A power transistor does not fail because it is warm to the touch; it fails because a few square millimetres of silicon inside it, which nobody can touch, spend their life at a temperature nobody measured. Every watt lost in the device has to get out through the package, across a mounting interface and off a heat sink into the air, and each step costs degrees per watt. The arithmetic is the same as Ohm's law and takes a minute. The judgement is in the numbers you feed it: the real loss, the real air temperature inside the box and the real conditions the heat sink datasheet assumed.
Why junction temperature is the number
The datasheet gives an absolute maximum junction temperature, 150 °C for most silicon and 175 °C for many MOSFETs and IGBTs, and that figure is where the guarantee stops, not a place to design to. The widely used rule of thumb, and it is only that, is that the failure rate of a semiconductor roughly doubles for every 10 °C, so a device run at 110 °C lasts of the order of sixteen times longer than one at 150 °C. Bond wires, die attach and the plastic itself age with temperature and with the number of heating and cooling cycles, and the datasheet's derating curve, a straight line from full rated power at 25 °C case temperature to nothing at the maximum junction temperature, is the manufacturer saying the same thing.
Heat also changes how the device behaves while it works. A silicon MOSFET's on-resistance rises with temperature, typically to 1.5–2 times its 25 °C value at 150 °C, so the conduction loss grows as the device warms, and a design that was marginal cold is worse hot. Bipolar transistors go the other way: the base–emitter voltage falls about 2 mV per degree and the gain rises, so a linear stage or a pass transistor at fixed bias draws more current as it heats, heats more, and can run away unless the design limits it. Diodes lose forward voltage as they warm, which helps their losses but makes paralleling them a bad idea. In every case the junction temperature is the variable that everything else depends on, and the whole purpose of a heat sink is to hold it where you decided it should be at the hottest ambient the equipment will meet.
The thermal chain: three resistances in series
Heat flowing through a material behaves like current flowing through a resistor: a temperature difference drives a heat flow, and the ratio of the difference to the flow is a thermal resistance in degrees per watt. Watts stand in for amperes, degrees for volts and °C/W for ohms, and resistances in series add. Between the junction and the surrounding air there are three.
Rθjc, junction to case, is inside the package: from the die through the solder or epoxy to the metal tab. The datasheet gives it, and it is the one figure you cannot change except by choosing a different device or package: 0.5–2 °C/W for a power MOSFET or transistor in a TO-220, 0.3–1 for a TO-247, and higher, around 3–5, for a small die such as a 78xx regulator in the same TO-220. Rθcs, case to sink, is the mounting interface: two surfaces that are nearly flat pressed together with something filling the roughness between them, 0.3 °C/W with grease on a TO-220 and up to 2 with nothing. Rθsa, sink to ambient, is the heat sink: the resistance of a piece of metal to warming the air around it, from 20 °C/W for a clip-on to below 1 for a large extrusion with a fan.
The ambient Ta is the air the heat sink actually sees, and the equation says everything the heat sink calculator does: given the power and the temperature you can allow, the heat sink must have a resistance no greater than (Tj − Ta) ÷ P minus the two resistances you do not control. If that comes out at zero or below, no heat sink will do and the loss itself has to change.
Where the heat comes from
The chain is only as good as the number of watts you put into it, and that number is often guessed low. A linear regulator dissipates the whole difference between input and output voltage times the load current, plus its quiescent current times the input voltage: a 7805 fed from 12 V and delivering 1 A burns (12 − 5) × 1 = 7 W to deliver 5 W to the load, which is the classic case of a small TO-220 asked to do a job it cannot do without a substantial heat sink. With Rθjc around 5 °C/W for that part, 45 °C air and a 110 °C junction, the sink must be below (110 − 45) ÷ 7 − 5 − 0.5 = 3.8 °C/W: a finned extrusion, not a clip-on.
A MOSFET loses I² × RDS(on) in conduction, with RDS(on) taken at the hot junction temperature, not the 25 °C headline, plus switching loss that grows with frequency, voltage, current and the switching times, plus a little in the gate. At 20 A through 20 mΩ hot that is 8 W before switching is counted. A diode loses Vf × I, so a 10 A bridge rectifier with two diodes conducting at about 1 V each is 20 W and needs a heat sink as surely as any transistor; a triac or thyristor at 1–1.5 V drop is the same story. Read the loss from the datasheet curves at the actual current and temperature, or measure it, before doing any of the thermal arithmetic; a 30 % error here is a 30 % error in every temperature.
Interfaces: grease, pads, mica and torque
Two machined surfaces touch at their high points only; the rest is air, which is a superb insulator. A thermal compound fills those gaps. Ordinary silicone grease with a zinc oxide or ceramic filler, applied as a smear thin enough to be translucent, brings a TO-220 down to 0.3–0.5 °C/W; a thick layer is worse, not better, because the grease itself conducts poorly and it is only there to displace air. A mica washer with grease on both sides adds an insulator good for a few kilovolts at 0.5–1 °C/W and needs an insulating bush on the screw. Silicone or ceramic-filled elastomer pads are cleaner and faster on a production line and insulate without grease, at 0.8–1.5 °C/W. Graphite sheets and phase-change pads sit between.
Torque matters as much as the material. The device datasheet gives a mounting torque, typically 0.5–0.8 N·m for an M3 screw on a TO-220; too little leaves air, too much bends the tab and cracks the die. A spring clip that presses on the plastic body over the die is better than a screw through the tab hole, because the pressure is where the heat is. Surface flatness matters too: an extruded heat sink is flat enough, a bent sheet of aluminium often is not, and a chassis with a paint or powder coat is an insulator until the coating is removed under the device. If the tab is at the drain or collector potential, which on a TO-220 it is, and the heat sink is earthed, the interface must insulate, and that costs a degree per watt; the alternatives are a fully insulated package (TO-220F, at a higher Rθjc built in) or floating the whole heat sink.
Heat sinks: natural convection, orientation, forced air
A heat sink in still air works by warming the air between its fins so that it rises and is replaced, and by radiating from its surface. Both depend on things the datasheet figure assumes silently: fins vertical, so the warm air can rise through the channels; 30–50 mm of clear air above and below; fin spacing of 6–10 mm, because natural convection through a narrower gap chokes; and a temperature rise of about 75 °C, at which the figure is usually quoted. At a smaller rise the same sink is worse, by roughly 20 % at a 35 °C rise, because natural convection improves with temperature difference. Lay the fins horizontal and it is worse again; put the sink in an enclosure with no path for the air and it can be twice as bad. Black anodising helps by radiation, noticeably in still air and hardly at all under a fan.
A fan changes everything. Forcing air through the fins divides the resistance by two to four, and the fins can be closer together, so a sink a third of the size does the same job; a 60 mm fan on a 100 mm extrusion reaches 1 °C/W where natural convection would need something the size of a book. The price is a moving part that stops, a filter that clogs, and dust that arrives anyway. In Lahore, Faisalabad or anywhere near a road the fin gaps of an unfiltered forced-air sink fill within months and the resistance climbs back towards the still-air figure, so a design that relies on a fan must either survive the fan's failure for long enough to shut down safely or detect it: an over-temperature switch on the sink that trips the load is the cheapest insurance there is. At altitude the air is thinner and a fan moves less mass of it; Quetta's 1 700 m costs a forced-air sink roughly a tenth of its performance.
Enclosures and the real ambient
The Ta in the equation is the air around the heat sink, not the air in the room and not the figure on the weather report. Inside a closed panel every device warms the same trapped air, and the panel itself sheds heat to the room only through its walls: enclosure makers reckon a painted steel box loses about 5.5 W per square metre of free surface per degree of wall-to-room difference in still air, so a 600 × 400 × 250 mm box mounted against a wall, with roughly 0.7 m² of useful surface, rises about 10 °C for every 40 W inside it. Add a summer afternoon in Multan or Sukkur, a 40 °C room and a panel in the sun, and 45–55 °C inside a sealed box is normal, which is why the calculator's default ambient is 45 °C and not 25.
A sealed IP65 or IP66 enclosure keeps the dust out and the heat in; a vented one with filters lets both move, and the filters need a maintenance schedule that will not be kept. The choices, in rising order of cost, are: keep the loss low enough that the box copes; use the enclosure wall as the heat sink, with the device bolted to a bare patch on the inside and fins or plain steel on the outside; fit a heat exchanger or a fan-and-filter set; or, for equipment in the sun, a second roof and a light colour, which are worth more than they cost. Whatever the arrangement, the design ambient is the air temperature inside the box at the worst hour of the worst month, and it should be measured on the first unit and not assumed.
Measuring instead of hoping
The junction cannot be reached, so its temperature is inferred from something that can. The standard method is a fine thermocouple on the case at the point the datasheet defines, which for a TO-220 is the centre of the tab: drill a small hole in the heat sink under the device, fill it with grease and bring the thermocouple bead up against the tab, then add P × Rθjc to what it reads. On the worked example the tab should read about 90 °C at full load in 45 °C air; if it reads 110, either the loss is more than 15 W or the interface is worse than 0.5 °C/W, and both are worth knowing. An infrared thermometer or camera reads surfaces, and bare aluminium reflects so well that it reads far too low; a patch of matte tape or paint, whose emissivity is close to one, gives a true reading of the sink, which is a few degrees cooler than the tab and tens of degrees cooler than the die.
For the junction itself there is the diode method described in JEDEC JESD51-1: the forward voltage of the body diode of a MOSFET, or the base–emitter junction of a transistor, falls by about 2 mV per degree at a fixed small measuring current. Calibrate it in an oven, run the device at load, switch briefly to the measuring current and read the voltage, and the junction temperature follows. It is more work than a thermocouple and it is how the datasheet figures were obtained. Whichever method, run the test at the design ambient, in the enclosure, with the door shut, for long enough for the sink to settle, which is typically half an hour or more, and log the result; a heat sink that is fine at 25 °C on the bench has proven nothing about July.
The example in numbers
A TO-220 MOSFET dissipating 15 W, Rθjc = 1.0 °C/W, mounted with grease (0.5 °C/W) on a 2.5 °C/W finned sink inside a panel whose air reaches 45 °C, with the junction to be held at 110 °C:
- The budget from junction to air is 110 − 45 = 65 °C, which over 15 W is 4.33 °C/W for the whole chain.
- The device and the interface take 1.5 °C/W, so the heat sink must be 4.33 − 1.5 = 2.83 °C/W or better. The 2.5 °C/W sink qualifies.
- With it the chain is 4.0 °C/W and the junction sits 15 × 4.0 = 60 °C above the air, at 105 °C. The tab is 105 − 15 = 90 °C and the sink under it 90 − 7.5 = 82.5 °C.
- The most this sink allows at 110 °C is 65 ÷ 4.0 = 16.25 W. With no sink at all, at Rθja = 62 °C/W, the same package could pass only 65 ÷ 62 = 1.05 W, and at 15 W the formula gives 975 °C: it would fail in seconds.
Swap the grease for an insulating pad at 1.2 °C/W and the junction rises to 115.5 °C, above the target; the pad has cost 10.5 °C and the sink must improve to 2.13 °C/W to pay for it. The heat sink calculator reproduces these figures and lets you trade the interface, the sink and the ambient against each other.
When a heat sink is the wrong answer
Metal is the last resort, not the first. The cheapest watt to dissipate is the one not generated, and the options are usually better than a bigger sink. A switching regulator in place of a linear one turns the 7805's 7 W into well under 1 W at 90 % efficiency and needs no heat sink at all; the same applies to any linear stage dropping more than a volt or two at more than a few hundred milliamps. A lower RDS(on) MOSFET cuts conduction loss in proportion, and the price of a 5 mΩ part against a 20 mΩ one is small compared with the sink it saves, though the gate charge and switching loss go up. Parallel MOSFETs share current naturally, because the positive temperature coefficient of RDS(on) steers current away from the hotter device, and two devices each dissipating half the loss, on their own tabs, get the heat into the sink through two Rθjc paths instead of one. Bipolar transistors and diodes do not share without ballast resistors.
Spreading the loss also works: a series resistor ahead of a linear regulator moves part of the drop into a component that is happy at 200 °C; a synchronous rectifier replaces a diode's 1 V with a MOSFET's tens of millivolts; a lower input voltage or a lower switching frequency shrinks the loss at its source. And sometimes the honest answer is that the design junction temperature was optimistic for the part, and a package with a lower Rθjc, or a different device, is the fix. Ahmedonics designs power and control hardware with the thermal budget settled before the schematic is finished, because a heat sink chosen afterwards is always larger, and a fan added later is always the part that fails first.
References
- JEDEC JESD51 series: JESD51-1 (electrical test method), JESD51-2A (natural convection test environment), JESD51-7 (high effective thermal conductivity test board) — definition and measurement of junction temperature, Rθja and Rθjc
- IEC 60747-1, Semiconductor devices — Part 1: General — ratings, thermal resistance and transient thermal impedance
- P. Horowitz and W. Hill, The Art of Electronics, 3rd ed., Cambridge University Press, 2015 — §9.4, heat and power design
- Manufacturer thermal design application notes, for example ON Semiconductor AN-1040 (Mounting Considerations for Power Semiconductors) and Infineon's thermal design guides — interface resistances, mounting torque, insulating washers and clips
- Heat sink manufacturers' catalogue data (Aavid Thermalloy, Fischer Elektronik and others) — Rθsa against length, temperature rise, orientation and air velocity
- Enclosure manufacturers' climate control guides (Rittal and others) — heat loss of sheet-steel enclosures, about 5.5 W/(m²·K), and the effective surface area rules