Sara Godfrey, Melcor Corporation

Figure 1: Cross Section of a Typical TE Couple

Introduction

Thermoelectric coolers are solid state heat pumps used in applications where temperature stabilization, temperature cycling, or cooling below ambient are required. There are many products using thermoelectric coolers, including CCD cameras (charge coupled device), laser diodes, microprocessors, blood analyzers and portable picnic coolers. This article discusses the theory behind the thermoelectric cooler, along with the thermal and electrical parameters involved.

How the Thermoelectric Works . . .

Thermoelectrics are based on the Peltier Effect, discovered in 1834, by which DC current applied across two dissimilar materials causes a temperature differential. The Peltier Effect is one of the three thermoelectric effects, the other two are known as the Seebeck Effect and Thomson Effect. Whereas the last two effects act on a single conductor, the Peltier Effect is a typical junction phenomenon. The three effects are connected to each other by a simple relationship.

The typical thermoelectric module is manufactured using two thin ceramic wafers with a series of P and N doped bismuth-telluride semiconductor material sandwiched between them. The ceramic material on both sides of the thermoelectric adds rigidity and the necessary electrical insulation. The N type material has an excess of electrons, while the P type material has a deficit of electrons. One P and one N make up a couple, as shown in Figure 1. The thermoelectric couples are electrically in series and thermally in parallel. A thermoelectric module can contain one to several hundred couples.

As the electrons move from the P type material to the N type material through an electrical connector, the electrons jump to a higher energy state absorbing thermal energy (cold side). Continuing through the lattice of material, the electrons flow from the N type material to the P type material through an electrical connector, dropping to a lower energy state and releasing energy as heat to the heat sink (hot side).

Thermoelectrics can be used to heat and to cool, depending on the direction of the current. In an application requiring both heating and cooling, the design should focus on the cooling mode. Using a thermoelectric in the heating mode is very efficient because all the internal heating (Joulian heat) and the load from the cold side is pumped to the hot side. This reduces the power needed to achieve the desired heating.

Thermal Parameters Needed

The appropriate thermoelectric for an application, depends on at least three parameters. These parameters are the hot surface temperature (T_h), the cold surface temperature (T_c), and the heat load to be absorbed at the cold surface (Q_c).

The hot side of the thermoelectric is the side where heat is released when DC power is applied. This side is attached to the heat sink. When using an air cooled heat sink (natural or forced convection), the hot side temperature can be found by using Equations 1 and 2.

The thermal resistance of the heat sink causes a temperature rise above ambient. If the thermal resistance of the heat sink is unknown, then estimates of acceptable temperature rise above ambient are:

The heat sink is a key component in the assembly. A heat sink that is too small means that the desired cold side temperature may not be obtained.

The cold side of the thermoelectric is the side that gets cold when DC power is applied. This side may need to be colder than the desired temperature of the cooled object. This is especially true when the cold side is not in direct contact with the object, such as when cooling an enclosure.

The temperature difference across the thermoelectric (T) relates to T_h and T_c according to Equation 3.

(3) T = T_h - T_c

The thermoelectric performance curves in Figures 2 and 3 show the relationship between T and the other parameters.

Estimating Q_c, the heat load in watts absorbed from the cold side is difficult, because all thermal loads in the design must be considered. Among these thermal loads are:

1. Active: I²R heat load from the electronic devices
   Any load generated by a chemical reaction
2. Passive: Radiation (heat loss between two close objects with different temperatures)
   Convection (heat loss through the air, where the air has a different temperature than the object)
   Insulation Losses
   Conduction Losses (heat loss through leads, screws, etc.)
   Transient Load (time required to change the temperature of an object)

Powering the Thermoelectric

All thermoelectrics are rated for I_max, V_max, Q_max, and T_max, at a specific value of T_h. Operating at or near the maximum power is relatively inefficient due to internal heating (Joulian heat) at high power. Therefore, thermoelectrics generally operate within 25% to 80% of the maximum current. The input power to the thermoelectric determines the hot side temperature and cooling capability at a given load.

As the thermoelectric operates, the current flowing through it has two effects: (1) the Peltier Effect (cooling) and (2) the Joulian Effect (heating). The Joulian Effect is proportional to the square of the current. Therefore, as the current increases, the Joule heating dominates the Peltier cooling and causes a loss in net cooling. This cut-off defines I_max for the thermoelectric.

For each device, Q_max is the maximum heat load that can be absorbed by the cold side of the thermoelectric. This maximum occurs at I_max, V_max, and with T = 0°C. The T_max value is the maximum temperature difference across the thermoelectric. This maximum occurs at I_max, V_max and with no load (Q_c = 0 watts). These values of Q_max and T_max are shown on the performance curve (Figure 3) as the end points of the I_max line.

An Example

Suppose a designer has an application with an estimated heat load of 22 watts, a forced convection type heat sink with a thermal resistance of 0.15°C/watt, an ambient temperature of 25°C, and an object that needs to be cooled to 5°C. The cold side of the thermoelectric will be in direct contact with the object.

The designer has a Melcor CP1.4-127-06L thermoelectric in the lab and needs to know if it is suitable for this application. The specifications for the CP1.4-127-06L are as follows (these specifications are at T_h = 25°C):

Imax = 6.0 amps

Qmax = 51.4 watts

Vmax = 15.4 volts

Tmax = 67°C

To determine if this thermoelectric is appropriate for this application, it must be shown that the parameters T and Q_c are within the boundaries of the performance curves.

The parameter T follows directly from T_h and T_c. Since the cold side of the thermoelectric is in direct contact with the object being cooled, T_c is estimated to be 5°C. Assuming a 10°C rise above ambient for the forced convection type heat sink, T_h is estimated to be 35°C. Without knowing the power into the thermoelectric, an exact value of T_h cannot be found. Equation 3 gives the temperature difference across the thermoelectric:

Figures 2 and 3 show performance curves for the CP1.4-127-06L at a hot side temperature of 35°C. Referring to Figure 3, the intersection of Q_c and T show that this thermoelectric can pump 22 watts of heat at a T of 30°C with an input current of 3.6 amps.

Performance Curve (T vs. Voltage)

T( °C)

Figure 2: Melcor CP1.4-127-06L, ^T vs. Voltage

Performance Curve (T vs. Qc)

T( °C)

Figure 3: Melcor CP1.4-127-06L, ^T vs. Qc

These values are based on the estimate T_h = 35°C. Once the power into the thermoelectric is determined, Equations 1 and 2 can be used to solve for T_h and to determine whether the original estimate of T_h was appropriate.

The input power to the thermoelectric, Pin, is the product of the current and the voltage. Using the 3.6 amp line in Figure 2 for the current, the input voltage corresponding to T = 30°C is approximately 10 volts.

Using Equations 1 and 2, T_h can now be calculated.

The calculated T_h is close enough to the original estimate of T_h, to conclude that the CP1.4-127-06L thermoelectric will work in the given application. If an exact solution needs to be known, the process of solving for T_h mathematically can be repeated until the value of T_h does not change.

Other Parameters to Consider

The material used for the assembly components deserves careful thought. The heat sink and cold side mounting surface should be made out of materials that have a high thermal conductivity (i.e., copper or aluminum) to promote heat transfer. However, insulation and assembly hardware should be made of materials that have low thermal conductivity (i.e., polyurethane foam and stainless steel) to reduce heat loss.

Environmental concerns such as humidity and condensation on the cold side can be alleviated by using proper sealing methods. A perimeter seal (Figure 4) protects the couples from contact with water or gases, eliminating corrosion and thermal and electrical shorts that can damage the thermoelectric module.

Figure 4: Typical thermoelectric from Melcor with a perimeter seal

The importance of other factors, such as the thermoelectric's footprint, its height, its cost, the available power supply and type of heat sink, vary according to the application.

Single Stage vs. Multistage

Given the hot side temperature, the cold side temperature and the heat load, a suitable thermoelectric can be chosen. If T across the thermoelectric is less than 55°C, then a single stage thermoelectric is sufficient. The theoretical maximum temperature difference for a single stage thermoelectric is between 65°C and 70°C.

If T is greater than 55°C, then a multistage thermoelectric should be considered. A multistage thermoelectric achieves a high T by stacking as many as six or seven single stage thermoelectrics on top of each other.

Summary

Although there is a variety of applications that use thermoelectric devices, all of them are based on the same principle. When designing a thermoelectric application, it is important that all of the relevant electrical and thermal parameters be incorporated into the design process. Once these factors are considered, a suitable thermoelectric device can be selected based on the guidelines presented in this article.

Sara Godfrey
Melcor Corporation, 1040 Spruce Street
Trenton, NJ 08648, USA
Tel: +1 (609) 393 4178
Fax: +1 (609) 393 9461
Email: tecooler@melcor.com

References
1. Levine, M.A., Solid State Cooling with Thermoelectrics, Electronic Packaging & Production, Nov. 1989.
2. Melcor Corporation, Thermoelectric Handbook, Sept., 1995.
3. Rowe, D. M., CRC Handbook of Thermoelectrics, CRC Press, Inc., 1995.
4. Smythe, Robert, Thermoelectric coolers take the heat out of today's hot chips, Electronic Products, Aug. 1995.

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