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**Note**Institute:
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West Bengal University of technology
**Course:
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B.Tech
**Specialization:
**Electronics and Communication Engineering**Offline Downloads:
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INTRODUCTION
The current-voltage characteristics is of prime concern in the study of semiconductor devices
with light entering as a third variable in optoelectronics devices.The external characteristics of
the device is determined by the interplay of the following internal variables:
1.
2.
3.
4.
5.
Electron and hole currents
Potential
Electron and hole density
Doping
Temperature
Semiconductor equations
The semiconductor equations relating these variables are given below:
Carrier density:
where
is the electron quasi Fermi level and
equations lead to
In equilibrium
=
is the hole quasi Fermi level. These two
= Constant
Current:
There are two components of current; electron current density
There are several mechanisms of current flow:
(i) Drift
(ii) Diffusion
(iii) thermionic emission
(iv) tunneling
and hole current density
.
The last two mechanisms are important often only at the interface of two different materials such
as a metal-semiconductor junction or a semiconductor-semiconductor junction where the two
semiconductors are of different materials. Tunneling is also important in the case of PN junctions
where both sides are heavily doped.

In the bulk of semiconductor , the dominant conduction mechanisms involve drift and diffusion.
The current densities due to these two mechanisms can be written as
where
constants.
are electron and hole mobilities respectively and
are their diffusion
Potential:
The potential and electric field within a semiconductor can be defined in the following ways:
All these definitions are equivalent and one or the other may be chosen on the basis of
convenience.The potential is related to the carrier densities by the Poisson equation: -
where the last two terms represent the ionized donor and acceptor density.
Continuity equations
These equations are basically particle conservation equations:
Where G and R represent carrier generation and recombination rates.Equations (1-8) will form
the basis of most of the device analysis that shall be discussed later on. These equations require
models for mobility and recombination along with models of contacts and boundaries.
Analysis Flow
Like most subjects, the analysis of semiconductor devices is also carried out by starting from

simpler problems and gradually progressing to more complex ones as described below:
(i) Analysis under zero excitation i.e. equilibrium.
(ii) Analysis under constant excitation: in other words dc or static characteristics.
(iii) Analysis under time varying excitation but with quasi-static approximation dynamic
characteristics.
(iv) Analysis under time varying excitation: non quasi-static dynamic characteristics.
Even though there is zero external current and voltage in equilibrium, the situation inside the
device is not so trivial. In general, voltages, charges and drift-diffusion current components at
any given point within the semiconductor may not be zero.
Equilibrium in semiconductors implies the following:
(i) steady state:
Where Z is any physical quantity such as charge, voltage electric field etc
(ii) no net electrical current and thermal currents:
Since current can be carried by both electrons and holes, equilibrium implies zero values for both
net electron current and net hole current. The drift and diffusion components of electron and hole
currents need not be zero.
(iii) Constant Fermi energy:
The only equations that are relevant (others being zero!) for analysis in equilibrium are:

Poisson Eq:
In equilibrium, there is only one independent variable out of the three variables :
If one of them is known, all the rest can be computed from the equations listed above. We shall
take this independent variable to be potential.
The analysis problem in equilibrium is therefore determination of potential or equivalently,
energy band diagram of the semiconductor device.
This is the reason why we begin discussions of all semiconductor devices with a sketch of its
energy band diagram in equilibrium.
Energy Band Diagram
This diagram in qualitative form is sketched by following the following procedure:
1. The semiconductor device is imagined to be formed by bringing together the various
distinct semiconductor layers, metals or insulators of which it is composed. The starting
point is therefore the energy band diagram of all the constituent layers.
2. The band diagram of the composite device is sketched using the fact that after
equilibrium, the Fermi energy is the same everywhere in the system. The equalization of
the Fermi energy is accompanied with transfer of electrons from regions of higher Fermi
energy to region of lower Fermi energy and viceversa for holes.
3. The redistribution of charges results in electric field and creation of potential barriers in
the system. These effects however are confined only close to the interface between the
layers. The regions which are far from the interface remain as they were before the
equilibrium
Analysis in equilibrium: Solution of Poisson’s Equation with appropriate boundary conditions Non-equilibrium analysis:
•
The electron and hole densities are no longer related together by the inverse relationship
of Eq. (5) but through complex relationships involving all three variables Y , , p

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