone explain the
concept behind effective mass...i mean how can mass vary???the prof
drew a graph of the second derivative of energy against k...and it was
a kind of a sinusoidal wave...the prof mentioned that the point where
the second derivative is 0 is the point where effective mass is
infinite....how can mass be infinite...if it is...wont the system
become heavy???

Also, i didn't understand the reason for drawing the graph of energy
against k....it seems to be of no real consequence....

thank you...
sunil

 

[Greg Neill]

Hi....We did energy bands in class a few weeks ago...i should say that
i am clueless to a certain extent....

I have no idea about what effective mass is...can someone explain the
concept behind effective mass...i mean how can mass vary???

Although not often covered overtly in your typical physics
classes, physics recognizes three types of mass:

1. Active gravitational mass
2. Passive gravitational mass
3. Inertial mass

They correspond to the m's in the formulae:

F = M*m/r^2

F = m*a

Thanks to what's called Einstein's equivalence principle
we say that 1, 2, and 3 are numerically equal.

Now, what you're concerned with for effective mass is the
inertial mass and the formula F = m*a. With a slight
rearrangement we have m = F/a.

Electrons in a material will interact with the material,
so that when you apply a force F to the electron (say via
an electric field), the acceleration of the electron will
be influenced not only by the applied force but its
interactions with the atoms in the material.

Think of a ball bearing in syrup. Although the ball
bearing still has the same gravitational mass, the
effective mass is increased due to the friction of
the bearing with the syrup (viscosity). To achieve the
same acceleration as a ball bearing in free space you
need to apply more force to the ball bearing in syrup,
so the m in m = F/a, the effective mass, is larger.

 

[Sunil]

Although not often covered overtly in your typical physics
classes, physics recognizes three types of mass:

1. Active gravitational mass
2. Passive gravitational mass
3. Inertial mass

They correspond to the m's in the formulae:

F = M*m/r^2

F = m*a

Thanks to what's called Einstein's equivalence principle
we say that 1, 2, and 3 are numerically equal.

Now, what you're concerned with for effective mass is the
inertial mass and the formula F = m*a. With a slight
rearrangement we have m = F/a.

Electrons in a material will interact with the material,
so that when you apply a force F to the electron (say via
an electric field), the acceleration of the electron will
be influenced not only by the applied force but its
interactions with the atoms in the material.

Think of a ball bearing in syrup. Although the ball
bearing still has the same gravitational mass, the
effective mass is increased due to the friction of
the bearing with the syrup (viscosity). To achieve the
same acceleration as a ball bearing in free space you
need to apply more force to the ball bearing in syrup,
so the m in m = F/a, the effective mass, is larger.

Yes....bt still...how can u assume effective mass to be 0 and infinite
in certain cases??

 

[James Beck]

Yes....bt still...how can u assume effective mass to be 0 and infinite
in certain cases??

Hmm, I don't know if this is applicable, but an electron in an insulator
can't be budged and one in a super conductor will move at the slightest
provication.