Electric field and C-V behaviour in simulated CNM device

 

A CNM device was simulated using ISE-TCAD. A section of the device with ¼ of an n+ column and ¼ of a p+ column was simulated, to keep the size of the simulated mesh as small as possible. Because of the device’s symmetry, this is sufficient to understand the behaviour of a much larger array.

 

Device structure

 

The device structure is similar to a regular 3D detector, except the n+ and p+ columns are etched from opposite sides of the substrate, and do not pass through the full thickness of the substrate.

 

 

 

Sketch of structure (not to scale)

 

Information about the sample:

 

Substrate:

Thickness 300μm

Type: p-

Resistivity: 20kΩ cm-1 (corresponds to doping density of 7*10-11cm-3)

 

Column:

Length: 250μm

Pitch: 55μm (diagram below indicates how pitch is measured).

Diameter: 10μm

n+ columns extend from front face, p+ columns extend from back face

 

Oxide:

Thickness: 500μm

Charge: 1011cm-2

 

p-stop: Forms ring around top of n+ column. The edges of the p-stop are at 10μm and 15μm radius.

 

Contacts

n+: Individual metal contacts to each n+ column. Used for readout.

p+: Metal contact connects all p+ columns together. Used for bias. Oxide layer covers back face of device except for small windows at each electrode. Then, oxide layer is covered in metal. So, bias is applied across oxide layer to entire backplane of device.

 

Electrode layout (not to scale)

 

 

 

Basic electrical characteristics

 

IV characteristics – with and without standard oxide charge

 

 

The leakage current increases rapidly at low voltages as the device depletes, then approximately levels out at around 10V, though there is still a gradual increase in I with V. At 40V, the leakage is 165pA per column.

The presence of the standard oxide charge of 1011cm-2 does not change the saturation current, but the current does reach saturation more quickly. In effect, the presence of the +ve oxide charge causes the p- bulk to deplete more rapidly.

 

CV characteristics (with oxide charge)

 

The capacitance of the column falls rapidly with increasing voltage as the device depletes. The intial period of rapid depletion takes place over a range of just 0-1V, though the log scale graph shows more clearly that the capacitance does not saturate until about 8V. The saturation value is 55fC per column. The coaxial cable approximation, which regards the column as being a coaxial cable with radius equal to the distance between n+ and p+ electrodes, predicts a value of between 65fC and 81fC (as the “cable length” can either be considered as the 250um column length or the 200um overlap region).

 

The C-V characteristics are much the same as for a regular 3D detector, except that the switch from rapidly falling capacitance to complete saturation is less abrupt here.

 

Depletion behaviour:

 

The video CNM_1Vdepletion.avi shows the growth in the depletion region over the range 0V to 1V. The colour shows the space charge in the device. Red is zero and positive charge, and the spectrum up to blue indicates increasing negative charge. The depletion region grows horizontally and vertically outwards from the n+ column .

 

By 1V, most of the volume of the device is depleted. However, particular undepleted regions persist beyond this, so complete depletion of the device does not occur until around 10V. This explains why the leakage current and the capacitance change rapidly from 0V to 1V but do not completely saturate until 10V.

 

 

The diagram above shows the spacecharge in the device at 1V. (Depleted bulk material has space charge of -7e11cm-3, and appears turquoise in the diagram.) There are still undepleted regions around the p+ column and at the base of the device. Note that the presence of the oxide charge produces regions of negative spacecharge at the top and bottom of the device.

 

 

Electric potential and field

 

Cross-sections and graphs of the field were taken at 20V and 100V. Generally, the coloured 2D graphs taken at 20V and 100V appear similar, apart from a difference in scale.

 

Vertical cross-sections of potential and field

 

These cross sections are taken parallel to the z-azis and pass diagonally through the n+ and p+ columns. Most of the cross-sections show the field at 20V, though in a few cases the 100V graphs are used, e.g. when looking at high-field regions where breakdown could occur.

 

 

Like in a regular 3D device, the field is greatest around the edge of the columns.

 

While the field and potential in the region where the columns overlap (50μm to 250μm) are much the same as in a regular 3D device, there are 2 notable differences at the top and bottom of the device;

1)      A region of high electric field at the tip of each electrode.

2)      A lower-field region, extending from about 0-30μm at the top of the device and from 270μm to 300μm at the bottom.

 

 

High-field region

The graph below shows the high-field region in greater detail, using a 100V bias rather than 20V. At 100V, the peak field is 1.3*105Vcm-1, much higher than the field along the length of the column (around 0.6*105Vcm-1) but significantly lower than the breakdown field of 3*105Vcm-1. The high field is probably due to the compression of field lines caused by the corner of the column. This simulation uses columns with an abrupt flat base. The maximum field at the base of the column would probably be reduced if the base was more rounded, which would spread the field lines more evenly.

 

 

Vertical streamtraces

 

All of the following streamtraces are plotted based on the direction of the electric field. They are continuous lines following the electric field vector, so they will trace out the paths that will be followed by charge carriers produced in the device. Note that these are not quite the same as electric field lines – in particular, their spacing does not reflect the strength of the electric field.

 

 

Carriers produced between the electrodes are swept horizontally to the appropriate electrode, like in a regular 3D device.

However, in the lower-field regions at the top and bottom of the device, the behaviour is more complicated, and varies depending on the bias and oxide charge. The following graphs show these regions in more detail.

 

Charge drift around backplane of device (variation with oxide charge and applied bias)

 

  

 

The carriers produced in this region generally have a longer drift distance than the carriers produced between the two columns.

 

The electric field points radially outwards from the tip of the n+ electrode. Electrons drift to the tip of the electrode. However, when following the streamtraces in the opposite direction (which indicates the direction of hole drift) some of the streamtraces end on the backplane, rather than the p+ column. This only occurs around the region directly below the electrode. In practice, since the electric field at the backplane still has a lateral component, these holes that end up at the backplane will then drift to the electrode. However, the low field in this region is likely to give a longer collection time.

 

The field at the backplane is affected by the presence of oxide charge and the potential applied to the entire backplane of the device across the oxide. The oxide charge repels holes, which means that fewer holes will drift to the backplane (as shown by the second graph above). However, at large biases this effect appears to be cancelled by the voltage applied to the backplane (third graph) In fact, some of the streamtraces curve slightly towards the backplane at this voltage.

 

Detail of electric field at backplane

 

The graph above shows the magnitude of the electric field in the lower region of the device when a 100V bias is applied. The contour levels have been chosen to make the variation in the field clearer (with the downside that the field magnitude immediately around the electrodes is “off the scale”). The magnitude of the field decreases substantially towards the backplane. In the region between the electrodes the field has a minimum values of about 25000V/cm, whereas at the back plane of the device the field falls to about 5000V/cm.

 

 

 

Charge drift around front of device (variation with oxide charge and applied bias)

 

  

 

In general, holes will drift to the tip of the p+ electrode and electrons will drift to the n+ electrode. However, the p-stop implant and the oxide charge affect the electric field in this region. In the simulation with no charge, electrons produced in the region directly above the column will take a complicated path around the p-stop, increasing their drift distance. When the oxide charge (which attracts electrons) is included, some of the electron paths end on the front plane of the device outside the p-stop ring.

 

Because of the p-stop, the electrons reaching the back plane will not simply drift along the back plane to the electrode. The graph below shows lines following the current density in the device, rather than the electric field. This rather complicated graph shows that the electrons produced directly above the p+ column will move to the back plane, drift laterally along the back plant until they near the p-stop, then drift round the p-stop. This will tend to give a long path length.

 

 

Detail of electric field at front of device

 

The graph above shows the magnitude of the upper field in the lower region of the device when a 100V bias is applied. Once again, the electric field decreases from a minimum of about 25000V/cm in the region between the electrodes to about 5000V/cm at the back plane of the device, though the field at the edge of the n+ column remains large regardless of depth.

 

 

 

Horizontal cross-sections of potential and field at 20V

 

These cross-sections were made horizontally through the device at a depth of 150um (half of the sample thickness). In this region, the two columns overlap.

 

 

Once again, the highest electric field is seen at the edge of the n+ and p+ columns.

There is also a low-field region at each corner. In a full-sized array, each of these low-field regions will be midway between pairs of n+ and p+ columns. (If charge carriers are produced at equal distance from 2 columns of the same type, their charge will be shared between them). This low-field region is also seen in standard 3D detectors.

 

Horizontal streamtraces

 

At the edge of each electrode the electric field points radially outwards. This means that rather than travelling directly towards the nearest electrode, charge carriers will follow a curved path as shown above.

 

 

Line graphs of electric field and potential

 

Horizontal graphs at 20V and 100V

 

Data was taken from a series of horizontal lines passing diagonally through the n+ and p+ columns as shown below.

 

The lines are taken from the midpoint of the columns (150um depth) and in the regions near the top and bottom where the columns do not overlap (5um and 295um depth). A final line was taken at 1um, passing though the p-stop ring.

 

 

The graphs below show the electrostatic potential and electric field along these lines at both 20V and 100V. There are separate graphs to show the magnitude of the electric field, and the component of the field parallel to the line between the columns (i.e. the component that will cause the carriers to drift to the nearest electrode).

Electrostatic potential at 20V and 100V

 

 

Electric field magnitude at 20V and 100V

 

 

Horizontal component of field at 20V and 100V

 

In the region between the electrodes, the electric field is high. The electric field magnitude peaks at the edge of the n+ and p+ columns (1.2*104V/cm at 20V, 6*104V/cm at 100V). The field is still reasonably large between them – the minimum field between the electrodes is about half of the maximum.

 

In the regions at the top and bottom of the device, the field is reduced significantly. In particular, there is a low-field region beneath the n+ column and above the p+ column. Since only one electrode is nearby in these regions, the electric field only has a single peak. In particular, the horizontal component of the electric field becomes small at 5um and 295um depth – less than 1000V/cm at 100V bias in some places. As noted earlier, the low field near the front and back planes will result in a longer collection time for charges produced in these regions.

 

At 100V, the electric field is both lower and more uniform near the back plane (295um depth) than it is at the top of the device (5um depth). This is because the -100V bias is applied to the entire back plane of the device (across a layer of oxide) rather than to just the columns.

 

At the very top of the device (1um depth) the electric field is larger between the horizontal positions of 5um and 10um. This is because there is just a 5um gap between the n+ column and the p-stop implant here. However, the field here is still lower than in the region between columns, so microdischarges between the n+ column and the p-stop are not likely to be a problem. There is also a small peak in the electric field where the outside edge of the p-stop meets the depleted bulk.

 

On the whole, the electric field patterns seen at 20V and 100V are very similar, aside from a change in scale.

 

 

Vertical graphs at 20V and 100V

 

Data was taken from a series of vertical lines passing diagonally through the n+ and p+ columns as shown below, to check the variation in the electric field with depth more thoroughly.

 

The lines are taken through the centres of the electrodes and along the midpoint between the electrodes, as shown below.

 

Electrostatic potential at 20V and 100V

 

 

Electric field magnitude at 20V and 100V

 


The field along the midpoint of between the columns is very uniform across the range of 50-250um (where the columns overlap). However, the field strength falls to nearly zero at the front and back surfaces of the device, which will increase charge collection times from these regions.

 

At the ends of the n+ and p+ columns, there are peaks in the electric field (90000V/cm at 100V). However, even in these regions the field drops rapidly towards the front and back faces.

 

 

Electric field and potential along the edge of the cell

 

The previous results have focused on a slice of the device passing through both the n+ and p+ electrodes. The following results are taken from a vertical cross-section along the edge of the basic cell of the device, indicated below. The line graphs were taken at a depth of 150um..

 

 

Like in a normal 3D device, the electric field along the cell edge falls from a maximum at the n+ column to a low field at the midpoint between two neighbouring n+ columns.

Unlike a regular 3D device the magnitude of the field at the midpoint between two n+ columns and two p+ columns does not fall to zero. This is because there is still a field running along the z-axis of the device, due to the layout of the columns.

 

 

 

Key points / conclusion

 

Electric field and carrier drift

 

In the region where the columns overlap (50um depth to 250um depth) the electric field is much the same as in a regular 3D device.

 

In the regions at the top and bottom of the device, there are a few factors which will increase the collection time.

Firstly, the straight-line distance to the electrodes is increased – e.g. an electron produced around the base of the p+ column will have to travel both horizontally and vertically to reach the tip of the n+ electrode.

Secondly, holes produced in the region below the n+ electrode tend to travel vertically towards the back plane of the device then drift laterally to the p+ electrode, increasing their drift distance. (The same applies to electrons above the p+ electrode.

Most importantly, the field strength is significantly smaller in these regions, particularly near the front and back planes of the device, where the field is approximately 5 times smaller than the minimum value seen in the region between the columns.

 

These results indicate that making the column length as close as possible to the substrate thickness will improve the charge collection. Further simulation work will be done to test this.

 

Depletion voltage, electric field and breakdown

 

A bias of 1V is enough to deplete most of the device volume, and 10V will deplete the full device.

At the ends of the n+ and p+ columns there are regions of high electric field. At a bias of 100V, the peak field reaches 1.3*105Vcm-1, which is safely below the breakdown value.

 

More simulation will be done to see if reducing the gap between the front and back faces of the substrate and the ends of the columns causes the field to become excessively large.

 

Further work to be done

 

As well as altering the lengths of the columns, simulations need to be done to test the effect of misaligning the two sets of columns.

Also, the effect of a MIP passing through the sample should be simulated.