2012 12th IEEE International Conference on Nanotechnology (IEEE-NANO)

The International Conference Centre Birmingham

20-23 August 20112, Birmingham, United Kingdom

Si/SiGe Nanoscale Engineered Thermoelectric Materials for Energy Harvesting

D.J. P aull, A. Samare11il, L. Ferre Llinl, J.R. Watlingl, Y. Zhangl, J.M.R. Weaverl, P.S. Dobsonl,

S. Cecchi2, J. Frigerio2, F. Isa2, D. Chrastina2, G. Isella2, T. Etzelstorfer3, J. Stang13, E. Muller Gubler4

Ahstract- Thermoelectric materials are one potential tech­nology that could be used for energy harvesting. Here we re­port results from nanoscale Ge/SiGe heterostructure materials grown on Si substrates designed to enhance the thermoelectric performance at room temperature. The materials and devices are aimed at integrated energy harvesters for autonomous sens­ing applications. We report Seebeck coefficients up to 279.S±1.2 f-l V IK at room temperature with electrical conductivites of 77,200 S/m which produce a high power factor of 6.02±0.OS mWm-1K-2• Methods for micro fabricating modules will be described along with techniques for accurate measurements of the electrical conductivity, Seebeck coefficient and thermal conductivity in micro- and nano-scale devices. The present thermoelectric performance is limited by a high threading dislocation density.

I. INTRODUCTION

The generation of electricity from thermal energy through

the Seebeck effect has been used for the last 50 years to

power a number of systems. Through the scaling of CMOS,

electronic circuits are now within reach of creating au­

tonomous sensors with sensing, control I analysis electronics,

radio communication and power management all integrated

into a single system-on-chip. For many sensing applications,

sensors require lifetimes of tens of years and the cost of

replacing batteries is orders of magnitude greater than the

cost of the system. Energy harvesting could potentially allow

fit and forget solutions where the battery never needs to be

replaced or indeed the battery may be completely removed

from the system.

The figure of merit for thermoelectric materials IS ZT

= 0;2 (}T / "" where 0; is the Seebeck coefficient, () IS the

electrical conductivity, T is the temperature and "" is the

thermal conductivity [I]. At present the best thermoelectric

materials for room temperature operation are based on bulk

Bi2Te3 and Sb2Te3with ZT :::::: I but tellurium is one of the

rarest elements on the planet and there is great demand for a

sustainable replacement [1]. The maximum power that can be

delivered to a load is related to the power factor, 0;2() so this

parameter must also be optimised for practical systems. More

importantly, when the temperature drop across the material

is small (i.e. for b..T < 25 K) and output power is more

1 University of Glasgow, School of Engineering, Rank-ine Building, Oakfield Avenue, Glasgow, Gl2 8LT, U.K. Douglas.Paul@glasgow.ac.uk

2L-NESS, Politecnico di Milano, Via Anzani 42, 22100 Como, Italy 3 Johannes Kepler Universitiit, Institute of Semiconductor and Solid State

Physics, A-4040 Linz, Austria 4ETH Zurich, Electron Microscopy ETH Zurich, Wolfgang-Pauli-Str. 16,

CH-8093 Zurich, Switzerland

important than efficiency, a high power factor can produce

significantly more output power from better electrical and

thermal impedance matching than optimization of ZT.

Large values of ZT requires a high electrical conductivity

and a low thermal conductivity. Due to the Wiedemann­

Franz rule, the two are proportional to each other in bulk 3D

materials and it is therefore difficult to engineer enhanced

thermoelectric materials. In lower dimensions, it is possible

to engineer structures in which there are weaker relation­

ships between the electrical and thermal conductivities. The

Seebeck coefficient is given by [2]

(I)

where q is the electron charge, kB is Boltzmann's constant,

JL is the mobility, g is the density of states, E is the energy

and EF is the Fermi energy. Therefore the use of quantum

wells, ID or OD nanostructures can also enhance the Seebeck

coefficient through the enhancement of the density of states

[2], [3].

Our approach uses Ge/SiGe heterostructures on Si sub­

strates to produce quantum wells and quantum dots which

have previously demonstrated high ZTs at high temperatures

[4] and can be easily integrated onto silicon chips through

back-end-of-line processing. Nanofabrication is also being

used to etch I D nanowires of Ge/SiGe heterostructures

to investigate potential enhancements. In this paper lateral

structures using Ge quantum wells will be investigated with

the aim of improving the ZT and power factor of the material.

II. FABRICATION

Ge/SiGe superlattices have been grown on Si substrates

using the low energy plasma enhanced chemical vapour

deposition (LEPECVD) growth technique which provides

very fast growth of up to 10 {Lm thick superlattices, ideal for

thermoelectric modules. A I {Lm Sio.2Geo.8 buffer was grown

at a rate of 5.5 nm Is and 525 °C [5]. This was followed

by 378 periods of modulation doped Ge quantum wells with

Sio.3Geo.7 barriers grown at the lower temperature of 475°C.

The compressively strained quantum well widths were varied

between 6.5 and 9.5 nm as measured by high-resolution x­

ray diffraction. The barriers in each structure were designed

to be tensile strained so that the total structure was strain

symmetrised and pseudomorphic to the relaxed buffer. The

sheet doping level of boron was 7.5 x 1012 cm-2 in between

100 nm

Fig. I. A TEM image of one of the lateral superlattice samples showing Ge quantum wells and SiGe barriers. The box indicates where a threading dislocation crosses a quantum well.

I I I I I I I I I I I 15 OkV 15 9mm x80 SEll) 500um

Fig. 2. A SEM image of a single free standing Hall bar sample for measuring the electrical conductivity. thermal conductivity and Seebeck coefficient for micro and nanoscale samples.

each quantum well and at the top and bottom of the structure

to screen the surface and substrate from the quantum wells.

Fig. I shows a transmission electron micrograph of Ge

quantum wells grown on a thin strain relaxation buffer on

top of a silicon-on-insulator substrate. Due to the thin virtual

substrate, the dislocation density is around 109 cm-2 as

measured by both transmission electron microscopy (TEM)

and counting the surface density using an optical microscope

after a decoration etch. Holes in this design are transported

along the quantum wells and so to characterise the material,

free standing Hall bars with electrical heaters at each end

to provide a temperature gradient along with thermometers

and electrical contacts to allow the electrical conductivity,

thermal conductivity and Seebeck coefficients to be extracted

on a single sample (see Fig. 2) were fabricated. The ther­

mometers consist of 20 nm of Ti with 100 nm of Pt and

are calibrated to obtain an accurate temperature coefficient

of resistance before being used. The thermal conductivity is

particularly difficult to measure and we use a novel technique

80000

E 70000 � Z. 60000 .s; � ::l

"C 50000 c: 0 <) iii 40000 <) .;: ti CI) iii 30000

20000 6 6.5 7.5 8.5 9.5 10

QW width (nrn)

Fig. 3. The electrical conductivity of the modulation doped samples as a function of quantum well width at 300 K. The errors are below I % and therefore any error bars are smaller than the plotted diamonds.

where the material in the Hall bar is measured before the

central part of the Hall bar is cut out leaving the heaters and

thermometers. Measurements are then made to obtain the

parasitic heat transport down the thermometers and heater

leads and this allows an accurate determination of the heat

flux which is transported down the material, essential to be

able to determine the thermal conductivity with a high level

of accuracy.

III. THERMOELECTRIC CHARACTERISATION

The electrical conductivity was measured on Hall bar

samples (see Fig 2) using a 4 terminal technique to remove

all series resistances from the measurement. The electrical

conductivity as a function of quantum well width is plotted

in Fig. 3. For bulk Ge doped at a comparable level the elec­

trical conductivity is 33,300 S/m [6] and so the modulation

doping technique has clearly produced higher values. As the

quantum well width is reduced, there is a sudden transition

to a reduced electrical conductivity which can be attributed

to an increase in interface roughness scattering [7]. This

spacer layer (the undoped spacer between the doping supply

layer and the quantum well) is not a constant and will also

decrease for the narrower quantum well. The position of the

dopant has not been measured in these samples and so the

thickness of the spacer layer between the quantum well and

the doping supply layer is unknown. Whilst the uncertainty

in the measurement of electrical conductivity is below 1%

of the measured values, the variation observed between the

samples is much larger than this value. It is believed that

local variations in the high threading dislocation density

for each sample results in the variability as the electrical

conductivity is very sensitive to the dislocation density in

this regime [8].

Two different techniques have been used to measure the

Seebeck coefficient. Both rely on an electrical heater at one

end of the Hall bar providing a temperature difference along

the Hall bar which will produce a Seebeck voltage. Heater

powers up to 25 m W were used which heats the hot side of

12

10 > .s (I) 8 CI S "0 >

-" 6 0 (I)

.c (I) (I)

(/J 4

8 10 12 14 16 18 20 22 Differential temperature (K)

Fig. 4. The Seebeck voltage as a function of temperature across a modula­tion doped sample at 300 K. The squares are temperature measurements from calibrated thermometers and the circles are measurements using a calibrated thermal AFM.

290

Q 280 -..... > -3 270 .... c OJ

'u <;:::: 260 -OJ 0

U -" 250 u OJ

..Q OJ OJ

Ul 240

230 6 6.5 7 7.5 8 8.5 9 9.5 10

QW width (nm)

Fig. 5. The Seebeck coefficient of the modulation doped samples as a function of quantum well width at 300 K with error bars plotted for each sample.

the Hall bar up to 335 K. As both ends of the Hall bars have

heaters, the heat was applied in both directions to provide

confidence in the measurements by producing symmetrical

results and in all cases the difference in measurement was

less than 1 %. All devices have calibrated thermometers

fabricated at either end of the Hall bar which allows the

temperature gradient to be measured. To provide a secondary

check, a calibrated thermal atomic force microscope (AFM)

where the Johnson noise in a resistor is used to provide a

calibrated reference [9] was scanned down the Hall bar. Fig.

4 presents the data from both techniques for a sample with

a 9 nm wide quantum well. Both techniques agree to better

than 1 % which provides confidence in the measurements

and the extracted Seebeck coefficients.

The Seebeck coefficient was taken as the gradient of the

Seebeck voltage versus the temperature difference measured

down the length of the Hall bar. Fig. 5 demonstrates the

variation of the Seebeck coefficient measured as a function

e-� [ ....

� J!! .... (I) � 0 a.

0.007

0.006

0.005

0.004

0.003

0.002

0.001 I....----L_--'-_-'-----''-----'-_--'-_-'------' 6 6.5 7 7.5 8 8.5 9 9.5 10

QW width (nm)

Fig. 6. The power factor of the modulation doped samples as a function of quantum well width at 300 K. The error bars are smaller than the plotted squares.

of the quantum well width. For this set of samples, the results

suggest that the Seebeck coefficient is near constant and it is

believed that the small variability in the results is related to

local changes in the threading dislocation across the samples

being characterized [8]. These results with values between

236.0±3.5 and 279.5±1.2I1Wm-1K-2 should be compared

with a bulk p-type Ge Seebeck coefficient of 90 ILV/K at

300 K with comparable doping density of rv 1 019 cm -3 [10]

and thin film p-Ge samples of 200 I1V/K [6]. As a high

dislocation density can also increase the Seebeck coefficient

[8], the present results do not yet demonstrate beyond all

reasonable doubt that the enhanced Seebeck coefficient is the

result of a larger asymmetry across the chemical potential

as suggested by equation (1). Further samples with lower

dislocation density are required before the true mechanism

for the enhanced Seebeck coefficient can be determined.

The power factor as a function of quantum well width has

been plotted in Fig. 6. The values need to be compared with

bulk p-Ge of 2.45 x 10-4 Wm-1 K-2 and for thin film p­

Ge of 1.33 x 10-3 Wm-1K-2. All the values demonstrate

enhancements with the best samples producing power factors

six times larger than bulk thin film Ge for a comparable

doping density [6].

To obtain the thermal conductivity, a measurement of the

heat flux being injected into the hot end of the Hall bar is

required. To obtain this, the temperature at each end of the

Hall bar was measured using the calibrated thermometers

(see Fig. 7). The Hall bar was then removed allowing the heat

that is being transported through parasitic channels such as

the electrical, heater and thermometer contacts to the Hall bar

to be measured. By evaluating how much additional power is

required with the Hall bar central section in place to get the

hot end of the device to the same temperature, an accurate

heat flux being injected into the Hall bar can be extracted.

Fourier's law can then be used to calculated the thermal

conductivity since the temperature gradient along the Hall

bar is known as well as the heat flux entering the Hall bar at

the hot end and the length of the measurement section. Fig.

340 r-----r---�----_,----_,--, • Hot Thermometer • Cold Thermometer •

330 •

•

E .a 320 E •

•

CI) Co E � 310 " ..... .

•

�

•

1..-••

:

•

300 � •• _ •• •

o 5 10

• • • • •

15 20

Power Heater (mW)

•

Fig. 7. The hot and cold side thermometers demonstrating the temperature gradient along a 9 nm wide quantum well Hall bar at 300 K substrate temperature.

� E ! z. .;;: � ::l

1J c: 0 0 iii E ... CI)

J:: I-

60

50

40

30

20

10

OL-� __ -L __ �� __ � __ �� __ � 6 6.5 7 7.5 8 8.5 9 9.5 10

QW width (nm)

Fig. 8. The thermal conductivity of the samples as a function of quantum well width at a 300 K substrate temperature.

8 presents the thermal conductivity results from the samples

as a function of quantum well width. There is a general trend

of lower thermal conductivities for narrower quantum wells.

As the electrical conductivity is also reducing, in the present

samples it is the hole contribution to the thermal conductivity

that dominates the reduction in thermal conductivity as the

quantum well width is reduced. The error bars have been

calculated from the measurements using standard statistical

methods. It is clear that the uncertainty for the thermal

conductivity measurements is significantly larger than the

uncertainty in the electrical and Seebeck measurements.

The ZT for the samples as a function of quantum well

width is presented in Fig. 9. For bulk Ge, the ZT is

1.15 x 10-3

[10] whilst for thin film Ge it is 6.23 x 10-3

.

The present results represent an order of magnitude increase

in the ZT figure of merit demonstrating the benefits of

low dimensional structures for improving the thermoelectric

figure of merit.

0.1 r-----,---,------r----,---,------,---,-----,

0.08

� 0.06 0 0 !:2. l-N

0.04

0.02

6 6.5 7 7.5 8 8.5 9 9.5 10 QW width (nm)

Fig. 9. The measured ZT at 300 K for the samples as a function of quantum well width.

Fig. 10. A SEM image of arrays of 50 nm wide etched Si/SiGe nanowires designed for vertical electron transport.

IV. DISCUSSION

These ZT values are still rather low compared to bulk

Bi2 Te3. Initial analysis suggests that all the present samples

have significant electrical conductivity in the Sio.3 Geo. 7 barriers and therefore optimising the spacer and doping sup­

ply layers should allow improved results especially through

enhancements to the Seebeck coefficient through the re­

duced doping. The modulation doped design will allow high

electrical conductivity for lower values of doping that bulk

samples due to the reduced Coulomb scattering. A second

issue is that the ZT is strongly dependent on the threading

dislocation density for densities above 107 cm-2 [8]. Theory

suggests that a reduction of the threading dislocation density

to 107 cm-2 or below would increase the ZT by an order of

magnitude [8] which would result in ZT values comparable

to Bi2Te3 at room temperature. The power factors are already

above bulk Bh Te3 at room temperature and these values

are expected to improve by an order of magnitude through

the reduction of the threading dislocation density and the

reduction in the doping in the samples.

The results also indicate that for the lower thermal con­

ductivities, the uncertainty in ZT increases significantly. This

makes accurate characterisation of material difficult with

the majority of the uncertainty in the measurement of the

Fig. I I. A TEM image of a Ge quantum dot grown directly by LEPECVD on a Si substrate.

thermal conductivity. There are many other potential methods

to improve the thermoelectric efficiency apart from the

straight quantum well modulation doping scheme discussed

above. SiGe superlattice material with much thinner quantum

wells and barriers has also been etched into nanowires to

investigate further reductions in the dimensionality where the

transport is vertical rather than lateral. Fig. 10 demonstrates

a SEM image of an array of 50 nm wide Ge/SiGe nanowires.

Such structures are being developed for vertical thermoelec­

tric superlattice transport to allow separate n-type and p-type

nanowires on Si chips to be flip-chip bonded to produce

complete thermoelectric modules. Finally, Ge quantum dot

structures have also been investigated. Multilayers of Ge

quantum dots have been produced in a Si matrix with heights

around 10 nm and widths around 25 nm (see Fig. 11). The

results from these ID and OD materials will be presented in

future publications elsewhere.

V. CONCLUSION

Nanoscale patterning of materials has been used to en­

hance the thermoelectric performance. Enhancements of the

Seebeck coefficients have been achieved using modulation

doped Ge quantum wells. Improvements of over an order of

magnitude in the power factor and ZT over bulk and thin

film Ge has been achieved but the ZT values are presently

limited by the threading dislocation density and parallel

electrical conduction in the barriers of the device. Modelling

suggest that reductions in the threading dislocation density

to 107 cm-2 or below would result in an order of magnitude

increase in ZT over the present results.

VI. ACKNOWLEDGEMENT

The work has been undertaken as part of the GREEN

Silicon project (No. 257750) funded by the EC ICT Fu­

ture Emerging Technologies Proactive Initiative "Towards

Zeropower ICT".

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