doping profiles and 1d approximations in the diode...
TRANSCRIPT
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-3
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-4
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-5
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 Page 6-6
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-7
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-8
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-9
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-10
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-11
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-12
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-13
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=
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-14
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≡
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-15
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?
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-16
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-17
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.
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-18
Example 6.2: Solution
•
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-19
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?
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-20
Example 6.3: Solution
•
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
ELEC 3908, Physical Electronics: Doping Profiles and 1D Approximations Page 6-21
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