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Seperate ion flux and yield
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@tobre1
tobre1 committed Jan 15, 2025
1 parent a89cdf8 commit 514e714
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Showing 3 changed files with 96 additions and 80 deletions.
13 changes: 7 additions & 6 deletions examples/holeEtching/config.txt
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Original file line number Diff line number Diff line change
Expand Up @@ -8,21 +8,22 @@ yExtent=100.0 # um

# Geometry
holeRadius=20.0 # um
maskHeight=20.0 # um
taperAngle=0.0 # degree
maskHeight=65.0 # um
taperAngle=1.5 # degree

# Process parameters
processTime=150 # seconds
processTime=50 # seconds

# all flux values are units 1e16 / cm²
ionFlux=1.
etchantFlux=180.
ionFlux=10.
etchantFlux=500.
oxygenFlux=30.

ionExponent=200
meanEnergy=100 # eV
sigmaEnergy=10 # eV
A_O=3 # passivation layer sputtering coefficient
A_O=3 # passivation layer yield constant
A_Si=7 # Si yield constant

etchStopDepth=-1000 # maximum etching depth
integrationScheme=EO_1
Expand Down
20 changes: 11 additions & 9 deletions examples/holeEtching/holeEtching.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -35,15 +35,17 @@ int main(int argc, char *argv[]) {
.apply();

// use pre-defined model SF6O2 etching model
auto model = ps::SmartPointer<ps::SF6O2Etching<NumericType, D>>::New(
params.get("ionFlux") /*ion flux*/,
params.get("etchantFlux") /*etchant flux*/,
params.get("oxygenFlux") /*oxygen flux*/,
params.get("meanEnergy") /*mean energy*/,
params.get("sigmaEnergy") /*energy sigma*/,
params.get("ionExponent") /*source power cosine distribution exponent*/,
params.get("A_O") /*oxy sputter yield*/,
params.get("etchStopDepth") /*max etch depth*/);
auto model = ps::SmartPointer<ps::SF6O2Etching<NumericType, D>>::New();
auto &modelParams = model->getParameters();
modelParams.ionFlux = params.get("ionFlux");
modelParams.etchantFlux = params.get("etchantFlux");
modelParams.oxygenFlux = params.get("oxygenFlux");
modelParams.Ions.meanEnergy = params.get("meanEnergy");
modelParams.Ions.sigmaEnergy = params.get("sigmaEnergy");
modelParams.Ions.exponent = params.get("ionExponent");
modelParams.Passivation.A_ie = params.get("A_O");
modelParams.Si.A_ie = params.get("A_Si");
modelParams.etchStopDepth = params.get("etchStopDepth");

// process setup
ps::Process<NumericType, D> process;
Expand Down
143 changes: 78 additions & 65 deletions include/viennaps/models/psSF6O2Etching.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -19,12 +19,12 @@ template <typename NumericType> struct SF6O2Parameters {
NumericType etchantFlux = 1.8e3;
NumericType oxygenFlux = 1.0e2;

NumericType etchStopDepth = std::numeric_limits<NumericType>::lowest();

// sticking probabilities
NumericType beta_F = 0.7;
NumericType beta_O = 1.;

NumericType etchStopDepth = std::numeric_limits<NumericType>::lowest();

// Mask
struct MaskType {
NumericType rho = 500.; // 1e22 atoms/cm³
Expand All @@ -44,13 +44,15 @@ template <typename NumericType> struct SF6O2Parameters {
// sputtering coefficients
NumericType Eth_sp = 20.; // eV
NumericType Eth_ie = 15.; // eV

NumericType A_sp = 0.0337;
NumericType B_sp = 9.3;
NumericType theta_g_sp = M_PI_2; // angle where yield is zero in rad
NumericType theta_g_sp = M_PI_2; // angle where yield is zero [rad]

NumericType A_ie = 7.;
NumericType B_ie = 0.8;
NumericType theta_g_ie =
constants::degToRad(78); // angle where yield is zero in rad
constants::degToRad(78); // angle where yield is zero [rad]

// chemical etching
NumericType k_sigma = 3.0e2; // in (1e15 cm⁻²s⁻¹)
Expand Down Expand Up @@ -99,9 +101,9 @@ class SF6O2SurfaceModel : public SurfaceModel<NumericType> {
coverages->insertNextScalarData(cov, "eCoverage");
coverages->insertNextScalarData(cov, "oCoverage");
if (Logger::getLogLevel() > 3) {
coverages->insertNextScalarData(cov, "ieComponent");
coverages->insertNextScalarData(cov, "spComponent");
coverages->insertNextScalarData(cov, "thComponent");
coverages->insertNextScalarData(cov, "ionEnhancedRate");
coverages->insertNextScalarData(cov, "sputterRate");
coverages->insertNextScalarData(cov, "chemicalRate");
}
}

Expand All @@ -113,18 +115,20 @@ class SF6O2SurfaceModel : public SurfaceModel<NumericType> {
const auto numPoints = rates->getScalarData(0)->size();
std::vector<NumericType> etchRate(numPoints, 0.);

const auto ionEnhancedRate = rates->getScalarData("ionEnhancedRate");
const auto ionSputteringRate = rates->getScalarData("ionSputteringRate");
const auto etchantRate = rates->getScalarData("etchantRate");
const auto ionEnhancedYield = rates->getScalarData("ionEnhancedYield");
const auto ionSputterYield = rates->getScalarData("ionSputterYield");
const auto ionFlux = rates->getScalarData("ionFlux");

const auto etchantFlux = rates->getScalarData("etchantFlux");
const auto eCoverage = coverages->getScalarData("eCoverage");

// save the etch rate components for visualization
std::vector<NumericType> *ieComponent = nullptr, *spComponent = nullptr,
*thComponent = nullptr;
std::vector<NumericType> *ieRate = nullptr, *spRate = nullptr,
*chRate = nullptr;
if (Logger::getLogLevel() > 3) {
ieComponent = coverages->getScalarData("ieComponent");
spComponent = coverages->getScalarData("spComponent");
thComponent = coverages->getScalarData("thComponent");
ieRate = coverages->getScalarData("ionEnhancedRate");
spRate = coverages->getScalarData("sputterRate");
chRate = coverages->getScalarData("chemicalRate");
}
bool stop = false;

Expand All @@ -134,25 +138,26 @@ class SF6O2SurfaceModel : public SurfaceModel<NumericType> {
break;
}

const auto sputterRate =
ionSputterYield->at(i) * ionFlux->at(i) * params.ionFlux;
const auto ionEnhancedRate = eCoverage->at(i) * ionEnhancedYield->at(i) *
ionFlux->at(i) * params.ionFlux;
const auto chemicalRate = params.Si.k_sigma * eCoverage->at(i) / 4.;

if (MaterialMap::isMaterial(materialIds[i], Material::Mask)) {
etchRate[i] =
-(1 / params.Mask.rho) * ionSputteringRate->at(i) * params.ionFlux;
etchRate[i] = -(1 / params.Mask.rho) * sputterRate;
if (Logger::getLogLevel() > 3) {
spComponent->at(i) = ionSputteringRate->at(i) * params.ionFlux;
ieComponent->at(i) = 0.;
thComponent->at(i) = 0.;
spRate->at(i) = sputterRate;
ieRate->at(i) = 0.;
chRate->at(i) = 0.;
}
} else {
etchRate[i] =
-(1 / params.Si.rho) * (params.Si.k_sigma * eCoverage->at(i) / 4. +
ionSputteringRate->at(i) * params.ionFlux +
eCoverage->at(i) * ionEnhancedRate->at(i) *
params.ionFlux); // in um / s
etchRate[i] = -(1 / params.Si.rho) * (chemicalRate + sputterRate +
ionEnhancedRate); // in um / s
if (Logger::getLogLevel() > 3) {
spComponent->at(i) = ionSputteringRate->at(i) * params.ionFlux;
ieComponent->at(i) =
eCoverage->at(i) * ionEnhancedRate->at(i) * params.ionFlux;
thComponent->at(i) = params.Si.k_sigma * eCoverage->at(i) / 4.;
spRate->at(i) = sputterRate;
ieRate->at(i) = ionEnhancedRate;
chRate->at(i) = chemicalRate;
}
}
}
Expand All @@ -170,11 +175,13 @@ class SF6O2SurfaceModel : public SurfaceModel<NumericType> {
// update coverages based on fluxes
const auto numPoints = rates->getScalarData(0)->size();

const auto etchantRate = rates->getScalarData("etchantRate");
const auto ionEnhancedRate = rates->getScalarData("ionEnhancedRate");
const auto oxygenRate = rates->getScalarData("oxygenRate");
const auto oxygenSputteringRate =
rates->getScalarData("oxygenSputteringRate");
const auto etchantFlux = rates->getScalarData("etchantFlux");
const auto oxygenFlux = rates->getScalarData("oxygenFlux");

const auto ionEnhancedYield = rates->getScalarData("ionEnhancedYield");
const auto ionEnhancedPassivationYield =
rates->getScalarData("ionEnhancedPassivationYield");
const auto ionFlux = rates->getScalarData("ionFlux");

// etchant fluorine coverage
auto eCoverage = coverages->getScalarData("eCoverage");
Expand All @@ -184,10 +191,11 @@ class SF6O2SurfaceModel : public SurfaceModel<NumericType> {
oCoverage->resize(numPoints);

for (size_t i = 0; i < numPoints; ++i) {
auto Gb_F = etchantRate->at(i) * params.etchantFlux * params.beta_F;
auto Gb_O = oxygenRate->at(i) * params.oxygenFlux * params.beta_O;
auto GY_ie = ionEnhancedRate->at(i) * params.ionFlux;
auto GY_o = oxygenSputteringRate->at(i) * params.ionFlux;
auto Gb_F = etchantFlux->at(i) * params.etchantFlux * params.beta_F;
auto Gb_O = oxygenFlux->at(i) * params.oxygenFlux * params.beta_O;
auto GY_ie = ionEnhancedYield->at(i) * ionFlux->at(i) * params.ionFlux;
auto GY_o =
ionEnhancedPassivationYield->at(i) * ionFlux->at(i) * params.ionFlux;

auto a = (params.Si.k_sigma + 2 * GY_ie) / Gb_F;
auto b = (params.Si.beta_sigma + GY_o) / Gb_O;
Expand All @@ -212,20 +220,23 @@ class SF6SurfaceModel : public SF6O2SurfaceModel<NumericType, D> {
// update coverages based on fluxes
const auto numPoints = rates->getScalarData(0)->size();

const auto etchantRate = rates->getScalarData("etchantRate");
const auto ionEnhancedRate = rates->getScalarData("ionEnhancedRate");
const auto etchantFlux = rates->getScalarData("etchantFlux");
const auto ionEnhancedYield = rates->getScalarData("ionEnhancedYield");
const auto ionFlux = rates->getScalarData("ionFlux");

// etchant fluorine coverage
auto eCoverage = coverages->getScalarData("eCoverage");
eCoverage->resize(numPoints);

for (size_t i = 0; i < numPoints; ++i) {
if (etchantRate->at(i) < 1e-6) {
if (etchantFlux->at(i) < 1e-6) {
eCoverage->at(i) = 0;
} else {
eCoverage->at(i) =
etchantRate->at(i) * params.etchantFlux * params.beta_F /
(etchantRate->at(i) * params.etchantFlux * params.beta_F +
params.Si.k_sigma + 2 * ionEnhancedRate->at(i) * params.ionFlux);
double tmp =
1 + (params.Si.k_sigma + 2 * ionEnhancedYield->at(i) *
ionFlux->at(i) * params.ionFlux) /
(etchantFlux->at(i) * params.etchantFlux * params.beta_F);
eCoverage->at(i) = 1 / tmp;
}
}
}
Expand All @@ -237,8 +248,8 @@ class SF6O2Ion
public:
SF6O2Ion(const SF6O2Parameters<NumericType> &pParams)
: params(pParams),
A(1. /
(1. + params.Ions.n_l * (M_PI_2 / params.Ions.inflectAngle - 1.))),
A_energy(1. / (1. + params.Ions.n_l *
(M_PI_2 / params.Ions.inflectAngle - 1.))),
sqrt_E_th_ie_O(std::sqrt(params.Passivation.Eth_ie)),
sqrt_E_th_ie_Si(std::sqrt(params.Si.Eth_ie)) {}

Expand All @@ -248,10 +259,7 @@ class SF6O2Ion
viennaray::TracingData<NumericType> &localData,
const viennaray::TracingData<NumericType> *globalData,
RNG &) override final {

// collect data for this hit
assert(primID < localData.getVectorData(0).size() && "id out of bounds");

const double cosTheta = -DotProduct(rayDir, geomNormal);
NumericType angle = std::acos(std::max(std::min(cosTheta, 1.), 0.));

Expand All @@ -277,7 +285,7 @@ class SF6O2Ion
std::cos(angle / params.Si.theta_g_ie * M_PI_2),
0.);

double sqrtE = std::sqrt(E);
const double sqrtE = std::sqrt(E);
NumericType Y_sp =
params.Si.A_sp * std::max(sqrtE - std::sqrt(Eth_sp), 0.) * f_sp_theta;
NumericType Y_Si =
Expand All @@ -290,13 +298,16 @@ class SF6O2Ion
assert(Y_O >= 0. && "Invalid yield");

// sputtering yield Y_sp ionSputteringRate
localData.getVectorData(0)[primID] += Y_sp * rayWeight;
localData.getVectorData(0)[primID] += Y_sp;

// ion enhanced etching yield Y_Si ionEnhancedRate
localData.getVectorData(1)[primID] += Y_Si * rayWeight;
localData.getVectorData(1)[primID] += Y_Si;

// ion enhanced O sputtering yield Y_O oxygenSputteringRate
localData.getVectorData(2)[primID] += Y_O * rayWeight;
// ion enhanced O sputtering yield Y_O ionEnhancedPassivationYield
localData.getVectorData(2)[primID] += Y_O;

// ion flux
localData.getVectorData(3)[primID] += rayWeight;
}

std::pair<NumericType, Vec3D<NumericType>>
Expand All @@ -318,11 +329,11 @@ class SF6O2Ion
// 0
NumericType Eref_peak;
if (incAngle >= params.Ions.inflectAngle) {
Eref_peak = (1 - (1 - A) * (M_PI_2 - incAngle) /
Eref_peak = (1 - (1 - A_energy) * (M_PI_2 - incAngle) /
(M_PI_2 - params.Ions.inflectAngle));
} else {
Eref_peak =
A * std::pow(incAngle / params.Ions.inflectAngle, params.Ions.n_l);
Eref_peak = A_energy * std::pow(incAngle / params.Ions.inflectAngle,
params.Ions.n_l);
}
// Gaussian distribution around the Eref_peak scaled by the particle energy
NumericType NewEnergy;
Expand All @@ -332,11 +343,12 @@ class SF6O2Ion
} while (NewEnergy > E || NewEnergy < 0.);

NumericType sticking = 1.;
if (incAngle > params.Ions.thetaRMin)
if (incAngle > params.Ions.thetaRMin) {
sticking =
1. - std::min((incAngle - params.Ions.thetaRMin) /
(params.Ions.thetaRMax - params.Ions.thetaRMin),
NumericType(1.));
}

// Set the flag to stop tracing if the energy is below the threshold
if (NewEnergy > params.Si.Eth_ie) {
Expand All @@ -360,12 +372,13 @@ class SF6O2Ion
return params.Ions.exponent;
}
std::vector<std::string> getLocalDataLabels() const override final {
return {"ionSputteringRate", "ionEnhancedRate", "oxygenSputteringRate"};
return {"ionSputterYield", "ionEnhancedYield",
"ionEnhancedPassivationYield", "ionFlux"};
}

private:
const SF6O2Parameters<NumericType> &params;
const NumericType A;
const NumericType A_energy;
// save precomputed square roots
const NumericType sqrt_E_th_ie_O;
const NumericType sqrt_E_th_ie_Si;
Expand Down Expand Up @@ -412,7 +425,7 @@ class SF6O2Etchant
}
NumericType getSourceDistributionPower() const override final { return 1.; }
std::vector<std::string> getLocalDataLabels() const override final {
return {"etchantRate"};
return {"etchantFlux"};
}
};

Expand Down Expand Up @@ -453,7 +466,7 @@ class SF6Etchant
}
NumericType getSourceDistributionPower() const override final { return 1.; }
std::vector<std::string> getLocalDataLabels() const override final {
return {"etchantRate"};
return {"etchantFlux"};
}
};

Expand Down Expand Up @@ -495,7 +508,7 @@ class SF6O2Oxygen
}
NumericType getSourceDistributionPower() const override final { return 1.; }
std::vector<std::string> getLocalDataLabels() const override final {
return {"oxygenRate"};
return {"oxygenFlux"};
}
};
} // namespace impl
Expand All @@ -509,7 +522,7 @@ class SF6O2Etching : public ProcessModel<NumericType, D> {
public:
SF6O2Etching() { initializeModel(); }

// All flux values are in units 1e16 / cm²
// All flux values are in units 1e15 / cm²
SF6O2Etching(const double ionFlux, const double etchantFlux,
const double oxygenFlux, const NumericType meanEnergy /* eV */,
const NumericType sigmaEnergy /* eV */, // 5 parameters
Expand Down

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