Dopant Diffusion Scaling down MOSFET by 1/K calls for smaller junction depths. high deposit activation (n  N d )  Resistance  in S/D. N d (x j ) = N asubstrate W t L Concept of Sheet Resistance of doped layers.  s [  /sq.]  4 point probe or van der Pauw In MOSFETs R contact + R source + R ext < 10% R chen  s  but keep x j small to avoid DIBL (conflicting requirements ResistivitySheet resistance L/W=# squares

VSLS: Shallow and Heavily Doped Junctions

Historical Development and Basic Concepts Development (40 years) in predeposition Solid-phase diffusion from glass layer. Gas phase deposition at high temperatures (B 2 H 6, PH 3, AsH 6 )  reproducibility; good only for solid sol. (too high N s ) Replace predeposition by ion implantation; good for bigger devices but difficult for small ones (TED) Return to diffusion 1960

Junction Formation – Process Choice

Dopant Solid Solubility Concentrations above SS limits result in inactive coplexes (defects,precipitates) Metastable electrical activation Practical concenrations for active P and As As complexes

Diffusion from a Microscopic Viewpoint Fick’s first law; D is a diffusivity, which depends on T not direction. Fick’s second law from: D = const. Fick’s II law in 3D

Analytic Solutions of the Diffusion Equation In steady state Gaussian Solution in an Infinite Medium

Gaussian Solution near a Surface Shallow implantation or deposited layer Delta layer’s thickness << X = 2 √(Dt) (final penetration) At the surface, if oxide growth occurs  dopant segregation

Error Function Solution in an Infinite Medium Tabulated (or approximated) Unlimited dopant supply from the source

Error – Function Solution near a Surface Surface concentration set by the solubility limits of the dopants C S (T) Q erfc increases with time. Q gauss is constant in time; it is set by a predeposition (erfc) preceding the diffusion (drive-in)

Intrinsic Diffusion coefficients of Dopants in Silicon Arrhenius fit Fast Diffusers Slow Diffusers Intrinsic Diffusion means that N dopant < n diffusion T 1000 °C, n i = 7.14 * cm -3 (1.45 * cm High dopant concentrations the diffusion is enhanced.

Successive Diffusion Steps T 1 followed by T 2 : Dt is a measure of thermal budget Transient Enhanced Diffusion (TED) and Concentration Enhanced Diffusion (CED) when D increases with C and/or crystallographic/point defects Computer Simulation includes diffusion enhancement Equiv. time

Design and Evaluation of Diffused Layer Surface Concentration determined from Rs (or  s ) and x j measurements Irvin’s curves for erfc and Gaussian profiles Example: Design a B diffusion process  s =900  /sq., xj = 3 µm for substrate C B = cm -3 Pick 1100 °C  D=1.5 * cm 2 sec -1 t = 6.8 hour (ex.: the well process) Use : Q=C(0,t)(  Dt) 1/2= 4.3*10 13 cm -2 implanted or predeposition From 950 °C, C sol.sol =2.5*10 20 cm -3, D=4.2*10 15 cm 2 sec -1 – not valid since C spread >>n i Delta function approx. Dt predep =2.3* << Dt drivein =3.7*10 -9 So Gaussian distribution is correct for the drive-in process

Manufacturing methods and Equipment Furnaces: horizontal,vertical (100 °C/min ramp) Temperatures: °C, N 2 (+O 2 low ) or Ar, O 2 when oxide must be grown °C/min to °C (  warpage) So  with T For TED defects induced by implantation show  D at low T than at high T. RTA goal:no diffusion but damage annealing/dopant activation Issues: 100 degC/sec ramp Single wafer processing sec process. Wafer T and uniformly measurement and control.

Measurement Methods SIMS – Secondary Ion Mass Spectroscopy – sensitivity –10 17 cm -3. Analysis of chemical concentration of dopants (both active and non active) Mass analyzed and counted  C(X) As, P, Sb  bombarded with Cs as primary ions  produce dopant ions. B, In  O (oxygen) “Knock on” – incident beam recoils atoms into the substrate(  with ion mass Cs>O  degrades depth resolution Sputtering rate at the surface increased by oxide  use lower energies down to 200 eV- 5keV to decrease sputtering (important for shallow junctions) Multilayer structures show matrix effect (sputtering yield and ion yield) and mixing (heavy Cs) Use oxygen bleed – keep ionization yield constant. Problems:

Spreading Resistance R(x)   (x)  n(x) Compare with C(x) from SIMS to get dopant activation. (information on defects, clusters etc.) 8’- 34’ From Wolf, VLSi Era

Sheet resistance Four point probe. (Figure 3.12); for shallow junctions use the Van De Pauw structure Capacitance Voltage C-V of a MOS Capacitor  C  X D (V)  x D (N)  N(x) TEM Cross Section Preparation of samples: Very complex Delineation by etching the doped silicon in HF: HNO3:CH3COOH 1 : 40 : 20 Doped silicon etch rate depends on dopant concentrations

2D Electrical Measurements Using Scanning Probe Microscopy Random distribution depends on the doping concentrations cm -3, cm -3, cm -3 STM – Scanning Tunneling Microscopy not useful  scanning capacitance (from STM or rather AFM) and Scanning Resistance. Problems: Cross-Section=preparation hard, Image interpretation (C  N) Inverse Electrical Measurements IV, CV of devices may not match simulated characteristics  make corrections as to the doping profiles.

Models and Simulations Numerical Solutions of the Diffusion Equations. No predetermined boundary conditions. Planar density of atoms Atoms jump between planes Hopping to a vacancy or exchange places with frequency For stable numerical solution Max. numerical interval means that we cannot have more than available number of atoms to jump in  t Adjacent concentrations calculated  SUPREM etc

Modification to Fick’s Loss to Account for Electric Field Effects. Set up by the increased concentrations Very strong effect of  at low concentrations The enhancement of diffusion by the electric field is by a factor of high concentrations. F.-II Law

Modifications to Fick’s Laws to Account for Concentration Dependent Diffusion ISO Concentration experiments: B 11 (substrate) B 10 diffusant give D A eff Neutral and charged point defects Different Activation Energies Ex: As at 1000°C For 1*10 18 cm -3  D As = 1.43* cm 2 sec -1 For 1*10 20 cm -3  D As = 1.65* cm 2 sec -1 5x10 20 cm cm -3 Experiment.

SUPREM Simulation deposition  Function doping CED Boxlike As Due to  filed effects

Segregation of Deposits at Interfaces Ex : Oxide Silicon Segregation h is the interface transfer coefficient. SIMS - for thick oxides can give k o (difficult measurements). - for thin oxides SIMS is inadequate (no steady state reached). So use V T or C-V areas. B segregates into the oxide P piles up at the Si Surface  Snowplow during oxidation. Flux:

Segregation; Interfacial Dopant Pileup. D AS << D p  steeper profile close to the interface. Dopant Loss at the surface - SIMS does not detect that. Important problem in small devices (dominant). Entrapped dopants can diffuse later. SUPREM includes a trapping flux. Very thin,  monolayer acts a sink for dopants (inactive there); Stripping of the oxide removes dopants.

The physical basis for diffusion on Atomic Scale Vacancy or exchange model. vacancy Typical diffusion in metals  use XRD to measure changes in lattice constant with T  extract vacancy concentration. For Si it is below the detection limit of XRD. V models used earlier for diffusion in Si especially CED; N v = f(E F ) Dopant and Si-I diffuse as bound pairs  split Dopant stays in the substitusional position, I released. Si – Interstitial (only) used in diffusion of dopants. Both are “Interstitial –” assisted diffusion. Kick - OutInterstitiency The role of interstitials-kick-out