Impurity Diffusion. Fundamental process step for microelectronics. We want Substitutional diffusion

Transcription

1 Diffusion

2 Impurity Diffusion Fundamental process step for microelectronics Controls majority carrier type Controls semiconductor resistivity We want Substitutional diffusion Needed to provide carriers

3 III IV V Silicon Dopant Types N-type (electron donor) P, As, Sb P-type (hole donor) B (Al+Ga have high diffusion constants/don t mask well) Sb

4 Methods for Doping Silicon Diffusion Ion-Implantation Combinations of the above

5 Diffusion Fick s First Law Particle flux J is proportional to the negative of the gradient of the particle concentration J D N x D = diffusion coefficient Same mathematical model as oxidation model

6 Diffusion Fick s Second Law Continuity Equation for Particle Flux : Rate of increase of concentration is equal to the negative of the divergence of the particle flux N t J x (in one dimension) Fick's Second Law of Diffusion : Combine First Law with Continuity Eqn. N 2 t D N x 2 D assumed to be independent of concentration! We use this because we are in a non-steady state situation, dopants continually diffuse Dose (Q) = Impurities/cm^2

7 Constant Source Diffusion Complementary Error Function Profiles erfcz1 erf z erf z 2 z 0 expx 2 dx Concentration : N x, t N 0 erfc 2 x Dt Total Dose : Q 0 N x, t dt 2N 0 Dt N 0 Surface Concentration D Diffusion Coefficient erfc = Complement ary Error Function Solve PDE with boundary conditions (No=const) Dose changes over time Furnace/chamber/etc

8 Limited Source Diffusion Gaussian Profiles Initial Impulse with Dose Q Concentration : Nx,t 2 x N 0 exp 2 Dt Q 2 Dt exp x 2 Dt N 0 Surface Concentration N 0 Q Dt D Diffusion Coefficient Gaussian Profile Solve PDE with boundary condition (Impulse dose at surf) Source never is replenished Area under each curve (dose) is constant

9 Diffusion Profile Comparison Complementary Error Function and Gaussian Profiles are Similar in Shape erfcz1 erf z erf z 2 z 0 expx 2 dx

10 Diffusion Coefficients Substitutional Diffusers Interstitial Diffusers

11 Diffusion Coefficients D D O exp E A kt Arrhenius Relationship E A activation energy k = Boltzmann' s constant =1.38 x10-23 J/K T = absolute temperature Dt product is the measure of driving force in the diffusion D is proportional to Temp Time (t) Increase either of these or both and you will change the diffusion parameters At high concentrations (~ni) diffusion constant becomes dependant on concentration

12 Two-step Diffusion Process Short, high concentration constant source pre-diffusion approximates impulse dose at surface Longer drive in step diffuses impurities into lattice If Dt for drive in >> Dt for predeposition Final profile will be Gaussian MOST CASES If Dt for drive in << Dt for predeposition Final profile will be Erfc fn.

13 Successive Diffusions Successive diffusions using different times and temperatures Any process which involves high temperatures also affect this Final result depends upon the total Dt product This (Dt)tot is plugged into the equation to determine final distribution Dt tot D i t i i

14 Diffusion Solid Solubility Limits There is a limit to the amount of a given impurity that can be dissolved in silicon (the Solid Solubility Limit) At high concentrations, all of the impurities introduced into silicon will not be electrically active

15 Diffusion p-n Junction Formation x j Metallurgical Junction Depth Gaussian Profile : x j 2 Dt ln N N 0 B Error Function profile : x j 2 Dt erfc -1 N N 0 B P-n junction occurs where the net impurity concentration is = 0 P doping cancels n doping/ etc. Set N(xj)=0 Solve equations for xj

16 Lateral Diffusion Under Mask Edge Original Mask

17 Concentration Dependent Diffusion Second Law of Diffusion N t x D x N x Profiles More Abrupt at High Concentrations

18 Concentration Dependent Diffusion Phosphorus diffusion is more complex, includes a Kink which makes it harder to use in actual devices Arsenic used instead

19 Diffusion Resistivity vs. Doping 1 q n n p p n type : q n p type : q p 1 N D N A N A N D 1 1

20 Resistors Sheet Resistance A W t R t L W L R S W R S t = Sheet Resistance [Ohms per Square] L Number of Squares of Material W

21 Resistors Counting Squares Top and Side Views of Two Resistors of Different Size Resistors Have Same Value of Resistance Each Resistor is 7 sq in Length Each End Contributes Approximately 0.65 sq Total for Each is 8.3 sq Figure 4.14

22 Resistors Contact and Corner Contributions Effective Square Contributions of Various Resistor End and Corner Configurations Figure 4.15

23 Sheet Resistance Irvin s Curves 1 1 x j 1 xdx R S x j x j x j xdx Irvin Evaluated this Integral and Published a Set of Normalized Curves Plot Surface Concentration Versus Average Resistivity R S x j R S x j 0 1 qnxdx Four Sets of Curves n-type and p-type Gaussian and erfc

24 Two Step Diffusion Sheet Resistance - Predep Step Initial Profile N o 1.1x10 20 /cm 3 N B 3x10 16 /cm 3 x j m p type erfc profile R S x j 50 - m R S 32 - m 850 /Square m

25 Two Step Diffusion Sheet Resistance - Drive-in Step Final Profile N o 1.1x10 18 /cm 3 N B 3x10 16 /cm 3 x j 2.73 m p type Gaussian profile R S x j m R S m 2.73 m 260 /Square

26 Doping Systems Spin on Glass containing the dopant impurity Not as uniform of a doping Furnaces (3 zone) Source material Liquid, Solid, Gas Boron Gas/solids react to supply impurities on surf Phosphorus Gas/solids react to supply impurities on surf Arsenic Hard to make high concentrations with furnace methods Use ion implantation