On-Chip Thermoelectric Cooling Tool
Contents
1. To Qm Qie RTEC H Sink RH Sink Amb Here in equation 2 we multiplied the thermal resistances Renip case Rease TEC by its corresponding thermal current and then added the temperature at the cold side of the TEC to get the total temperature at the chip junction Similarly to find the temperature at the hot side of the TEC we multiply the thermal resistances RTEC H Sink Ru sink Amp times the corresponding heat current and then add the ambient temperature Analyzing these equations we realize that there are four unknowns Tp Te Tenip and Qie The user can fix Qm and J on the simulation Thus a system of four equations and four unknowns is developed The recommended method to solve this system is by using the rref row reduce echelon form function from MatLab once the corresponding matrix has been found Below the code used to solve these equations is shown Matrix 2 N alpha I K G 2 N K G O O Qm N I 2 rho G 2 N alpha 1 2 N alpha xI 1 0 2 N I 2 rho G 0 1 R2 R3 O TO Qm R2 R3 1 0 O 1 Qm RO R1 M rref Matrix This would yield the result for each of the variables for given values of Qm and J A full copy of the code is available under request 6 Input amp Output Default values are set for a common device There are three categories for user input 1 TEC characteristics 2 Thermal Resistances 3 Analysis Type Each of them is briefly discussed below 62. 2 3 5 And multiplying by the number of thermocouples the equation becomes Qm 2N 1 2 3 6 Where 1 aTl 2 I p 2G 3 kG T T Where T and T are the cold and the hot side of the TEC respectively and k is the thermal conductivity of the thermoelectric elements The negative side indicates backflow of heat And we get our first equation for heat current looking something like this Qm 2N aT I I p 2G kG Th Te 7 Now let s analyze the flux after the TEC Let s say now that Q is the power dissipated by the thermoelectric cooler Thus we would have to take into account two heat current contributions to the system 1 Power dissipation due to joule heating in the device 2 Power dissipation due to Seebeck voltage drop Just as before we have to multiply the total addition of the fluxes by the number of thermocouples The equation for the TEC heat contribution would then look like Qte 2N 1 2 8 Where 1 I p G 3 al T And we get our second equation for heat current Qie 2N 1 p G aI Thn T 9 Now we just need to calculate the localized temperatures at each of the interfaces by multiplying the corresponding flux addition times each thermal resistance and adding any preexisting heat Equations would look like 1 Qm 2N aT I p 2 G kG Ti T 2 Qie 2N I7p G aI Tr Te 3 Tehip Ig Qm Rechip case Rease TEC A Thot
3. current through the device in opposite direction to the existing current and a voltage drop is developed throughout Furthermore this would turn out to be a complicated relation but we will keep it simple In a few words the voltage source would have to overcome the voltage drop produced by the heat flow generated through the TE device Seebeck voltage and the one produced 3 by the actual device to make current flow This process will dissipate heat according to the ohm s law W V x I Other heat source would be the chip power dissipation Qie Then one can map the heat currents through the layout ad come up with equations describing the flow of heat Let s start with a simple one couple device Figure 4 Thermoelectric Heat Pump Dual Semiconductor Pellet For each metal semiconductor metal junction two in the above figure Heat will be pumped from the hot side according to the formula q nl 1 Where q can be called the heat current and 7 is the peltier coefficient which describes the amount of heat current per unit charge J is just the electric current through the materials In turn while powering the device the power dissipated as heat flows half towards the hot side and half towards the cooled side This is simple joule heat described by ohm s law as PR 2 But we find convenient to express the electrical resistance R as a function of the geomet rical dimensions of the thermocouples Assuming th
4. parallel 2 Current flows through the circuit in the direction indicated to transfer heat from the top part to the bottom part Common Peltier devices are made of several of this junction connected electrically in series and thermally in parallel as shown in the picture below lel Heated E Figure 2 Peltier Cell Schematic The contacts and semiconductor materials are sandwiched in between two slabs of insu lating material commonly ceramic A real life device is shown below Figure 3 Real Peltier Device If we take a close look to the edges of the device we will be able to identify the several couples of semiconductor Normally a protective material is put on these edges to avoid damage to the semiconductor couples Also when using these devices one must be careful not to exceed a maximum working temperature specified by the manufacturer so to keep the soldier connecting the device from being melt or other irreversible damage to the device 4 Thermoelectric theory Thermoelectric phenomena arise out of inter coupled electrical and thermal currents in a material As stated in the introduction Seebeck and Peltier effects are the main thermoelec tric effects They both happen simultaneously in a thermoelectric device One can connect a TE device to a voltage source and make an electrical current flow through the junctions inside to generate a heat flow Peltier effect At the same time such heat flow produces an electrical
5. 1 TEC Characteristics e No of N P couples This is the number of thermoelectric n and p type material couples in the Peltier cell e Seebeck Coefficient This is the coefficient of proportionality indicating how much voltage is generated through the device per temperature difference Units are in volts per kelvin V K e Electrical Resistivity An average resistivity of n and p type materials In units of ohm per meter ohm m e Gamma Factor The ratio of a thermoelectric element single cube of semiconductor element to its length In units of meters m 9 e Thermal Conductivity A measure of the ability of the TEC to transfer heat per 6 2 unit time given one unit area and the temperature gradient through the thickness of the device In units of watts per meter per degree Kelvin W m k Thermal Resistances In here the user specifies the thermal resistances of each of the junctions in the device in units of degree kelvin per Watt K W Chip to Case Case to TEC TEC to Heat Sink Heat Sink to Ambient 6 3 Analysis Type e Analysis Here the user can choose whether to sweep for maximum cooling capacity or current input to the TEC e Ambient Temperature The temperature of the heat sink surroundings in degrees Kelvin K e Current Feed Current through TEC only for Sweep Power Dissipation analysis in units of Amperes A e Power Dissipation The maximum power pumped out of the chip only for Sweep Curre
6. On Chip Thermoelectric Cooling Tool User manual David Saenz March 28 2011 1 Introducion Thermoelectricity is the study of the relationship between heat and electrical energy There are two main thermoelectric effects one on which a heat current through a thermocouple produces an electrical current Seebeck effect and one on which an electrical current pro duces a heat current Peltier effect Thermoelectric devices make use of these two effects to either produce power out of a temperature gradient or generate a temperature difference between the two sides of the device by the use of electrical power This simulation tool is intended to exemplify one of the main applications of the Peltier effect A thermoelectric cooler or heat pump commonly known as Peltier cell is localized on the top of a micropro cessor s casing Then a heat sink is attached right on the top of it this is a common layout on cooling applications The Peltier cell will take heat from the chip and pump it towards the heat sink which dissipates it to the ambient when an electric current is made to flow trough it We can compare the way this Peltier cooler works with a common refrigerator We spend some amount of electrical energy to transport heat from one place to another We can measure the process efficiency by taking the ratio of the useful work performed heat being removed to the energy expenditures This efficiency is commonly represented by a Coef
7. e p and n type elements within the TEC are the same shape and size and neglecting contact resistance we can express the electrical resistance of the single pellet cooler module as R p length area p G 3 4 where p stands for the electrical resistivity of the semiconductor material And although in reality n and p type pellets have different p we will assume uniformity between both Also we will call the ratio of the area to length of the element gamma factor G for simpli fication The last heat contribution to the system is the one generated by the voltage drop due to the Seebeck voltage through the TEC It is easily calculated by multiplying this thermo electrically generated voltage by the total current flowing through the device V x J QV Seebeck IaAT 4 Where a is the Seebeck coefficient and AT is the difference in temperature between the hot and cold side of the TE device heated and cooled respectively J is again the electrical current that flows through the TEC Now that we have found the heat current through the system and explained how the single coupled TEC works we can turn our attention to the simulation and the math 5 Simulation Thermal resistances are present within a junction of two objects These resistances will make heat not to flow uniformly through the components and will develop a change in temperature This is what we are interested in knowing the temperatures at the different stages of
8. ficient of Performance COP In common Peltier devices this is very small which means that we would have to invest a lot of energy to move a small amount of heat from one side to the other This is why they are only used in applications where heir use is imprescindible Otherwise we can recur to a common gas compression refrigerator or other air conditioning systems Cooling a chip with these devices is an example on which we need of these devices due to its small size durability and maintenance free feature 2 How to use this manual While science underlying thermoelectrics is quite complex in this manual you will find an initial perspective of one of the applications of a thermoelectric cooler by keeping most of the intrincacies apart And although an explanation of the formulas and the code embedded in this tool is provided in this manual it has to be noted that these are only approximations to what it actually happens and it is a good example of a real life case which is the objective of the tool This manual is presented as a step by step explanation on how to use the tool as well as interpret the outputs 3 Thermoelectric Device The layout of a common single couple Peltier device is shown below Figure 1 Thermoelectric Heat Pump This picture explains how this cooling business works The process can be outlined as follows 1 Cooper connects the n and p type semiconductor materials electrically in series and thermally in
9. n this case 1 One dimensional system 2 Heat flows only due to conduction processes 3 Temperature is absolute and invariable on each part of the setup 4 Temperature independent thermoelectric parameters 5 No thermal resistance between electrical junctions within the TEC 6 No thermal masses instant heat transmission no transient state The image below shows the heat currents through the device and the thermal resistances at the junctions Rinip case Rease TEC Reec 1sink RB sink Amb E s n Ambient k b i Figure 6 Thermal Profile Heat currents are the big red arrows each labeled with a number on the tail 1 and 2 Thermal resistances are represented as electrical resistances through the diagram The temperature at each junction can be found by multiplying the total heat current through the junction by the corresponding thermal resistance and adding the corresponding temperature from the past junction Let s first find the equations describing the thermal fluxes For the total heat current 1 the total cooling capacity of the thermocouple we have to take into account the following fluxes 1 Heat being pumped by the TEC away from the chip case 2 Heat dissipated by the TEC towards the chip case 3 Heat transmission from hot side of the TEC to the cold side due to Fourier s law Thus if we say that Q is the total heat current on the bottom side of the single ther mocouple TEC Qm 1
10. nt Input analysis in units of Watts W e Maximum Plot Range Maximum range for each kind of simulation e Minimum Plot Range Minimum range when plotting in sweep current mode 6 4 Output There is a graph for each of the variables in the equations solved earlier in the manual There is also a plot of the temperature difference across the TEC labeled as Thot Tcold as well as one for the figure of merit of the device Below summary of output graphs 1 Cold Side Temperature of the TEC 10 2 Hot Side Temperature of the TEC 3 Thot Tcold 4 Chip Temperature 5 Power Dissipated by the TEC 6 Figure of Merit Each of these graphs is self explanatory References 1 D K C MacDonald Thermoelectricity an introduction to the principles Dover New York 1st Edition 2006 2 Mark Lundstrom Thermoelectric Nanotechnology https nanohub org resources 9421 2010 3 TXL Group Inc Thermoelectric Generation Developer s Kit TXL Group Inc Texas 1st Edition 2009 11
11. our layout If we want to know the temperature at a certain point on the system we just need to multiply the heat current at the interested stage by the thermal resistance at the corresponding junction This process can be compared to electrical circuit calculations One can take heat current as being electrical current voltage at a resistance as the temperature of the junction and electrical resistances as thermal resistances we can use this analogy due to the 1D system assumption As an example lets take the heat current flowing from the TEC to the heat sink q and multiply it by the thermal resistance between that specific junction The result would yield the junction temperature just as multiplying the electrical current times an electrical resistance yields the voltage drop across it To find the temperature at the heat sink ambient junction we would just have to add the ambient temperature to the temperature resulting by multiplying the thermal resistance in the heat sink to ambient junction and we are good Now we can come up with heat balance equations describing the temperature at each section of our layout In the application mentioned in the introduction the TE cooler TEC is put in between the chip case and the heat sink as shown below Ambient Mari Figure 5 Chip Layout Heat flows from the chip to the case then it is pumped through the peltier device and then dissipated by the heat sink Some assumptions are made i
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