Drift and Diffusion Transport

DRIFT AND DIFFUSION TRANSPORT

The net current flow in a semiconductor is due to two types of transport, viz.

1. Drift transport

2. Diffusion transport

1. Drift transport

In general, the movement of a charge carrier will be like a wave model rather than a particle model in a defect free crystal. i.e., the electrons move freely in a defect free crystal.

However, in the absence of external electric field the random motion of charge carriers will not contribute current, because, the charge movement in one direction will be balanced by the charge movement in the other direction.

Now, when the external field is applied, then the electrons are attracted to the positive terminal and the holes are attracted to the negative terminal. This net movement of charge carriers are termed as drift transport.

Here, it should be noted that the drift transport overcomes the thermal movement and result in the current flow through the material.

The current density due to electron drift is

J_e = n_e ev_d …..(1)

Since drift velocity v_d ∞ E (Field applied)

V_d=μ_e E ……(2)

Substituting eqn (2) in eqn (1) we can write

J_e = n_ee μ_e E ……(3)

Similarly,

The current density due to hole drift is

J_h=n_he μ_hE …...(4)

Total drift current is J=J_e+J_h …..(5)

Substituting equations (3) and (4) in equation (5) we get

J = n_ee μ_e E + n_he μ_hE

[or] J = [n_ee μ_e + n_he μ_h] E ……(6)

We know J = σ E ……(7)

Comparing equations (6) and (7) we can write the σ = n_eeμ_e+ n_he μ_h

For intrinsic semiconductors n_e= n_h= n_i

 σ_i = n_i e [μ_e + μ_h] ……(8)

2. Diffusion transport

We know, while doping excess charge carriers are introduced in the material, which may cause non-uniform distribution of charge carriers at some places.

Now, when electric field is applied to the semiconductor, in addition to the drift motion, the charge carrier also move by diffusion at the places where we have non-uniform concentration of charge carrier in the material.

The charge carriers move from the region of higher density to lower density, in order to attain uniform distribution. This transport phenomena is called as diffusion transport.

Thus we can say that the concentration of charge carrier (Δn_e) varies with distance (x) in a semiconductor.

i.e., The Rate of flow of charge carriers is ∞ ∂/∂x(Δn_e)

The negative sign indicates that the movement of charge carries is in the direction of negative gradient.

Rate of flow of electrons

Rate of flow of electrons = -D_e∂/∂x(Δn_e)

Where D_e→ electron diffusion coefficient

Current density due to electrons

We know Current density J_e = Charge of electron ×  Rate of flow of electrons

J_e = [-e] [-D_e ∂/∂x (Δn_e)]

(or) J_e = e D_e ∂/∂x (Δn_e) ….(9)

Similarly, we can write

Rate of flow of holes

Rate of flow of holes = -D_h∂/∂x(Δn_h)

Where D_h→ hole diffusion co-efficient.

Current density due to holes

We know Current density due to holes, J_h = Charge of hole ×  Rate of flow of holes

J_h = [+e] [-D_h∂/∂x(Δn_h)]

J_h = [-eD_h∂/∂x(Δn_h)] .....(10)

Drift and diffusion current

Thus, if an electric field is applied to the semiconductor, the total current contribution is due to both drift and diffusion transport.

Total current due to electrons

The total current density due to electrons can be written as

J_e (Total) = J_e (drift) + J_e (diffusion)

Substituting equations (3) and (9) in the above equation, we get

 ………(11)

Total current due to holes

Similarly the total current density due to holes can be written as

J_h(Total) = J_h (drift) + J_h (diffusion)

Substituting equations (4) and (10) in the above equation, we get

 ………(12)

J(Total) = J_e (Total) + J_h (Total)

Net current due to both electrons and holes

The Net current due to both electrons and holes can be obtained by adding equations (11) and (12), as

………(13)

The above equation (13) represents the total current density due of drift and diffusion of electrons and holes in semiconductors.