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class04SolarCells2020-08p-njunctions1.pptx

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p-n junctions (1)

Prof. Richard R. King

Solar Cells

EEE 565

Arizona State University

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A pn junction is a non-linear device, a “valve” with an “easy”and a “difficult” current direction

It has an on voltage and a breakdown voltage

Circuit element

p-n junction introduction

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Different types of junctions

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p-n Junction consists of p-type and n-type material in contact with each other

Thermal equilibrium means that there are no inputs – no voltage, no extra heat, no light

When n and p-type material come into contact, electrons diffuse from n-type to p-type and vice versa (i.e., majority carriers cross junction)

Once the majority carriers have crossed the junction, they become minority carriers, and have a limited lifetime

Dopant atoms are fixed and cannot diffuse (at normal operating temperatures)

Movement of electron and holes across junction

p-n junction in equilibrium

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Electrons and holes are assumed to satisfy Poisson’s equation together with the drift-diffusion equations

Poisson’s equation (Gauss’ Law):

Transport (drift-diffusion) equations:

Continuity equations:

The following simplifications

are made here:

1) 1-dimensional device

2) Thermal equilibrium

3) Steady-state

4) Depletion approximation

Basic semiconductor equations

Recall that:

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In two- or three D, the density of states is very low at

Space-Charge Region (or depletion region)

Due to the large concentration gradient, holes in p-type region (and electrons in n-type region) diffuse across junction and leave behind ionized dopant atoms

The field due to the ionized acceptors and donors left behind creates an electric field

In equilibrium, the current is zero, therefore a space charge region (SCR) is established where the forces due to drift and diffusion exactly cancel

This region is called the depletion region in equilibrium since it is depleted of carriers, but space charge region (SCR) is a more general term that applies in forward bias as well, when the region is not depleted of carriers

Remember the direction of the arrow of the electric field points in the direction a POSTIVE charge (i.e., a hole) would move

p-n junction in equilibrium

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In two- or three D, the density of states is very low at

For a system in equilibrium, the average energy must be constant and so the Fermi level must be constant

Well away from the junction, bulk conditions dominate such that the Fermi levels are at their bulk values, E1 and E2.

At the junction, the slope in the band diagram indicates the presence of the electric fields

Band diagrams in equilibrium

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In two- or three D, the density of states is very low at

The electric field across the interface of a p-n junction gives rise to a voltage across the interface, called the built-in voltage, V0 (= o in diagram)

The built-in voltage cannot be measured by externally connecting probes to the device

V0 is due to the difference between the Fermi levels of the joined materials, and can be calculated from this

using

gives

Built-in voltage

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In two- or three D, the density of states is very low at

The difference between the Fermi level and the conduction band (valence band) gives the electron (hole) concentration

From the band diagram, we can sketch the carrier concentration

Outside of the depletion region, carriers retain their equilibrium values

Since the built-in voltage depends on the difference between the doping on either side of the junction, the carrier concentrations are related to each other by the built-in voltage

Carrier concentration in equilibrium

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In two- or three D, the density of states is very low at

The depletion region consists of a region of fixed charge corresponding to the ionized dopant atoms cores that “lost” their electrons or holes due to the diffusion current

The depletion region tails off exponentially away from the junction edge

Assuming that the depletion region charge density is zero a certain distance away from the junction edge (called the depletion region width) results in greatly simplified analysis

The above assumption is called the depletion region approximation: The depletion approximation assumes that the electric field is confined to a finite region

For constant doping it approximates the charge density as constant in the transition region and zero everywhere else

The amount of charge on the two sides of the depletion region must be equal

Depletion region properties

See, for instance, Section 6.3 in Nelson

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In two- or three D, the density of states is very low at

The width of the depletion region can be calculated by integrating the charge density in the depletion region to get the electric field, and then integrating again to get an expression for the built-in voltage, whose value we already know from the difference in the Fermi levels

Integrating once gives the maximum electric field

Integrating from -xp to xn gives the built in voltage, V0 (the area under the electric field curve)

Depletion region width

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In two- or three D, the density of states is very low at

The depletion region width is given by:

The maximum electric field increases as the doping increases and is controlled by the doping of the more lightly doped side

The depletion region width is also controlled by the more lightly doped side

Depletion region width

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In two- or three D, the density of states is very low at

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