To find the ratio of the drift velocity of holes to the drift velocity of electrons, we need to analyze the given information about the current and the number densities of electrons and holes.
Let's denote the following:
Number density of electrons:
neNumber density of holes:
nhDrift velocity of electrons:
veDrift velocity of holes:
vh According to the problem, the ratio of the number density of electrons to holes is:
‌=2:1So we can write:
ne=2nhThe total current density
J can be expressed as the sum of the current densities due to electrons and holes:
J=Je+JhWe also know the relationship for the current density for electrons and holes:
Je‌=neeveJh‌=nhevh Given that
‌ th of the total current is due to holes, we write:
Jh=‌JTherefore, the remaining current due to electrons is:
Je=J−Jh=J−‌J=‌J Now substituting the expressions for
Je and
Jh, we get:
‌neeve=‌J‌nhevh=‌J Dividing these two equations, we have:
‌‌=‌‌‌=‌ Substitute the ratio of the number densities
‌=‌ :
‌‌⋅‌=‌‌‌=‌⋅2=‌ Therefore, the ratio of the drift velocity of holes to the drift velocity of electrons is:
‌=‌So, the correct answer is Option D:
‌.