DE1464073A1 - Semiconductor thermocouple - Google Patents

Description

Semiconductor thermocouple

PB-Mr. 25 52Q

(It becomes the priority of January 3, 1961 from the British Patent application Application No. 229/61, Case A-HIi 819 claimed)

The present invention relates to semiconductor materials with improved electrical properties for use in thermoelectric devices

Certain semiconductor materials have recently had a high thermoelectric power compared to metals Gaining increasing importance as a material for thermocouples. Semiconductor thermoelectric devices generally consist of two bodies of semiconductor intermetallic compound with different leadership character, which at one end are connected by a metal plate and have separate metal plates at their other ends. You two bodies can be of the same or different semiconductor material. In a typical thermocouple, this forms the two Body common metal plate the hot contact point, with the relative, high and low temperatures of the contact points a decisive factor for the efficiency of the thermocouple represent,,

In the practical application of thermoelectric phenomena the semiconductor it turned out that the same « the early presence of holes and electrons is inexpedient when hole and electron mobility are approximately equal. Moreover, it is advantageous to have semiconductors with high electrical

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Conductivity & to use "Both requirements are met" by introducing impurities into the semiconductor, which either generate free electrons or holes in the material · In this way an improvement in the thermoelectric properties of the semiconductor is achieved · The thermoelectric power of a semiconductor (sucked on The thermal SSK produced varies greatly with the purity and perfection of the sample and therefore depends on the concentration of the imprinting agent, on which in turn the conductivity depends. The properties required of a semiconductor material which is to be used for thermoelectric applications include not only a high thermoelectric force, but also the lowest possible resistance and the lowest possible thermal conductivity. The desired material should therefore have a low Lorens number Xi >> K / # T (where ¹ S is the temperature of the material / ° K, K is the thermal conductivity and C ^ is the electrical conductivity)

Ui s S ² At d.ho <Sää m- S% T / K - S ² T.

can therefore be as high as possible, whereby the specific resistance of the material and S dsr Seebeckkoeffizisnt (thermal EMF generated in the material / BinlrvSit Temperaturöifferenz / ° O) a measure of the thermoelectric ^, K ;. ^: & ft is. The so-called figure of merit is a decisive factor for the efficiency of the thermocouple and of course has its highest value only at a very specific temperature Thermocouple that acts as a theraoelectric generator requires greater temperature differences than with a thermocouple for thermoelectric cooling: and therefore the temperature dependency of the corresponding parameters (K, ® * and S) as theraoeltktrieohan materials cannot be neglected »In a situation where temperature differences of several hundred degrees being viewed «it is not always possible

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ZWP 25th 520

•a. to use a single material in the thermocouple because the iSigenleitung achieved the desired with the material can prevent highest figures of merit.

The present invention is a semiconductor thermocouple, higher fourth of the figure of merit in the opposite of the confessed can be achieved.

According to the present invention, in a semiconductor thermocouple, in which the conductivity is preferably of the n- or p-Iyp, the level of impurities progressively graded so that the maximum figure of merit of the material corresponding to that of the Operating conditions in the body created temperature distribution remain.

The theoretical determination of the optimal distribution of the impurity level in the thermocouple appears difficult at first glance, since the temperature distribution does not depend on the chosen impurity distribution. If, however, the optimum values of the Seebeck coefficient S, of the electrical resistance f and of the thermal conductivity E are known over the temperature range in which the thermocouple is operated, then the problem of determining the required distribution is only a numerical one.

From a consideration of the simple theory theπαοelectric Devices can be shown that the Seebeck coefficient S for the maximum (Kiteza & l at a given temperature in the thermocouple given the following equation, it is 2

is there

k the Boltzmaiine 2hö Komstante

K ^ the thermal conductivity of G-it e

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If aleo KJ&C ^ t * ^so * ^B * ^{der rfer} * ^{Von s} aahesu constant, wit always be the operating conditions, if the figure of merit should be at its optimal value at every point of the thermocouple. If S is assumed to be exactly constant, the above condition requires that the carrier concentration n, ie the level of the impurity, varies such that η er T, where I is the operating temperature. Furthermore, since the carrier concentration η does not vary with the temperature in the conduction state with little interference, corresponding to the saturated n or p conductivity, the equation of the heat flow along the thermocouple in the stable state can be used

di * (K degrees T) + j ² / cf »0 ..... ·.«. (2)

(where;} is the density of the electric current) can be integrated in its one-dimensional range, eo that the relative distribution of donors and acceptors in and / or along the thermocouple is obtained The following simplification would give an expression for the temperature distribution along the thermocouple. Since nCf3 / 2 _f fcaan ai _e desired distribution of free electrons or holes along the conductor can be calculated mathematically with the following equation:

n / n ₀

£ the length of the thermocouple T the temperature at a .distance χ from the cold

End of the thermocouple T * the temperature at χ «^ f T the temperature at χ = ο η the carrier concentration: ui an -uJntferaiing

x from the cold find of the thermocouple and n ₀ the carrier concentration at 2: «c

0 9 9 0 1/042 6

ZWF 25 520

the upper one

a function of the figure of merit &> - j _t the temperature T-, eren limit of the efficiency ^ () of the thermocouple £ - (^ ₁ -I ₀ ) A ₁ J and T ₁ A ₀ * that a modified figure of merit

represents

(B -ο * O) ₁ da Τ— ^ T ₀ )

belongs (Cp ₀ is the figure of merit corresponding to the upper limit of the efficiency λ)

ft. ²

Now at high temperature the thermal conductivity of the lattice K ^ is usually inversely proportional to the temperature » and so K ^ - AAf where λ is a constant; Ke will neglected, on the assumption »that S is constant · · * ■

becomes <3TT if S is constant

As an example, consider a specific case: Ee. let S "120O ⁰ K, T ₀ " 300 ⁰ K unaω ^ (figure of merit at temperature T ₁ ) * 10o DaßxrT ² , iu _Q (corresponding to T ₀ ) is equal to 0.6251 which is close to the value for bismuth telluride Bi ₂ Te ₅ at 30O ⁰ K comes up. Bi ₂ Te ^ is a heavy intermetallic compound that has gained importance as a semiconductor material for thermoelectric applications due to its low thermal conductivity and high thermoelectric power.In practice, however, the performance is dee Bi ₃ Te ₅ due to its small forbidden band and low melting point limited; the above example is therefore intended to illustrate “how matter can behave when it is not so limited. They correspond to variations of T and g along the

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Thermocouple Bind for Bi ₃ Te _{5 shown} in Figure 1 of the accompanying drawing.

The efficiency of such a graduated thermoelectric generator (Bi ₂ Te ₅ ) is shown graphically in Figure 2 as a function of the upper figure of merit ^, at a temperature S ₁ (^ ₁ = S ² T ₁ <T / K) * Ist6O ₁ = 10 » so h · 36 #, Although an efficiency of this order of magnitude would be very desirable, especially if such an efficiency could be maintained up to a temperature of 1200 ^° K, it is unlikely that a semiconductor material like that shown by Bi ₂ Te, at low temperatures has efficiency even at these temperatures · Mn such a material would be particularly suitable for thermoelectric applications. In general, the efficiency of semiconductor thermocouples between 10 and 10

In practice, it is also likely that the thermocouple is made from at least two different semiconductors o However, since S would still be approximately constant, the above general theory could still be used in determining the required variation in impurity level when the integration of equation (2) is performed in parts.

The above method is of interest because it illustrates how a particular temperature and carrier concentration distribution can be achieved across the thermocouple. It however, it can be shown that the condition that S is constant should be, represents an undue restriction, and that this Condition only applies to the case in which the figure of merit has a low value · If S is not constant, the optimal Values of all parameters appearing in the heat flow equation can still be determined as a function of temperature · The heat flow equation then has the

d / dx (κ _ö dT / dx) + j ² / e- _o - js-P- SSL. 0. (4)

■ dT dx

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for the SqJLI ₉ da © K _f ^ * «AS t & re fcftiaalen rferte S ^ ^ _% halsen. Since the latter are functions of the temperature $, this equation can be evaluated numerically if the boundary conditions are chosen, Me boundary conditions are the two temperatures T _Q (at χ = 0) and SJ ₁ (at x = <£) between the Tharmocouple should work, where T _{1 is} greater than $ ₀ and the length of the thermocouple £ is. The temperature and carrier concentration distributions along the thermocouple can then be calculated for a given current density%.

The efficiency is calculated from the absorbed heat t at a temperature T ₁ and the _{heat repelled at T Q} , as well as the work Φ determined from their difference * The efficiency is then £ = ^ Vq ₁ »which is a function of the current density J ( or the external load). This value j is then chosen so that rt remains at its maximum.

The variation can be determined from the corresponding temperature distribution of S, € T and K along the thermocouple both under the operating conditions under which the thermocouple is to operate and can also be calculated at room temperature. So the variation of the impurity level along the thermocouple for a maximum degree of effectiveness can be obtained. In practice would this required variation in the level of the storage location the thermocouples are made in such a way that one the known method for varying the impurity level of a semiconductor crystal is used.

It may also be desirable to measure the cross-section of the Graduating the thermocouple in order to obtain the maximum figure of merit according to the temperature distribution created in the thermocouple. It has been found that by grading the crosswise order in the case where the material parameters are constant, nothing is won; however, this need not apply if the Parameters are not constant.

Claims (5)

1Λ64073 Q ZVYF 25 520 ! Patent claims 11 Λ semiconductor thermocouple with preferably ρ- or n-conductivity character, characterized in that to increase the value of the figure of merit, the impurity level is graded so that the maximum figure of merit of the material corresponds to the temperature distribution that occurs during operation. 2. Semiconductor thermocouple according to claim 1, characterized in that » that the equation of the heat flow along the thermocouple in stable condition diV (K degrees T) + $ ² / <r * O linearly integrated, which gives the relative distribution of donors and acceptors in 'and / or along the thermocouple. 3. Semiconductor thermocouple according to claim 1 and 2 _r, characterized in that the figure of merit by means of the equation certainly! that for high temperatures the grid conductivity K is inversely proportional to the temperature and thus at constant Seebeck coefficient S is asymptotically equal to the figure of merit the square of the temperature T iat " 4 · Semiconductor thermocouple according to Claims 1 to 3, characterized in that, in the case of thermocouples, there are at least two different Semiconductors to determine the required variation of the impurity level, the integration carried out in parts the equation diy (K degrees T) + $ ² / <r «O sufficient. 809901/0426 * 3 5. Semiconductor thermocouple, naoh Anepruoh 1 to 4, characterized daduroh that the efficiency by the choice of current density Is kept at its maximum 6, semiconductor thermocouple according to claim t "bie 5, characterized in that the variation of the impurity level along the Thermocouple are designed for maximum efficiency. $ 901/042