**Explain Conduction in Intrinsic Semiconductors:**

Explain Conduction in Intrinsic Semiconductors – As already explained, conduction through a semiconductor is due to two mechanisms viz. drift and diffusion. The movement of charge carriers (electrons and holes) under the influence of an applied electric field E is termed as the **drift current**.

The conductivity of Ïƒ_{e }of the semiconductor due to electrons in conduction band is given as

where n is the number of electrons per unit volume of the conductor (i.e., electron density or concentration), e is the electron charge and Î¼_{e}Â is the electron mobility.

Similarly, the conductivity Ïƒ_{h}Â of the semiconductor due to holes is given as

where p is the number of holes per unit volume and Î¼_{h}Â is the hole mobility.

Since Conduction in Intrinsic Semiconductors is by free electrons as well as by holes, total conductivity Ïƒ is given as

Since in **intrinsic semiconductors** n = p = n_{i,}Â the Conduction in Intrinsic Semiconductors of holes or free electrons in the semiconductor, **intrinsic semiconductor conductivity**

Current density,

Current,

where E is applied electric field, V is the applied potential difference across the two ends of the conductor and A is the cross-sectional area of the conductor.

In case of N-type semiconductor hole concentration p_{h} is negligible and electron concentration n_{n }= N_{D}. So conductivity in N-type semiconductor

Similarly in case of P-type semiconductor electron concentration is negligible and hole concentration p_{h} = N_{A}. So conductivity in P-type semiconductor

Total current density due to drift of electrons and holes on application of electric field E,

**Intrinsic Concentration:** It has been established that the intrinsic concentration n_{i} varies with temperature according to the relation

where A_{0} is a constant and is independent of temperature, k is a Boltzmann constant in eV per K and E_{GO }is the energy gap in electron volts at zero absolute temperature, T is temperature in degrees absolute and n_{i} is concentration in number per cubic metre. A_{0} is taken as 2.33 x 10^{43}.

**Mobility:** The mobility Î¼ of charge carriers (electrons and holes) varies as T^{-m}Â over a temperature range of 100 K and 400 K. For silicon m = 2.5 for electrons and 2.7 for holes. For germanium m = 1.66 for electrons and 2.33 for holes.

The carrier currents are also due to concentration gradients in the doped material which leads to **diffusion of carriers** from high concentration region to low concentration region.

A concentration gradient exists if either the number of holes or electrons is greater in one region as compared to the rest of the region. As already explained, when a concentration gradient of carriers exists in a material, the charge carriers tend to move from the region of high concentration to the region of lower concentration. The process is called the **diffusion** and the current due to this process is called the **diffusion current**.

Let us assume that at reference plane x, the density of holes is p per m^{3}. Let the carriers have a mean free path of Î”x and mean free time of Î”t between collisions. Assuming uniform density gradient of holes as -dp/dx.

The average density of holes in the region x – Î”x and x

Flow of holes to the right per unit time,

Left directed hole flow across reference plane x per unit time,

The net rate of flow of holes is to the right and is given as

where

called the **diffusion current**.

The current density due to diffusion of holes is given as

Similarly current density due to diffusion of electrons is given as

**Total Current in a Semiconductor: **It is possible that a potential gradient and a concentration gradient may exist simultaneously within a semiconductor. In such a case, the total current is the sum of drift current due to potential gradient and the diffusion current due to charge carrier concentration gradient.

Thus,

and

The constants E_{G0}, Î¼_{e}, Î¼_{h}, D_{e}, D_{h}Â and many other important physical quantities for silicon and germanium are given in tabular form (Table 6.4).

**Einstein Relationship:** Diffusion constant D and mobility Î¼ are statistical thermodynamic phenomena. Hence they are not independent of each other. The diffusion constants D_{h} and D_{e }and mobilities Î¼_{h}Â and Î¼_{e}Â are related by Einstein’s equation given as

where V_{T} is the **volt-equivalent of temperature** and is defined as

where kâ€² is Boltzmann constant in joule/K and k is Boltzmann constant in eV/ K.

At room temperature (300 K)

**Properties of Intrinsic Semiconductors:**

The important properties of silicon and germanium are given below in tabular form (Table 6.4)