Modeling and control of size distribution for fluidized bed silane decomposition

Christy M. WhiteB. Erik Ydstie

Department of Chemical EngineeringCarnegie Mellon University

Pittsburgh, PA

1400

Inst

alle

d C

apac

ity

(MW

)

020021992

Photovoltaic Industry

Industry GrowthIEA-PVPS, ‘03

Missing Link

Solar Cell Production

Raw Material SiHCl3 (TCS) Decomposition CrystallizationDistillation

Wafers IC’s

Metallurgical Grade $3-5 per kg Electronic Grade $40-60 per kg

Wafers PV CellsSolar Grade Aim: $20 per kg

Remelt/Cryst

Insufficient

2

Silicon Production

H2

SiH4H2 Si

HEAT

HEAT

Fluid Bed ReactorContinuous Process

650°CLarge surface area

Dense PhaseSiH4 Decomposition

Particle GrowthSize Distribution

SiHCl3 or SiH4

Si HEAT

HEAT

Siemens ReactorBatch Process

1100°C

3

Modeling Particulate Processes

space, timeexternal coordinates

(mass balance)

CrystallizationAerosol Formation

Cell GrowthFluidization

Population Balance

internal coordinates size, age, composition

continuousphase

distributedphase

internalflux

death andbirth terms

densitydistribution

externalflow terms

4

Overall Reaction and Gas PhaseThermal Decomposition of Silane:

Ideal operation: dense zone is a CSTRGas phase balance equations (SiH4, H2)

Reaction rate defined by Lai et al. (1986)

Accounting for loss through entrainment → Total reaction:

η is fraction of product (powder) lost

Behavior along external coordinate axes: position and time5

Solid PhaseInterval i … Interval nfi-1 fi

fai,j

fan

qirxni

Size interval mass balance

Assume Derive fiassuming continuous number:

can obtain:

Interval j

Behavior along internal coordinate axis: size 6

Solution Strategy for Discrete Model

Ordinary differential equations for mass in gas and solid phases

Algebraic constitutive equations+

DAE system solved by MATLAB’s ode15s

Adjustable Parameters Example ValuesFraction of powder lost

Aggregation proportionality constant

7

Experimental Data for Validation

Operation of pilot scale reactorSi powderH2

SiH4H2 Si

HEAT

HEAT

Load known initial distribution– sieves used to measure distribution

Continuous feed to fluidized bed

Withdraw samples regularly~8-12 samples per run

8

Silicon in Reactor

9

Particle Size Distribution

10

Controlling Continuous Operation

SiH4H2

feed

Si powder

H2

Si seed

Si product

Objectivecontrol: mass of silicon manipulate: external flow rates

System

Controller

–

11

Inventory Control of Population Balance

Apply inventory control to system:

Constant mass in reactor:

Constant seed mass:12

Response to Set Point Changes

13

System Dynamics

14

Silicon Size Distribution

15

Summary

• Size interval mass balance predictions of particle distribution compare well with data

• Simulations of continuous operation and inventory control indicate that size is controllable

• Further investigate measurability and stability

• Application to other particulate processes or multi-scale modeling is significant

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Acknowledgements

• NSF Graduate Research Fellowship Program

• Solar Grade Silicon LLC

• Reactech Process Development Inc.

• Ydstie Research Group

Any opinions, findings, conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the National Science Foundation

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