Introduction
Solar cell contacts are ideally ohmic and with little contact resistance. The metal contact is often wider and more conductive than the thickness of the semiconductor layer, which gives rise to the concept of a transfer length. As shown in the figure below, current is not spread evenly across the metal silicon contact and crowds at the edges. Modeling and measurement needs to take account of the crowding.
like any other semiconductor devices have contact and all contacts have contact resistance. Contacts can be metal-semiconductor or semiconductor-semiconductor. Contacts can be either ohmic or Schottky. Ohmic contacts have linear or quasi-linear current-voltage characteristics while Schottky ones have non-linear characteristics. Ohmic contacts should not inject minority carriers and the voltage drop over them should be small compared to the voltage drops across the active device regions. The following figure shows IV characterization for a typical Silicon heterojunction cell in dark conditions. As seen, some of the contacts can behave both as an ohmic or Schottky under varying applying conditions. For low applied voltages the current is governed by the bulk property of the material whereas for higher voltages (and low doping) the space charge accumulated inside the device changes the current to space charge limited current (SCLC) which typically varies nonlinearly with the applied voltage. (see Ref. 1)
Contact Resistance
Current in metal-semiconductor contacts can flow either vertically or horizontally and so can behave differently. In the following figure, the different resistance component in a solar cell and among them the contact resistance which for measuring that we need to apply current to the two metal contacts on the front and then measure the voltage over that. The total resistance can then be divided into three components: (1) the resistance of the metallic conductor Rm, (2) the contact resistances RC, and (3) the semiconductor or emitter resistance Rsemi.
The contact resistance is usually not well defined. It includes several components including metal-insulator contact, a portion of metal immediately above the metal-semiconductor interface, a part of the semiconductor below that interface, current crowding effects, and any interfacial oxide or other layers that may be present between the metal and the semiconductor. The semiconductor resistance is mainly determined by the sheet resistance of the semiconductor (n-layer in the above figure)
Measurement techniques
There are different techniques to measure contact resistance including transfer length method (TLM) measurements [9], circular transfer length method (CTLM) measurements [10], or the through-the-absorber measurement introduced by Cox and Strack [11]. Here, we focus on the transfer length method (TLM) measurements as it is the most prevalent technique for solar cells.
Transfer Length Method (TLM)
As shown in figure.1, the resistance of a single contact would be Rm + RC. However, in most situations, the resistivity of the metal in the contact is so low that RC >>Rm, and so Rm can be ignored.
So, Eq.1 can be replaced with:
$$R_{T}=2 R_{C}+R_{\text {sheet}} \frac{L}{W}, \quad\left(\text {Rsemi}=R_{\text {sheet}} \frac{L}{W}\right)$$
Above suggest that total resistance has a linear dependency to the length of the resistor which means if we construct several of them with different lengths, the total resistance can be measured and plotted. Then by extrapolating back to L = 0 in the graph, in the limit of a zero-length resistor, the residual resistance would be just twice the contact resistance. The sheet resistance of the semiconductor can be found from the slope of the line as well.
Contact Resistivity
The advantage of measuring contact resistance instead of the contact resistivity is that we can have a standard quantity as a point of comparison. It can be written as ρC=ACRC and it would have units of Ω·cm2. Assuming we know the area of the contacts, finding contact resistivity should be straight-forward. However, in practice, the physical contact area is not usually equal to the effective contact area. This is because the current does not flow uniformly in the contact.
Current Crowding
A phenomenon known as current crowding occurs at the edge of the contact (see figure.4). As we move away from that edge, the current drops off until, at the far edge, there is no current. The current flow through the semiconductor is still uniform, but the flow into the contacts is not. Since the current does not flow uniformly in the contact, we can’t use the physical length and width of the contact to determine the contact area. Based on the analysis provided in Ref. 1, the average distance that an electron (or hole) travels in the semiconductor beneath the contact before it flows up into the contact can be determined as below:
$$L_{T}=\sqrt{\frac{\rho_{C}}{R_{\text {sheet}}}}$$
We call this transfer length, LT. So for the cases that LT < contact pad dimensions, the effective area of the contact can be calculated as LTW. The contact resistance is then:
A typical arrangement for a TLM test pattern is shown below. There is a single rectangular region (blue in the figure) that has the same doping (i.e. same sheet resistance) as the contact areas of the devices. An array of contacts (darker gray in the figure), with various spacings, is formed over the doped region.
The plot of RT vs resistor length can also give the transfer length, by extrapolating back to the horizontal axis, where the intercept = –2LT. Thus, we know everything needed to find contact resistivity.
Typical contact resistivity values for multi-layer heterojunction silicon stacks are between 10 to 500 mΩcm2 and for diffused junction solar cells can be as low as 1 mΩcm2.
References
- Inorganic Photovoltaics - Planar and Nanostructured Devices, Progress in Materials Science, 2016.
- Semiconductor material and device characterization by Dieter Schroder, John Wiley, 1998.
- Contact resistance and TLM measurements.