Godt&Blandet

Question 1

What is the expression for the Fermi-Dirac distribution?

Answer 1

f(E) = 1/(exp(E - E_F/(kT))+1)

Question 2

What is the expression for the electron and hole concentration?

Answer 2

n = N_C * exp(-(E_C - E_F)/(kT))

p = N_V * exp(-(E_F - E_V)/(kT))

Question 3

What is the charge neutrality condition?

Answer 3

p + N_D = n + N_A

Free holes p + bound positive charge N_D = free electrons n + bound negative charge N_A

Question 4

What is the expression for the number of vacancies in a crystal?

Answer 4

N_v = N * Exp(-E_a/(kT)) N = total number of lattice sites in crystal (Si: 5e22 cm^-3)

E_a = activation energy (Si: ~ 2.6 eV)

Question 5

What is an intermetallic?

Answer 5

A material that has two solid phases that melt to form only one liquid phase.

Question 6

What is a Frenkel defect?

Answer 6

A vacancy and a nearby self-interstitial.

Question 7

What is the expression for the number of charged and doubly charged vacancies?

Answer 7

N_v- = N_v * n/n_i * exp((E_i - E_v-)/(kT))

N_v– = N_v * (n/n_i)^2 * exp((E_i - E_v–)/(kT))

Question 8

What are the grades of Si and the purity of them?

Answer 8

Metallurgical grade: 95-98% pure Electronic grade 11N: 99.999999999% pure

Question 9

What is the reaction for creating metallurgical Si?

Answer 9

SiO2 + 2C -> Si + 2CO

Question 10

What is a boule?

Answer 10

The grown crystal in Czochralski growth.

Question 11

What is the expression for the 1D analysis of Czochralski growth?

Answer 11

(-k_l * A * (dT/dx)_l) - (-k_s * A * (dT/dx)_s) = L * dm/dt

k_l and k_s = heat conductivity in liquid and solid

A = crossectional area of boule

L = latent heat ( ~ 340cal/g for Si)

Question 12

What happens if a crystal is pulled faster than the maximum pulling rate?

Answer 12

The heat will not be conducted away fast enough, and the crystal will not solidify in one single crystal.

Question 13

How is the temperature gradient in the melt minimized?

Answer 13

By rotating the boule and melt in opposite directions.

Question 14

What happens if the pull rate is too low?

Answer 14

Point defects will agglomerate.

Question 15

How can the oxygen level in the boule be reduced during the Czochralski process?

Answer 15

By placing the boule in a magnetic field. (The Lorentz force F = qv x B will keep the oxygen atoms away from the boule)

Question 16

What is the segregation coefficient?

Answer 16

k = C_s/C_l, the impurity concentration at solid surface over the impurity concentration at liquid surface.

Question 17

How is the crystal heated in float zone growth?

Answer 17

By a high energy RF coil which leads to currents and Joule (resistive) heating.

Question 18

Name one disadvantage with float zone growth.

Answer 18

Difficult to introduce uniform doping.

Question 19

What is the solid solubility?

Answer 19

The maximum concentration of an impurity that can be dissolved in another material in equilibrium without forming a compound.

Question 20

What is quenching?

Answer 20

Quenching is the process where the wafer is cooled rapidly, so that precipitates can not form, and the doping concentration exceeds the solid solubility limit.

Question 21

What are common impurities in Si?

Answer 21

Al, As, B, O, P, Sb (Al and B are acceptors, B, P and Sb are donors)

Question 22

What happens at the solid/liquid interface with a segregation coefficient k < 1, and how can that be exploited?

Answer 22

When k < 1, impurities at the interface will diffuse to the liquid region. This can be exploited in zone melting, to purify the boule.

Question 23

What is the heat of fusion, L?

Answer 23

The latent energy that is released when going from liquid to solid state. (The temperature is constant, but the enthalpy decreases, which corresponds to the latent heat L)

Question 24

What is necking?

Answer 24

Necking is the extension of the seed which eliminates dislocations caused by thermal shock.

Question 25

What is a typical oxygen concentration in Si wafers?

Answer 25

10-40 ppm, 10¹⁸ cm^-3

Question 26

What is gettering (extrinsic/intrinsic)?

Answer 26

The process of trapping defects and unwanted impurities in gettering sites. Extrinsic: gettering sites are added damaged areas on the back side. Intrinsic: gettering sites are oxygen precipitates.

Question 27

What are the sources of metal contamination in wafers?

Answer 27

Chemicals, oxidation, resist removal, ion implantation, reactive ion etching.

Question 28

What are the effects of metal contamination in wafers?

Answer 28

Leak current of pn-junction, reduction in minority carrier lifetime, degradation of device.

Question 29

Which dopants diffuse faster of intersititals and substitutionals?

Answer 29

Interstitials :)

Question 30

Hva er fused silica?

Answer 30

Amorf silica (amorphous). Fire oksygenatomer i en pyramide, med et Si-atom i midten. Kovalent bonding.

Question 31

Hvilke metoder har man for å måle tykkelsen på et oksyd?

Answer 31

• Etsing: Etser vekk en del av oksydlaget, og måler størrelsen på steget, f.eks. med SEM/TEM eller mekanisk scanning med nål.
• Ellipsometri: Sender inn kollimert lys, og ser på refleksjon. Refleksjonen avhenger av polarisasjon og fasevinkel, dvs. tykkelsen.
• Breakdown voltage: Måler strøm med gradvis økende spenning. Ingen ledningsevne før breakdown voltage er nådd. Finner tykkelsen fra dielekstrisk feltstyrke, 12MV/cm.
• CV-karakteristikk. C = eplison_ox·A/t_ox