# Temperature Coefficients: Negative vs Positive

Semiconductors exhibit different types of temperature coefficients. In order to valuable parameters such as resistance or forward voltage drop and the associated change in temperature, one must understand temperature coefficients for various devices.

First however, it is best to explain the difference between positive temperature coefficients and negative temperature coefficients. As usual, Wikipedia does a good job of explaining the difference. Here are the basics:

• A component that becomes less resistive with temperature has a negative temperature coefficient.
• A component that becomes more resistive with temperature has a positive temperature coefficient.
• The polarity of the temperature coefficient is easy to spot in a graph of resistance versus temperature. As temperature increases, a positive slope indicates a positive temperature coefficient. A negative slope indicates a negative temperature coefficient.

In this blog we’ll look at the temperature coefficients of popular power semiconductors as well as how to deal with them in a circuit. This excerpt from the Wikipedia post provides a top level statement about semiconductor temperature coefficients”

Negative temperature coefficient of resistance of a semiconductor

An increase in the temperature of a semiconducting material results in an increase in charge-carrier concentration. This results in a higher number of charge carriers available for recombination, increasing the conductivity of the semiconductor. The increasing conductivity causes the resistivity of the semiconductor material to decrease with the rise in temperature, resulting in a negative temperature coefficient of resistance.”

This is true for the base semiconductor theory especially junction based devices such as bipolar junction transistors (BJTs) and diodes. However, components such as (Metal Oxide Semiconductor Field Effect Transistors (MOSFETs) and Insulated Gate Bipolar Transistors (IGBTs) actually have resistive channels that affect the behavior of the temperature coefficient.

In engineering school, semiconductor theory always started with references to energy gaps created by a semiconductor junction with different levels of p and n concentrations. By injecting energy into a semiconductor, electrons gained thermal energy which in turn supplemented the amount of electrical energy thus requiring less forward biasing current for conduction to occur. Similarly, while blocking voltage, a diode junction’s leakage current increases with temperature. I saw this first hand as some 600V silicon Schottky diodes started to disintegrate before my eyes in a power factor correction circuit. The waveforms did a lava lamp style expansion as they rapidly expanded. Fortunately, I killed the circuit before the whole thing blew up. Suffice it to say that Motorola is no longer in the semiconductor business. Go figure.

Forward voltage decreases with increasing temperature as shown in the Figure. This change in forward voltage is so predictable that it’s often used as a method for measuring junction temperature within a separate device.

The aforementioned temperature coefficient tendencies relate to silicon. Newer materials such as silicon carbide (SiC) and gallium nitride (GaN) will act differently with temperature changes than silicon.

As for MOSFETs, they have a positive temperature coefficient as shown in the figure where the Rds(on) is shown increasing with temperature. This is due to the resistance of the MOSFET substrate itself as well as the thickness of the device. Thicker devices withstand higher voltages and therefore have higher ON resistance.

The increasing resistance of a MOSFET with temperature is not all bad. It helps balance up currents for MOSFETs that are placed in parallel as current will follow the path of least resistance.

IGBTs are sort of hybrid devices that can lightly be described as a cross between a BJT and a MOSFET. The IG or Insulated Gate part of IGBT refers to the MOSFET that triggers the device. The BT refers to the bipolar transistor (actually two of them) that conduct most of the current. The IGBT curves show this in the IC versus VCE figure below rather than provide a resistor based graph like a MOSFET. Note the cross over point where slopes change.

Copper has a positive temperature coefficient whereas it gets more resistive with increasing current. I’m going to borrow some text from one of the references as it is explained rather well here: “Whereas in the case of conductors, when temperature increases resistivity increases as electrons collide more frequently with vibrating atoms. This reduces drift speed of electrons (and thus current reduces). Thus, conductors have positive temperature coefficient of resistance .”

Temperature coefficient affects from major power circuit components can enhance or reduce efficiency. Furthermore, they change temperature rise of the component. Understanding these behaviors benefits the reliability and performance of your design.

References

2. Why is temperature coefficient of resistance negative for semiconductor? Quora answer blog
3. BAV99 diode data sheet IF vs. VF graph
4. “Use Forward Voltage Drop To Measure Junction Temperature.” Electronic Design, Jason Chonko, Dec 15, 2005.
5. MOSFET Rds(on) question”, Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts
6. IGBT Basics”, Fairchild Application note AN-9016

## 1 comment on “Temperature Coefficients: Negative vs Positive”

1. Victor Lorenzo
May 1, 2017

Nice post, Scott.

I agree with your final comment “Understanding these behaviors benefits the reliability and performance of your design “. The temperature of a body is somehow an external, or macroscopic, view of its internal state. We need to understand the internal effects that are induced on our components when their internal temperature changes. In many cases we use these effects for creating temperature and flow sensors. But in the vast majority of situations when the components temperature changes, due to external influences or due to self heating, it produce undesired deviations which negatively impact the circuit's performance.

Power supplies and instrumentation systems are, from my point of view, two classes of circuits which are very sensitive to variations in component parameters originated by temperature changes and governed by their temperature coefficients.

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