HW-QA-2020 issues https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues 2020-06-06T13:31:24Z https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/38 [HW5 Q2.5] 2020-06-06T13:31:24Z lcartocci [HW5 Q2.5] Hi, I'm unsure how to go about question 2.5 (and as far as I've seen, other people are having the same problem as well). I'm guessing it's the LHS of the conditions we have to rewrite, so I've managed to find a relation between both $E_{CB}(x\rightarrow\infty)$ and $E_{CB}(x=0)$ based on $\psi_{B0}$ but struggle to make use of the bandgap and especially $n_{B0}$ (do we even need it in the expression since B is intrinsic?). What I have so far is the following: $\psi_{B0}=-E_{FB}/e$ with $E_{FB}=E_{CB}-1/2*E_{gB}$ -- but here $E_{CB}$ corresponds to conduction band energy before contact, so this is where I get stuck (unless we can assume that it's equal to the $E_{CB}$ far from the interface after contact??)... Could you please let me know if I'm going in the right direction, or if there's something wrong in my reasoning? Hi, I'm unsure how to go about question 2.5 (and as far as I've seen, other people are having the same problem as well). I'm guessing it's the LHS of the conditions we have to rewrite, so I've managed to find a relation between both $E_{CB}(x\rightarrow\infty)$ and $E_{CB}(x=0)$ based on $\psi_{B0}$ but struggle to make use of the bandgap and especially $n_{B0}$ (do we even need it in the expression since B is intrinsic?). What I have so far is the following: $\psi_{B0}=-E_{FB}/e$ with $E_{FB}=E_{CB}-1/2*E_{gB}$ -- but here $E_{CB}$ corresponds to conduction band energy before contact, so this is where I get stuck (unless we can assume that it's equal to the $E_{CB}$ far from the interface after contact??)... Could you please let me know if I'm going in the right direction, or if there's something wrong in my reasoning? https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/30 [HW5 Q3.4] Determining power conversion efficiency 2020-05-25T09:29:21Z lcartocci [HW5 Q3.4] Determining power conversion efficiency Hi again, I have a question regarding the solar cell power conversion efficiency. According to the lecture, to calculate this value, we should also take into account the photons that are not absorbed by the semiconductor due to their energy being lower than the bandgap. However, in the question itself, it says to calculate the number of photons radiated by the blackbody as a function of frequency "which are all absorbed by the solar cell" -- I take this as meaning we should only consider the energy of the photons within the light frequency range referred to in Question 3.2. Which approach should we take here? In principle I would assume we should consider the entire solar spectrum (ie. including the energy of photons which do not get absorbed) to compute the overall conversion efficiency... I hope this makes sense! Hi again, I have a question regarding the solar cell power conversion efficiency. According to the lecture, to calculate this value, we should also take into account the photons that are not absorbed by the semiconductor due to their energy being lower than the bandgap. However, in the question itself, it says to calculate the number of photons radiated by the blackbody as a function of frequency "which are all absorbed by the solar cell" -- I take this as meaning we should only consider the energy of the photons within the light frequency range referred to in Question 3.2. Which approach should we take here? In principle I would assume we should consider the entire solar spectrum (ie. including the energy of photons which do not get absorbed) to compute the overall conversion efficiency... I hope this makes sense! https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/29 [HW5 Q2.1] Calculation of Fermi energies 2020-06-02T16:14:32Z lcartocci [HW5 Q2.1] Calculation of Fermi energies Hi, I have a question with respect to Question 2.1, where we have to calculate the Fermi energies of A (n-doped) and B (intrinsic). In principle, to do this we would need the density of states of the conduction and valence bands Nc and Nv, which are in turn related to the effective carrier masses... Can we assume those to be the same in those calculations, such that Nc=Nv? If not, I would be unsure how to proceed in order to answer the question. Hi, I have a question with respect to Question 2.1, where we have to calculate the Fermi energies of A (n-doped) and B (intrinsic). In principle, to do this we would need the density of states of the conduction and valence bands Nc and Nv, which are in turn related to the effective carrier masses... Can we assume those to be the same in those calculations, such that Nc=Nv? If not, I would be unsure how to proceed in order to answer the question. https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/26 HW4 Q3.5 Setting up dP/dx 2020-05-12T19:34:25Z etzoldk HW4 Q3.5 Setting up dP/dx I managed to set up $\eta \nabla^2 v_\mathrm{f} = \frac{\partial p}{\partial x} + c \frac{\partial U}{\partial x} = \frac{\Delta p - \Delta \Pi_\mathrm{eff}}{L} = \frac{\Delta P}{L}$ but now I am stuck because I don't know how I should set up $dP/dx$. Could you give me a hint? I managed to set up $\eta \nabla^2 v_\mathrm{f} = \frac{\partial p}{\partial x} + c \frac{\partial U}{\partial x} = \frac{\Delta p - \Delta \Pi_\mathrm{eff}}{L} = \frac{\Delta P}{L}$ but now I am stuck because I don't know how I should set up $dP/dx$. Could you give me a hint? https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/25 [HW4] Q3.4 2020-05-19T12:43:34Z Gianluca Lombardini [HW4] Q3.4 Hi, at some point I get the equation $\frac{d^2 g(x)}{d x^2} - \beta\frac{d g(x)}{d x}\frac{d U(x)}{d x} = 0$. Could you tell if I am on the right path? An if yes, could you maybe give a hint on how to solve it analytically? Thanks! Hi, at some point I get the equation $\frac{d^2 g(x)}{d x^2} - \beta\frac{d g(x)}{d x}\frac{d U(x)}{d x} = 0$. Could you tell if I am on the right path? An if yes, could you maybe give a hint on how to solve it analytically? Thanks! celebik celebik https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/23 [Lecture 16] Eq. 16.5 and [HW4] Q3.1 2020-05-19T12:43:51Z aandreotti [Lecture 16] Eq. 16.5 and [HW4] Q3.1 Dear Tian, Can I ask you a question about eq. 16.5 of Lecture 16? During the lecture Prof. Shih provided us with this expression for the solute flux N=-w*D/L*delta(C)+w*c*v Why eq.16.5 has the term D/L that multiplies c*v too? In other words, the solute carried by the solvent isn't independent from diffusion? And sorry, for what concerns the term delta(c), on the assignment it is written that it is c1-c2. But in this case, when c1>c2 the first term on the right hand side is negative but the diffusive flux is from reservoir 1 to 2. So shouldn't it be delta(c)=c2-c1? Thank you in advance! Best regards Alessandro Andreotti Dear Tian, Can I ask you a question about eq. 16.5 of Lecture 16? During the lecture Prof. Shih provided us with this expression for the solute flux N=-w*D/L*delta(C)+w*c*v Why eq.16.5 has the term D/L that multiplies c*v too? In other words, the solute carried by the solvent isn't independent from diffusion? And sorry, for what concerns the term delta(c), on the assignment it is written that it is c1-c2. But in this case, when c1>c2 the first term on the right hand side is negative but the diffusive flux is from reservoir 1 to 2. So shouldn't it be delta(c)=c2-c1? Thank you in advance! Best regards Alessandro Andreotti vaglig vaglig https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/21 [Important] L16 Clarification 2020-05-15T08:07:15Z atapia [Important] L16 Clarification ![Screenshot_2020-05-04_at_19.00.00](/uploads/e70409be348d126b7607ff357f6a366f/Screenshot_2020-05-04_at_19.00.00.png) I don not follow how you plug Eq 16.10 into Eq 16.7. The integrals do not match at all anywhere. If I plug c(x)(from Eq. 16.7) directly into Eq. 16.10 I do not see how you resolved the arising double integral and how you treated the partial derivative ($\partial U / \partial x$). Is there a c(x) term missing in eq 16.17 or are there some other steps that you have omitted. If so could you help me understand how you got this result? Because it is proving hard to follow this lecture in order to solve Q3 in HW4 Also there seems to be a typo in page 151 ![Screenshot_2020-05-04_at_19.09.34](/uploads/12c8fcd4ad76c93b17bb036dc979ba0b/Screenshot_2020-05-04_at_19.09.34.png) should it be here 'we plug Eq. 16.10 into Eq 16.13' for the second integral on the RHS? ![Screenshot_2020-05-04_at_19.00.00](/uploads/e70409be348d126b7607ff357f6a366f/Screenshot_2020-05-04_at_19.00.00.png) I don not follow how you plug Eq 16.10 into Eq 16.7. The integrals do not match at all anywhere. If I plug c(x)(from Eq. 16.7) directly into Eq. 16.10 I do not see how you resolved the arising double integral and how you treated the partial derivative ($\partial U / \partial x$). Is there a c(x) term missing in eq 16.17 or are there some other steps that you have omitted. If so could you help me understand how you got this result? Because it is proving hard to follow this lecture in order to solve Q3 in HW4 Also there seems to be a typo in page 151 ![Screenshot_2020-05-04_at_19.09.34](/uploads/12c8fcd4ad76c93b17bb036dc979ba0b/Screenshot_2020-05-04_at_19.09.34.png) should it be here 'we plug Eq. 16.10 into Eq 16.13' for the second integral on the RHS? celebik celebik https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/18 [HW4 Q2.5] What is F 2020-05-04T10:05:23Z atapia [HW4 Q2.5] What is F ## Details In this question we are asked to denote a matrix linear system of form: $ AY = F $ I understand $Y$ are the solutions of the PBE Eq at the evaluated points. For example the Gouy-Chapman in the forms of $tanh(ze\psi/k_b T) = \Lambda _0 exp(-\kappa x)$, so we could use these as guess solutions for the starting solutions. But I do not understand what $f(x_i)$ is, would this be the RHS of the PB equation, i.e.: $\sum _j \frac{e}{\epsilon _0 \epsilon _r}exp(-z_j e \psi (x_i) / k_B T)$ Also, I noticed that in the enunciate of the problem you set that we are solving: $- \frac{d^2\psi}{dx^2} = f(x_i)$ Why have we moved the sign here to the LHS? Is this so that the coefficients for the A matrix match accordingly? Finally, I do not understand what $\alpha$ and $\beta$ are. Are these simply the BC conditions at x=[0, H]? So we would have the same potential at both ends? ## Details In this question we are asked to denote a matrix linear system of form: $ AY = F $ I understand $Y$ are the solutions of the PBE Eq at the evaluated points. For example the Gouy-Chapman in the forms of $tanh(ze\psi/k_b T) = \Lambda _0 exp(-\kappa x)$, so we could use these as guess solutions for the starting solutions. But I do not understand what $f(x_i)$ is, would this be the RHS of the PB equation, i.e.: $\sum _j \frac{e}{\epsilon _0 \epsilon _r}exp(-z_j e \psi (x_i) / k_B T)$ Also, I noticed that in the enunciate of the problem you set that we are solving: $- \frac{d^2\psi}{dx^2} = f(x_i)$ Why have we moved the sign here to the LHS? Is this so that the coefficients for the A matrix match accordingly? Finally, I do not understand what $\alpha$ and $\beta$ are. Are these simply the BC conditions at x=[0, H]? So we would have the same potential at both ends? https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/14 [HW4 Q2.2/2.3] 2020-05-04T07:55:06Z fiscmark [HW4 Q2.2/2.3] ## Summary Initial boundary conditions / Implementation of $\dfrac{d\psi (x=h/2)}{dx}=0$. ## Details Q2.2: I solved the Poisson-Boltzmann equation with initial boundary conditions for $\psi (x=0)=\psi(0)$ and $\dfrac{d\psi (x=0)}{dx}$ being my guessing parameter and it works well. I then looked for a value of $\dfrac{d\psi (x=0)}{dx}$ giving a solution satisfying $\dfrac{d\psi (x=h/2)}{dx}=0$, which must be valid in the middle between the two plates. The solution I obtained satisfies equation 6 as well. Q2.3: My result is not realistic ($\psi$=40mV over whole gap). It seems that my solution doesnt work for realistic parameter values. Is the implementation of the boundary condition $\dfrac{d\psi (x=h/2)}{dx}=0$ correct? I hesitated with this part cause we are looking for a solution to satisfy eq. 6. However, I couldnt find another way to implement both conditions simultaneously. ## Summary Initial boundary conditions / Implementation of $\dfrac{d\psi (x=h/2)}{dx}=0$. ## Details Q2.2: I solved the Poisson-Boltzmann equation with initial boundary conditions for $\psi (x=0)=\psi(0)$ and $\dfrac{d\psi (x=0)}{dx}$ being my guessing parameter and it works well. I then looked for a value of $\dfrac{d\psi (x=0)}{dx}$ giving a solution satisfying $\dfrac{d\psi (x=h/2)}{dx}=0$, which must be valid in the middle between the two plates. The solution I obtained satisfies equation 6 as well. Q2.3: My result is not realistic ($\psi$=40mV over whole gap). It seems that my solution doesnt work for realistic parameter values. Is the implementation of the boundary condition $\dfrac{d\psi (x=h/2)}{dx}=0$ correct? I hesitated with this part cause we are looking for a solution to satisfy eq. 6. However, I couldnt find another way to implement both conditions simultaneously. https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/13 [HW4 Q2.5] 2020-05-01T15:46:35Z bpopa [HW4 Q2.5] ## Summary >1. I don't know if my thoughts on **HW4, Q2.5** are correct. Below are my thoughts ## Details I was able to set-up my matrix in **HW4, Q2.4** Then I tried to write a solver with this information and it just gives me non-sense. I have a question regarding the BCs. So for me $\alpha=\psi(x=0)=\psi_{0}=40mV$ and for me $\beta=\psi(x=h/2)$ which I can take from **Q2.3** as I was planing to solve f(x) from x=0:h/2. My last question is regarding to the initial condition $\Psi(\psi_{1},\psi_{2}...)$ - this initial condition I have generated by solving $\psi(x)$ with GC at x=points in space where I am interested in solution math \psi_{init}(x)=\frac{4k_{B}T}{ze}*atanh(\exp(-\kappa x)*tanh(ze\psi_{0}/ek_{B}T))  ## Summary >1. I don't know if my thoughts on **HW4, Q2.5** are correct. Below are my thoughts ## Details I was able to set-up my matrix in **HW4, Q2.4** Then I tried to write a solver with this information and it just gives me non-sense. I have a question regarding the BCs. So for me $\alpha=\psi(x=0)=\psi_{0}=40mV$ and for me $\beta=\psi(x=h/2)$ which I can take from **Q2.3** as I was planing to solve f(x) from x=0:h/2. My last question is regarding to the initial condition $\Psi(\psi_{1},\psi_{2}...)$ - this initial condition I have generated by solving $\psi(x)$ with GC at x=points in space where I am interested in solution math \psi_{init}(x)=\frac{4k_{B}T}{ze}*atanh(\exp(-\kappa x)*tanh(ze\psi_{0}/ek_{B}T))  https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/12 [HW4 Q1.2] Not sure if my approach is correct 2020-05-01T15:07:42Z atapia [HW4 Q1.2] Not sure if my approach is correct I am not sure if this is what you mean that we use Gauss' Law. Also, I am not sure how to integrate this to obtain a BC at r=R (how do I integrate something with f(g(x)dx when I do not know how g(x) depends on x?). Form this I can only gather that at R, we must have a surface charge density but not sure how to express it. Is this the right approach? I am not sure if this is what you mean that we use Gauss' Law. Also, I am not sure how to integrate this to obtain a BC at r=R (how do I integrate something with f(g(x)dx when I do not know how g(x) depends on x?). Form this I can only gather that at R, we must have a surface charge density but not sure how to express it. Is this the right approach? https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/10 [HW4 Q3] Definition of $V_m$ 2020-04-24T13:23:44Z Tian Tian [HW4 Q3] Definition of $V_m$ # Clarification for $V_m$ in Q3 needed. The parameter $V_m$ that comes in Q3.2 (and following sub-questions) is not defined in the text. From my understanding $V_m$ is the membrane potential (i.e. $U$ inside the membrane). @chshih @vaglig could you confirm? # Clarification for $V_m$ in Q3 needed. The parameter $V_m$ that comes in Q3.2 (and following sub-questions) is not defined in the text. From my understanding $V_m$ is the membrane potential (i.e. $U$ inside the membrane). @chshih @vaglig could you confirm? Tian Tian Tian Tian https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/9 [HW4 Q1.4] 2020-04-24T13:13:02Z bpopa [HW4 Q1.4] ## Summary >4. **HW4, Q1.4**: Not sure how to understand r=0 and to show $c_{max}$ ## Details >4. I cannot plug r=0 in the equation that I got from 1.3 because then all is 0 which makes sense bc the other BC states $\frac{d\psi}{dr}\bigg|_{r=0}=0$ - I would also lose $R^{2}$ from the equation of $c_{max}$. How should one proceed with this question? ## Summary >4. **HW4, Q1.4**: Not sure how to understand r=0 and to show $c_{max}$ ## Details >4. I cannot plug r=0 in the equation that I got from 1.3 because then all is 0 which makes sense bc the other BC states $\frac{d\psi}{dr}\bigg|_{r=0}=0$ - I would also lose $R^{2}$ from the equation of $c_{max}$. How should one proceed with this question? https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/8 [Lecture notes] Eq. 11.7 2020-04-21T09:32:18Z aandreotti [Lecture notes] Eq. 11.7 Dear Tian, I have one doubt about eq 11.7 of the lecture notes. In this step, you simply converted Ci,o into Mi,o. But the factor 1000 shouldn't be at the denominator? Cio= #/m^3 => Cio= mol x Na/m^3 => Cio= Mio x Na/1000 I ask you because I found the same expression also on the Wikipedia link you provided us this afternoon. Thank you in advance for your help! Best regards Alessandro Andreotti Dear Tian, I have one doubt about eq 11.7 of the lecture notes. In this step, you simply converted Ci,o into Mi,o. But the factor 1000 shouldn't be at the denominator? Cio= #/m^3 => Cio= mol x Na/m^3 => Cio= Mio x Na/1000 I ask you because I found the same expression also on the Wikipedia link you provided us this afternoon. Thank you in advance for your help! Best regards Alessandro Andreotti https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/4 [HW3 Q2.7] Clarification of symbols 2020-04-20T08:40:46Z Tian Tian [HW3 Q2.7] Clarification of symbols ## Clarification of symbols $c$ and $nu_n$ In the following equation of Q2.7 ![image](/uploads/28436348541f890c6c3c77142f69f387/image.png) - $c$ is the speed of light in vacuum - $\nu_n$ is the n-th Matsubara frequency (in Hz or s$^{-1}$). Overall $r_n$ is a *unitless* number. Larger $r_n$ means the separation $d$ is too long for the EM wave to travel compared with $\nu_n$, hence the retardation effect. ## Clarification of symbols $c$ and $nu_n$ In the following equation of Q2.7 ![image](/uploads/28436348541f890c6c3c77142f69f387/image.png) - $c$ is the speed of light in vacuum - $\nu_n$ is the n-th Matsubara frequency (in Hz or s$^{-1}$). Overall $r_n$ is a *unitless* number. Larger $r_n$ means the separation $d$ is too long for the EM wave to travel compared with $\nu_n$, hence the retardation effect. https://gitlab.ethz.ch/IEM-course/2020-iem-hw-qa/-/issues/3 [HW3 Q2] Typo in eps-data.zip files 2020-04-20T08:40:54Z Tian Tian [HW3 Q2] Typo in eps-data.zip files ## There are a few typos in the files of eps-data.zip - Typo in the Readme.txt The following line contains a typo: > In each file, the first column is the energy h\*nu h*nu should be changed to h\*omega - Data files The header should be changed to: > #h\*omega, eps'' ## There are a few typos in the files of eps-data.zip - Typo in the Readme.txt The following line contains a typo: > In each file, the first column is the energy h\*nu h*nu should be changed to h\*omega - Data files The header should be changed to: > #h\*omega, eps''