Van der Pauw module¶

Van der Pauw resistivity measurement.

Four-point measurement bypass resistance of ohmic contacts.
To find resistivity from sheet resistance, use
physicslab.electricity.Resistivity.from_sheet_resistance method.
Pay special attention to enum Geometry.

physicslab.experiment.van_der_pauw.process(data, thickness=None)[source]¶

Bundle method.

Parameter data must include geometry voltage and current. See Columns for details and column names.

The optional parameter allows to calculate additional quantities: resistivity and conductivity.

Supplying None for data returns pandas.Series of the same columns with values being units.

Parameters

data (pandas.DataFrame or None) – Measured data. If None, return units instead
thickness (float, optional) – Sample dimension perpendicular to the plane marked by the electrical contacts, defaults to None

Returns

Derived quantities listed in Columns.process() or units

Return type

pandas.Series

class physicslab.experiment.van_der_pauw.Solve[source]¶

Van der Pauw formula and means to solve it.

static implicit_formula(Rs, Rh, Rv)[source]¶

Van der Pauw measurement implicit function.

The function reads:
\(func(R_s) = exp(-\pi R_v/R_s) + exp(-\pi R_h/R_s) - 1\).
This function’s roots give the solution.

Parameters

Rs (float) – Sheet resistance. Independent variable - MUST be first
Rh (float) – Horizontal resistance
Rv (float) – Vertical resistance

Returns

Quantification of this formula is meant to be zero

Return type

float

static square(Rh, Rv)[source]¶

Compute sheet resistance from the given resistances.

Accurate only for square sample: \(R_h = R_v\).

Parameters

Rh (float) – Horizontal resistance
Rv (float) – Vertical resistance

Returns

Sheet resistance

Return type

float

classmethod universal(Rh, Rv, Rs0)[source]¶

Compute sheet resistance from the given resistances.

Universal formula. Computation flow for square-like samples is as follows:

Rs0 = van_der_pauw.Solve.square(Rh, Rv)
Rs = van_der_pauw.Solve.universal(Rh, Rv, Rs0)

Parameters

Rh (float) – Horizontal resistance
Rv (float) – Vertical resistance
Rs0 (float) – Approximate value to start with.

Returns

Sheet resistance

Return type

float

classmethod analyze(Rh, Rv)[source]¶

Solve Solve.implicit_formula() to find sample’s sheet resistance. Also compute resistance symmetry ratio (always greater than one). The ratio assess how squarish the sample is, quality of ohmic contacts (small, symmetric) etc.

Parameters

Rh (float) – Horizontal resistance
Rv (float) – Vertical resistance

Returns

Sheet resistance and symmetry ratio

Return type

tuple(float, float)

class physicslab.experiment.van_der_pauw.Columns[source]¶

Bases: physicslab.utility._ColumnsBase

Column names.

classmethod mandatory()[source]¶

Get the current mandatory column names.

Return type: set(str)

classmethod process()[source]¶

Get the current values of the process() output column names.

Return type: lits(str)

class physicslab.experiment.van_der_pauw.Measurement(data)[source]¶

Van der Pauw resistances measurements.

Parameters: data (pandas.DataFrame) – Voltage-current pairs with respective geometries.
Raises: ValueError – If data is missing a mandatory column

analyze()[source]¶

Classify geometries into either Geometry.Horizontal or Geometry.Vertical. Then average respective hall resistances.

Additionally save Hall resistances to data.

Returns: Horizontal and vertical sheet resistances
Return type: tuple(float, float)

class physicslab.experiment.van_der_pauw.Geometry(value)[source]¶

Resistance measurement configuration Enum.

Legend: Rijkl = \(R_{ij,kl} = V_{kl}/I_{ij}\). The contacts are numbered from 1 to 4 in a counter-clockwise order beginning at the top-left contact. See Van der Pauw method at Wikipedia. There are two additional group values: Vertical and Horizontal.

classmethod parse(text)[source]¶

Parse string to Geometry.

Parameters: text (str) – Any valid permutation of digits 1-4, e.g. 4123 or vertical or horizontal
Raises: ValueError – If there is no corresponding Geometry
Returns: Enum corresponding to text
Return type: Geometry

reverse_polarity()[source]¶

Reverse polarity of voltage and current.

Returns: Reversed geometry
Return type: Geometry

rotate(number=1, counterclockwise=True)[source]¶

Shift measuring pins counterclockwise.

Parameters

number (int, optional) – Number of pins to jump, defaults to 1
counterclockwise (bool, optional) – Direction of rotation, defaults to True

Returns

Rotated geometry

Return type

Geometry

is_horizontal()[source]¶

Find whether the geometry describes horizontal configuration.

Returns: Is horizontal?
Return type: bool

is_vertical()[source]¶

Find whether the geometry describes vertical configuration.

Returns: Is vertical?
Return type: bool

classify()[source]¶

Sort the Geometry to either vertical or horizontal group.

Returns: One of the two group configurations
Return type: Geometry

physicslab.experiment.van_der_pauw.plot(data_list, results)[source]¶

Plot individual measurements and results with quality coefficients.

For plotting details, see: https://matplotlib.org/stable/tutorials/intermediate/gridspec.html#a-complex-nested-gridspec-using-subplotspec

Parameters

data_list (list[pandas.DataFrame]) –
results (pandas.DataFrame) – Analysis data from physicslab.experiment.process()

Returns

Same objects as from matplotlib.pyplot.subplots(). Axes are: grid axis array, right plot left axis, right plot right axis

Return type

tuple[Figure, numpy.ndarray[Axes]]