1 ENS/PHY463 Lab1. Resolution and Throughput of Ion Beam Lithography. (SRIM 2008/2013 computer simulation) Objective The objective of this laboratory work is to evaluate the exposure depth, resolution, and throughput of focused ion beam (FIB) processing of lithographic resist using SRIM simulation software. This objective is achieved by performing simulation of the process of ion irradiation of positive photoresist and determination of the size of ion beam exposed area. Principles Exposure of lithographic resist to ion irradiation results in its chemical modification. In case of positive resist, the ion-irradiated area of the resist becomes more soluble and can be removed in a solvent. Energetic ions propagating through target material collide with atoms of the target losing their energy. If the collisions are strong enough and the energy transferred to the target atoms exceeds a certain threshold energy Ed (displacement energy), these atoms leave their regular positions producing vacant atomic sites (vacancies). The knocked-out atoms and vacancies are the defects responsible for the changes of the properties of the ion-irradiated resist. A common software used for simulation of ion irradiation and the irradiation-induced defect production is SRIM [http://www.srim.org]. Below, Fig. 1 shows an example of simulation of propagation of one Ga ion of initial energy 100 kev in a solid carbon target of density 1.2 g/cm 3.
2 Fig. 1. SRIM2008 simulation of defect production in solid carbon of density 1.2 g/cm 3 by one Ga ion of initial energy 100 kev. Red trace shows trajectory of Ga ion. Green lines and dots show trajectories of knocked-out carbon atoms of the target and the created vacancies. Bacause of the collisions with the atoms of target, the ion does not proparate along straight line. It experiences multiple collisions (scatterings). Some target atoms are knocked out of their regular sites violently and may move over long distances sometimes penetrating deeper than the initial ion. Since the energy loss of the ion and knock-outs is random process, every ion has its unique pathway and unique pattern of the created defects. The result of simulation of ion irradiation with many ions is shown in Fig. 2. Fig. 2a shows trajectories of the primary (implanted) ions. Fig. 2b shows pathways of the knock-out atoms of the target and the created defects. Fig. 2. SRIM2008 simulation of irradiation of solid carbon target of density of 1.2 g/cm 3 by 200 Ga ions of initial energy 100 kev. (a) Trajectories of ions are shown by red traces. Final positions of the ions are shown by black dots. (b) Trajectories of knock-out carbon atoms and distribution of created defects are shown by green lines and dots respectively. The distribution of the implanted ions through the depth has approximately gaussian shape the two main parameters of which are the depth of the maximum density Rp (projected range of ions, or ion range) and the width of the gaussian 2ΔRp. ΔRp is the longitudinal straggling, or average scattering of ions through the depth (Fig. 3a).
3 Fig. 3. SRIM2008 simulation of irradiation of solid carbon of density 1.2 g/cm 3 by 10000 Ga ions of initial energy 100 kev. (a) Depth distribution of density of the implanted Ga ions. (b) Depth distribution of density of the defects (vacancies). Depth distribution of the defects is shown in Fig. 3b. A considerable defect production starts from the very surface of the irradiated resist. The defect distribution curve does not have a gaussian shape. However, its tale towards greater depths can be approximated by gaussian distribution. Comparing distributions of the implaned ions and the created defects one can see that average penetration of the ions in deeper than that of the defects. The depth of the maximum density of the implanted ions is about 110 nm (1100 Å), whereas the maximum density of defects is at a depth of 70 nm (700 Å). Exposure Depth Since the radiation defects are the primary reason for the change of solubility of resist, the defect distribution through the depth determines the depth of the exposure and hence the thickness of the resist layer which can be processed with given ion species of given energy and given exposure dose. From the graph on Fig. 3b one can conclude that the maximum penetration depth of defects is about 200 nm. However, the density of defects at depths greater than 130 nm drops down rapidly. Thus, the effective depth of penetration of defects Rd is only about 130 nm. A simple estimation of the magnitude of Rd can be done calculating sum of the depth of the maximum concentration of implanted ions Rp (projected range of ions, or ion range) and the longitudinal straggling ΔRp: Rd = Rp +ΔRp. The results of the simulation shown in Fig. 3 yields in Rp = 114.7 nm and ΔRp = 28.1 nm. Correspondingly Rd = 142.8 nm. Thus, the thickness of the resist layer which can be used for this ion irradiation is about 140 nm. More precise calculation takes into account the dose of the ion irradiation and the critical concentration of defects corresponding to clearance dose Dc. With the increase in the ion dose, the
4 layer in which the concentration of defects exceeds Dc expands in depth and ultimately can be as deep as 200 nm. In order to calculate the ion dose required for the exposure of resist of a given depth d, the efficiency of defect production nd at this depth is determined from Fig. 3b. For instance, at a depth of 160 nm nd = 0.1 vacancy/ion*å = 10 7 vac/ion*cm. Then, the ion dose needed to achieve the critical defect concentration Nc at depth d is Dc = Nc/nd. A common critical defect concentration (clearing defect concentration) corresponding to the clearing dose Dc of polymeric resist is about Nc = 10 19 cm -3. Thus, Dc = 10 12 cm -2 at depth 150 nm. For a resist layer of thickness 100 nm, nd = 1.25 vacancy/ion*å = 1.25 10 8 vac/ion*cm. Then the corresponding Dc = 8 10 10 cm -2. Resolution Fig. 2 shows that even when the ions enter target in one and the same point, they do not propagate along one and the same straight line because of lateral (side) scattering. The lateral scattering broadens the damaged area and this broadening is especially pronounced for ion beams of small diameter. The lateral scattering of ions is described by lateral range Rl and lateral straggling ΔRl. The lateral deviation of ions from straight propagation shown in Fig. 2a is about 30 nm, whereas it is about 70 nm for defects (Fig. 2b). The lateral distribution of defects can be described in the same way as we did it for the depth distribution. Thus, we assume that the effective depth of the lateral propagation of defects equals the sum of the lateral range and the lateral straggling: Rdl = Rl +ΔRl. The simulation of lateral scattering is shown in Fig. 4. It is seen that the lateral scattering increases with depth. For simple modeling, average values of lateral range and lateral straggle can be taken: Rl = 15.7 nm and ΔRl = 19.9 nm. Correspondingly, Rdl = 35.6 nm.
5 Fig. 4. SRIM2008 simulation of lateral scaterring of 100 kev Ga ions in solid carbon of density 1.2 g/cm 3. Lateral scattering causes broadening of the area exposed to ion irradiation and consequently deteriorates resolution of ion lithography. The effective resolution of lithography R utilizing exposure with ion beam focused to diameter D can be estimated as: R = D + 2Rdl. In case of our simulation example, an ion beam of diameter 20 nm can provide resolution of 90 nm in 140 nm thick resist. Clearing dose An important parameter of any lithography method including ion beam lithography is the clearing dose Dc. Dc correspond to the number of particles per unit area sufficient for chemical modification of the resist in the irradiated area through the whole resist depth. Clearing dose can be also presented as the density of energy losses deposited by ions. Energy losses of energetic ions propagating through target material have to components: energy losses in elastic collisions with the target atoms (nuclear stopping) and energy losses in inelastic interaction with the target electrons (electronic stopping). The main result of nuclear stopping is the production of defects and heating the target (generation of phonons). Depth distribution of energy losses in our simulation example is shown in Fig. 5.
6 Fig. 5. SRIM2008 simulation of electronic (a) and nuclear (b) energy losses of 100 kev Ga ions in solid carbon of density 1.2 g/cm 3. Red traces show direct losses by Ga ions. Blue areas show losses by carbon recoils. Comparing Figs. 3, 4 and 5 one can conclude that effective deposition of energy and generation of defects occur in a layer of thickness Rd. The value of the clearing dose is specific for every combination ion specie and type of resist. It is established experimentally. Let us assume that Dc of 100 kev Ga ion beam lithography is 10 12 cm 2. Then, for a 140 nm thick resist, average density of energy losses Eaverage is: Eaverage = (Dc Eion)/Rd = (10 12 cm -2 * 10 5 ev * 1.6 10-19 J/eV)/140x10-7 cm = 1.14 10 3 J/cm 3. Area density of the deposited energy, or the clearing dose is: Dc = Eaverage * Rd = 16 mj/cm 2. Thoughput Throughput of lithographical procedure T is the speed of exposure of resist at the clearing dose: T = A/t = I/(eDc) where A is the irradiated area and t is the time required for this irradiation, e is the electron charge and I is the ion beam current. For ion beam I = 10 pa, T = 100 µm 2 /s. If an ion beam of diameter 20 nm is used for making a pattern of straight lines, this pattern can be produced with a speed of 5 cm/s. Tasks of the lab work 1. Compare parameters of two lithography techniques which utilize Ga and He ion beams. In both cases a carbon-based resist of density 1.4 g/cm -3 and clearance dose 100 J/cm 3 is used. Displacement energy if carbon atoms in resist is 15 ev.
7 Input parameters of Ga ion beam lithography: Ion energy - 50 kev. Ion beam current is 20 pa. Nominal diameter of the ion beam is 10 nm. Sensitivity of resist Nc = 2 10 19 cm -3. Input parameters of He ion beam lithography: Ion energy - 30 kev. Ion beam current is 10 pa. Nominal diameter of the ion beam is 5 nm. Sensitivity of resist Nc = 3 10 19 cm -3. 2. Calculate thickness of the resist layer corresponding to the given clearing dose 2 10 12 cm -2. 3. Calculate maximum thickness of the resist layer for the irradiation dose 5 10 13 cm -2. Parameters to be found and compared: 1. Parameters of distribution of ions. 2. Parameters of distribution of damage. 3. Lithography resolution. 4. Clearing dose in units [ion/cm 2 ] and [J/cm 2 ]. 5. Throughput for areal exposure and line exposure. Questions 1. Which parameters of ion beam exposure are to be changed in order to process a thicker resist layer? 2. What are the advantages and disadvantages of using heavy ions for ion beam lithography? 3. What are the advantages and disadvantages of using light ions for ion beam lithography? 4. Lateral scattering makes resolution of ion beam lithography greater than ion beam diameter. Is it possible for ion beam lithography to achieve resolution less that ion beam diameter? Lab2. Ion Implantation. (SRIM 2008/2013 computer simulation) 1. Objectives - To give students hand-on experience of numerical simulation of ion doping used for fabrication of semiconductor nanodevices. - To familiarize students with SRIM software used for numerical simulation of ion implantation. - To perform numerical simulation of ion doping of planar structure of bipolar transistor.
8 5.2. Principles 5.2.1. Parameters of ion-doped layer Ion implantation is the main doping method used for fabrication of in microelectronic devices. Over all, it is the most precise and controllable method of impurity doping of solids. In ion implantation, impurity toms are introduced into semiconductor substrate by ionizing them (creating ions), accelerating the ions to energies ranging from kiloelectronvolt (kev) to megaelectronvolt (MeV), and then literally shooting these ions onto the substrate surface (Fig. 1). Fig. 1. Principle of local doping of semiconductor using ion implantation and masking technique. Openings in the mask define the ion-doped areas. Mask must be thick enough to protect the masked areas from doping. Ions penetrate into semiconductor substrate to a certain doping depth Ri. This way a buried ion doped layer is created. Distribution of density of the implanted ions N(x) through the depth x is not uniform. It is approximately described by a Gaussian function (1): Thus, the distribution of ions through the depth on the implanted layer is described by a broad peak, the parameters of which are the maximum concentration Ni located below the surface at a depth Rp (the projected range) and the spread Rp (implantation straggle) (Fig. 2). (1)
9 2 Rp Rp Fig. 2. Depth distribution of boron ions implanted into silicon with equal dose 10 15 cm -2, but at different energies. Depth of the doped layer and its width (2 Rp) increase with the implantation energy. Projected range Rp and straggling Rp are shown for 400 kev ions. The doping depth Ri primarily depends on the mass of the implanted ions, their energy and the chemical composition of the substrate. It is roughly proportional to the ion energy and inversely proportional to the ion mass. The ion-doped layer is buried under the substrate surface. The average depth of the doped layer is Rp, and its effective width is 2 Rp. In order to dope selected areas, masking technique is used. Mask covers the areas which must remain undoped. The openings in the mask define the areas of ion doping (Fig. 1). The mask must be thick enough to stop the ions completely and prevent from doping in the masked areas. Using ion implantation, layers doped with donors (e.g. phosphorous ions, P + ) and acceptors (e.g. boron ions, B + ) can be created. Using multiple implantations with appropriate energies through corresponding masks a multilayer doped structure can be made. Fig. 3 shows an example of threelayer ion-doped structure of bipolar transistor.
10 Fig. 3. Structure of planar bipolar transistor made by two implantations of B + ions and one implantation of P + ions. 5.2.2. Numerical simulation of ion doping with SRIM computer code Stopping and Range of Ions in Matter (SRIM) is a group of computer programs which calculate interaction of ions with matter. The essential program of these is Transport of Ions in Matter (TRIM). SRIM is very popular in the ion implantation research and technology community. The programs were developed by J. F. Ziegler and J. P. Biersack around 1983 and are being continuously upgraded. SRIM is based on a Monte Carlo simulation method, namely the binary collision approximation with a random selection of the impact parameter of the next colliding ion. The main output data of the SRIM simulation used in this lab work are three-dimensional distribution of the implanted ions and the implantation induced damage. The output data of simulation can be viewed in plots (while the calculation is proceeding) and also in detailed numerical files. The plots are especially useful to see if the calculation is proceeding as expected, but are usually limited in resolution. Most of the data files can be requested in the Setup Window for TRIM (menus at the bottom of the window), or can be requested during the calculation. All calculated averages are made over the entire calculation. Simulation of fabrication of planar bipolar p-n-p structure Simulation of ion doping of p-n-p structure starts with the calculation of the depth distribution of boron acceptors in the deepest p-type collector layer. Energy of the boron ions and the ion dose are chosen so that they ensure formation of the collector layer at the required depth with the required concentration of acceptors. An example is shown in Fig. 4. Collector layer is formed at a depth range from 260 to 500 nm by implantation of 100 kev B + ions (Fig. 4a). The maximum acceptor concentration of 5.7 10 17 cm -3 is achieved at a depth of 350 nm (collector depth RC). The second step is the simulation of formation of the phosphorous-doped n-type base layer. The energy of P + ions and their dose have to be adjusted so that the distribution of the implanted phosphorous overlaps with the boron distribution in the collector layer only partially. The maximum concentration in the phosphorous-doped layer must correspond to the required density of donors in the base layer. In the depth range of overlapping, boron acceptors and phosphorous donors compensate each other. At the depth RCB, where the boron and phosphorous concentrations are equal, complete compensation occurs. At this depth the collector-base p-n junction is formed. In Fig. 5a the base layer is formed at depths from 10 to 250 nm by implantation of 130 kev P + ions. The maximum donor concentration in the base layer is about 6.8 10 17 cm -3 at a depth of 180 nm (base depth RB). Collector-base junction is formed at a depth of 260 nm (RCB). Once RCB is determined, the simulation of the boron ion doping of the emitter layer is performed. The ion energy and dose are to be adjusted so that the emitter boron-doped layer has the required acceptor concentration and forms the emitter-base p-n junction at the required depth REB. The emitter layer in Fig. 4b is formed by 25 kev B + ion implantation. The maximum acceptor concentration in the emitter layer is about 1.2 10 18 cm -3 at a depth of 110 nm (emitter depth RE) The emitter-base junction is formed at a depth of 160 nm (REB).
Phosphorous concentration, cm -3 Dopant Concentration, cm -3 Boron Concentration, cm -3 Boron Concentration, cm -3 11 6.0x10 17 B 100 kev 1.2x10 18 B 25 kev 4.0x10 17 8.0x10 17 2.0x10 17 4.0x10 17 0.0 0 100 200 300 400 500 600 Depth (nm) 0.0 0 100 200 300 400 500 600 Depth (nm) Fig. 4. Depth distribution of ion-implanted boron. (a) Implantation of 100 kev boron ions. (b) Implantation of 25 kev boron ions. 1.0x10 18 8.0x10 17 P 130 kev 1.2x10 18 1.0x10 18 Boron 6.0x10 17 8.0x10 17 Phosphorous 6.0x10 17 Boron 4.0x10 17 4.0x10 17 2.0x10 17 2.0x10 17 0.0 0 100 200 300 400 500 600 Depth (nm) 0.0 0 100 200 300 400 500 600 Depth (nm) Fig. 5. (a) Depth distribution of ion-implanted phosphorous. (b) Distribution of implanted boron and phosphorous plotted on one graph. There is considerable overlapping of the distribution profiles.
Concentration, cm -3 12 1.0x10 18 EB junction 8.0x10 17 6.0x10 17 BC junction 4.0x10 17 2.0x10 17 p n p 0.0 0 100 200 300 400 500 600 Depth, nm Fig. 6. Distribution of non-compensated boron acceptors (blue) and non-compensated phosphorous donors (red). Position of p-n junctions are shown with arrows. The ion dose which is required to achieve maximum concentration Nmax is calculated using formula: (2) 5.3. Procedure 1. Open SRIM simulation program. Open Stopping/Range Table option. Generate table of projected ranges and stragglings for boron ions. Determine ion energy EC corresponding to the chosen collector depth, e.g. RC = 400 nm. This depth corresponds to the projected range RpC of the boron ions in the collector layer. 2. Perform simulation of implantation of silicon with boron ions of energy EC. Obtain value of straggling RpC for the collector layer. Save the simulation data. 3. Calculate difference RCB = RpC - RpC. This is an approximate depth of the CB junction. 4. In the Stopping/Range Table option, generate table of projected ranges and stragglings for phosphorous ions. Determine energy EB of P + ions, for which RpB + RpB RCB. This is the energy of phosphorous ions implanted into base layer. 5. Perform simulation of implantation of silicon with phosphorous ions of energy EB. Obtain value of straggling RpC for the base layer. Save the simulation data.
13 6. Calculate difference REB = RpB - RpB. This is an approximate depth of the EB junction. 7. In the table of projected ranges and stragglings for B + ions find the energy of boron ions EE, for which RpB - RpB REB. This is the energy for boron ions implanted into emitter layer. 8. Perform two separate simulations of implantation in silicon of boron ions with the energies EC and EE. Perform simulation of implantation in silicon of phosphorous ions with the energy EB. Save the simulation data. 9. Plot the obtained three simulation profiles on one graph in coordinates Ion Concentration versus Depth. 10. Adjust each simulation profile so that the maximum concentrations correspond to the chosen values: e.g. NCmax = 3 10 17 cm -3, NBmax = 8 10 16 cm -3, and NEmax = 2 10 18 cm -3. 11. Sum up the boron concentration profiles and subtract the phosphorous concentration profile. The depths where the total concentration is zero (complete compensation) are the junction depths. 12. Using the values of NC, NB and NE calculate the ion doses DC, DB and DE, which are required to achieve these concentrations. 5.4. Calculations and Discussion 1. Discuss the obtained distributions of boron and phosphorous over the depth of the transistor structure. 2. Compare the nominal depths of the CB and EB junctions found from Stopping/Range Tables with those obtained from the simulation profiles of implanted ions. 3. Calculate average concentrations of the implanted boron and phosphorous in collector, base and emitter layers. 5.5 Questions How you would change the parameters of ion doping in order to: a) reduce the width of the base layer? b) reduce concentration of active phosphorous in base layer?