Page 194 - Materials Science and Engineering An Introduction

166 • Chapter 5 / Diffusion

0.75 wt% at a position 0.5 mm below the surface. gives a junction depth x j of 2.35
m. Compute
Estimate the diffusion time required at 900 C the predeposition diffusion time at 925 C if the
(1173 K) to achieve this same concentration also surface concentration is maintained at a constant
26
3
at a 0.5-mm position. Assume that the surface car- level of 2.5 10 atoms/m . For the diffusion of
bon content is the same for both heat treatments, In in Si, values of Q d and D 0 are 3.63 eV/atom and
which is maintained constant. Use the diffusion 7.85 10 m /s, respectively.
2
5
data in Table 5.2 for C diffusion in a-Fe.
5.41 An FCC iron–carbon alloy initially containing Spreadsheet Problems
0.10 wt% C is carburized at an elevated tempera- 5.1SS For a nonsteady-state diffusion situation (con-
ture and in an atmosphere in which the surface stant surface composition) in which the surface and
carbon concentration is maintained at 1.10 wt%. If, initial compositions are provided, as well as the
after 48 h, the concentration of carbon is 0.30 wt% value of the diffusion coefficient, develop a spread-
at a position 3.5 mm below the surface, determine sheet that allows the user to determine the diffusion
the temperature at which the treatment was car- time required to achieve a given composition at
ried out. some specified distance from the surface of the solid.
Diffusion in Semiconducting Materials 5.2SS For a nonsteady-state diffusion situation (con-
5.42 For the predeposition heat treatment of a semi- stant surface composition) in which the surface
conducting device, gallium atoms are to be dif- and initial compositions are provided, as well as the
fused into silicon at a temperature of 1150 C for value of the diffusion coefficient, develop a spread-
2.5 h. If the required concentration of Ga at a sheet that allows the user to determine the distance
3
position 2
m below the surface is 8 10 atoms/m , from the surface at which some specified composi-
23
compute the required surface concentration of Ga. tion is achieved for some specified diffusion time.
Assume the following: 5.3SS For a nonsteady-state diffusion situation (con-
stant surface composition) in which the surface
(i) The surface concentration remains constant
and initial compositions are provided, as well as
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(ii) The background concentration is 2 10 Ga the value of the diffusion coefficient, develop a
atoms/m 3 spreadsheet that allows the user to determine the
(iii) Preexponential and activation energy values composition at some specified distance from the
are 3.74 10 5 m /s and 3.39 eV/atom, respec- surface for some specified diffusion time.
2
tively. 5.4SS Given a set of at least two diffusion coefficient
5.43 Antimony atoms are to be diffused into a silicon values and their corresponding temperatures,
wafer using both predeposition and drive-in heat develop a spreadsheet that will allow the user to
treatments; the background concentration of Sb calculate the following:
20
in this silicon material is known to be 2 10 (a) the activation energy and
3
atoms/m . The predeposition treatment is to be (b) the preexponential.
conducted at 900 C for 1 h; the surface concentra-
tion of Sb is to be maintained at a constant level
of 8.0 10 atoms/m . Drive-in diffusion will be DESIGN PROBLEMS
25
3
carried out at 1200 C for a period of 1.75 h. For Fick’s First Law
the diffusion of Sb in Si, values of Q d and D 0 are It is desired to enrich the partial pressure of
2
5
3.65 eV/atom and 2.14 10 m /s, respectively. 5.D1 hydrogen in a hydrogen–nitrogen gas mixture
(a) Calculate the value of Q 0 . for which the partial pressures of both gases are
(b) Determine the value of x j for the drive-in dif- 0.1013 MPa (1 atm). It has been proposed to ac-
fusion treatment. complish this by passing both gases through a thin
sheet of some metal at an elevated temperature;
(c) Also, for the drive-in treatment, compute the inasmuch as hydrogen diffuses through the plate
position x at which the concentration of Sb atoms at a higher rate than does nitrogen, the partial
23
3
is 5 10 atoms/m . pressure of hydrogen will be higher on the exit
5.44 Indium atoms are to be diffused into a silicon side of the sheet. The design calls for partial pres-
wafer using both predeposition and drive-in heat sures of 0.051 MPa (0.5 atm) and 0.01013 MPa
treatments; the background concentration of In (0.1 atm), respectively, for hydrogen and nitrogen.
20
in this silicon material is known to be 2 10 The concentrations of hydrogen and nitrogen (C H
3
3
atoms/m . The drive-in diffusion treatment is to be and C N , in mol/m ) in this metal are functions of
carried out at 1175 C for a period of 2.0 h, which gas partial pressures (p H 2 and p N 2 , in MPa) and