Dr. Nasim Zafar Electronics 1 EEE 231 – BS Electrical Engineering Fall Semester – 2012 COMSATS Institute of Information Technology Virtual campus Islamabad

Semiconductor device lab.KwangwoonUniversity Semiconductor Devices. Carrier Transport in Semiconductors Lecture No: 5  Diffusion of Carriers  Diffusion Processes  Diffusion and Recombination  Continuity Equations  Einstein Relation Nasim Zafar

Carrier Diffusion: Introduction:  When excess carriers are created non-uniformly in a semiconductor, a “concentration gradient” results due to this non-uniformity of the carrier densities in the sample. This concentration gradient, for electrons and holes, will cause a net motion of the charge carriers from the regions of high density to the regions of low carrier density. This type of carrier motion is called Diffusion and represents an important charge transport process in semiconductors.  Thus, the charge carriers in a semiconductor diffuse, due to the concentration gradient by random thermal motion and under going scattering from:  The lattice vibrations and  Ionized Impurity atoms.

Carrier Diffusion: Introduction:  When excess carriers are created non-uniformly in a semiconductor, a concentration gradient results due to this non-uniformity of the carrier densities in the sample. This concentration gradient, for electrons and holes, will cause a net motion of the charge carriers from the regions of high density to the regions of low carrier density.  This type of carrier motion is called Diffusion and represents an important charge transport process in semiconductors.

Carrier Diffusion: Introduction:  Thus, the charge carriers in a semiconductor diffuse, due to the concentration gradient by random thermal motion and under going scattering from:  The lattice vibrations and  Ionized Impurity atoms.

Carrier Diffusion: How can we produce a concentration gradient in a semiconductor?  By making a semiconductor or metal contact.  By illuminating a portion of the semiconductor with light, (next slide).  As the carriers diffuse, a diffusion current flows. The force behind the diffusion current is due to the random thermal motion of the carriers.

Photo Generation and Diffusion: Current mechanisms Drift Current Diffusion Current photons Contact with a metal

Photo Generation and Diffusion:  By shining light, electron-hole pairs can be produced when the photon energy>E g.  The increased number of electron-hole pairs will move toward the lower concentration region, until they reach their equilibrium values.  So there is a net number of the charge carriers crossing per unit area per unit time, which is called flux.  Units: [Flux] = m -2 – S -1

Diffusion Flux : Fick’s first law Diffusion Flux ∞ Concentration Gradient dn/dx [Flux] = m -2 – S -1 D = v th l, [ D] = m 2 /S  D measures the ease of carrier diffusion in response to a concentration gradient.  D limited by vibrations of lattice atoms and ionized dopant impurities.

Diffusion Flux :  For Electrons: F n = - D n dn/dx  For Holes: F p = - D p dp/dx D n = electron diffusion coefficient D p = hole diffusion coefficient

Einstein Relationship:  Einstein relation relates the two independent current mechanicms of mobility  with diffusion D.  n = q  n /m n * D n = kT  n /m n * ½ m*v 2 = ½ kT D n = v 2  n = l 2 /  n

Einstein Relation: Constant value at a fixed temperature

Diffusion Current Density: J Diffusion current density = charge x carrier flux

Total Current:  Diffusion Current within a semiconductor consists of: i. hole component and ii. electron component  Total Current flowing in a semiconductor is the sum of: i. drift current and ii. diffusion current:

Diffusion Current Densities:

Total Current Density: When both electric field and the concentration gradient are present, the total current density, for the electron, is given as:

Summary  Current flowing in a semiconductor consists of drift and diffusion components:  Mobility and Conductivity are highly temperature dependent.  Generation and Recombination processes were discussed. Nasim Zafar18

19 Resistivity formula J = J n + J p Drift current density Diffusion current density Total hole and electron current density Total current density Summary