Format And Type Fonts


 

 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 39, 2014 

A publication of 

 
The Italian Association 

of Chemical Engineering 

www.aidic.it/cet 
Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Peng Yen Liew, Jun Yow Yong  

Copyright © 2014, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-30-3; ISSN 2283-9216 DOI: 10.3303/CET1439276 

 

Please cite this article as: Kozin K.A., Goryunov A.G., Manenti F., 2014, Siemens-reactor’s high-frequency power supply, 

Chemical Engineering Transactions, 39, 1651-1656  DOI:10.3303/CET1439276 

1651 

Siemens-Reactor’s High-Frequency Power Supply 

Kirill A. Kozin*
a
, Alexey G. Goryunov

a
, Flavio Manenti

b
 

a
Tomsk Polytechnic University, Dept. of Electronics and Automation of Nuclear Plants, 30 Lenina St, Tomsk, 634050, 

Russia 
b
Politecnico di Milano, Dept. di Chimica, Materiali e Ingegneria Chimica „Giulio Natta“, Piazza Leonardo da Vinci 32, 

20133 Milano, Italy 

kozin@tpu.ru 

A detailed mathematical model is developed to calculate the radial temperature profile in silicon rods by 

heating currents of different forms. The model is based on the heat and Maxwell equations and on an 

expansion in Fourier series. Sinusoidal, pulsed unipolar and bipolar-like currents and their combinations as 

well were adopted to investigate the effect. Mathematical models and laboratory devices have been built to 

implement high-frequency power supply (frequency higher than 50 kHz). The power supply is a resonant 

inverter with two cells (sub-modules) that contains new technology with modern IGBT-transistors, low 

induction capacitors and toroidal core from amorphous nanocrystalline alloys. New high frequency 

transport technology with twisted-pair cable has been used to decrease reactive and active loss power. 

1. Introduction 

One of the key issues for the development a modern society is sustainable development and renewable 

energies including the photovoltaic sources (Tiepoloa et al., 2013). On one side, sustainable development 

and the reduction of greenhouse gas emissions are matters of great concern in process development and 

design (Sha et al., 2013). On the other, side PV industry experiencing a deep crisis at the moment. 

Despite it, the research has been conducted in order to reduce production costs and increase the future 

polysilicon market competition for polysilicon plants reconstruction and transformation. Analysis of energy 

consumption in main plants of polysilicon by Ke et al. (2013) shown that multi-effect distillation, reducing 

heat energy comprehensive utilisation system, and cold hydrogenation process can save energy and 

reduce polysilicon cost greatly. Huang and Liu (2013) was developed a novel Chemical Vapour Deposition 

(CVD) reactor. The energy consumption of the novel reactor was < 8% than that of the traditional reactor 

by simulation results. It is well known that Siemens technology, based on CVD, is the most widespread 

process for the production of high-purity polycrystalline silicon. It consists of batch reactors where a set of 

polysilicon rods are heated by intensively supplying electrical energy and they are progressively increased 

in volume (Ceccaroli, 2003). The main limitation of this technology is related to the relevant internal 

temperature gradient within the silicon rods due to the poor conductivity of silicon and the growing 

diameter as well. The fact that the electrical conductivity of pure silicon increases with increasing 

temperature (Fan et al., 2008) leads to a greater increase of the current density flowing in the centre of the 

rod (Mitrasinovic et al., 2009) and thereby this region becomes hotter (del Coso et al., 2007). Such a 

temperature gradient induces mechanicals stresses and limits the possibility to obtain large rods without 

melting the core of the rod, with consequent losses of the polycrystalline nature of silicon inside the rod 

(Hou et al., 2013). An effective way to overcome this limitation, without the inclusion of design changes in 

the Siemens-reactor, is the use of high-frequency current sources (Dawson et al., 2003). In this case, the 

temperature profile within the rod is smoother because most of the current density migrates to the rod's 

outer region (the so-called skin effect). The result is a high overall deposition rate of silicon, with optimum 

temperature deposition, and a minimized breakdown risk; this allows reducing the process time, thus 

reducing energy costs and technological expenses.  

The state-of-the-art provides one invention of high-frequency current sources, which addresses the 

relevant internal temperature gradient problem inside silicon rods, proposed by company “AEG Power 



 

 

1652 

 
Solutions” (Wallmeier, 2009). This power supply is implementing AC as a superposition of two harmonics 

with a carrier frequency of 50-60 Hz. 

In this context, the aim of this work is the development of a new resistive heating method for silicon rods, 

which ensures the reduction of the internal temperature gradient, and its practical implementation to test 

different power supplies.  

2. Mathematical model of the radial temperature profile 

The temperature profile inside the silicon rod is influenced by two key factors: the distributed nature of the 

sources of internal heating by Joule effect and the heat transfer with the environment. The mathematical 

model of the radial-dependent temperature distribution T(r) uses an approach proposed by del Coso 

(2007). The model uses the differential equation of stationary heat conduction in a cylindrical coordinate 

system with a radially distributed heat source: 

 
21

( ) ( ) 0
T

r T T E r
r r r

 
  

     
  

, (1) 

with boundary equations: 

   
0

4 4

Si

0,

( )     ,  









     




r

g B wcon

T

r

T
T T T T T on r R

r
k

 (2) 

where r – radial coordinate, mm; λ – silicon thermal conductivity, W/(m·K); σ – silicon specific conductivity, 

S/m; E – electric field, V/m; R – rod radius, m; Tg – gas temperature, K; kcon – convection coefficient, 

W/(K·m
2
); σB – Stephan-Boltzmann constant, W/(K

4
·m

2
); εSi – silicon emissivity; Tw – reactor’s wall 

temperature, K. 

Maxwell equation leads to the Helmholtz equation since the problem is symmetric, thus the differential 

equation related to the electric field E(r)=J(r)/ σ(T) for a current of sinusoidal form may be obtained: 

1
( , ) 0

E
r k T E

r r r


  
   

  
 (3) 

with boundary conditions: 

0

0
r

E

r 





, (4) 

( ) ( ) , 
rod

tot

S

I T E r dS  
(5) 

where ω – current angular frequency, rad/s; k(T,ω)=–jµωσ(T); μ – silicon magnetic permeability, H/m; Srod 

– cross-sectional area of the rod, m
2
; Itot – RMS current, A; J(r) – current density, A/m

2
. 

However, Eq(5) cannot be easily used for a numerical simulation. Using Eq(3), Eq(4) can be written in the 

following simple form of boundary condition: 

2
tot

r R

E jµ
I

r R









. (6) 

Sinusoidal, pulsed unipolar and bipolar-like currents and their combinations, proposed in Wallmeier (2009), 

were adopted to investigate the skin effect in polysilicon rod. The electric field E for a non-sinusoidal 

current was computed through the superposition method applied to electric fields, generated by harmonic 

currents derived from a Fourier-series expansion of the original current. The required number of terms in 

the Fourier-series expansion was determined by ensuring at least 99 % of the original RMS current. A set 

of conditions used for the simulations is given in Table 1. A general block diagram, relating to different 

current trends, that shows the algorithm employed for the evaluation of the radial temperature profile in the 

polysilicon rod is presented in Figure 1.  



 

 

1653 

Table 1: Set of conditions used in the simulations of the radial temperature profile 

Parameter  Value  Parameter  Value  

Rod surface temp. Ts 1,423 K Convection coefficient kcon 25 W/(K·m
2
)  

Gas temp. Tg 673 K Silicon emissivity εSi -2.79·10
-4

·Ts + 0.93 

Wall temp.Tw 373 K Silicon thermal conductivity λ 39,5·e
-T/62.7

 + 108·e
-T/332.7

 W/(m·K) 

Magnetic permeability 4π*10
-7

 H/m Specific conductivity σ 1.85·10
6
 e

-56300/(8.314·T) 
S/m 

 

 

Figure 1: Polysilicon rod temperature profile evaluation block diagram 

The temperature trends in the rod center and surface, achieved via simulation as a function of frequency, 

depending on the studied current shape, are given in Figure 2. Here the best results coming from the 

superposition of two harmonics with equal amplitudes, which can be implemented by the current source 

proposed by Wallmeier (2009), are shown. The mentioned current source has a low frequency component 

so the skin effect is small while the unipolar pulse current owns a DC component. As observed, the skin 

effect is best manifested in the resistive heating generated by harmonic or bipolar pulse current. Unlike the 

results of del Coso (2007) the skin effect is already evident at frequencies of 50 kHz (Figure 3).  

The temperature gradient within the silicon rod as a function of frequency, for several diameters of the rod, 

is shown in Figure 4. As a result of the reported trends, it is convenient to develop source of bipolar 

currents with frequencies above 50 kHz. 

 

 
 

Figure 2: Temperature trend in the rod center and 

surface as a function of frequency (R = 75 mm) 

Figure 3: Volumetric heat power distribution in the 

silicon rod with its resistive heating as a function of 

frequency harmonic current 

 

 

 1 1 1

1

0

1 1 1

1
, 0;

0;

;
22

r

r R

E
r k T E

r r r

E

r

E a jµ

r R











  
  

  










st
R

I

 

0

1

1
, 0;

0

;
22

n

n n

n

r

n n

r R

E
r k T E

r r r

E

r

E a jµ

r R











  
  

  










...
   

   

2

0

0

4 4

Si w

( )1
0;

2

( )
0;

( )     ;

 

  







  
  

  







   





n

m

m

r

g B

r R
con

E rT
r T T

r r r

T r

r

T
T T T T T

r
k

Fourier-series 

expansion

n
a

1
a

...ia
j

a

( )T r

( )
i

E r

( )
j

E r

1
( )E r

( )
n

E r

...

 

0 50 100 150 200

1260

1290

1320

1350

1380

1410

T
e

m
p

e
ra

tu
re

 (
K

)

Frequency (kHz)

  superposition of two harmonics

  pulsed unipolar

  sinusoidal

  pulsed bipolar

 

0 15 30 45 60 75
0

1

2

3

4

5

6

7

V
o

lu
m

e
tr

ic
 h

e
a

t 
p

o
w

e
r,

σ
(T
)|
E
(r
)|
2
 (

М
W

/m
3
)

Distance (mm)

 10 Hz

 10 kHz

 50 kHz

 100 kHz



 

 

1654 

 

 

Figure 4: Temperature difference between the rod center and surface as a function of frequency 

3. Power supply 

Mathematical models and laboratory devices have been realized to implement a high-frequency power 

supply (frequency higher than 50 kHz). In Figure 5 a schematic structure is presented, in Figure 6 a 3D-

model of a high-frequency power supply is shown, and in Figure 7 a photo of a real laboratory device is 

displayed. 

The power-generation-related portion of the inverter model and the control system are based on 

"SimPowerSystem" (SPS) blocks of MATLAB / SIMULINK. This approach, in contrast to circuit simulation 

packages, allows to greatly simplify the entire model and to enhance its stability and speed.  

The power supply is equipped with a resonant inverter with two cells (sub-modules); moreover, it contains 

new technology with modern IGBT-transistors, low induction capacitors and a toroidal core from 

amorphous nanocrystalline alloys. A new high frequency technology with twisted-pair cable is used to 

decrease reactive and active loss power in the transformer. A high-power cable is used to transmit high-

frequency energy; the 
 

 

Figure 5: Laboratory device of high-frequency power supply: 1 – power rectifier, 2 – power switch, 4 – 

inverter, 5 – resonant capacitance, 6 – equivalent high-power high-frequency cable, 7 – equivalent load, 8 

– driver, 9 – control unit, Iamr – amplitude current reference, f – frequency 

  

Figure 6: 3D-model of a high-frequency power 

supply 

Figure 7: Photo of a real laboratory device 

 

0 50 100 150 200
20

40

60

80

100

120

140

160


T

, 
K

Frequency (kHz)

  sinusoidal

  pulsed bipolar

R
rod

=25 mm

I
rms

=350 A

R
rod

=50 mm

I
rms

=1100 А

R
rod

=75 mm

I
rms

=2000 А

 

+

Driver

V

V V V

А

В

С

Three-phase electric 

power 

380V 50Hz

Start power

1 2 3 4 5 6 7

8

9

Iamr f

V

 – current sensor

 – voltage sensor



 

 

1655 

cable has a plurality of strand pairs where these pairs are bundled so as to run in parallel to each other 

and the individual wires of the strands are twisted (Wallmeier and Niehaus, 2012). 

The power supply automatic control system (ACS) includes two channels (Figure 8): the first includes 

extreme ACS frequencies; the second includes cascading ACS with PI-controlling of the average current 

load. Cascading ACS is constituted by two-control loops: the first (main loop) is made of the fast control 

loop of the amplitude current load; the second includes the control loop of the average current load. The 

introduction of the fast control loop provides a significant increase in the device reliability for short circuits 

in the load (i.e. rods fall in Siemens-reactor). 

A transient analysis of ACS (Figure 9) provides the following evidences: a transient overshoot is not 

detected; the stabilization time is the less than 1.5 ms, at an error of less than 1 % and 30 us, at an error 

less than 10 %. The RLC circuit is used in a laboratory device, where R = 0.5 Ohm – load resistance, 

L = 2 mH – load inductance, C = 4 uF – resonant capacitor. 

The power supply simulations highlighted that ± 50 % change in the parameters of the RLC-circuit does 

not result in a significant decrease of the quality control. Consequently, the ACS has the necessary control 

robustness. 

Experimental evidence has shown that the transformer current secondary winding (Figure 10) and burden 

is sinusoidal out of the direct component, under the pulsing voltage in the output of a power supply (Figure 

11), at a frequency from 20 to 100 kHz, without sacrificing the inverter effectiveness more than 3 %. 

 

V

V

3

4 5CC

FC

1

2

Iavr

I

U
Uс

m

f
U

 

Figure 8: Control system of high-frequency power supply: 1 – frequency control, 2 – current control, 3 – 

inverter, 4 – resonant capacitance, 5 – equivalent load, U – load voltage, Uc – capacitance voltage, U – 

error voltage, f – frequency pulse, Iavr – average current reference, m – pulse width 

 

Figure 9: Experimental time evolution of current, frequency and pulse width 

4. Conclusions 

Different alternative current shapes have been analyzed in order to reduce the internal temperature 

gradient of the polysilicon rods of Siemens reactor. Simulations have shown that the most effective current 

in realizing the skin effect in polysilicon rods is a harmonic and bipolar pulse current with frequencies 

above 50 kHz. Simulations and experimental research by laboratory devices has afforded the possibility to 

study a high-frequency power supply with the following parameters: average load current from 0 to 1 kA; 

voltage from 1 kV to 200 V; active load power higher than 200 kW; efficiency higher than 95 %. High-

frequency power supplies can be used in induction furnaces with long electrical lines for saline solution 

heating in pyro-chemistry processes to purify fission material from other fusion side-components (in this 

 

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6
0

20

40

60

80

100

120

Время, мс

Ч
а
с
то

та
, 
к
Г

ц
Ш

И
М

, 
%

0

0,1

0,2

0,3

0,4

0,5

0,6

Т
о

к
 н

а
гр

у
зк

и
, 
к
А

 

 

ШИМ

Частота

Ток нагрузки

f, kHz I, kA

· · · · · · · · · · 
· 

· 

· 

· 
· 

· 

· 

· 

· 

· 

m ,%

Time, ms

Pulse width

Frequency

Current

0.2 0.4 0.6 0.8 1.2 1.4 1.6

0.1

0.2

0.3

0.4

0.5

0.6

0



 

 

1656 

 
case the current frequency is more than 50 kHz). Moreover, power supply can be used in the compact 

induction furnaces of chemo-metallurgical plants. 

 

  

Figure 10: Experimental current shape on the 

secondary and primary transformer winding 

Figure 11: Experimental voltage shape on the out of 

power supply 

Acknowledgment 

This work was funded as part of Federal government-sponsored program “Science” by Tomsk Polytechnic 

University. 

References 

Braga A.F.B., Moreira S.P., Zampieri P.R., Bacchin J.M.G., Mei P.R., 2008, New processes for the 

production of solar-grade polycrystalline silicon: A review, Solar Energy Materials and Solar Cells, 92, 

418-424. 

Ceccaroli B., 2003, A. Luque, S. Hegedus (Eds.), 2003, Handbook of Photovoltaic Science and 

Engineering, Wiley, New Jersey, USA. 

Dawson H., Keck D., Russell R., 2003, Chemical vapor deposition system for polycrystalline silicon rod 

production, US Patent 2003/ 0127045. 

del Coso G., Tobias I., Canizo C., Luque A., 2007, Temperature homogeneity of polysilicon rods in a 

Siemens reactor, Journal of Crystal Growth, 299, 165-170. 

Fan S., Plascencia G., Utigard T., 2008, High temperature electric conductivity of pure silicon, Canadian 

Metallurgical Quarterly, 47(4), 509-512. 

Huang Z., Liu C., 2013, Numerical simulation in a novel polysilicon CVD reactor, 2013 AIChE Spring 

Meeting and 9th Global Congress on Process Safety, San Antonio, United States, 28 Apr -2 May 2013. 

Hou Y.Q., Xie G., Nie Z.F., Li N., 2013. Direct current heating model for the Siemens reactor, Advanced 

Materials Research, 881-883, 1805-1808. 

Ke Z.-P., Yang Z.-G., Liu J.-S., 2013, Discussion on energy-saving measures in polysilicon plants, Huaxue 

Gongcheng/Chemical Engineering (China), 41, 75-78. 

Mitrasinovic M., Li. A., Utigard T., Plascencia G., Warczok A., 2009. Silicon rod heat generation and 

current distribution, Journal of Crystal Growth, 312, 141-145. 

Sha S., Melin K., Hurme M., 2013, Computer aided solar energy based sustainability evaluations in 

process design, Chemical Engineering Transactions, 32, 1225-1230. 

Tiepolo G.M., Junior O.C., Junior J.U., 2013, Analysis of the electricity generation potential by solar 

photovoltaic source in the state of Paraná – Brazil, Chemical Engineering Transactions, 32, 601-606. 

Wallmeier P., 2009, Device and method for producing a uniform temperature distribution in silicon rods 

during a precipitation process, US Patent 2009/0229991. 

Wallmeier P., Niehaus B., 2012, High-power high-frequency cable, US Patent 2012/0292075. 

 

 

Primary transformer winding

Secondary transformer winding

C
u
rr

e
n

t,
 k

A

Time, ms
0.04 0.05 0.06 0.07 0.08 0.09 0.1

-0.5

0.5

-1

-1.5

1

1.5

2

0

 

Time, ms

V
o

lt
a
g

e
, 

V

0.04 0.05 0.06 0.07 0.08 0.09 0.1
-300

-200

-100

100

200

300

0