Doping Profiles and 1D Approximations in the Diode...

Doping Profiles and 1D Approximations

in the Diode Structure

ELEC 3908, Physical Electronics, Lecture 6

ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-2

Lecture Outline

•

Previous lecture examined the fabrication of three planar diode structures

•

Now look in some detail at two aspects of the basic structure–

Doping profile: the spatial (with distance) variation of doping concentration within the structure, and one-dimensional or 1D approximations

–

The flow and spreading of current, and the relevant area to use in scaling currents in varying sized devices

–

The concept of current density, an area-independent quantity


Dopant

Diffusion in Three Dimensions (3D)•

When dopant

is introduced into the substrate, atoms can move in all 3 directions (3D)

•

The doped region therefore extends down into the substrate and outside the masking window

•

Following terminology used:–

Internal region: the area inside the window opening, away from the area of lateral diffusion

–

Peripheral region: the area outside the window, i.e. at the edges


Constant Doping Contours in 3D•

In the internal area, constant doping contours are flat sheets, since concentration is uniform across a given depth

•

In the peripheral area, contours bend upwards to reflect lateral diffusion outwards from window

•

A doping vs. dimension characteristic is called a doping profile


2D Approximation to 3D Doping Profile•

If a slice in the x-y plane is taken through the device at a value of z away from the end regions, a two-dimensional (2D) approximation is obtained (i.e. the “front”

of the previous structure)

•

Constant doping contours represent the effect of lateral diffusion towards the sides of the device

•

Internal region is again characterised by flat contours -

no lateral component

ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations -6

Surface Plot of 2D Doping Profile•

The spatial variation of doping can also be visualized using a surface plot

•

For generality, plot ln

of the absolute value of the difference NA -ND vs. position in the x-y plane

•

When NA =ND , ln(|NA -ND |) →

−∞, so a change in doping between n and p-type is indicated by a sharp drop towards -∞

•

Lateral diffusion is evident from the curved side regions


Surface Plot of 2D Doping Profile -

Half Plot•

Plot to the right is the same as the previous, but only half the surface is shown -

from the middle of the internal region outwards

•

The front edge of this plot illustrates the variation of doping density with depth in the internal region

•

This 1D doping profile holds for any point in the internal region


1D Doping Profile

•

Plotting |NA-ND | (log scale) vs. depth intothe substrate (x) in the internal regionleads to the plot shown to the right

•

The presence of the metallurgical junction is indicated by the drop of the curve at x=1.0 μm

•

When the doping of the implanted region is much higher than that of the substrate, the junction is termed one-sided


1D Doping Plot –

Implant and Substrate Dopings•

The figures on the right show how the doping profile is constructed, on linear axes (so the negative portion can be shown)

•

Nimplant -

Nsubstrate is positive where, Nimplant > Nsubstrate and negative where Nimplant < Nsubstrate

•

The absolute value of the difference |Nimplant –

Nsubstrate | passes through zero where the two are equal –

on a log ordinate, the curve dips to -∞

NsubstrateNimplant

N - Nimplant substrate |N Nimplant - substrate|

x

x x

x


Uniform Doping Approximation•

Analytic models difficult to derive if accurate doping variation taken into account

•

Use a uniform approximation to the characteristic -

assume implanted region has constant doping at maximum value

•

Not the only possible choice for the approximation -

could use average value, etc.

•

Note that although this profile is shown for the substrate diode, it would be found in the diffusion regions of the other structures


2D Current Flow in pn-Junction•

Flow lines tend to spread as current passes through substrate

•

Current flow is therefore inherently two dimensional

•

This is another effect which is difficult to model accurately


1D Internal Current Flow Approximation•

To obtain first order analytic solutions, assume that all current flow is 1D (through substrate) and confined to the internal region

•

Current flow area is then the internal area of the junction, labelled AD

•

Accuracy of approximation depends on diode area:–

large area structure is dominated by internal

–

small area structure has significant peripheral effect


Current Density•

The diode area AD can be used to define a current density JD given by

•

Current density is useful since it allows comparison between different area devices

•

In the diagram below, all devices have the same current density:

1 mA/μm2

= 105

A/cm2.

JIAD

D

D=


Simple Ideal Diode Equation with Current Densities

•

By dividing both sides of the original simple ideal diode equation by the diode area, the relationship can be expressed in terms of current densities

•

The term JS is the saturation current density, normally in A/cm2, given by

( )J J eD SqV kTD= −/ 1

JIAS

S

D≡


Example 6.1: Basic Current Density

Which is carrying more current, a device with a current density of 100 A/cm2

and an area of 30 μm by 10 μm, or a device with a current density of 75 A/cm2

and a square area 20 μm on a side?


Example 6.1: Solution

•

The absolute currents are calculated as (note the conversion of μm to cm)

•

The currents are therefore identical, 300 μA

I J AI J A

D D D

D D D

= = ⋅ × ⋅ × = ×

= = ⋅ × ⋅ × = ×

− − −

− − −

100 30 10 10 10 3 1075 20 10 20 10 3 10

4 4 4

4 4 4

AA


Example 6.2: Area Calculation

What area is required if an integrated diode is to conduct 100 μA

of current at a junction potential of 0.7V? The

saturation current of a 500 μm by 500 μm device is 3.75x10-14

A.



•

The saturation current density is found as

•

Using the simple ideal diode equation, at 0.7 V of bias

•

The required area is therefore

•

This would correspond to a square area approx. 34 μm on a side

( ) 202586.0/7.011 A/cm55.81105.1 =−×= − eJ D

( )211

24

14

A/cm105.1105001075.3 −

−

−

×=×

×==

D

SS A

IJ

AIJD

D

D= =

×= × =

−−100 10

8 55117 10 1170

65

.. cm m2 2μ


Example 6.3: Maximum Current Density Spec.

An IC process for power applications specifies that a diode’s current density cannot exceed 106

A/cm2. The saturation current density is 1.5x10-11

A/cm2. If an application requires a diode to conduct 1A of current at a terminal voltage of 0.9V, can a diode from this process be used?



•

To find the necessary area from the current spec., write

•

Substituting values gives

•

The corresponding current density is then

•

The process is therefore suitable for this requirement

( ) ( )JIA

J e AI

J eDD

DS

qV kTD

D

SqV kT

D

D= = − → =

−/

/11

( ) ( )AeD =

× −= × = ≈−

−115 10 1

51 10 5120 71511 0 9 0 025865 2

.. .. / . cm m m2 2μ μ

JIAD

D

D= =

×≈ ×−

1512 10

2 1054

.A / cm2


Lecture Summary

•

A doping profile

is a plot of the spatial variation of dopant concentration in a device, usually |NA -ND | on a log scale

•

A uniform doping approximation

ignores the spatial variation and assumes a constant value, in our case the peak value

•

For devices with larger internal areas, a 1D approximation ignores the peripheral region in favor of the internal

region, and considers current to be determined by the internal area

•

Current density

is the current per unit internal area, and is a useful means of comparing devices with different areas and currents

Doping Profiles and 1D Approximations in the Diode...

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