## What is Drift Current : Derivation & Its Calculation

- Frank
- May 25, 2022
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The movement of charge carriers or electric current within the condensed matter physics & electrochemistry is known as drift current. This can be occurred because of the applied electric field over a given distance. This is frequently called the electromotive force. In a semiconductor material, once an electric field is applied then current can be generated because of the charge carriers flow within the semiconductor. The charge carrier’s average velocity within the drift current is known as drift current. The resulting current & drift velocity can be described through electron or electrical mobility. This article discusses an overview of the drift current.

### What is Drift Current?

**Derivation:** The flow of charge carriers in response to the electric field is known as drift current. This concept is frequently used in the electrons & holes context in the semiconductor. Even though, this concept is also used in metals, electrolytes, etc.

Once an electric field is applied to a semiconductor, charge carriers will begin to flow for generating current. The holes in the semiconductor will flow through the electric field whereas the electrons will flow opposite to the electric field. Here, each charge carrier flow can be described as a constant drift velocity (Vd). The sum of this current mainly depends on the attention of charge carriers & their mobility within the material.

Please refer to this link to know about What is Diffusion Current in Semiconductors and Its Derivations

### Drift Current in Semiconductor

We know that there are two types of charge carriers present in semiconductor namely electrons & holes. Once the electric field is applied to a semiconductor, then the flow of electrons will be in the direction of +Ve terminal of a battery whereas holes will flow in the direction of –Ve terminal of a battery.

In a semiconductor, the negative charge carriers are electrons and positively charged carriers are holes. We have already discussed that the direction of electrons flow will be attracted by the positive terminal of the battery whereas the holes are attracted by the negative terminal of the battery.

In a semiconductor material, the flow of electrons direction will be changed because of the continuous collision through the atoms. Every time the electron flow will strike an atom & bounces back within a random way. The voltage applied to a semiconductor doesn’t prevent the collision as well as random electrons motion; however, it causes the electrons to drift in the direction of the positive terminal.

Because of the electric field or applied voltage, the average velocity can be achieved by electrons or holes are known as drift velocity.

### Calculation

The electrons drift velocity can be given as

**V _{n} = µ_{n}E**

Similarly, the holes drift velocity can be given as

**V _{p} = µ_{p}E**

From the above equations

Vn & Vp are drift velocity of electrons & holes

µn & µp are the mobility of electrons & holes

‘E’ is applied electric field

### Drift Current Density Derivation

The density of this current because of free electrons can be written as

** J _{n}= enµ_{n}E**

The density of this current because of holes can be written as

**J _{p}= epµ_{p}E**

From the above equations,

Jn & Jp are drifting current density because of electrons & holes

e = electron charge (1.602 × 10-19 Coulombs).

n & p are no. of electrons & holes

So the density derivation of this current can be given as

**J = Jn + Jp**

Substitute the Jn & Jp values in the above equation, then we get

** = enµnE + epµpE**

** J = eE(nµn + pµp) **

### The Relation between Current and Drift Velocity

In a conductor, the length and area are denoted with l & A. Thus, the conductor volume can be given as **AI**

If the no. of free electrons for each unit volume in the conductor is ‘n’, then the whole no. of free electrons within the conductor will be A/n.

If the charge on every electron is ‘e’ then the whole charge on the electrons within the conductor is given as

**Q=A/ne**

When a voltage supply is applied across the two terminals of the conductor using a battery, then the electric field can occur across the conductor

**E = V/l**

Because of this electric field, the flow of electrons within the conductor will start to flow through a drift velocity toward the positive terminal of the conductor. Thus the time taken to cross the conductor through the electrons can be given as

**T = l/vd**

When current **I = q/t **

Substitute the Q & T values in the above equation, then we get

**I = (A/ne)/( l/vd) = Anevd**

In the above equation, A, n & e are constant. So ‘I’ is directly proportional to the drift velocity (I∞vd)

Please refer to this link to know about the What is Drift and Diffusion Current & Their Differences

### FAQs

**(1). What is drift & diffusion current within semiconductor?**

The flow of currents in a semiconductor is drift & diffusion currents.

**(2). What is the main difference between drift & diffusion current?**

This current mainly depends on the applied electric field applied: if there’s no electric field, there’s no drift current whereas diffusion current happens even though there is an electric field in the semiconductor

**(3). What is the definition of current?**

The flow of charge carriers is known as current. This can be calculated from Ohm’s law (V = IR)

**(4). What are the types of current?**

They are AC (alternating current) & DC (direct current)

**(5). What is the drift velocity formula?**

It can be calculated using the formula I = nqAvd

**(6).What are the factors that will affect the drift velocity?**

Factors like high temperature & high carrier concentration.

**(7). What are the types of semiconductors?**

They are intrinsic semiconductors & extrinsic semiconductors

**(8). Does the velocity of drift depend on the cross-sectional area?**

No, it does not depend on the cross-sectional area or the length of the wire

**(9). How diffusion current will occur in a semiconductor?**

Diffusion current can be caused by a semiconductor due to the charge carrier’s diffusion.

**(10). What is knee voltage?**

If the voltage is higher than a certain threshold, then the current will flow throughout the diode, so this is called knee voltage.

Thus, this is all about an overview of drift current in semiconductor, calculation, and its derivation. Thus, this is all about an overview of drift current in semiconductor, calculation, and its derivation. This concept mainly involves within a doped semiconductor where it includes charge carriers like electrons and holes. Once the voltage supply is given to semiconductor then we can observe the flow of the charge carriers. Depending on the charge carrier’s polarity, it gets attracted to the battery terminals. Therefore, the electric field can be applied because of the flow of charge carriers to generate the current. The essential velocity for the flow of charge carriers can be called as drift velocity. Here is a question for you, what is diffusion current?